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付録 B

Flare-Substorm/Space Weather Topics(Earth, Planets and Space, Vol. 61,
No. 5, 2009)“Flare-Substorm/Space Weather Topics” (Earth, Planets and Space, Vol. 61, No. 5, 2009) は、2007 年 3 月にアラスカで開催された「CAWSES Space Weather Workshop」（本報告書 88 ページを参照）の集録として出版されたものである。

掲載論文• Preface,
Earth Planets Space, Vol. 61 (No. 5), pp. 553, 2009
• A two-step scenario for both solar flares and magnetospheric substorms: Short duration energy
storage,
Bruce T. Tsurutani, Kazunari Shibata, Syun-Ichi Akasofu, and Mitsuo Oka,
Earth Planets Space, Vol. 61 (No. 5), pp. 555–559, 2009
• Modeling of substorms and flares by the fast reconnection mechanism,
M. Ugai, K. Kondoh, and T. Shimizu,
Earth Planets Space, Vol. 61 (No. 5), pp. 561–564, 2009
• Coronal loops, flare ribbons and aurora during slip-running,
Brigitte Schmieder, Guillaume Aulanier, Pascal Demoulin, and Etienne Pariat,
Earth Planets Space, Vol. 61 (No. 5), pp. 565–568, 2009
• Three-dimensional non-linear instability of spontaneous fast magnetic reconnection,
T. Shimizu, K. Kondoh, and M. Ugai,
Earth Planets Space, Vol. 61 (No. 5), pp. 569–572, 2009
• Patchy reconnection in a Y-type current sheet,
M. G. Linton, C. R. DeVore, and D. W. Longcope,
Earth Planets Space, Vol. 61 (No. 5), pp. 573–576, 2009
• Flares and the chromosphere,B–2
Hugh S. Hudson and Lyndsay Fletcher,
Earth Planets Space, Vol. 61 (No. 5), pp. 577–580, 2009
• Development of the global simulation model of the heliosphere,
Satomi Kamei, Aoi Nakamizo, Takashi Tanaka, Takahiro Obara, and Hironori Shimazu,
Earth Planets Space, Vol. 61 (No. 5), pp. 581–584, 2009
• The interplanetary magnetic decrease automatic detection (IMDAD) code,
F. L. Guarnieri, B. T. Tsurutani, and E. Echer,
Earth Planets Space, Vol. 61 (No. 5), pp. 585–588, 2009
• Impacts of torus model on studies of geometrical relationships between interplanetary magnetic
clouds and their solar origins,
Katsuhide Marubashi, Suk-Kyung Sung, Kyung-Suk Cho, and Ronald P. Lepping,
Earth Planets Space, Vol. 61 (No. 5), pp. 589–594, 2009
• Halo coronal mass ejections and geomagnetic storms,
Nat Gopalswamy,
Earth Planets Space, Vol. 61 (No. 5), pp. 595–597, 2009
• Numerical simulations of the solar corona and Coronal Mass Ejections,Stefaan Poedts, Carla Jacobs, Bart van der Holst, Emmanuel Chane, and Rony Keppens,
Earth Planets Space, Vol. 61 (No. 5), pp. 599–602, 2009• Non-thermal electrons at the Earth’s bow shock: A ’gradual’ event,
M. Oka, T. Terasawa, M. Fujimoto, H. Matsui, Y. Kasaba, Y. Saito, H. Kojima, H. Matsumoto, andT. Mukai,Earth Planets Space, Vol. 61 (No. 5), pp. 603–606, 2009
• Influence of the foreshock of the Earth’s bow shock on the interplanetary shock propagation
during their mutual interaction,
Lubomı́r Přech, Zdeněk Němeček, and Jana Šafránková,Earth Planets Space, Vol. 61 (No. 5), pp. 607–610, 2009
• Three dimensional configuration of earthward fast plasma flow in the near-Earth plasma sheet,
Koji Kondoh, Masayuki Ugai, and Tohru Shimizu,
Earth Planets Space, Vol. 61 (No. 5), pp. 611–614, 2009
• Timing of substorm related auroral oscillations,P. Martin, N. E. Turner, and J. Wanliss,
Earth Planets Space, Vol. 61 (No. 5), pp. 615–619, 2009
• Statistically predicting Dst without satellite data,
A. S. Parnowski,
Earth Planets Space, Vol. 61 (No. 5), pp. 621–624, 2009
• Properties of dayside nonlinear rising tone chorus emissions at large L observed by GEOTAIL,
Olga P. Verkhoglyadova, Bruce T. Tsurutani, Y. Omura, and S. Yagitani,
Earth Planets Space, Vol. 61 (No. 5), pp. 625–628, 2009
• Proxy for the ionospheric peak plasma density reduced by the solar zenith angle,
T. L. Gulyaeva,

B–3
Earth Planets Space, Vol. 61 (No. 5), pp. 629–631, 2009
• Investigation of ionospheric gradients for GAGAN application,
K. Ravi Chandra, V. Satya Srinivas, and A. D. Sarma,
Earth Planets Space, Vol. 61 (No. 5), pp. 633–635, 2009
• The total failures of GPS functioning caused by the powerful solar radio burst on December 13,
2006,
E. L. Afraimovich, V. V. Demyanov, and G. Ya. Smolkov,
Earth Planets Space, Vol. 61 (No. 5), pp. 637–641, 2009
• Aeronomic eﬀects of the solar flares in the topside ionosphere,
L. A. Leonovich and A. V. Taschilin,
Earth Planets Space, Vol. 61 (No. 5), pp. 643–648, 2009

Preface
Under the sponsorship of CAWSES, a Workshop was held on the topic of solar flares, magnetospheric substorms (particularly the relationship between the two) and other space weather topics. The workshop was held under the sponsorship of
the University of Alaska, Fairbanks from 18 to 20 March, 2007. This special issue is a result of this workshop. Auroras
were observed nightly during the workshop interval. Many presentations given at the workshop showed detailed images ofsolar flares. This special issue includes, but is not limited to, papers presented at the Workshop. We hope that the following
papers will be stimulating to the readership of Earth, Planets and Space.
Guest Editors: Bruce T. Tsurutani
Kazunari Shibata
Syun-Ichi Akasofu
Mitsuo Oka

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LETTER

Earth Planets Space, 61, 555–559, 2009

A two-step scenario for both solar flares and magnetospheric substorms:
Short duration energy storage
Bruce T. Tsurutani1 , Kazunari Shibata2 , Syun-Ichi Akasofu3 , and Mitsuo Oka4
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
2 Kyoto University, Kyoto, Japan
3 International Arctic Research Center (IARC), Univ. Alaska, Fairbanks, AK
4 University of Alabama in Huntsville, Huntsville, AL(Received September 16, 2008; Revised February 25, 2009; Accepted March 12, 2009; Online published May 29, 2009)

The basic observations for magnetic storms and substorms at Earth and for flares at the Sun are reviewed forbackground. We present a common scenario of double magnetic reconnection for both substorms and flares basedon previous interplanetary observations and substorm-triggering results. Central to the scenario is that the firstmagnetic reconnection phase is the source of energy loading for possible substorms and flares. The energy placedin the magnetotail or magnetosphere/at the sun lasts for only a short duration of time however. The energy getsdissipates away rapidly (in some less dramatic form). This scenario predicts that if the initial reconnection process
is sufficiently intense and rapid, concomitant substorms and flares occur soon thereafter. If the energy input isless rapid, there may be lengthy delays for the onset of substorms and flares. If external influences (shocks, etc.)
occur during the latter energy buildup, the “trigger” will cause a sudden release of this energy. The model also
explains reconnection without subsequent substorms and flares. The model addresses the question why strong
triggering events are sometimes ineffective.
Key words: Solar flares, substorms, magnetic storms, magnetic reconnection.

1.

Introduction

It has been well established that major geomagnetic
storms do not occur at Earth unless the upstream interplanetary magnetic field (IMF) is southward for durationsof hours (Gonzalez and Tsurutani, 1987; Gonzalez et al.,
1994, 2007). There have been no exceptions to this rule
found to date. On the other hand, if the upstream IMF isnorthward, the magnetosphere and auroras becomes very
quiet (Tsurutani and Gonzalez, 1995). It can be assumed
that the energy input into the magnetosphere/magnetotail
does not occur during such intervals (or takes place at amuch lower rate). The implication of both of these observations is that magnetic reconnection (Dungey, 1961) is the
major mechanism for solar wind energy input into the magnetosphere (Echer et al., 2008) and is a direct or indirectsource of the energy powering magnetic storms.
Substorms are much smaller intensity geomagnetic
events, and there the situation is less clear. Tsurutani andMeng (1972) and Meng et al. (1973) found that southward IMFs preceded substorms by ∼10 to 40 min, and concluded that southward IMFs are both the ultimate energy
source and trigger for the substorms that follow. Alternatively Lyons et al. (1997) have suggested that some substorms are “triggered” by northward IMF turnings due tobraking of the magnetospheric convection process. Freeman and Morley (2004) have demonstated that substorms
c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

may occur spontaneously and may not be triggered at all.
We will argue that all of these positions are correct and are
not contradictory to each other.
The strongest external impact on the magnetosphere andpotential substorm triggers are interplanetary fast forward
shocks (Kennel et al., 1985) impinging on the dayside magnetopause. The solar wind ram pressure can increase by
an order of magnitude across a shock. Such pressure pulses
will compress the magnetosphere in a dramatic fashion suchthat magnetic increases (sudden impulses or SIs) are detected on the ground (Araki, 1994). As the shock propagates further downstream, it will compress the magnetotail
and thereby increase currents within and bounding the tail(Tsurutani et al., 1986; Tsurutani and Zhou, 2003). Shockcompression will also enhance field-aligned currents fromthe magnetosphere to the ionosphere (Araki, 1994). These
shocks can immediately trigger substorms with little or nodelay (Heppner, 1955; Kawasaki et al., 1971; Kokubun etal., 1977). However there are also times when they do not
trigger substorms. What does this mean?
Zhou and Tsurutani (2001) and Tsurutani and Zhou
(2003) have found that if the IMF is southward or ∼zeronT a few hrs prior to shock impingement, a substorm will
occur. If the IMF is northward, one will not. These observations have been somewhat of a mystery. The Earth’s magnetotail has enough stored magnetic energy to supply a dozen
or more substorms. Why don’t shocks trigger substorms irrespective of preceding IMF directionality? A similar question can be asked about solar flares. The energy stored in
the coronal loops is sufficient for many solar flares. Why

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B. T. TSURUTANI et al.: A COMMON SCENARIO FOR FLARES AND SUBSTORMS

Fig. 1. A schematic of two-step reconnection at Earth (on left) and at the sun (on right). For the Earth’s case the solar wind from the sun (at bottom
out of the figure) convects interplanetary magnetic fields to the Earth. Magnetic reconnection at the magnetopause (indicated in red at the bottom)
allows the transfer of solar wind energy to the ionosphere/magnetosphere/magnetotail. If this first reconnection process is intense enough, a substorm
will occur. Magnetic reconnection in the tail (indicated in red at the top) may either drive the substorm or be a consequence of the substorm. This iscurrently being debated in the literature. An analogous solar flare schematic is shown on the right. An emerging flux region occurs on the far right of
the figure. Magnetic reconnection between it and the neighboring (central) loop leads to an increase of magnetic stress between the central loop andthe large loop at the left. Release of this stress occurs in the form of a solar flare.

cipitating into the upper atmosphere colliding with neutral
atoms and molecules. The electrons lose their kinetic energies through electron-electron collisions resulting in the excitation of the atoms and molecules. The excited atoms andmolecules relax to emit visible and UV photons. To a muchlesser extent (∼1 to 2% of the total radiated energy), the incoming energetic electrons are accelerated by interactions
with atmospheric nuclei to form bremsstrahlung X-rays.
The processes accelerating the electrons to 1–10 keV
occurs above the ionosphere. Electric fields with components aligned along the geomagnetic field (so called “parallel electric fields”) have been detected at low altitudes
by satellites such as FAST (Carlson et al., 1998). Theseelectric fields accelerate thermal electrons to monoenergetic
beams of ∼keV kinetic energies (Evans, 1968). The causesof these electric fields are due to processes occurring in themagnetosphere, at higher altitudes still. The lack of sufficient current carrier densities is the cause of the parallel
electric fields generated above the ionosphere (Carlson etal., 1998).
Large scale convection of magnetotail (plasmasheet)plasma also occurs simultaneous with auroral substorms.
2. Results
The plasmasheet is convected inward towards the Earth,
2.1 Substorms
Substorms were first identified and described by Akasofu compressing (heating) the plasmasheet plasma. Due to cur(1964) (see also Akasofu and Chapman, 1972) by all sky vature and gradients in the magnetospheric magnetic field,
images measured from the ground. Substorms are isolated the electrons drift from the midnight sector towards dawn
midnight sector auroral zone (∼60◦ to 65◦ magnetic lati- and the ions from the midnight sector to dusk. The energies
tude) events. Akasofu (1964) found that a substorm was of these particles are ∼10 to 100 keV. Through plasma infound to consist of the following sequence: 1) a brightening stabilities and plasma wave growth, these magnetosphericof the equatorward arc (the arc width typically is ∼1 km), particles are pitch-angle scattered and some precipitate into2) a breakup of the arc, and then poleward, eastward and the ionosphere. This is the “diffuse” component of the auwestward expansions of auroral forms. This sequence takes rora.
It is well documented that the energy for substorms ultibetween ∼10 and ∼30 min to complete, with no definite
mately comes from the solar wind Poynting flux (discussed
time interval identified.
Auroral light is created by ∼1–10 keV electrons pre- previously). The magnetic field directionality serves as
don’t flares occur continuously until the loop energy is exhausted? The loop configuration often looks remarkably
similar before and after the flare.
We present a scenario of double magnetic reconnection
for substorms and solar flares. Our scenario follows theabove empirical findings that magnetic reconnection is the
major process transferring solar wind energy into the magnetosphere. That is a standard, well-accepted concept (seeTerasawa et al., 2000 for a discussion of the similarities
and differences between substorms and flares). However
we also follow the Zhou and Tsurutani (2001) and Tsurutani and Zhou (2003) result that the energy stored in someform in the magnetosphere/magnetotail/ionosphere is being
dissipated rapidly. If the energy is not released in the formof a substorm within several hrs, it gets released in a lessdramatic manner. In this scenario, the quiet-time tail lobe
energy does not play a prominent role. In this paper we explore the consequences of this idea, assuming that the sameprocesses occur at the sun. We will hypothesize under what
condition solar flares occur and when they do not.

B. T. TSURUTANI et al.: A COMMON SCENARIO FOR FLARES AND SUBSTORMS

an energy gate. If the interplanetary magnetic fields areoriented in a southward direction, opposite in direction to
the magnetopause magnetic fields, reconnection will takeplace. A second site of reconnection occurs in the magnetotail. A schematic of this model is shown on the left-handside of Fig. 1.
Although sufficient energy may be transferred into themagnetosphere/magnetotail system by the first reconnection process, substorms may not take place immediately
or even at all. Our scenario is that if energy is supplied
at a rapid enough rate, e.g., if the IMF is intensely southward, substorms will result (Tsurutani and Meng, 1972). If
sufficient energy has recently been put into the magnetosphere and the IMF turns northward, this current disruption
can cause a substorm (Lyons et al., 1997). Or if there isenergy being put into the magnetosphere/magnetotail continuously, substorms will occur sporadically (Freeman andMorley, 2004). However if the IMF is northwardly directed
for hours prior to the “trigger” arriving at the magnetopause,neither IMF southward turnings, northward turnings nor
shocks will trigger substorms. In our scenario, the important feature is the rate of energy input into the magnetosphere/magnetotail system. The “triggers” are less important.
In the above substorm scenario, there is less emphasis on
the second reconnection event. It may occur as a byproductof the substorm or may lead to the substorm. There aremany ongoing debates of the timing of the events. In our
point of view, it is the first reconnection event that is theimportant one. This leads to energy input from the solar
wind to the ionosphere/magnetosphere/magnetotail.
2.2 Solar flares
Solar flares were first observed (1859) and reported independently by R. C. Carrington (1860) and R. Hodgson(1860) as localized brightenings in a sunspot group. The
brightening lasted only ∼5 min. No changes in the sunspot
orientation or intensity was noted after the flare had occurred. This is similar to the case of substorms, viewed
from a great distance. Differences in the magnetosphere before and after substorms would be difficult to discern froma viewing distance of 108 km.
Since the above 1859 observations, numerous flare events
have been recorded by ground-based, balloon-borne andspacecraft telescopes. Today, a solar flare is defined as “atransient phenomenon showing a rapid increase followed byeither a rapid or gradual decay” (Tajima and Shibata, 1997).
The “rapid” time scale normally corresponds to 10 sec to
10 min, although it varies largely from event-to-event. It is
often accompanied by quasi-periodic variations, or pulsations, with the time-scale as small as 20 msec. These observations are similar to those of substorms.
The wavelength of the electromagnetic emission covers
radio wavelengths at the low end to γ - rays at the upper end.
The γ -rays are produced by precipitating high energy ions,a feature far more energetic than that in substorms. The
low end includes Hα photons, a feature often used in flarediagnostics. Recent progress has come from spectral andimaging observations of X-rays (e.g., Svestka, 1976). Soft
X-rays (SXR) are thought to be thermal emission from plasmas of 107 K temperature whereas hard X-rays are “non-557

thermal”. The latter are bremsstrahlung emissions createdby 10 keV to 1 MeV electron collisions with ions.
The whole duration of a flare depends on the type offlare. Long duration event (LDE) flares typically last morethan 1 hr while impulsive flares are short-lived ones thatlast far less. The latter is characterized by impulsive hard
X-ray emission whereas the former shows a softer X-ray
spectrum.
Generally, the LDE flares have larger characteristic scale
sizes of ∼105 km. SXR observations show cusp-type
loops associated with their rise and expansion motion (e.g.,
Tsuneta et al., 1992). The temperature was found to besystematically higher in the outer loops. The loops gradually shrink with time (Forbes and Acton, 1996). Someother phenomenon such as plasmoid ejections (Hudson,1994), downflows (McKenzie and Hudson, 1999; Asai etal., 2004), and inflows (Yokoyama et al., 2001) were also
observed.
Impulsive flares, on the other hand, are relatively small
with characteristic scales of ∼104 km but occur much more
frequently than LDE flares. A notable feature of these
events is that they do not show clear cusp-shaped loop structures, so some researchers considered the two types of flares
to be different phenomena. From the mid-1990s, however, many features similar to LDE flares were found in
impulsive flares (e.g., see a review by Shibata, 1999). In
1994, a careful comparison between SXR and HXR images revealed an above-the-looptop HXR source so-called
Masuda-type source (Masuda et al., 1994). It was soon discovered, from the time-of-flight (TOF) analysis, that the acceleration site of energetic electrons is situated high above
the Masuda type sources (Aschwanden et al., 1996). Other
important findings in impulsive flares are plasmoid ejections (Shibata et al., 1995; Ohyama and Shibata, 1998),
temperature distributions, upward and shrinking motions of
SXR loops, and increasing footpoint/double-ribbon separation (Sakao, 1994; Fletcher and Hudson, 2001; Asai etal., 2002). A detailed analysis of spatial distribution of
the coronal sources has provided evidence of a large scalecurrent sheet (Sui and Holman, 2003). It is only recently
that the γ -ray line observations revitalized the discussionof the differences between ions and electrons in acceleration and/or propagation (Lin et al., 2003).
In both types of flares, plasma heating and particle acceleration are primary processes of solar flares that take placein the solar corona (very recent observations by Hinodeclarified many small-size flares not only in the solar corona
but also in the chromosphere (e.g., Shibata et al., 2007).
The impact of such ubiquitous presence of flares, causedby reconnection, should be discussed in the future literature. During the peak time of flares, the accelerated particles and thermal conduction fronts propagate to and heat thechromosphere. The heated chromospheric plasma results inan upward flow or ‘chromospheric evaporation’. It is thisphase that the highest energy emission such as HXR and γ rays are prominently observed. In the later phase of flares,
a cooling process dominates heating. The typical temporalvariation of energy spectra shows the “soft-hard-soft” sequence (e.g. Fletcher and Hudson, 2002).
The magnetic field configuration for our solar flare model

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B. T. TSURUTANI et al.: A COMMON SCENARIO FOR FLARES AND SUBSTORMS

is shown on the right-hand side of Fig. 1. Our model isa double reconnection event, similar to the process of reconnection at Earth (reconnection occurs first at the magnetopause and then in the tail). We note that double reconnection models for solar flares have been previously proposed by Wang and Shi (1993), Aulanier et al. (2000), Kusano et al. (2004) and Zhang et al. (2006). We include thetether cutting model (Moore and Roumeliotis, 1992) andthe breakout model (Antiochos et al., 1999) because in a
broader sense, they are double reconnection models too (seereview by Shibata, 2005). In this paper we build on thismodel to draw a schematic for solar flares that is similar to
the magnetospheric case. The initial condition is two magnetic loops adjacent to each other. These are the large loops
on the left and center. The source of the loops and theirintrinsic magnetic energy is magnetic buoyancy.
The emergence of a new loop on the far right leads to energy transfer to the system (e.g., Chen and Shibata, 2000).
This loop has a polarity that is conducive to magnetic reconnection (indicated by an “x”) between the emerging loop
and the right-hand initial loop. This reconnection corresponds to the dayside reconnection in the Earth’s case. Reconnection between the small emerging loop and the central
loop enlarges the initial right-hand loop and increases themagnetic stress between it and the left-hand loop. If significant stress builds up between the two loops, magnetic
reconnection will take place between them and the energy
will be abruptly released in the form of a flare. If on theother hand the stress build up is slow such that the magnetic
stress is being dissipated more rapidly than increased, nosudden release of energy will occur.
If the rate of energy input (reconnection between the newloop and central loop) is rapid enough, a flare will occur
with short delay. If the energy input is less rapid but theamount of accumulated energy is sufficient for a flare, coronal disturbances may “trigger” it. As one example, coronalshocks propagating from distant regions of the sun can trigger “sympathetic” flares, much in the way an interplanetaryshock can trigger a substorm at Earth. If however the energy input is at a relatively low rate or there is no energy
being added, even strong triggers may be ineffective.

3.

Summary

We have developed a scenario for double reconnection
involving three coronal loops at the sun which has an analog
to the case of interplanetary magnetic reconnection at the
Earth’s magnetosphere and reconnection in the magnetotail.
Our scenario emphasizes short duration energy storage timescales in both the magnetosphere/ionosphere and at the sun.
If the energy input is rapid, flares/substorms occur. This
scenario is based on detailed observations made for storms
and substorms at Earth.
At this time, the authors do not speculate on what specific form the resultant energy from the (first) magnetic reconnection process is stored at Earth and at the Sun. For
the Earth’s case, energy storage in the magnetotail, magnetosphere and in the ionosphere have been suggested. The
literature is extensive. For the solar case, Zirin and Tanaka(1973), Neidig (1979), Hagyard et al. (1983) and Moore etal. (2001) have suggested that shear in the magnetic field

is one mechanism. This may be the case for our model between the central and left-hand loop of Fig. 1. Kusano etal. (2002) have suggested flux emergence was an importantfeature for a November 1997 interval. Similarly Schrijver etal. (2008) have indicated that electrical currents associatedwith the emerging flux is important. In our model, the existence of the right-hand side emerging loop is such a feature.
All of the energy storage mechanisms mentioned above(and more) may occur to varying degrees, depending on theparticular solar preconditions. It is possible that the pathof energy storage and release may be different for different
events.

4.

Final Comments

We have proposed a double reconnection model that canbe applied to both substorms at Earth and to solar flares. We
emphasize that the rate of the first reconnection process isimportant to determine if the substorm/flare: 1) will occur
immediately, 2) will occur with some delay, 3) could occur
if there is an external “trigger” and 4) may not occur at all.
Key to this scenario is that the energy input leaks away fromthe storage site (as implied from magnetospheric results)
and the preexisting magnetotail/loop energy is not the main
source for the substorm/flare. The ideas presented in thispaper are readily testable.
One can envision obvious simple variations to this double
reconnection model. Flux emergence enhancing the central loop will eliminate the need for the emergence of thesmall right-hand loop. Otherwise, the scenario is the same.
Again, the rate of free energy input into the system will be
critical for the occurrence/lack of occurrence of a flare.
Acknowledgments. Portions of this work were performed at the
Jet Propulsion Laboratory, California Institute of Technology under contract with NASA. This work was supported by the Grantin-Aid for Creative Scientific Research “The Basic Study of Space
Weather Prediction” (17GS0208, Head Investigator: K. Shibata)from the Ministry of Education, Culture, Sports, Science, andTechnology of Japan. Copyright 2009. All rights reserved.

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LETTER

Earth Planets Space, 61, 561–564, 2009

Modeling of substorms and flares by the fast reconnection mechanism
M. Ugai, K. Kondoh, and T. Shimizu
Research Center for Space and Cosmic Evolution, Ehime University, Matsuyama 790-8577, Japan(Received October 2, 2007; Revised March 29, 2008; Accepted June 4, 2008; Online published May 29, 2009)

The 3D spontaneous fast reconnection model is applied to well-known signatures of geomagnetic substorms
and solar flares. First, it is applied to the traveling compression regions (TCRs) associated with plasmoids
propagating down the tail plasma sheet, known as a definite signature of geomagnetic substorms, and the in-situ
satellite observations can be precisely explained, both qualitatively and quantitatively. Then, it is demonstrated
that the magnetospheric current wedge drastically evolves through field-aligned currents to link the tail current
to the auroral electrojet. It is also found that the well-known morphological features of two-ribbon flares canbe explained by the fast reconnection model. In particular, the joule heating, associated with the flare current
wedge, is shown to be important for the two-ribbon heating. Therefore, it is suggested that both solar flares andgeomagnetic substorms result from the same physical mechanism, i.e., the fast reconnection mechanism.
Key words: Fast reconnection, substorms, flares, TCR, current wedge.
The fast reconnection mechanism involving standing
slow shocks should be most responsible for explosive events
observed in space plasmas (Shibata, 1999). Then, questionis how the fast reconnection mechanism is realized in spaceplasmas of extremely large magnetic Reynolds number. A
possible fast reconnection configuration was first proposedby Petschek (1964), and it was suggested that the fast reconnection mechanism may be determined by external boundary conditions (Vasyliunas, 1975). However, it can be realized only when a localized resistivity is applied (Ugai andTsuda, 1977), and we have proposed the spontaneous fastreconnection model and demonstrated by 2D and 3D MHD
simulations that the fast reconnection mechanism can berealized as an eventual solution by the nonlinear instability due to positive feedback between current-driven anomalous resistivities and global reconnection flows (Ugai, 1984,
1986, 1992, 1999; Ugai and Zheng, 2005).
In general, the energy conversion principle can directly
be derived from Maxwell Equations as 2
∂ 0 E2B+(1)= −∇ · (E × B)/µ0 − E · J∂t 2µ02
The electric energy is negligible for the Alfven time scale,so that E × B indicates the magnetic energy flow, and E · J
the rate of conversion between magnetic and plasma energies. Any fast reconnection process involves magnetic energy inflow E × B toward the diffusion region and hence
requires the dissipation mechanism E · J > 0 in the diffusion (reconnection) region. Hence, the reconnection electric field E at the X reconnection point must be sustainedby some dissipation mechanism. If there is no dissipation
mechanism, the reconnection electric field should readilyc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

be short-circuited by electrons in the small diffusion regionof electron inertial length of c/ωpe .
The generalized Ohm’s law may be written as
E + u × B = R, where R is composed of the resistivity
term Rη , the Hall term RH , the electron pressure-tensor term
Rp , and the electron inertial term Ri . For the Hall term,
RH · J = 0, so that it cannot have any direct influence on
the reconnection process, since it has no dissipation mechanism. In the diffusion region (u × B ∼ 0), R can be described as ηJ since E · J > 0, where η(> 0) is the effective resistivity. The effective resistivity, usually provided
by Coulomb collisions, is extremely small in space plasmas, and if current densities are notably intensified, it may
result from wave-particle collisions due to current-driven
microinstabilites, such as ion acoustic, two-stream (Buneman), lower-hybrid drift instabilities (Lui, 2001). In fact,
anomalous resistivities are detected in laboratory plasmas(Ono et al., 2001).
First, let us examine the physical conditions for the fastreconnection evolution to be realized in actual 3D systems. Initially, we assume a current sheet system that contains antiparallel magnetic fields Bx and a sheet current in|y| < 1. Initiated by a small disturbance, all the phenomena grow by the self-consistent interaction between the reconnection flow and the effective resistivity. In order toexamine how magnetic reconnection is influenced by theeffective resistivity, we may assume the following resistivity models. For the current-driven anomalous resistivity model (A), η(r, t) = kR [Vd (r, t) − VC ] for Vd > VC
(Vd = |J/ρ|), where ρ is plasma density, and Vd the relativeelectron-ion drift velocity. For another anomalous resistivity model (B), η(r, t) = kJ [|J(r, t)| − JC ] for |J| > JC .
For the model (C), the Spitzer resistivity is assumed as,η(r, t) = kC [T (r, t)/T0 ]−3/2 , where T is the temperature.
We find that for the anomalous resistivity model (A) or(B), if the threshold VC or JC is sufficiently large, the fast

561

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Fig. 2. ISEE 3 magnetic field observations taken in the north lobe of thetail at x = −73Re in GSM coordinates (after Slavin et al., 1993).
Fig. 1. (Upper) Magnetic field configuration with the isosurface of theplasma pressure P, and (lower) plasma flow vectors for the anomalous
resistivity model (A), where the X neutral point is located at the origin.

reconnection mechanism fully evolves as a nonlinear instability because of the positive feedback, since the reconnection flows grow so as to enhance the current density at
the X point by the pinch effect (Ugai, 1984, 1986, 1999).
Figure 1 typically shows the resulting configuration for the
anomalous resistivity model (A), where the fast reconnection mechanism involving slow shock builds up, and a largescale plasmoid is formed ahead of the Alfvenic fast reconnection jet. Here, the simulation domain is a rectangularbox, 0 ≤ x ≤ L x = 20, 0 ≤ y ≤ L y = 6, and 0 ≤ z ≤L z = 9.8, with the mesh sizes x = 0.04, y = 0.015 andz = 0.1, and the conventional symmetry boundary conditions are assumed on the z = 0, x = 0, and y = 0 planes
with the other outer planes being free boundaries. For the
Spitzer resistivity model (C), no effective reconnection occurs because of the negative feedback, since the resistivity
becomes reduced because of the increase in temperature T
in the diffusion region (Ugai and Zheng, 2005). Note thatmagnetic reconnection is strongly influenced by the effective resistivity, and the fast reconnection mechanism can berealized for current-driven anomalous resistivities even ingeneral three dimensions.
Next, let us apply the spontaneous fast reconnection
model to substorm signatures observed by satellites. The
so-called traveling compression regions (TCRs) have beenclearly observed in the tail lobe of the Earth’s magnetosphere, and they were qualitatively expected to result fromthe plasmoid bulge propagating down the central plasma
sheet. The TCR signatures have been studied in detail(Slavin et al., 1993), and Fig. 2 typically shows the observed magnetic field variations, which indicates the pulselike compression of the earthward (Bx ) field component aswell as the northward to the southward tilting of the Bz fieldcomponent. These fundamental features of TCR have beentheoretically discussed by Birn (1992) and by Young andHameiri (1992), but have not been verified in detail by nu-

Fig. 3. Temporal variations of magnetic fields observed by virtual satellites located in the magnetic field (low-β) region, where Bx , B y and Bz
correspond to −Bx , −Bz and −B y in GSM coordinates, respectively.

merical simulations.
In order to clarify the physical mechanism of TCR, 3D
MHD simulations of the spontaneous fast reconnection
model are performed with the same simulation model as inFig. 1. It should be noted that unlike the traditional plasmoid, the resulting plasmoid contains no closed field lines
and is caused and sustained by the Alfvenic fast reconnection jet. Then, in order to directly compare the simulation results with the satellite observations, virtual satellites
are located in the magnetic field region outside the central
plasma sheet in the simulation domain, which can readilymeasure the temporal variations of magnetic fields in accordance with the plasmoid propagation (Ugai and Zheng,
2006a). Figure 3 shows the field components, measured
by the virtual satellites, which indicate the pulse-like fieldcompression Bx with the bipolar changes in B y and Bz .
Then, another tearing suddenly occurs, leading to a small
plasmoid propagating outward, so that a small TCR is observed at t ∼ 56. These results are in good agreement withthe actual satellite observations (Fig. 2) (Ugai and Zheng,
2006b).
Other well-known substorm signatures are the earthward
jet and the magnetic field dipolarization. In particular, whena substorm builds up, the tail current sheet may suddenly

M. UGAI et al.: MODELING OF SUBSTORMS AND FLARES

563

Fig. 5. (Color online) Plasma flow vectors and contour lines of the joule
heating ηJ2 , where the fast reconnection flow velocity u x < 0 attains
the Alfven velocity, VA ∼ −2.7, measured in the low-β region.

Fig. 4. (Color online) Current flow lines starting from the segment,
2.16 < x < 2.72 at y = 0.27 and z = 13, at different times,
where contour lines of the reconnected field component B y and the flow
velocity vectors u in the (z, x) plane are also shown, where the X neutral
point is located at x = L x = 10.

be disrupted so that a substorm current wedge evolves tolink the tail current to the auroral electrojet through fieldaligned currents (McPherron et al., 1973). The importanceof current wedge has widely been recognized by satellite
and ground observations, but this long-standing question
has never been resolved theoretically. Recently, it is demonstrated on the basis of the 3D spontaneous fast reconnection
model that when the fast reconnection jet collides with theclosed field lines in the near-Earth magnetosphere, the drastic current wedge evolution can be realized (Ugai and Kondoh, 2006).
We have also found that only when the east-west width of
the tail current sheet is 3–4 times larger than its thickness,the 3D fast reconnection mechanism and the current wedge
can fully be set up (Ugai and Shimizu, 1996; Ugai, 2007).
For this case, Fig. 4 shows the resulting current flow lines,
where the contour lines of the reconnected field component
B y and the flow velocity vectors u in the (z, x) plane arealso shown. In this model, magnetic reconnection is initiated at x = L x = 10, and the x = 10 plane as well as thex = 0 plane is assumed to be the symmetry boundary. We
readily see that when the closed field lines in the near-Earthmagnetosphere is compressed by the 3D fast reconnection
jet, the sheet current (Jz < 0) ahead of the closed field lines
drastically turns its direction toward the foot points of close
field lines through field-aligned currents. This is generally
consistent with the predicted substorm current wedge.
In view of morphological similarities between flares andsubstorms, the spontaneous fast reconnection model may
also be applied to two-ribbon flares. Unlike in-situ observations in the Earth’s magnetosphere, magnetic fields canhardly be measured in the solar corona. In this sense, any
theoretical model of solar flare is circumstantial, so that it isessential to clarify the well-known morphological featuresthat have been obtained from satellite observations. The
previous theories were mostly based on the cartoon model
based on the 2D Petschek reconnection configuration, andit was supposed that the chromospheric flare heating should
be caused directly from the coronal plasma heated and accelerated by 2D reconnection shocks.
The solar surface is modeled as follows. An antiparallel
magnetic field B = [Bx (y), 0, 0] is initially assumed as:
Bx (y) = sin(π y/2) for 0 < y < 1; Bx = 1 for 1 < y < 4;
Bx = cos [(y − 4)π/1.2] for 4 < y < 4.6; Bx = 0 for y >4.6; also, Bx (y) = −Bx (−y) for y < 0. Fluid velocity u =(0, 0, 0), and plasma pressure P(y) satisfies the pressurebalance condition, P + Bx2 = 1 + β0 , where β0 = 0.15 istaken.
Also,
plasma density ρ initially satisfies ρ(x, y) =R0 exp −(x/0.4)4 + 1 P(y)/(1 + β0 ), where R0 = 100
is taken, so that x = 0 corresponds to the chromosphere,
and the corona is for x
0.4. In the chromosphere, placedin the x = 0 plane, the plasma density is assumed to be
100 times larger than in the corona for x > 0.4, so thatthe temperature in the corona is 100 times larger than in thechromosphere.
An initial disturbance is imposed at x = L x = 10 on theinitial configuration, and then the current-driven anomalous
resistivity models are assumed. Figure 5 illustrates theresulting plasma flow vectors and contour lines of the joule
heating ηJ2 . The joule heating in the (x, y) plane mostly
indicates the standing slow shock layer, across which theplasma is accelerated to the Alfven velocity. The plasmoid,
propagating in the negative x direction (at t = 39), collides
with the chromosphere (x = 0) at t ∼ 42, leading tosudden current wedge evolution, which may be called theflare current wedge by analogy with the substrom current
wedge. For t > 42, distinct plasma downflows (u x < 0)
toward the chromosphere (x = 0) occur along the magnetic
loop boundary.
The flare current wedge causes an extreme increase in
the current density (hence an anomalous resistivity) in thechromosphere (x = 0). Hence, Fig. 5 indicates that re-564

M. UGAI et al.: MODELING OF SUBSTORMS AND FLARES

sults suggest that both solar flares and geomagnetic substorms result from the same physical mechanism, i.e., thefast reconnection mechanism.
Acknowledgments. This work was supported by Grant-in-Aids
for Creative Scientific Research ‘The Basic Study of Space
Weather Prediction’ (17GS0208, Head Investigator: K. Shibata)from the Ministry of Education in Japan, Mitsubishi Foundation, RISH of Kyoto University, and Solar-Terrestrial Environment
Laboratory of Nagoya University.

References

Fig. 6. (Color online) Temperature distributions, shown by contour lines
at x = 0, where the maximum temperature becomes more than 20 times
its initial value.

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Lui, A. T. Y., Current disruption in the Earth’s magnetosphere: observations and models, J. Geophys. Res., 101, 13067–13088, 1996.
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345, 2001.
McPherron, R. L., C. T. Russel, and M. P. Aurbry, Satellite studies ofmagnetospheric substorms on August 15, 1968. 9. Phenomenologicalmodel for substorms, J. Geophys. Res., 78, 3131–3149, 1973.
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the Physics of Solar Flares, NASA Spec. Pub., SP-50, 425–439, 1964.
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model of flares, Astrophys. Space Sci., 264, 129–144, 1999.
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Ugai, M., Self-consistent development of fast magnetic reconnection withanomalous plasma resistivity, Plasma Phys. Controlled Fusion, 26,
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markable joule heating occurs along the thin layer in thechromosphere near the seperatrix, which bounds the preand post-reconnection field lines. In particular, the strongest
heating occurs impulsively at times t = 42 and 43. Accordingly, Fig. 6 shows the resulting temperature distributions,and demonstrates that at t = 42 the temperature is suddenly enhanced distinctly in the chromospheric thin layer,
which presents the two-ribbon structure because of the symmetry boundary conditions. Hence, the plasma pressure isnotably enhanced in the chromosphere to cause distinct upward flows (u x > 0) from the chromosphere at t = 48
inside the loop, which is consistent with the so-called chromospheric evaporation observed during flares. The joule
heating layer moves in the positive y direction as the reconnected field lines are piled up, and the cusp-shaped flare
loop expands outward. These results are consistent with thewell-known morphological features of two-ribbon flares.
In summary, in-situ satellite observations of TCR signatures can exactly be explained by the 3D spontaneous fastreconnection model (Figs. 2 and 3). Also, the 3D fast reconnection jet causes drastic evolution of magnetosphericcurrent wedge (Fig. 4). For this theoretical model, currentdriven anomalous resistivities are essential, and the current
disruption occurs just ahead of the closed field lines to form
the current wedge (Fig. 4). Interestingly, these basic features are rather consistent with those of the current disruption model (Lui, 1996). In addition, it is demonstrated thatthe well-known morphological features of two-ribbon flares
are pertinently explained by this theoretical model (Figs. 5
and 6). In particular, the drastic increase in the chromospheric temperature occurs in the shape of two ribbons, andM. Ugai (e-mail: ugai@cosmos.ehime-u.ac.jp), K. Kondoh, and T.
the resulting coronal flare loop is expanding outward. Also, Shimizu
the definite chromospheric evaporation occurs. These re-LETTER

Earth Planets Space, 61, 565–568, 2009

Coronal loops, flare ribbons and aurora during slip-running
Brigitte Schmieder1 , Guillaume Aulanier1 , Pascal Démoulin1 , and Etienne Pariat2
1 Observatoire de Paris, LESIA, 92195 Meudon, France
2 NRL, Washington DC, USA(Received September 12, 2007; Accepted August 16, 2008; Online published May 29, 2009)

Solar two ribbon flares are commonly explained by magnetic field reconnections in the low corona. During
the reconnection energetic particles (electrons and protons) are accelerated from the reconnection site. These
particles are following the magnetic field lines down to the chromosphere. As the plasma density is higher inthese lower layers, there are collisions and emission of radiation. Thus bright ribbons are observed at both ends
of flare loops. These ribbons are typically observed in Hα and in EUV with SoHO and TRACE. As the timeis going, these ribbons are expanding away of each other. In most studied models, the reconnection site is aseparator line, where two magnetic separatrices intersect. They define four distinct connectivity domains, acrosswhich the magnetic connectivity changes discontinuously. In this paper, we present a generalization of this model
to 3D complex magnetic topologies where there are no null points, but quasi-separatrices layers instead. In thatcase, while the ribbons spread away during reconnection, we show that magnetic field lines can quickly slip along
them. We propose that this new phenomenon could explain fast extension of Hα and TRACE 1600 Å ribbons,
fast moving HXR footpoints along the ribbons as observed by RHESSI, and that it is observed in soft X rays with
Hinode/XRT.
Key words: Sun: flares, magnetosphere: aurora.

1.

Introduction

Eruptions occur at locations on the Sun where there
is a build-up of a large amount of magnetic energy andwhen this energy is released via some reconnection process. Many models deal with how this energy release is accomplished; for example Forbes and Isenberg (1991), Lin etal. (1998) discuss on the convergence of magnetic flux below a flux tube situated along a magnetic polarity inversion
line that leads to enhancement of the flux tube and eruption. Chen and Shibata (2000) presents a model where eruption results when the tension of the sheared arcade or flux
tube field is weakened via reconnection between the main
magnetic field and emerging flux (kind of “tether-cutting”
mechanism). Antiochos et al. (1999) discuss instead disruption of field lines and reconnection above flux tubes. To determine which of the mechanism is predominantly responsible for eruptions it is necessary to observe the onset andthe evolution of flares. The coronal plasma is frozen into
the magnetic field almost everywhere except where current
sheets can be formed and then dissipated. Current sheets develop along separatrices when the magnetic configuration
evolves quasi-statically or dynamically. A very powerfultool to understand where the energy could be deposited is to
study the magnetic topology of the active region, since it defines where magnetic reconnection is expected to occur (seereviews of Démoulin, 2005; Longcope, 2005; Schmieder,
2006).
In the first section, magnetic topology models are prec The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

sented. In the second and third sections, we review eruptive
and compact flares showing that their dynamics cannot be
neglected to interpret the formation of long ribbons withevolving Hα, UV brightenings and X-ray kernels. New
simulations are briefly described. Slip-running reconnection simulation explains the fast motion of X-ray sourcesalong flare.

2.

Magnetic Topological Models

Coronal activities such as flares, eruptions and general
heating are often attributed to the manner in which the coronal field responds to photospheric motion. The coronalplasma has a low resistivity and to release efficiently thefree energy, small length scales have to be created. Coronal magnetic fields are forced to evolve continuously byslow photospheric velocities (0.1 km/s), faster velocities
still lower to the typical Alfvén velocity (∼1000 km/s) may
exist during magnetic flux emergence. In this context magnetic configurations, with a slow evolution at the boundary
leads to the formation of very thin current layers play a keyrole (review of Démoulin, 2006). Let us recall some classical definitions of magnetic configuration and reconnection.
Separatrices are magnetic surfaces where the magnetic field
line linkage is discontinuous, thus where the field lines canchange abruptly of connectivity. In 2D configuration the reconnection occurs at a X-point (null point) where the magnetic vanishes, in 3D configuration the intersection of the
field lines occur along the separator, intersection of the separatrices. Current sheet form along the whole separatrices
when shearing flows are present in the photosphere. The
flare ribbons are found at the intersections of the separatrices and the chromosphere.

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Flare ribbons and loops evidence the locations where thestored energy is released. For testing the spatial localizationof the energy release sites, it is needed to extrapolate thefield lines in the corona using photospheric magnetograms
as a boundary condition. When the magnetic field is no
more represented by point charges but maintained continuously as observed, there are not necessarily separatrices
to interpret the ribbons: a generalization of the concept of
separatrices does provide an interpretation of 3D magnetic
reconnection (Démoulin et al., 1996a, 1997). This new concept is based on the existence of quasi-separatrice layers(QSL) for general magnetic fields anchored to a boundary.
QSLs are defined as volumes where magnetic field lines canchange of connectivity abruptly. There are no coronal nullpoints in such configurations. Such topological properties
are insensitive to detailed geometry of the magnetic field,
and thereby create a very robust tool to understand the lociof flare energy release. The intersections of QSLs and thechromosphere are restricted to smaller regions than in thecase of separatrices and match better the shape of the ribbons (Schmieder et al., 1997).

al., 2006b). It was shown that the later arcades are less andless sheared (Su et al., 2006). During cooling process thetwo ribbon distance is increasing. In complex active regions
different systems of ribbons can be formed and developedin a fast time, of the order of few minutes (14 July 2000,
28 October 2003, 13 September 2005, 27 May 2003). In
the event of 13 September 2005 a series of 10 flares occur
within one day and even a series of 3 flares (X1.4, X 1.5,
X1.7) in three hours. The concerned active regions are allcomplex containing a spot with constant new emerging fieldwith fast moving polarities. It is difficult to identify thetrigger of each flare of the series.
Nevertheless, we are able to find the locations where themagnetic reconnection is possible and produce flares byanalyzing the topology either by lfff (linear-force-free field)
extrapolation when the shear is weak enough, otherwise by
nlfff (non linear-force-free field) methods of extrapolation
have to be applied (Régnier and Canfield, 2007).
Many models of flare onset are developed based ontether-cutting or straining forces (Klimchuk, 2001). For
large quadrupolar configuration, the breakout model proposed by Antiochos (1999) seems to be successful for some
3. Eruptive Flarescases (Aulanier et al., 2000). The existence of null pointFirstly we investigated the regions of large flares, we which was pointed out in the Antiochos model does notcalled eruptive flares when a coronal mass ejection (CME) seem to be a necessary condition for breaking the overlyis related to the flare. In this frame, Chen and Shibata ing lines (Schmieder et al., 2006; Mandrini et al., 2006).
(2000) and Lin (2004) proposed unified models. As the Reconnection could occur in quasi separatrices layers withmagnetic field lines are reconnected, a plasmoid is escaping no null points (Li et al., 2006; Schmieder et al., 2007).
and forming the CME. During the reconnection, electrons
are precipiced downwards to denser layers. They heat the 4. QSL Reconnection with Slippage of Magnetic
Field Lines
plasma and form the so-called two bright ribbons in thechromosphere (visible in Hα, in Ca II H by Hinode/SOT,In the previous section we have shown complex examples
the 1600 Å continuum by TRACE), in the transition region of flares with multiple ribbons formed at different places(CDS, EIT and TRACE). Between the ribbons, loops are successively. Here we present a simple compact flare withobserved in different wavelengths: bright X ray loops, in no CME in order to study in details the dynamics of thecoronal lines 171 Å and 195 Å and bright or dark in Hα as ribbons, not the well known increasing distance of the ribthey are cooling (Schmieder et al., 1996; DelZanna et al., bons versus time but the fast lateral extension of the ribbons.
2006a). The loops form growing arcades with higher and The flare occurs in a sheared active region at the location ofhigher hot loops while the reconnection point is rising. In a small emerging flux (Berlicki et al., 2004). The obserthe ribbons, kernels are the footpoints of loops (DelZanna et vation in Hα shows two ribbons, one of them is relatively

Fig. 1. Magnetic field lines extrapolated in a linear force free configuration and Hα ribbons of the 22 October 2003 flare for two times observed with
the VTT in Canaries showing the fast extension of the ribbons (Berlicki et al., 2004).

B. SCHMIEDER et al.: CORONAL LOOPS, FLARE RIBBONS AND AURORA

567

Fig. 2. Quadrupolar magnetic reconnection with slip-running field lines for three different times. The darker field lines have a fixed footpoint anchoredin a fixed point in the right source, the other footpoint is slip-running continuously along the quasi-separatrice layer. During the reconnection, theplasma in the different field lines will be successively heated with footpoints visible as bright kernels. This behaviour explains the fast extension ofribbons (Aulanier et al., 2006).

Fig. 3. Sketch of the formation of aurora due to magnetic reconnection in a QSL configuration.

short and stays short, the other one is developing an extension in a few minutes. The conclusion of the Berlicki et al.
(2004)’s paper was that there was a series of reconnectionsin the corona. The question arises to know if this was really
due to multiple reconnections. We performed a lfff extrapolation using the data base of FROMAGE and pointed out
the existence of loop-like field lines growing with one fixed
footpoint and the other footpoint was slip-running along theribbon (Fig. 1).
Aulanier et al. (2006) propose a new idea with the slippage of the field lines along the QSLs (Fig. 2). Using timedependent MHD simulation it is shown the possibility offield lines to change connectivity in a continuously way
and not abruptly like in the classical null point reconnection where field lines clearly connect by pair. This process
can take place in many solar flares. Magnetic field configurations with fields weakly stressed by asymmetric line-tied
twisting motions are considered. When the line-tied driving is suppressed, magnetic reconnection is solely due tothe self-pinching and dissipation of current layers formed
along QSLs. For thin QSLs and high resistivity, the field
line footpoints slip-run at super-Alfvénic speeds along theintersection of the QSLs with the chromosphere. Since particles are probably accelerated in reconnection regions orin the vicinity, slip-running reconnection could explain thefast extension of the ribbons in all the wavelengths, being
the result of heat of the plasma as particles travel in denser
plasma. Recently Hinode observed moving loops movingthat have been interpreted as due to the slippage of magnetic field lines (Aulanier et al., 2007).

5.

Reconnection in the Magnetosphere in QSLs

Making an analogy between solar flares and magnetospheric substorms, we can conjecture that QSL reconnection may very well occur in the latter. Indeed, the geometryof the Earth magnetosphere can possibly make the appearance of real 3D null points impossible in the magneto-tailwhen it is stretched anti sunward. This does not preclude
the development of rotational discontinuities in the tail, i.e.
of 2D null points with an azimuthally guide field, as often
reported in global models of the magnetosphere. But solar models teach us that the latter configurations can correspond to a hyperbolic flux tube (HFT), hence to QSLs when
the system is viewed globally. Assuming that substorms
correspond, on large scales, to the formation of a fully 3D
twisted flux rope rooted in the ionosphere (and not a 2D
plasmoid), we can transpose the solar Cartesian 3D modelof Démoulin et al. (1996a) to the Earth spherical geome-

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B. SCHMIEDER et al.: CORONAL LOOPS, FLARE RIBBONS AND AURORA

try, replacing the solar photosphere by the ionosphere andthe solar corona by the magnetosphere. This topology naturally possesses QSLs between the flux rope and the outerfields, that intersect at a HFT located between the Earth andthe flux rope, and whose footprints have J shapes. In thispicture, polar auroras are the equivalent to chromosphericflare ribbons, i.e. they are due to the impact of particles accelerated from the reconnection site, i.e. the HFT.
Transposing our recent findings about slip running reconnection in the corona to the magnetosphere, we predict andinterpret by the latter model the following evolution of aurorae: (1) the aurora starts to form a point-like brightening
at the ionospheric footpoint of the HFT, where QSL reconnection is the most efficient since that is where the strongest
field aligned currents (i.e. parallel electric fields) naturally
develop, according to Aulanier et al. (2005); (2) the aurora brightnings expand along the footprint of the J-shaped
QSLs predicted by Démoulin et al. (1996b), azimuthally in
the Earth case; this fast development is due to slip-runningreconnection at the HFT (as described in Aulanier et al.,2006) in the magneto-tail during the formation of the flux
rope that it later ejected anti-sunward. We do not knowwhether these dynamics of polar aurorae are frequently observed or not, so we would like to encourage further studies
to test our present transposition of solar slip-running reconnection models to magnetospheric models (Fig. 3).

6.

Conclusion

Flares and eruptions are dynamical events which evolvewith a fast speed. Past flare models were static in 2D and
3D. They provided good insight on the magnetic topologyof active regions and the loci of possible deposit of energy.
We have shown that MHD simulations explain some particular aspects of the dynamics of flares. In one case wehave shown how slip-running magnetic field lines in quasiseparatrice can mimic fast extension of Hα and UV ribbons
observed by THEMIS and TRACE and running XRT loops
observed by Hinode. Finally, making an analogy between
solar flares and magnetospheric substorms, we can conjecture that QSL reconnection may very well occur in the latter.
Acknowledgments. I would like to thank Dr. Akosufu and Dr.
Shibata, the organizers of the CAWSES workshop in Alaska where
I present this work.

References
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Lundquist, N. Nakurage, T. Sakao, and M. Weber, Science, 2007 (submitted).
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gradual phase of the X17 flare on October 28, 2003, Sol. Phys., 239,
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Démoulin, and E. Pariat

LETTER

Earth Planets Space, 61, 569–572, 2009

Three-dimensional non-linear instability of spontaneous fastmagnetic reconnection
T. Shimizu, K. Kondoh, and M. Ugai
Department of Computer Science, Ehime University, Bunkyo town, Matsuyama City 790-8577, Japan(Received November 2, 2007; Revised June 23, 2008; Accepted August 24, 2008; Online published May 29, 2009)

Three-dimensional instability of spontaneous fast magnetic reconnection is studied using MHD (magnetohydro-dynamic) simulation. Previous two-dimensional MHD studies have demonstrated that, if a current-driven
anomalous resistivity is assumed, two-dimensional fast magnetic reconnection occurs and two-dimensional largescale magnetic loops, i.e., plasmoids, are ejected from the reconnection region. In most two-dimensional MHD
studies, the structure of the current sheet is initially one-dimensinal. On the other hand, in recent space plasma
observations, fully three-dimensional magnetic loops frequently appear even in the almost one-dimensional
current sheet. This suggests that the classical two-dimensional fast magnetic reconnection may be unstable toany three-dimensional perturbation, resulting in three-dimensional fast magnetic reconnection. In this paper,
we show that a three-dimensional resistive perturbation destabilizes two-dimensional fast magnetic reconnection
and results in three-dimensional fast magnetic reconnection. The resulting three-dimensional fast reconnection
repeatedly ejects three-dimensional magnetic loops downstream. The obtained numerical results are similar tothe pulsating downflows observed in solar flares. According to the Fourier analysis of the ejected magnetic loops,
the time evolution of this three-dimensional instability is fully non-linear.
Key words: Magnetic reconnection, solar flare, MHD simulation.

1.

Introduction

Fast magnetic reconnection provides a physical mechanism by which magnetic energy is explosively converted
into plasma kinetic and thermal energies. This mechanism
has been considered to play a crucial role in solar flares andgeomagnetic substorms. Fast magnetic reconnection has
been reported in many numerical magneto-hydro-dynamic(MHD) studies (e.g., Ugai and Tsuda, 1977). On the other
hand, the plasma jets and magnetic loops associated with
fast magnetic reconnection have been also reported in spacesatellite observations of solar flares (Masuda et al., 1994;
Shibata et al., 1995; Shibata, 1996; Yokoyama et al., 2001;
Asai et al., 2004). In particular, in some observation reports, the three-dimensional (3D) structure of fast magnetic
reconnection was discussed (Shibata et al., 1995; Asai etal., 2004). Asai et al. (2004) reported that the intermittent
plasma downflows observed in solar flares may be caused
by fast magnetic reconnection in the high-altitude corona.
In order to theoretically explain the observation data, theysuggested that 3D fast magnetic reconnection may occur
even in a uniform (1D) current sheet and, hence, the ejected
3D magnetic loops may be strongly localized in the current sheet direction. To explain the formation of impulsive
plasma downflows, Linton and Longcope (2006) proposed atheoretical 3D model. However, it is still unclear how sucha 3D fast magnetic reconnection process occurs in the 1D
current sheet.
c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

In this paper, the 2D spontaneous fast magnetic reconnection model proposed by Ugai is numerically developed
to a 3D model. At this point, note that the study shownin this paper is basically different from the 3D studies reported by Ugai and collegues (Ugai et al., 2004, 2005). In
the studies reported by Ugai, since the initial resistive disturbance is strongly localized in the sheet current direction,
it directly results in a “single” 3D fast magnetic reconnection. In contrast, in the work presented here, the initial resistive disturbance is almost 2D but only includes a “veryweak non-uniformity (perturbation)” in the sheet current direction, resulting in “multiple” 3D fast magnetic reconnection processes. In other words, this paper shows that the
2D fast reconnection process is basically unstable for a 3D
perturbation. As a result, the destabilized 2D fast magnetic
reconnection can be three-dimensionally localized even in
a 1D current sheet. At the time, some 3D magnetic loops
are repeatedly ejected from the reconnection region. Thesefeatures of 3D fast reconnection seem to be consistent withthe observation data of intermittent plasma downflows observed in solar flares.

2.

Simulation Setup

In the spontaneous fast magnetic reconnection model, thereconnection process is initiated by a small resistive disturbance in the current sheet (Ugai and Shimizu, 1996; Ugai,
1999). After the initial disturbance is removed, fast reconnection spontaneously develops by a current-driven anomalous resistivity enhanced by the nonlinear tearing instability.
Hence, no external driven mechanism is required to keep thereconnection process going.

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T. SHIMIZU et al.: THREE-DIMENSIONAL FAST MAGNETIC RECONNECTION

The MHD simulation procedures are basically the sameas in Ugai (1987), except for the initial resistive disturbanceshown later, in this article i.e., Eq. (1). The 3D compressible
MHD equations are used. The computational region isrestricted to the first quadrant and set to be a rectangularbox, (0 ≤ x ≤ L x , 0 ≤ y ≤ L y , 0 ≤ z ≤ L z ), becauseof the conventional symmetry boundary conditions withrespect to the x z-plane at y = 0, yz-plane at x = 0, andx y-planes at z = 0 and L z . On the other boundaries, freeboundary conditions are assumed, where all the quantities
are determined by the state of the inner region, so that thefirst derivatives of the quantities in the direction normal
to the boundaries vanish (the normal component of B isdetermined by the solenoidal condition). Because of thesymmetry boundary conditions for x y-planes at z = 0 and
L z , the simulation box is closed in the z-direction. In otherwords, the simulation box may be considered to be periodic
in the z-direction, where 2L z is the maximum wave length
for all the z-directional MHD waves. The computational
region L x = 30, L y = 10, and L z = 20 are taken with the Fig. 1. Some of magnetic field lines, a contour map of B y field intensity,and a pattern of flow velocity at T = 48.
mesh points N x = 880, N y = 1000, and Nz = 100.

3.

Simulation Results

3.1 The initial stage
The simulation starts with β0 = 0.15 in the magnetic
field region, which consists of Bx0 = 1.0 and P0 = 0.075.
Initially, every magnetic field line is exactly set up in thex-direction. The current sheet is initially formed on the x zplane and the current is flowing in the negative z-direction.
In the initial current sheet, Bx monotonously varies from
Bx0 at y = +1 to zero at y = 0. Then, Bx = Bx0 is
set for y > +1. There is no initial plasma flow. The
Alfven speed VA is unity in the initial upstream magnetic
field region based on Bx0 = 1.0, and the Alfven transit time
to pass the distance of L x = 30 is set as T = 30 in the timescale.
The initial resistive disturbance shown below initiates atearing instability in the current sheet during 0 < T < 4,
which is strongly localized around the z-axis.

η0 = 0.04 exp −α x 2 + y 2 {1 + 0.01 cos (π z/L z )}(1)
where α = 0.01. In this initial resistive disturbance, themagnetic Reynolds number is estimated to be 25 at theorigin. Note that this resistive disturbance fluctuates only by
1% in the z-direction, which is the sheet current direction.
Accordingly, the resulting reconnection process is expected
to be nearly 2D. In fact, the magnetic loop ejected firstly
from the reconnection region is almost 2D, as shown laterin Fig. 1.
After T = 4, η0 is removed and, instead, the currentdriven anomalous resistivity η1 shown below is switched
on, which starts to drive the fast magnetic reconnection after
about T = 20.
(2)= 0.002(Vd − Vc ) for Vd ≥ Vc
η1
= 0.0
for Vd < Vc
(3)

Fig. 2. The figure format is the same as Fig. 1 but at T = 60.

rotB and is unity at the center of the initial current sheet,i.e., y = 0. Also, the uniform plasma density ρ is initially
set to be unity.
3.2 The first stage (2D fast reconnection)
Figure 1 shows magnetic field lines on three x y-planes
for z = 0, 0.5L z , and L z with a B y contour map and plasma
flow vectors on an x z-plane for y = 0 at T = 48. Alongthe z-axis, the magnetic neutral line for fast reconnection
process is formed. The magnetic field lines in all three x yplanes are very similar. In addition, the B y contour map andplasma flow vectors are almost uniform in the z-direction.
Hence, at this time, the fast magnetic reconnection process
where Vd = |J |/ρ is the ion-electron drift velocity and is 2D, and a 2D large-scale magnetic loop is formed beVc = 4.0 is set. The current density J is obtained from tween 15 < x < 30.

T. SHIMIZU et al.: THREE-DIMENSIONAL FAST MAGNETIC RECONNECTION

Fig. 3. B y contour map on the x z-plane at y = 0 and T = 45.

Fig. 4. B y contour map at T = 60.

571

Fig. 6. Z -directional Fourier analysis of B y contour map on x z-plane at
T = 45.

Fig. 7. Z -directional Fourier analysis at T = 60.

Fig. 5. B y contour map at T = 75.
Fig. 8. Z -directional Fourier analysis at T = 75.

3.3 The second stage (3D fast reconnection)
Figure 2 shows the numerical result similar to Fig. 1
but for T = 60. The 2D large-scale magnetic loop in
20 < x < 30 corresponds to the one in 15 < x < 30 ofFig. 1, so the loop is propagating with the reconnection jets.
More exactly, the propagating speed is about 0.6VA and isa little slower than the jet speed VA . In addition, anothersmall magnetic loop is observed in the vicinity of the origin,which is marked by “A” in Fig. 2. Since this magnetic loop
is not observed in the magnetic field lines of z = 0.5L z and
L z , the loop structure is evidently 3D. This 3D magnetic
loop is a result of the z-directional perturbation in the initialresistive disturbance Eq. (1). In Fig. 2, the B y contour
map on the x z-plane at y = 0 is also shown, which is
the intensity of the reconnected magnetic field. Clearly, the3D magnetic loop marked by “A” corresponds to a highintensity island on the B y contour map, which is a little
extended in the z-direction and largely curved in the positive
x-direction.
3.4 Time variation of By contour map
Figures 3, 4, and 5 show B y contour maps on the x z-plane
for y = 0 at T = 45, 60, and 75. In Fig. 3, no 3D magnetic
loop is observed and a 2D magnetic loop is only observed
as vertical bands at 13 < x < 17. This is consistent
with Fig. 1. Figure 4 is exactly the same as the contour
map in Fig. 2, where L z = 20. In Fig. 4, a 3D magnetic

loop appears and then, in Fig. 5, slightly propagates in thepositive x-direction. In addition, in Fig. 5, considering thesymmetry boundary condition on the x-axis, i.e., z = 0, two
3D magnetic loops are also observed as small round-shapeislands at (x, z) = (5, 5) and (7, 0).
3.5 z-directional Fourier analysis
Figures 6, 7, and 8 respectively show the z-directional
Fourier analysis of Figs. 3, 4, and 5 as the contour mapof the Fourier components. These figures show the time
variation from T = 45 to 75. The vertical axis Rz of thesefigures is scaled as the inverse of the z-directional wave
length λz , where unity Rz = (1/λz ) = 1 is equivalent to
1/(2L z ). Note that 2L z corresponds to the wave length of
the z-directional resistive perturbation in Eq. (1). In Fig. 6,
the growth of the Fourier components 1 ≤ Rz < 10 related
to the 2D magnetic loop is observed at x = 13. In Fig. 7,
the Fourier components move to x = 21, and new Fouriercomponents 1 ≤ Rz < 10 widely appear in the 3D magnetic
loop region located in 2 < x < 5. Next, in Fig. 8, the
new Fourier components widely spread in the x-direction,
because of the multiple formations of 3D magnetic loops
in Fig. 5. Since the initial resistive disturbance Eq. (1)only has Rz = 1 component, the higher-order components
Rz ≥ 2 are generated by the non-linear instability of the fastmagnetic reconnection. In Figs. 6 and 7, the 2D magnetic

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T. SHIMIZU et al.: THREE-DIMENSIONAL FAST MAGNETIC RECONNECTION
Log (int By)

7.0

K=1

6.0
K=2
5.0
4.0

k=4

3.0
2.0

k=10
20

30

40

50

60

70

80

Time

Fig. 9. Time variation of some z-directional Fourier components which
are averaged over 0 < x < L x .

loop also generates the higher-order components Rz ≥ 2.
However, evidently, the higher-order Fourier components
related to 3D magnetic loops are spread more widely thanthose of the 2D magnetic loop.
Figure 9 shows the time variation of four typical zdirectional Fourier components for the B y contour map,
where k = Rz . On the 2D stage (T < 50), the k = 1 component that corresponds to the z-directional perturbation in
Eq. (1) linearly grows up and, on the 3D stage (50 < T ), almost saturates. As mentioned in Figs. 7 and 8, since Eq. (1)has no Rz = k ≥ 2 components, such higher-order components should be created from the k = 1 component, due tothe non-linear instability in the 3D fast magnetic reconnection. In fact, the higher-order components rapidly grow up
after the linear growth of k = 1.

4.

Summary

may be repeatedly ejected even on the 1D current sheet, due
to the fast magnetic reconnection.
In the next step of this study, the temporal dynamics
of ejected magnetic loops must be studied. In the temporal dynamics, some of the ejected magnetic loops may
merge into a magnetic loop in the downstream region. Finally, few large-scale magnetic loops can only survive. At
this point, the 3D fast reconnection model shown in thispaper may be closely related to the fractal and intermittent reconnection model that was proposed by Shibata andTanuma (2001) to explain the solar flare observation data
as a time-development from micro-reconnection processes
to a macro-reconnection process. Since their basic concept
is a 2D model, the 3D fast reconnection shown here should
give a new view point to their model.
Acknowledgments. This work was supported by grant-in-aidsof the Japanese education ministry; Ehime Univ. T. Shimizu,“Study of Multi-scale Plasma Simulation of Magnetic Reconnection” (15540475) and Kyoto Univ. K. Shibata, Creative Scientific Research, “The Basic Study of Space Weather Prediction”(17GS0208). In addition, this work is supported by Research Institute for Sustainable Humanosphere (RISH) of Kyoto University
and Solar-Terrestrial Environment Laboratory (STEL) of Nagoya
University. The numerical calculations were performed on the
KDK computer system at RISH and FUJITSU HP2500 parallel
computer system at Nagoya and Kyoto University Data Processing Centers.

References
Asai, A., T. Yokoyama, M. Shimojo, and K. Shibata, Downflow motions
associated with Impulsive nonthermal emissions observed in the 2002
July 23 Solar Flare, Astrophys. J., 605, L77, 2004.
Linton, M. and D. Longcope, A Model for Patchy Reconnection in Three
Dimensions, Astrophys. J., 642, 1177–1192, 2006.
Masuda, S., T. Kosugi, H. Hara, S. Tsuneta, and Y. Ogawara, Loop-top
impulsive hard X-ray source of a solar flare as evidence for magnetic
reconnection, Nature, 371, 495–497, 1994.
Shibata, K., New Observational Facts about Solar Flares from Yohkoh
Studies—Evidence of Magnetic Reconnection and a Unified Model of
Flares, Adv. Space Res., 17, 9–18, 1996.
Shibata, K. and S. Tanuma, Plasmoid-induced-reconnection and fractal
reconnection, Earth Planets Space, 53, 473–482, 2001.
Shibata, K., S. Masuda, M. Shimojo, H. Hara, T. Yokoyama, S. Tsuneta,
T. Kosugi, and Y. Ogawara, Hot plasma ejections associated with
Compact-Loop solar flares, Astrophys. J., 451, L83, 1995.
Ugai, M., Strong loop heating by the fast reconnection in a closed system,
Geophys. Res. Lett., 14, 103–106, 1987.
Ugai, M., Basic physical mechanism of reconnection development andmagnetic loop dynamics, J. Geophys. Res., 104(A4), 6929–6939, 1999.
Ugai, M. and T. Tsuda, Magnetic field-line reconnexion by localized enhancement of resistivity, 1. Evolution in a compressible MHD fluid, J.
Plasma Phys., 17, 337–351, 1977.
Ugai, M. and T. Shimizu, Computer studies on the spontaneous fast reconnection mechanism in three dimensions, Phys. Plasmas, 3, 853–862,
1996.
Ugai, M., K. Kondoh, and T. Shimizu, Computer studies on the threedimensional spontaneous fast reconnection model as a nonlinear instability, Phys. Plasmas, 11, 1416–1423, 2004.
Ugai, M., K. Kondoh, and T. Shimizu, Spontaneous fast reconnection inthree dimensions, Phys. Plasmas, 12, 042903, 2005.
Yokoyama, Y., K. Akita, T. Morimoto, K. Inoue, and J. Newmark, Clear
evidence of reconnection inflow of a solar flare, Astrophys. J., 546, L69,
2001.

In this paper, we have shown that 2D fast magnetic reconnection caused by a current-driven anomalous resistivity is
unstable to a 3D resistive perturbation. In fact, in this MHD
model, the initial current sheet has exactly a 1D structure,and every setup is exactly prepared for 2D fast magnetic reconnection, except for the initial 3D resistive perturbation
η0 . At this point, note that the 3D fast reconnection processreported by Ugai (Ugai et al., 2004, 2005) is largely different because the initial resistive disturbance employed in
his papers includes a largely non-uniform component along
the neutral line and, hence, the resulting fast reconnection
processes is fully 3D even on the first stage. In contrast,
as shown in Fig. 1, the fast reconnection studied in this paper is still 2D on the first stage. The 3D fast reconnectionis spontaneously caused after the 2D fast reconnection has
been established. In addition, as shown in the time variationof Fig. 9, the z-directional higher-order Fourier components
generated by the 3D instability rapidly grows after the 2D
stage. This means that the 3D instability shown here is fully
non-linear.
As shown in Fig. 5, the appearance of the multiple 3D
magnetic loops means that 3D fast reconnection process
is pulsating. This may support the intermittent downflow
T. Shimizu (e-mail: shimizu@cosmos.ehime-u.ac.jp), K. Kondoh, andreported by Asai et al. (2004), where 3D magnetic loops M. Ugai

LETTER

Earth Planets Space, 61, 573–576, 2009

Patchy reconnection in a Y-type current sheet
M. G. Linton1 , C. R. DeVore1 , and D. W. Longcope2
1 Naval Research Laboratory, Washington, DC, U.S.A.
2 Montana State University, Bozeman, MT, U.S.A.

(Received November 21, 2007; Revised March 24, 2008; Accepted June 20, 2008; Online published May 29, 2009)

We study the evolution of the magnetic field in a Y-type current sheet subject to a brief, localized magnetic
reconnection event. The reconnection produces up- and down-flowing reconnected flux tubes which rapidly
decelerate when they hit the Y-lines and underlying magnetic arcade loops at the ends of the current sheet. This
localized reconnection outflow followed by a rapid deceleration reproduces the observed behavior of post-CME
downflowing coronal voids. These simulations support the hypothesis that these observed coronal downflows are
the retraction of magnetic fields reconnected in localized patches in the high corona.
Key words: Solar, corona, flare, reconnection.

1.

Introduction

Reconnection is believed to be a key process allowing
the excitation of solar flares and coronal mass ejections(CMEs). The reconnection releases significant magnetic
energy, leading to solar flare heating, and changes magnetic
topologies, allowing CME magnetic fields to erupt and escape the solar corona into interplanetary space. Observations of the flaring which occurs behind recently erupted
CMEs show downflowing voids (see, e.g., McKenzie andHudson, 1999; Gallagher et al., 2002; Innes et al., 2003;
Asai et al., 2004; Sheeley et al., 2004) which push their way
through the heated flare plasma in the high corona. These
downflowing voids, observed by TRACE, Yohkoh SXT,
and Hinode XRT, have been shown to be evacuated structures. They are therefore not cool, dense plasma blobs being
pulled down by gravity, but rather appear to be evacuatedloops of magnetic field being pulled down by the magnetic
tension force (McKenzie and Hudson, 1999). The three dimensional (3D) structure of these voids breaks up the twodimensional (2D) symmetry of the flare current sheet andarcade, implying that the reconnection which creates thesevoids occurs in localized 3D patches rather than uniformly
along the current sheet. The reconnected field from thispatchy reconnection takes the shape of individual 3D flux
tubes rather than extended 2D sheets of field. In this letter, we study whether the formation of magnetic loops highin the corona via a 3D patch of reconnection creates structures consistent with the morphology and dynamics of thesecoronal voids.
In Linton and Longcope (2006), we showed that theshapes and evolutions of such magnetic loops in a one dimensional (1D) Harris type current sheet are consistent withobservations of these downflowing loops. The cross sections of the simulated magnetic loops form teardrop shapes,c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

similar to that of the voids, while the 3D structure of theloops is similar to the structure of the coronal loops whichappear below these voids, e.g., as seen by Sheeley et al.
(2004).
However, there is a key aspect of the void dynamics
which the initial 1D nature of the Harris current sheet
cannot reproduce. This is the rapid deceleration of thevoids once they reach the post-flare arcade loops in the low
corona. Sheeley et al. (2004) have shown that the speeds ofthese voids through the high corona are relatively constantuntil they hit the coronal arcade, when they rapidly decelerate. As the Harris current sheet continues unchanged tothe edge of the simulation, there is no arcade of loops at
the base of such a current sheet with which the voids collide. To study this deceleration, we therefore now simulate
this patchy reconnection in a Y-type current sheet (Green,1965). The Y-type current sheet terminates at a set of magnetic arcade loops, as shown in Figs. 1(a) and 2(a). Theintersections of the current sheet and the outermost of these
arcade loops forms the two Y-lines, at z = ±L in Fig. 1(a).
These arcades make the current sheet more representativeof a post-CME coronal current sheet with underlying arcade fields. Note that these Y-lines are not Y-type nulls, as
there is a uniform guide field in both the current sheet andthe arcade, so the field strength does not go to zero at the Ylines, even though the reconnection component of the field
does go to zero here.
We study the effect of a localized reconnection event inthis current sheet, focusing on the form of the reconnected
field, and on whether it decelerates once it hits the Y-line
and the coronal arcade below it. The current sheet configuration and the simulation setup are discussed in Section 2,
the results are described in Section 3, and our conclusions
are summarized in Section 4.

2.

Simulations

The simulations were performed using the magnetohydrodynamic (MHD) code ARMS (Adaptively Refined

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Fig. 1. Magnetic field of the Y-type current sheet in the y = 0 plane, with a magnetic reconnection patch imposed at z = 2L/3 for a time tv A0 /L = 0.6.
The vectors show the magnetic field in the plane, while the greyscale shows the guide field component, with white representing maximum positive
field. The panels show the simulation at times tv A0 /L = [0.2, 0.7, 1.1, 1.6, 2.1, 2.6, 3.1, 3.5]. The x boundaries of each panel shown are at
x = ±3L/4π .

MHD Solver) on the Cray XD1 supercomputer at the Naval
Research Laboratory. The code was used to solve the resistive MHD equations. See Welsch et al. (2005) for a discussion of the code, and a presentation of the equivalent ideal
MHD equations. We include an explicit resistivity η in the
induction equation, ∂B/∂t = ∇ × (v × B − η∇ × B), andan ohmic heating term in the energy equation.
The Y-type magnetic field (e.g., Priest and Forbes, 2000)is
Bx + i Bz = −B0 ω2 /L 2 − 1,(1)√where i is the positive value of −1, ω ≡ z + i x, and L
is the current sheet half-length. The guide field is uniform
at B y = B0 /π . Here Bz (z = 0, x ∼ 0) = B0 = 44 inunits where the pressure is p0 = 20/3. Due to the guidefield, the magnetic fieldlines on either side of the current
sheet form a half angle ζ = arctan(Bz /B y ) ∼2π/5. The
reconnection field strength |Bz | decreases as 1 − z 2 /L 2
along the current sheet, going to zero at the Y-lines at z =±L , x = 0. This magnetic configuration is force-free, so
the density and gas pressure are initially set to be uniform
at ρ = ρ0 = 1/2 and p = p0 , which sets the ratio ofplasma to magnetic pressure near the center of the current
sheet at β ≡ 8π p/|B|2 ∼ 0.08.
√ The Alfvén speed used
for normalization, v A0 = |B|/ 4πρ, is measured near thecenter of the current sheet at z = 0, x ∼ 0.
Extrapolative, zero gradient, open boundary conditions
are imposed in the ẑ and x̂ directions, while periodic boundary conditions are imposed in the ŷ direction. The computational mesh is adaptively refined in areas of high current magnitude. This gives a resolution ranging from 64 to
512 cells in the ŷ, and ẑ directions [−1.9L , 1.9L], and a
resolution ranging from 32 to 256 cells in the x̂ direction[−.95L , .95L]. The current sheet is at the highest resolu-

tion, and it is effectively one cell wide, so its thickness is
l = 0.007L.
The simulation is run with a uniform background resistivity η0 . To initiate the reconnection, we impose asphere of enhanced resistivity on the current sheet for the
first tv A0 /L = 0.6 of the simulation.
This resistiveen−r 2 /δ 2, for r =hancement has the form η = η0 1 + 99e

x 2 + y 2 + (z − 2L/3)2 < 2δ, with δ/L = 0.087. The
Lundquist number of the background resistivity is Sη ≡
δv A0 /η0 = 5000, while for the peak resistivity at the centerof the reconnection region Sη = 50. Note that Ugai (2007)
have found that reconnection induced by locally enhanced
resistivity is inhibited if δ < 4l. As δ ∼ 10l here, the reconnection should not be inhibited by this mechanism.

3.

Results

The effects of the magnetic reconnection event on the Ytype current sheet are shown in Figs. 1 and 2. Figure 1
shows a vector magnetogram view of the field in a plane
perpendicular to the current sheet at y = 0. Figure 1(a)is taken soon after the reconnection event is turned on.
The guide field, shown by the greyscale, is enhanced in
two small spots on either side of the reconnection eventat z = 2L/3. These spots are the cross sections of thetwo recently reconnected flux tubes flowing away from thereconnection site. The guide field is enhanced in thesereconnected flux tubes because the reconnection componentof the magnetic field has been annihilated, and the guidefield must increase to make up for the lost magnetic pressure(see Hesse et al., 1996).
Figure 2(a) shows the fieldlines on either side of thiscurrent sheet just before the reconnection starts. Three
topologically distinct sets of fieldlines are shown. One set

M. G. LINTON et al.: PATCHY RECONNECTION IN A Y-TYPE CURRENT SHEET

575

Fig. 2. Fieldlines of the reconnecting Y-type current sheet. The blue color shows where the electric current parallel to the magnetic field is strong.
The panels show the simulation at times tv A0 /L = [0.0, 1.3, 2.1, 2.8, 3.4, 3.9]. Panel (a) shows fieldlines traced from both the front and back sideof the current sheet, at the bottom boundary. The rest of the panels show only fieldlines traced from the back side of the current sheet, at the bottom
boundary.

runs just behind the current sheet from the bottom to the topof the panel, while a second set runs in front of the current
sheet from the top to the bottom of the panel, as marked
by the arrows. The third set arches below the current sheet,running from the back of the simulation to the front, andcoming close to the Y-line and the base of the current sheet
at its apex. All three sets of fieldlines are canted graduallyfrom left to right: this is the effect of the uniform guide fieldin the ŷ direction. The arched set of fieldlines represents thepost-CME arcade loops while the two other sets of fieldlines
represent the coronal current sheet fieldlines, which may
still be connected to the CME above the second Y-line at the
top of the simulation. For the remaining panels of Fig. 2,
only the first and third sets of these fieldlines are traced,
so that the second set, which lies in front of the current
sheet, does not obscure the dynamics. Both of these setsof fieldlines are traced from the bottom boundary, behindthe current sheet and arcade. Therefore, any section of afieldline which appears in front of the current sheet above
the arcade fieldlines is purely due to reconnection of frontside fieldlines with the back-side fieldlines.
The reconnection event was initiated very close to theupper Y-line, so the upflowing reconnected field quickly
hits the Y-line, in Fig. 1(b). The corresponding upward
retracting fieldlines are not shown in Fig. 2, since they
are not connected to the lower boundary from which thefieldlines are traced. The upflow halts when it hits the upper
Y-line and the arcade fieldlines lying above it. This is theequivalent of the upgoing fieldlines hitting and merging into
the recently erupted CME, though this would only happen

if the CME were erupting at a slower rate than the fieldlines
retract.
The downflowing part of the reconnected flux is displayed in Fig. 2(b) as the fieldlines which trace upwards
with all the field on the back side of the current sheet, butthen suddenly take a hairpin turn and trace back down to thebottom boundary on the front side of the current sheet. The
blue color of the fieldlines at these hairpin turns shows thatthe parallel electric current is enhanced and therefore reconnection is strong there (see, e.g., Schindler et al., 1988).
The high placement of the initial reconnection region allows
the cross section of the flux tube carrying this downflowing reconnected flux to fully take shape. Figures 1(b)–1(f)show how the cross section of the tube forms into an oblong shape, reminiscent of the coronal void observations,just as it did in the Harris sheet experiments of Linton andLongcope (2006). Note that the area of the downflowing
flux tube cross section continues to grow as it absorbs more
reconnected flux, even though the enhanced reconnection
spot was turned off at tv A0 /L = 0.6, just before Fig. 1(b).
Apparently the disturbance caused by the initial reconnection event spontaneously excites subsequent patchy reconnection events.
When this downflowing flux tube hits the Y-line and thearcade field below it, in Fig. 1(f), it decelerates and compresses the arcade field, in Fig. 1(g), and eventually joins
the arcade, in Fig. 1(h). The reconnected flux which hits
and joins the lower arcade is shown in Figs. 2(d)–2(f) as thefieldlines which now lie on top of the original arcade.
To illustrate the downflow and deceleration of the recon-

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M. G. LINTON et al.: PATCHY RECONNECTION IN A Y-TYPE CURRENT SHEET

not expand significantly in this direction. From these preliminary results, it appears that the guide field can play animportant role in expanding the reconnection region along
the current sheet.

4.

Conclusions

We have studied the effect of a brief, localized burst ofreconnection in a Y-type current sheet with guide field. The
up- and down-flowing flux this creates decelerates rapidly
when it hits the Y-lines and the arcade fields beyond them.
This gives strong support to the theory that the downflowing
post-CME voids observed by TRACE, Yohkoh, and Hinodeare in fact downflowing reconnected magnetic flux loops.
This model gives a clear mechanism to explain why downflowing post-CME voids decelerate rapidly when they reachthe post-flare arcades, as observed by Sheeley et al. (2004).
We also find that the velocities of the voids change as
they propagate through regions of different magnetic field
Fig. 3. Height-time plot of the guide field at x = y = 0. The white strength in the current sheet. Finally, we find that the perturbation created by the initial burst of reconnection is suftickmarks at the top mark the times of the vector plots of Fig. 1.
ficient to excite spontaneous patchy reconnection events inthe current sheet.
nected flux tubes, we show a height-time plot of the guidefield along the x = y = 0 line in Fig. 3. Here, the upward Acknowledgments. This work was funded by NASA and ONR,
with a grant of computer time from the DoD High Performanceor downward propagating voids are displayed as diagonal Computing program.
white streaks of concentrated guide field. The first pair of
up- and down-flowing streaks, starting at tv A0 /R = 0, are References
the tracks of the two initial reconnection voids. The up- Asai, A., T. Yokoyama, M. Shimojo, and K. Shibata, Downflow motions
associated with impulsive nonthermal emissions observed in the 2002
flowing track rapidly hits the upper Y-line and decelerates,
July 23 solar flare, ApJL, 605, 77–80, 2004.
while the downflowing track starts off at about v A0 /2, acGallagher, P. T., B. R. Dennis, S. Krucker, R. A. Schwartz, and A. K.
celerates as it passes the current sheet midpoint, and thenTolbert, Rhessi and trace observations of the 21 April 2002 x1.5 flare,also rapidly decelerates as it hits the lower Y-line. Guidoni
Sol. Phys., 210, 341–356, 2002.
and Longcope (2007) suggest that a reconnected flux should Green, J. M., Geometrical properties of three-dimensional reconnecting
magnetic fields with nulls, in Solar and Stellar Magnetic Fields, edited
accelerate near z = 0 as seen here because the magnetic
by R. Lüst, 7 pp., North-Holland Publishing Co., Amsterdam, 1965.
field strength, and thus the accelerating Lorentz force, peaks Guidoni, S. and D. Longcope, Dynamics of post-reconnected thin flux
there.
tubes, Am. Astron. Soc. Meeting Abstracts, 210, #93.27, 2007.
After the reconnection is turned off at tv A0 /L = 0.6, Hesse, M., J. Birn, M. M. Kuznetsova, and J. Dreher, A simple model ofcore field generation during plasmoid evolution, J. Geophys. Res., 101,no new tracks appear at the height of the initial reconnec10797–10804, 1996.
tion site until about tv A0 /L = 1.3. Then patchy recon- Innes, D. E., D. E. McKenzie, and T. Wang, SUMER spectral observationsof post-flare supra-arcade inflows, Sol. Phys., 217, 247–265, 2003.
nection spontaneously sets in, as several reconnection outflow pairs appear in rapid sequence. This is supported by Isobe, H., M. Takehiro, K. Shibata, and T. Yokoyama, Filamentary structure on the Sun from the magnetic Rayleigh-Taylor instability, Nature,
the more detailed views of Figs. 1 and 2. Figures 1(f)–1(h)434, 478–481, 2005.
show the corresponding newly reconnected flux tube cross Linton, M. G. and D. W. Longcope, A model for patchy reconnection inthree dimensions, ApJ, 642, 1177–1192, 2006.
sections flowing up and down at these times. Meanwhile,Figs. 2(c)–2(e) show the continual generation of newly re- McKenzie, D. E. and H. S. Hudson, X-ray observations of motions andstructure above a solar flare arcade, ApJL, 519, 93–96, 1999.
connected fieldlines high up in the current sheet, well after Schindler, K., M. Hesse, and J. Birn, General magnetic reconnection,
the initial reconnection has been turned off and those reconparallel electric fields, and helicity, J. Geophys. Res., 93, 5547–5557,
1988.
nected fields have retracted. The source of this secondary
Sheeley, N. R., H. P. Warren, and Y.-M. Wang, The origin of postflare
patchy reconnection may be numerical resistivity due to theloops, ApJ, 616, 1224–1231, 2004.
finite grid-scale of the simulation, in tandem with perturba- Priest, E. and T. Forbes, Magnetic Reconnection, MHD Theory and Applitions excited by the initial reconnection event, and will becations, Cambridge University Press, Cambridge, UK, 2000.
explored in a future paper. Isobe et al. (2005) found a simi- Ugai, M., Conditions for drastic evolution of magnetospheric current
wedge, Phys. Plasmas, 14, 062902.1–062902.8, 2007.
lar spontaneous patchy reconnection, but in their case it was Ugai,
M., K. Kondoh, and T. Shimizu, Spontaneous fast reconnection
due to an interchange instability, which cannot occur here.
model in three dimensions, Phys. Plasmas, 12, 042903.1–042903.7,
2005.
Interestingly, Fig. 1 also shows the reconnected fieldlines
spreading in the ŷ direction along the current sheet, also Welsch, B. T., C. R. DeVore, and S. K. Antiochos, Magnetic reconnection
models of prominence formation, ApJ, 634, 1395–1404, 2005.
in a patchy fashion, instead of remaining near the initial reconnection site. This is in contrast with the findings of Ugai
M. G. Linton (e-mail: linton@nrl.navy.mil), C. R. DeVore, and D. W.
et al. (2005) for a Harris current sheet without guide field.
Longcope
Their results show that initially localized reconnection does

LETTER

Earth Planets Space, 61, 577–580, 2009

Flares and the chromosphere
Hugh S. Hudson1,2 and Lyndsay Fletcher2,1
1 SSL, UC Berkeley, CA 94720-7450, USA
2 University of Glasgow, UK(Received December 2, 2007; Revised August 24, 2008; Accepted August 31, 2008; Online published May 29, 2009)

The chromosphere (the link between the photosphere and the corona) plays a crucial role in flare and CME
development. In analogies between flares and magnetic substorms, it is normally identified with the ionosphere,
but we argue that the correspondence is not exact. Much of the important physics of this interesting region
remains to be explored. We discuss chromospheric flares in the context of recent observations of white-lightflares and hard X-rays as observed by TRACE and RHESSI, respectively. We interpret key features of theseobservations as results of the stepwise changes a flare produces in the photospheric magnetic field.
Key words: Solar flares, solar chromosphere, solar corona, Alfvén waves.

1.

Introduction

The chromosphere historically has been the origin ofmuch of what we understand about solar flares. The reason for this was the recognition, in the 19th and early 20th
centuries, of the extreme sensitivity of Hα, a strong Fraunhofer absorption line formed in the chromosphere, to solar
magnetic activity. Spectroscopic observations of this line
and its imaging led to exciting discoveries regarding active
prominences, ejecta, flare brightenings etc. (Hale, 1930).
Eventually it was realized that the original flare observation of 1859 (Carrington, 1859) was simply the tip of theiceberg, and that the entire solar atmosphere was participating in events that have now come to be defined moreby their coronal X-ray emission (the GOES classification)rather than their Hα importance levels (Thomas and Teske,1971). Research attention, indeed, has largely left the chromosphere layers in favor of coronal and even interplanetary
effects (CMEs and ICMEs; see Schwenn, 2007, for a recent
review).
Our understanding of the chromosphere, until recently,
has been limited to the “semi-empirical” models, based on
1D radiative-transfer physics. Such an approach omits dynamics except for the “microturbulence” factor and muchof the interesting plasma physics; for example these models assume Te = Ti everywhere. See Berlicki (2007) andHudson (2007) for recent reviews about the flaring chromosphere, and for references to the abundant literature on thissubject.
In the often-discussed but imperfect analogy between solar flares and auroral substorms, the chromosphere plays
the role of the ionosphere, but these regions have substantially different properties and the detailed physics may not
produce analogous effects (e.g., Haerendel, 2007). On thelarger scale there is also no analog of the solar wind flowc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

ing around an active-region field concentration in the solar
corona, so that the convective (v×B) electric field across thegeotail does not have an appropriate analog. The presenceof a highly conductive solar atmosphere below the chromosphere also distinguishes it from the ionosphere. Thus, although striking observational parallels between flares andaurorae have been noted by many authors (e.g., Obayashi,1975), the basic physics may be quite different in regard tocausation or the dynamical development of the phenomena.
In this paper we touch on flare energetics (Section 2), energy build-up (Section 3), and energy release (Section 4),
attempting to use magnetospheric concepts as a guide tounderstanding.

2.

Chromospheric Flare Energetics

The radiative energy of a solar flare appears mainly in the
optical and UV continuum, which form in the lower solar
atmosphere, most probably the chromosphere (e.g. Allred etal., 2005; Fletcher et al., 2007). This is in spite of the factthat the chromosphere itself (for this purpose, all regionsof the solar atmosphere between photospheric and coronaltemperatures) cannot contain sufficient energy to power aflare (see Hudson, 2007, for discussion). For example,
the gravitational energy contained in coronal filaments does
not play a strong role in flare energization. The radiatedflare energy appears in compact emission patches that ourcurrent observations do not resolve either in space or intime (Hudson et al., 2006), and Fletcher et al. (2007) haveconfirmed that the immediate source of the radiated energy
lies in the electrons accelerated in the impulsive phase of
the flare. Of this energy the chromospheric Hα component
and the coronal soft X-ray component each comprise lessthan about 10% of the total (Thomas and Teske, 1971).
Zeeman-splitting observations (Wang, 1993; Sudol andHarvey, 2005) have shown convincingly that flares result inlarge-scale perturbations of the photospheric magnetic field(see Fig. 1). This would generally be expected from any
model of energy release from the coronal magnetic field,

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Fig. 1. GONG observations of the line-of-sight solar magnetic field prior to the X-class flare of 2003 October 29 (panel a); a difference map showing
flare-related changes in the field (panel b); after Sudol and Harvey (2005). The field changes are of order 10% of the line-of-sight field and can bedetected in essentially all X-class flares, according to Sudol and Harvey.

Fig. 2. Snapshots of TRACE observations (white light filter) of the C4.8 flare of 24 July 2004, showing the intermittency of the continuum emissions
in both space and time. Spatial scale for each frame is 32 × 68 ; the times shown on the figure span 30 s (from Hudson et al., 2006).

which will requirerestructuring in order to reduce the stored
magnetic energy (B 2 /8π)d V (e.g., Hudson, 2000), as
for example with large-scale magnetic reconnection. The
main contribution to the coronal magnetic energy and its
stress are concentrated strongly in the lower solar atmosphere (e.g., Régnier and Priest, 2007). Thus we need atheoretical understanding of how the coronal stored energy
can flow to and focus itself into the chromospheric emission
regions (see Fig. 2). Heretofore this coupling has been understood as the result of beams of electrons coming from an
unknown coronal acceleration site, for which there are several possibilities (e.g., Miller et al., 1997). These ideas underlie the “thick target” model for the impulsive phase of aflare, which envisions electron beams capable of transporting energy from the coronal storage site into the dissipation
regions (Brown, 1971; Hudson, 1972). We do not know yet
how the particle acceleration relates to the magnetic restructuring needed to release coronal energy.

3.

Cross-field Currents

Another aspect of flare energetics and the chromosphereis the mapping of subphotospheric magnetic twist into coronal currents (Longcope and Welsch, 2000). This in principle involves the use of the full conductivity tensor, though
there is little discussion of this yet in the solar literature(e.g., Kazeminezhad and Goodman, 2006; Arber et al.,2007) at least as regards flares. Haerendel (2007) points
out that the large ion-neutral coupling in the chromospheremakes the perpendicular conductivity is smaller than theparallel conductivity, at least for slowly-varying currents,

and yet cross-field current systems must develop slowly insuch a way as to match the conflicting boundary conditions
at the two independent footpoints of a coronal flux tube.
Auroral models make use of ionospheric currents to close
coronal current systems, but in the case of the Sun we believe that the significant currents are injected through thephotosphere in a slowly-evolving manner, and that thesecurrents serve to energize the non-potential fields in thecorona. In this sense the chromosphere must play the rolesof both the ionosphere and the magnetopause.
We can write the perpendicular conductivity asσ⊥,x =

νxn
N e2
2 + ω2m e νxncx(1)with x representing either ions or electrons (Banks, 1966),2
where ωcx
represents the Larmor frequency for particle
species x and n denotes neutrals. The neutral collision frequencies νxn largely determine the perpendicular conductivity and it is not clear at present which particle species dominates the steady-state perpendicular current system. In any
case for “normal” chromospheric and coronal conditions, as
inferred from standard semi-empirical models, the Larmor
frequencies greatly exceed the neutral collision frequencies
so that the perpendicular conductivity is small relative to theparallel term. So far as we are aware, the questions posedby the requirement to establish slowly varying cross-fieldcurrents in the chromosphere have not been discussed in
the literature, and we do not know the role that they play inenergy storage or dissipation.

H. S. HUDSON AND L. FLETCHER: FLARES AND THE CHROMOSPHERE

579

Fig. 3. Sketch of flare mechanisms as discussed in the text. Deformation of a flux tube results in Alfvén waves that transport energy into the footpoint
regions via the Poynting flux. The wave deformation also perturbs the global structure to produce effects such as those seen in Fig. 1. Particle
acceleration results either directly from parallel electric fields produced by the waves, or in tubulent cascades developing from their interactions.

4.

Field Restructuring, Waves, and Energy Transport

Changes of the coronal magnetic structure imply thetransport of energy via Poynting fluxes (Melrose, 1992).
The observations indicate that coronal energy dissipates in
the chromosphere, and the hard X-ray signature directly implicates weakly relativistic electrons. Thus the magnetic restructuring, and the energy transport it implies, must somehow result in the acceleration of electrons to non-thermalenergies. We sketch how this may happen in Fig. 3 (Fletcher
and Hudson, 2008). The sudden reconfiguration of the field,in the ideal MHD approximation, would launch Alfvénwaves. Emslie and Sturrock (1982) argue that the suddenness of flare energy release requires that the Alfvén modeand the fast mode predominate in the partition of this energy. The Alfvén mode is particularly interesting in thiscontext, because as a transverse wave its Poynting flux E×Bmust be strictly parallel to B and thus be strongly ducted
into the footpoint regions.
The mechanism for electron acceleration remains illunderstood. Because it is energetically so important (Kaneand Donnelly, 1971; Lin and Hudson, 1971), its identification is fundamental to understanding the physics of solar
flares. In the view of Fig. 3, the acceleration must happen asa result of the Alfvén-wave energy flux ducted along the arcade loops that result from the restructuring. This suggests
several possible acceleration mechanisms, some of whichhave been recently reviewed by Miller et al. (1997).
Our scenario suggests additional acceleration mechanisms. Alfvén waves in the lower corona may propagate dispersively (e.g., Stasiewicz et al., 2001), inducing
parallel electric fields directly. If the plasma beta, β =2nkT /(B 2 /8π ), is smaller than m e /m i , where m e /m i is theelectron/ion mass ratio, then the Alfvén mode can become
dispersive in the form of a kinetic Alfvén wave and develop
a parallel field directly. Fletcher and Hudson (2008) review
how this happens. The waves may also cascade into formsof turbulence suitable for stochastic particle acceleration,and this cascade may develop promptly under some conditions. First-order Fermi acceleration and the betatron effectmay also play roles in the “collapsing trap” (e.g., Veronig

Fig. 4. Sketch showing how magnetic reconnection may excite Alfvénwaves. From Haerendel (2007).

et al., 2006), and finally the disruption may create shockwaves that may also accelerate particles.
Our preferred scenario (Fig. 3) has the virtue of linking the observed magnetic-field variations with the powerful energy release seen in the visible and UV continua.
The sketch by Haerendel (2007), reproduced in Fig. 4, illustrates the generation of Alfvén waves from the reconnection
process. Particle acceleration, in this picture, could readily occur in the lower solar atmosphere, where the ambient electrons are numerous enough to overcome the “number problem” and concerns about electron beam dynamics.
One weakness may be the apparent time-of-flight signature
noted by Aschwanden (2002), which—though somewhat
ambiguous—provides the main observational evidence forthe existence of the intense coronal electron beams the580

H. S. HUDSON AND L. FLETCHER: FLARES AND THE CHROMOSPHERE

thick-target model requires. Type III radio bursts also require beams, but of significantly lesser intensity.

5.

Conclusions

Research in solar flares and terrestrial aurorae has long
been stimulated by the observational analogies one candraw between the phenomena (e.g., Obayashi, 1975). The
analogous elements include ribbon-like optical emissions,electron acceleration to keV energies, and similar magnetic
geometries. There are observational differences though,and theoretically there also are good reasons not to havea strict analogy. Nevertheless we feel it important to discuss the physics of chromospheric flares, both in the energy build-up and release stages, in ways that exploit someof ideas auroral physics offers to the understanding of solar problems. We interpret the observed photospheric magnetic field changes as the result of large-scale Alfvén waves
created during coronal magnetic restructuring (Fletcher andHudson, 2008). Particle acceleration, a key observable insolar flares because of hard X-ray and γ -ray emission, thenbecomes secondary to the transport of energy via the Poynting fluxes of the waves. There are different ways in which
the necessary particle acceleration may happen, most directly if the waves become dispersive in nature, but the identification of the acceleration mechanism remains an open
problem.
Consideration of wave transport of energy in solar flaresand CMEs seems like a logical and necessary development
for the advancement of theoretical ideas. Some large-scale
manifestations of waves are readily observable, originallyas type II bursts and Moreton waves (e.g., Uchida et al.,1973), but now also at higher resolution in the EUV as the
EIT waves (Thompson et al., 1999). The EIT waves introduce new kinds of behavior not seen before and it has become clear that not all of the motions can be identified with
the Moreton-wave phenomenon (Biesecker et al., 2002).
Small-scale waves such as those that could be directly responsible for particle acceleration are difficult to observe
remotely, but their presence may be just as fundamental tosolar-flare physics as comparable structures are in auroral
physics. We therefore urge theoretical work involving theideas discussed here.
Acknowledgments. This work was carried out at the Universityof California, Berkeley, during a sabbatical leave of LF from the
University of Glasgow, as well as at the University of Glasgow
where HSH is grateful for hospitality. We are grateful to K. Shibata and the organizers of the workshop in Fairbanks, Alaska,
where this paper was originally presented. LF gratefully acknowledges financial support by the European Commission through the
SOLAIRE Network (MTRN-CT-2006-035484) NASA provided
support under grant NAG-5-12878 and contract NAS5-38099.

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H. S. Hudson (e-mail: hhudson@ssl.berkeley.edu) and L. Fletcher

LETTER

Earth Planets Space, 61, 581–584, 2009

Development of the global simulation model of the heliosphere
Satomi Kamei1,4 , Aoi Nakamizo2,4 , Takashi Tanaka2,4 , Takahiro Obara3,4 , and Hironori Shimazu3,4
1 Department of Earth and Planetary Sciences, Graduate School of Sciences, Kyushu University, 6-10-1 Higashi-ku, Fukuoka 812-8581, Japan
2 Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu University, 6-10-1 Higashi-ku, Fukuoka 812-8581, Japan
3 National Institute of Information and Communications Technology, 4-2-1 Koganei-shi, Tokyo 184-8795, Japan
4 CREST, Japan Science and Technology Agency, Kawaguchi-shi, Saitama 332-0012, Japan(Received September 28, 2007; Accepted February 7, 2008; Online published May 29, 2009)

The heliospheric structure ranging from the solar surface to the earth’s orbit is self-consistently reproduced
from a time-stationary three-dimensional (3D) magnetohydrodynamic (MHD) simulation. The simulation model
incorporates gravity, Coriolis, and centrifugal forces into the momentum equation, and coronal heating and fieldaligned thermal conduction into the energy equation. The heating term in the present model has its peak at 2.8
solar radius (Rs ) and exponentially falls to zero at greater distance from the solar surface. The absolute value ofheating depends on the topology of the solar magnetic field so as to be in inverse proportion with the magnetic
expansion factor. The results of the simulation simultaneously reproduce the plasma-exit structure on the solar
surface, the high-temperature region in the corona, the open- and closed-magnetic-field structures in the corona,the fast and slow streams of the solar wind, and the sector structure in the heliosphere.
Key words: Solar wind, MHD simulation, CIR.

1.

Introduction

There is a long history associated with the developmentof sun-earth-system models that try to predict the changes
in the terrestrial environment caused by the disturbances on
the solar surface following propagation through the interplanetary space (Dryer, 1998). Many early studies applied
the physics-based model. Among these, the pioneering
Hakamada-Akasofu-Fry kinematic model (Hakamada andAkasofu, 1982) is still currently in use by the U.S. space
weather system. Since the large-scale structure and dynamics of the solar corona is dominated by the magnetic field,
the source surface current sheet model was developed as anobserved magnetic field data-driven model for the corona.
This model can predict not only the sector structure but also
the solar wind speed from the expansion factor (Wang andSheeley, 1990). By extending the results up to the earth’s
orbit, model outputs can be compared directly with satellite
observations.
In recent years, increases in computing speed have enabled the development of first-principle-based models. The
hybrid model developed by Detman et al. (2006) combined
the source surface current sheet model for the corona with
the MHD solar wind model to predict the MHD parametersat the earth’s orbit. Full MHD models from the solar surface
to the solar wind region have also been developed by several
authors (Linker et al., 1999; Riley et al., 2001; Manchester
et al., 2004; Tóth et al., 2005; Shen et al., 2007). Although
there are differences in the details for each model, thesemodels can extrapolate the surface magnetic field together
with self-consistently described plasma into the interplane-tary space.
In this paper, we report an attempt to develop an improved MHD simulation that unitedly reproduces quasistationary heliosphere from the solar surface to the earth’s
orbit from the observed solar surface magnetic field. When
we try to reproduce the heliosphere extending form the solar surface to the earth’s orbit, we must calculate both thefine structure around the corona and a global structure fromthe sun to near the earth’s orbit simultaneously. In the following part of this paper, we first show how these difficulties are solved in our simulation model, and then we present
some calculation results for a typical solar rotation period.

2.

Simulation Model

2.1 Basic equation
The basic equations of the simulations are the modified
MHD equations written by dividing magnetic field B as
B = B0 +B1 with B0 a fixed potential field and B1 deviationfrom B0 (Tanaka, 1994).

c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

581∂ρ+ ∇ · (ρv) = 0,
∂t

(1)



B 2 − B02
BB − B0 B0∂(ρv)
I−+ ∇ · ρvv + PI +
∂t
2µ0
µ0
= ρg − 2ρ × r − ρ × ( × r),(2)∂B1+ ∇ × (v × B) = 0,
(3)
∂t

 
B12
∂U1
B1 (v · B1 ) B0 (v · B1 )−+ ∇ · v· U1 + P +
−
∂t
2µ0
µ0
µ0

v(B1 · B0 )= Q − ρv ·  × ( × r)+ρv · g, (4)
+
µ0

582

S. KAMEI et al.: DEVELOPMENT OF THE GLOBAL SIMULATION MODEL OF THE HELIOSPHERE

Table 1. Boundary conditions of the MHD and Poisson equations.
Distance form the Sun
Density
Velocity (parallel)
Velocity (perpendicular 1)
Velocity (perpendicular 2)
B1 (radial)B1 (tangential 1)
B1 (tangential 2)
U1
B0 (line-of-sight)
B0 (perpendicular 1)
B0 (perpendicular 2)

U1 =

1Rs
Fix
∂/∂r = 0000∂/∂r = 0∂/∂r = 0Fixobservation
free
free

B2
ρv 2
P
+
+ 1 ,
2
γ − 1 2µ0

200Rs∂/∂r = 0∂/∂r = 0∂/∂r = 0∂/∂r = 0∂/∂r = 0∂/∂r = 0∂/∂r = 0
Fix (P → 0)
free
free
free

Fig. 1. Grid system made from a dodecahedron. One pentagon surface ofregular dodecahedron is first divided into five right triangles, and thenthe generated triangles are divided into four smaller triangles.

(5)

where ρ, v, P, r, µ0 , g, and γ are the density, velocity,
plasma pressure, position vector, the vacuum magnetic permeability, acceleration of gravity, angular velocity of solar
rotation and polytropic index set as 5/3, respectively. Theseequations are generally called as continuity equation (1),equation of motion (2), induction equation (3), and energy
equation (4). The energy equation (4) written through themodified total energy of plasma U1 (Tanaka, 1994) includes
the heating term Q . The equations are written in the rotating system, and they include the Corioli’s force as well as
the centrifugal force and gravity force.
2.2 Boundary condition
The inner boundary of the heliosphere is set at coronalbase, which is approximately assumed to be 1 solar Radii(Rs ), and the outer boundary is set at the near earth’s orbit at
200Rs . On the inner boundary, the density and total energyof the plasma are fixed, and field perpendicular velocities
are set to 0. The field parallel velocity is obtained fromthe Neumann condition. For the magnetic field, we put theobservation data, which were obtained from Wilcox Solar
Observatory, to the line-of sight component of B0 . For B1 ,the radial component is set to 0. On the outer boundary,
total energy of the plasma is set so as the pressure becomesa small value near 0. Other variables are solved under the
Neumann condition. The boundary conditions of the MHD
equation used for the present simulation are summarized inTable 1.
2.3 Coronal heating
To obtain a realistic solar wind with γ = 5/3, some
additional energy input is required (Lionello et al., 2001;
Sittler et al., 2002). For the purpose of accelerating the solar
wind to a high enough speed, we included an additional
heating term to the energy Eq. (4) as−r/L
2.5 ∇T · B
Q = ρq0 (r − 1.0)e· B, (6)+ ∇ ξT
B2

it is clear that heating has its peak at L + 1 = 2.8Rs andsubsequently decreases with a distance from the sun.
The magnetic field topology of the solar surface is important for solar wind speed. Therefore, we consider themagnetic field topology into the calculation of heating amplitude q0 . It is known that the flux tube expansion factor f s ,which is the ratio of the magnetic field intensity on the photosphere to that of respective points at extension along magnetic field, is inversely correlated with the velocity (Wangand Sheely, 1990). So, we set q0 to be inversely proportional to f s written in the form
 2
 
Brs
rs
rs
fs ≡
fs ,
=
(7)
rs
Brs
rs

where rs and Brs are 1Rs and field intensity at the photosphere, and rs and Brs denote distance from the solar center and field intensity at rs . Given the magnetic field B, theexpansion factor f s is calculated by solving ∇ · (n f s ) = 0(∇ · (−n f s ) = 0) with n = B/|B| along the away (toward)
field lines, together with the boundary condition f s = 1.0
on the inner boundary. In addition to this inverse correlationconsidered through Eq. (7), q0 is additionally reduced in theplace where temperature is higher than 2.8 million K.
2.4 Grid system and numerical scheme
When calculating a global system with a centrifugal configuration like the heliosphere, it is desirable to construct
a spheroidal unstructured grid system having no apparent
singularity. The grid system must also be tolerable for the
calculation which treats both the fine structure around thecenter and wide-range structure extending the whole area
simultaneously. To realize such a grid system, we first divide one pentagon surface of regular dodecahedron into fiveright triangles, adding a central point that inscribes a sphere.
Next, we divide the generated triangles into four smaller
triangles with all new points inscribing a sphere. Figure 1
shows this process of how we generate higher order splitting successively. By the fourth order splitting, 1922 grid
points are generated. Stacking such spheres radially, a 3-D
where q0 , L, and T are amplitude of heating, decay distance grid system is generated.
The control volume for the Finite Volume Method (FVM)
of heating (set to 1.8Rs ), and temperature (Sittler et al.,2002). The first term of the right handed side shows the calculation is hexagonal columns connecting the exocentric
ad hoc heating, while the second term shows Spitzer’s heat points of triangles on interfacing spheres. For each control
conduction term parallel to the magnetic field line. This volume, data for volume, area of interfacing surface, andheat conduction is applied only inside 10Rs . From Eq. (6), normal and tangential vectors on the interfacing surface are

S. KAMEI et al.: DEVELOPMENT OF THE GLOBAL SIMULATION MODEL OF THE HELIOSPHERE

583

prepared for the FVM calculation.
The numerical scheme used in the present simulation
for the time integration of the conservative MHD equation is the FVM total variation diminishing (TVD) schemewith the monotonic upstream scheme for conservation laws
(MUSCL) method, and the Van Leer’s differentiable limiter originally developed by Tanaka (1994). For details, see
Tanaka (1994).

3.

Numerical Results

Here, we show the simulation results for 3-D structuresof the solar corona and the solar wind for a typical solar rotation period. We have calculated the period of Carrington
Rotation (CR) 2028 (2005, March 25–April 21) and thencompared it with the observation is made at the earth’s orbit using the solar wind data obtained by ACE (OMNI web
service).
Figure 2 shows a 3-D close up view of the solar surface
and solar corona as viewed from the earth on 2005 March
29. In this figure, the contour surface shows an isotemperature surface at 2.8 and inside of it is higher than 2.8. Thistemperature value is normalized by the surface temperature
0.8 × 106 K. These high temperature regions correspond tothe closed field regions, where the plasma is trapped. Red
and blue lines show magnetic field lines. Here red (blue)lines show the away (toward) field lines. We can observe
the origin of sector structure in the corona where toward andaway sectors are separated by the high temperature region.
Open field lines extending from one continuous region havea same color. The area of another-color open field lines isseparated by the high-temperature region. These structures
are a 3-D generalization of 2-D field, temperature and flow
structures shown by Sittler et al. (2002).
Color shading on the solar surface shows plasma flux
emitted from the solar surface. Yellow and red colors show
the region from where solar wind plasma is supplied tothe interplanetary space. Consequently, these regions canbe looked upon as the coronal hole. Coronal holes are
situated at the center of one continuous region having samecolor field lines. Compared with SOHO extreme ultraviolet
image observed during CR 2028, positions of these coronalholes estimated from the flux exiting region almost coincidewith dark regions seen in X-ray images.
From Fig. 2, we can see that the calculation has reproduced the solar and coronal fine structures near the sun. The
coronal hole, sector structure, and high temperature corona
are organized as a combined structure. As will be shownin Fig. 3, sector and high-speed flow structures in the interplanetary space are the extension of this organized structurenear the sun.
Figure 3 shows the global solar wind structure on theecliptic plane from the solar surface to the earth’s orbit.
White lines show the start longitudes of each quarter whichwere face to face with the earth on March 25, April 1,
April 15, and April 22. The shading and contour lines inFig. 3 show the magnetic sector and solar wind speed in
the interplanetary space. Velocity is shown by the contour
lines after the conversion from the rotating (calculating)frame to the non-rotating (observing) frame. In Fig. 3,
the interplanetary magnetic structure exhibits four sectors.

Fig. 2. A 3-D close up view of the solar surface and solar corona viewed
from the earth on 2005 March 29. The contour surface shows an
isotemperature surface at 2.8. Temperature value is normalized by thesurface temperature 0.8 × 106 K. The coronal temperature outside thecontour surface is about 1.7. Red lines show the away field lines andblue lines show the toward field lines. Color shading on the solar surface
shows plasma flux emitted from the solar surface. The outward-flux area
is indicated by warm colors.

Fig. 3. The global solar wind structure in the ecliptic plane from the solar
surface to near the earth’s orbit. White lines show the start longitudesof each quarter which were face to face with the earth on March 25(right), April 1 (top), April 8 (left), and April 15 (top). The shading andcontour lines shows the magnetic sector (green-away, blue-toward) andsolar wind speed (color bar: red-fast, blue-slow) in the interplanetary
space.

Fig. 4.
Top pannel shows observed (pink) and calculated result(navy) of solar wind speed and bottom shows Bφ for ovserved data
and Br > 0 (upper) or Br < 0 (lower) for calculation result.
Observed near-Earth solar wind speed and magnetic field data by
OMNI (http://omniweb.gsfc.nasa.gov). From the observed data during
CR2028, it seems to have three speed peaks and 4 sectors including onevery narrow sector around Apr 10.

This four sector structure reflects, in the ecliptic plane, thesectors shown in 3D in Fig. 2. The away sector seen on theright of Fig. 2 corresponds to the first away sector in thefirst quarter of Fig. 3 that starts on March 25 at the earth,584

S. KAMEI et al.: DEVELOPMENT OF THE GLOBAL SIMULATION MODEL OF THE HELIOSPHERE

as the beginning of CR 2028, and the toward sector seen on
the left of Fig. 2 corresponds to the second toward sector
in the second quarter of Fig. 3 that starts on April 1 at theearth. The third away sector seen in the third quarter at theearth is a very narrow away sector, and the fourth sector in
the third and fourth quarter at the earth are both a toward
sectors with a normal width.
Due to the solar rotation, the solar wind blows like asprinkler seen in the non-rotating frame. In Fig. 3, threehigh-speed flows can be seen at the earth with their positions in the first away, second toward and fourth toward
sectors. There is no high-speed flow in the third narrow
away sector. In one sector, only one high-speed flow appears without consecutive high speed flows (Neugebauer etal., 2004). These flow and sector structures can be quite
reasonably understood from the coronal structure shown in
Fig. 2. The time recognized on the earth for the increasing of wind speed is shorter than that for decreasing. This
characteristic resembles the observed feature of solar windvariation in the increasing and decreasing of speed (Goslingand Pizzo, 1999). In Fig. 3, no shock is generated associated with the CIR. Actually, there may not be an obvious
CIR formation in the interval treated in this paper. However,
we cannot draw a firm conclusion, because grid spacing in
the present model is still too sparse for the shock resolution.
Figure 4 shows observed and calculated results for variations in solar wind speed and sector near the earth’s orbit.
Comparing the calculation results with these observation
data, it is clear that the four sectors and three high speed
winds seen in calculation are also observable . A narrow
third away sector in the third quarter is similarly seen bothin the calculation and in the observation data. As for the
relative position of the sector boundary and fast flow, similar features are seen in Figs. 2, 3 and 4. At the earth, fast
flow starts after the sector boundary has been passed, andfast flow does not restart until the passage of the next sector
boundary. However, some discrepancies are seen. However, provided that the calculated and observed magnitudeof the low-speed solar wind is the same, the magnitude of
the calculated high-speed solar wind value is lower than theobserved value. In other words, the contrast between highand low-speed flows is not sufficient in the calculated result. In addition, the decreasing speed of third fast flow is
too rapid in the calculated than the observed data. These results suggest a further necessity for the improvement of themodel. There are many uncertainties that prevent a modelobservation coincidence. There may still be many unknown
factors in heating term, expansion factor, radiation energybalance, and magnetic field observation.

4.

Summary

been well reproduced in the model. Whereas three velocity
peaks are seen at the earth’s orbit in both the calculated andobserved solar winds, the calculated results are still insufficient for the absolute speed of solar wind. This means that
we need to improve this model further when using it for thereal prediction of solar wind. For this purpose, we are going to continue variations and improvements of the model.
In future research, we are going to adopt this model for the
space weather prediction system operated in the National
Institute of Information and Communication Technologies(NiCT), Japan.
Acknowledgments. Wilcox Solar Observatory data used inthis study was obtained via the web site (http://quake.
stanford.edu/∼wso) courtesy of J. T. Hoeksema. The OMNI
data were obtained from the GSFC/SPDF OMNIWeb interface at(http://omniweb.gsfc.nasa.gov).

References
Brio, M. and C. C. Wu, An upwind differencing scheme for the equationsof ideal magnetohydrodynamics, J. Comput. Phys., 75, 400–422, 1988.
Detman, T., Z. Smith, M. Dryer, C. D. Fry, C. N. Arge, and V. Pizzo, A hybrid heliospheric modeling system: Background solar wind, J. Geophys.
Res., 111, A07102, doi:10.1029/2005JA011430, 2006.
Dryer, M., Multidimensional, magnetohydrodynamic simulation of solargenerated disturbances: space weather forcasting of geomagnetic
storms, AIAA J., 36, 365–370, 1998.
Gosling, J. T. and V. J. Pizzo, Formation of corotating interaction regions
and their three dimensional structure, Space Sci. Rev., 89, 21–52, 1999.
Hakamada, K. and S. Akasofu, Simulation of three-dimensional solar wind
disturbances and resulting geomagnetic storms, Space Sci. Rev., 31, 3–
70, 1982.
Linker, J. A., Z. Mikic, D. A. Biesecker, R. J. Forsyth, S. E. Gibson,
A. J. Lazarus, A. Lecinski, P. Riley, A. Szabo, and B. J. Thompson,
Magnetohydrodynamic modeling of the solar corona during Whole Sun
Month, J. Geophys. Res., 104, 9809–9830, 1999.
Lionello, R., J. A. Linker, and Z. Mikic, Including the transition region
in models of the large-scale solar corona, Astrophys. J., 546, 542–551,
2001.
Manchester, W. B., T. I. Gombosi, I. Roussev, D. D. De Zeeuw, I. V.
Sokolov, K. G. Powell, G. Toth, and M. Opher, Three-dimensional
MHD simulation of a flux rope driven CME, J. Geophys. Res., 109,
A01102, doi:10.1029/2002JA009672, 2004.
Neugebauer, M., P. C. Liewer, B. E. Goldstein, X. Zhou, and J. T. Steinberg, Solar wind stream interaction regions without sector boundaries,
J. Geophys. Res., 109, A10102, doi:10.1029/2004JA010456, 2004.
Riley, P., J. A. Linker, and Z. Mikic, An empirically driven global MHD
model of the solar corona and inner heliosphere, J. Geophys. Res., 106,
15,889–15,901, 2001.
Shen, F., X. Feng, S. T. Wu, and C. Xiang, Three-dimensional MHD
simulation of CMEs in three-dimensional background solar wind withthe self-consistent structure on the source surface as input: Numericalsimulation of the January 1997 Sun-Earth connection event, J. Geophys.
Res., 112, A06109, doi:10.1029/2006JA012164, 2007.
Sittler, Jr., E. C., L. Ofman, S. Gibson, M. Guhathakurta, J. Davila, R.
Skoug, A. Fludra, and T. Holzer, Development of multidimensional
MHD model for the solar corona and solar wind, Solar wind 10, 2002.
Tanaka, T., Finite volume TVD scheme on an unstructured grid system forthree-dimensional MHD simulation of inhomogeneous systems including strong background potential fields, J. Comput. Phys., 111, 381–389,
1994.
Tóth, G., I. V. Sokolov, T. I. Gombosi, D. R. Chesney, C. R. Clauer, D. L.
De Zeeuw, K. C. Hansen, K. J. Kane, W. Manchester, R. C. Oehmke,
K. G. Powell, A. J. Ridley, I. I. Roussev, Q. F. Stout, O. Volberg, R. A.
Wolf, S. Sazykin, A. Chan, B. Yu, and J. Kóta, Space Weather Modeling
Framework: A new tool for the space science community, J. Geophys.
Res., 110, A12226, doi:10.1029/2005JA011126, 2005.
Wang, Y. M. and N. R. Sheely Jr., The solar wind speed and coronal fluxtube expansion, Astrophys. J., 355, 726–732, 1990.

We have succeeded in constructing an MHD model to reproduce the heliospheric structure extending from the solar
surface to the earth’s orbit using a uniform triangular grid
system with no apparent singular point. The calculation results have reproduced both of the fine structure around thecorona and global structure from the solar surface to theearth’s orbit. The tendency of a rapid increase and slow decrease of velocity seen on the earth and the relative position
S. Kamei (e-mail: satomi@geo.kyushu-u.ac.jp), A. Nakamizo, T.
of the sector boundary, including the narrow sector, have Tanaka, T. Obara, and H. Shimazu

LETTER

Earth Planets Space, 61, 585–588, 2009

The interplanetary magnetic decrease automatic detection (IMDAD) code
F. L. Guarnieri1 , B. T. Tsurutani2 , and E. Echer3
1 Universidade do Vale do Paraiba (UNIVAP), Sao José dos Campos, SP, Brazil
2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
3 Instituto Nacional de Pesquisas Espaciais, INPE, Sao Jose dos Campos, SP, Brazil(Received February 7, 2008; Revised April 15, 2008; Accepted May 5, 2008; Online published May 29, 2009)

A new code, called the interplanetary magnetic decrease (MD) automatic detection (IMDAD) code, has beendeveloped to enable researchers in the field to rapidly identify MD events for further analyses. The criterion
used for MD selection is Bmin < X B0 , where X is a variable value and B0 is the ambient magnetic fieldmagnitude. The code can be applied to data sets from different instruments/missions located in different spaceplasma environments in the heliosphere. The code has been tested during slow solar wind, fast solar wind and
CIR intervals at ∼5 AU (from November 28 to December 03, 1992). For this test, we used a sliding window
with a width of 300 seconds applied to 1-second high-resolution magnetic field data. The events identified by thecode have been confirmed by hand analyses. The routine was able to identify 57 of the 118 MDs identified byhand (∼50%). The selection criteria for IMDAD and hand-analyses MDs were not exactly the same, accounting
for the different rates of occurrence. What is particularly encouraging is that IMDAD did not falsely identify any
events. The discrepancies between the two methods are discussed in the text. This code will be made available
to the general public.
Key words: Interplanetary magnetic decreases, solar wind, Alfvén waves.

1.

Introduction

Magnetic Decreases (MDs; Turner et al., 1977) havebeen defined as ∼50% decreases in the interplanetary magnetic field magnitude (Winterhalter et al., 1994; Fränz etal., 2000; Tsurutani et al., 2003). These structures havebeen called a variety of names (magnetic holes, holes, magnetic dips, magnetic cavities, magnetic bubbles, etc.) due
to their discovery at different times and in different locations of the heliosphere/Earth’s magnetosphere (Sugiura etal., 1969; Turner et al., 1977; Luhr and Klocher, 1987;
Winterhalter et al., 1994; Fränz et al., 2000). For events
that have been examined to date, the magnetic pressure decreases have been supplanted by plasma thermal pressure
increases, so that the entire structure is generally in pressurebalance (Winterhalter et al., 1995; Burlaga, 1995; Fränz etal., 2000).
Most past studies have focused on large decreases of themagnetic field magnitude, events where the decrease magnitudes are larger than 0.5 times the ambient field. It is clearthat this is an arbitrary threshold. Similar structures generated by the same mechanism, but lesser in intensity, are alsopresent in the interplanetary medium. To allow the rapid
detection of MDs of arbitrary intensity, a computer code
called Interplanetary Magnetic Decrease Automatic Detection (IMDAD) has been developed for the space research.
This code allows variable magnetic field decreases, variableinter-MD spacing, and can be applied to variable data rates.
The code can be used to identify MDs of arbitrary lengthc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

by adjusting its window size (here we discuss only MDs oflength up to 300 s to compare results to previous works).
Although previous workers have developed routines to automatically identify MDs (Winterhalter et al., 1994; Fränz
et al., 2000), those codes did not have the special featuresof IMDAD. The codes are also not available to the generalpublic.

2.

Method of Analyses

A general routine to identify MDs using high time resolution magnetometer data has been developed. The aim ofthe development of the IMDAD computer code is to be able
to correctly identify MDs present in the data. In this paper,
the routine will be described in detail. Pitfalls will also be
discussed.
We have used the Ulysses high-resolution magnetometerdata as our test sample. The data used for this test is nominally one-second (the Ulysses sampling rate varies) resolution magnetic field vector data for the interval from November 25 (day 330) to December 3 (day 338), 1992. Ulysses
had recently encountered Jupiter (February, 1992) and wasstarting its first south polar pass. Ulysses was at ∼−20◦ andat 5.1 AU from the sun during the selected test data interval.
This 9-day interval contained a variety of solar wind types.
There are ∼4 days of quiet solar wind, ∼3 days of Corotating Interaction Region (CIR) solar wind, and ∼1 day of
non-CIR (pure) high speed stream solar wind.
IMDAD was tested on the above data interval. The MDs
were identified by hand analyses and they were also independently identified by computer analyses. The MDs identified by hand but missed by computer were carefully examined to understand the reasons why.

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F. L. GUARNIERI et al.: INTERPLANETARY MAGNETIC DECREASE AUTOMATIC DETECTION CODE

The definition of a MD used in this test is a decreaseof field magnitude of 50% of the ambient magnetic fieldstrength (0.5B0 ). This is the same general criterion used byWinterhalter et al. (1994). This criterion is kept so there will
be continuity of methods used in the literature (however,
we will latter show that even with this simple definition,slightly different selection methods may yield significantly
different results). We also hope to intercompare our resultswith those of others. It should also be noted by the reader
that different decrease levels can be easily implemented.
This program can be used by other scientists for analyses of
MDs in the heliosphere and magnetosphere. Interested persons should contact F. L. Guarnieri at guarnieri@univap.br.
2.1 Details of the IMDAD routine
A sliding window of 300 seconds was used to calculate
the average field magnitude (B0 ) during the interval. All
points that have values less than 0.5B0 are identified. The
window is shifted by 1 second and the process repeated.
This analysis is done for the entire data set. After thedata has been initially processed in this manner, the samedata points identified by different window placements andadjacent potential MD candidates are deleted (keeping only
the beginning and end points). Single isolated points arealso deleted, assuming that they are spurious data errors.
The window size of 300 seconds and the minimum MD
separation of 30 seconds were empirically selected for thisdata set. We caution the reader that he/she might have tochange these parameters for applications to different plasma
regions. It would also be important that they empiricallyhand check the accuracy of the code as done in this paper.
A schematic showing the basics of the routine is indicatedin Fig. 1. A nine-point interval with a sliding window sizeof three points is illustrated (only as an example) to givethe reader a general idea of how the routine works. The
sliding windows are represented by brackets A (black), B(blue), C (red), etc. For bracket A, the first 3 points are
examined. The magnetic field average of the first threepoints is calculated. Any points that have values less than
50% of the average of the field are identified. In this case no
points meet this criterion. Next, the window is slid by one
point in time to give a new analysis subinterval (bracket B in
the figure). The result of the subsequent calculation is thatpoint 4 satisfies the MD criterion. A blue star is noted above
the point (for visualization). For the subinterval bracket C,
the average magnetic field is low, so no points are identified.
The same is true for bracket D. For bracket E, point 5 will
be detected as an MD. A yellow star is indicated above thispoint. After the entire interval has been analyzed, there are
2 points identified, points 4 and 5.
The program next considers single MD points. If there is
only a single isolated MD point, this is discarded assumingthat it is a spurious data spike. In the example shown above,
two adjacent points were selected, so there are no suchsingle point cases.
The next step of the routine is to consider cases where
there are several adjacent points. Point 5 is adjacent topoint 4 so the program considers the deletion of point 5.
Next point 6 is examined. Since it is not identified as anMD, point 5 is retained and identified as the end of the MD.
Thus, the program identifies point 4 as the beginning of the

4
A

5

B
C

1

D

E

F

2

7

8

9

3
6

4

5

Fig. 1. Illustration of the general features of the routine. The stars over thebrackets indicate the points that were identified as following the MDs
criteria.

MD and point 5 as the end. This allows us to automaticallydetermine the MD width.
The window width selected in our final analysis of thereal Ulysses data was 300 seconds rather than 3 points, as
shown in Fig. 1. The much shorter interval was chosen only
to illustrate the general features of the program.
To be able to handle waves inside the MD or highly turbulent data, the program examines adjacent MDs that arecloser than 30 seconds. Several different separation timescales, from 5 to 50 seconds were tested. The interval of
30 seconds was found to be the one with best correspondence to the hand-analyzed MD set, and it was selected
for the present version of the program. If candidate MDs
are closer together than 30 seconds, they are considered asa single MD. The two MDs are “merged” and the beginning of the first event and the end of the second become theboundaries of the new (merged) MD.
The MD duration indicated by the program is based onlyin the points that follow the MD criteria. The user would
have to define what method he/she may find appropriate to
identify the edges. Tsurutani et al. (1999), in their hand
analyses of MDs, assumed an 1/e decay from the B0 calculated outside the MD. This is the criteria used in this paper in order to check the IMDAD code. Although we havestated the method used here, we state this as only an example. Other users can select their own criteria for edge
detection.
2.2 Hand analyses of MDs
To test the accuracy of IMDAD MD selection, the same
9-day Ulysses magnetic field interval was examined by visual inspection (without reference to the computer results).
For a potential MD, a background field on both sides of the
MD was estimated by drawing line “averages” on a dataplot. These were determined by visual inspection. Of thetwo “background fields”, the higher value was used for the
calculation. Next, the minimum field was determined by thesame method. The 1/e value of the difference between thehighest background field and minimum field was required
to be greater than 0.5B0 . This is the same method applied
by Tsurutani et al. (1999).

3.

Results of the Intercomparison Between
Computer-selected Events and Hand-selected
EventsFigure 2 shows the Ulysses data interval of the test. From
top to bottom are the solar wind speed, proton density,

F. L. GUARNIERI et al.: INTERPLANETARY MAGNETIC DECREASE AUTOMATIC DETECTION CODE

BR [nT]

0,1
0,0
-0,1
-0,2
0,2

1
0
6

0,1
0,0
-0,1
-0,2
0,2

3

BN [nT]5

Tp (1E K)

Br (nT)FS HCSIF RW

BT [nT]

Vsw (km/s)

Np (cm )

2

-3

800
700
600
500
400

0,2

HSS

SSS

587

0
3

0,1
0,0
-0,1

0

-0,2

-3

Bt (nT)|B| [nT]

Bn (nT)

0,2

2.5
0.0
-2.5
3

0,0
333,753

333,7540333,756

333,757

Fig. 3. Example of a MD identified by the program. The blue square
marks the MD event, and the red box the MD identified by the program.

2
0
330

333,755

DOY 1992-3
4
B (nT)

0,1

339

85

25Nov 26Nov 27Nov 28Nov 29Nov 30Nov 01Dec 02Dec 03Dec 04Dec

331

332

333

334

335

336

337

338

80
75

1992

hand analyses
computer analyses

70
65
60
55
50

N. MDsFig. 2. Ulysses data interval (November 25 to December 3, 1992) used
to test the routine. The panels are, from top to bottom, the solar windspeed, proton density, proton temperature, magnetic field components,
R, T and N , and at the bottom, is the magnetic field magnitude. The
slow speed stream is identified by SSS. The high speed stream is marked
by HSS, and IF indicates the interface between the two regions. Present
in the interval is a heliospheric current sheet, marked as HCS.

45
40
35
30
25
20
15
10

proton temperature, magnetic field components (in Solar
Heliospheric R, T , and N coordinates), and at the bottom,
the magnetic field magnitude. At the top of the figure,the slow speed stream (SSS) and high speed stream (HSS)
intervals are indicated by horizontal arrows. The slow speed
stream is present from November 25 to 29 and the highspeed stream from December 2 through 3. The CIR is
the region of interaction of the two types of streams andis the interval between the slow and high speed streams
proper. Some of the CIR structures are indicated for theinterested reader. The CIR boundaries are a fast forward
shock (FS, blue line) at the anti-solar direction boundary. A
reverse wave (RW, blue line) is present at the solar direction
boundary. The CIR occurs from 02:35 UT November 29(day 334) to 11:30 UT December 1 (day 336). Several
structures within the CIR are also indicated. There is anembedded heliospheric current sheet (HCS) indicated by agreen line. The interface between the high speed stream andthe slow speed stream is denoted by “IF” (for “interface”).
The IF is indicated by a red line.
Figure 3 shows an example of a MD identified by the program. The panels are, from top to bottom, the magnetic fieldcomponents B R , BT , and B N , and the B magnitude. ThisMD event, clearly visible in the B magnitude panel, occurred on November 28, 1992 (DOY 333). The blue square

5
0
330

331

332

333

334

335

336

337

338

339

1992

Fig. 4. MD occurrence rates using the two methods of analyses. The
results from the computer analyses are plotted in dashed red and thosefrom hand analyses are in solid black.

marks the MD event and the red box the MD identified by
the program. There is a discontinuity in BT and B N components at the time of the MD occurrence. The BT component
changes from ∼0.125 nT to ∼−0.1 nT across the discontinuity. The change in B N is from ∼−0.125 nT to ∼0.15 nT.
The MD identified by the computer routine (red box) has
a shorter duration when compared with hand analysis due
to different identification procedures. In the IMDAD identification, the edges are based only in the points following
the criteria, while in the hand analysis the inspectors used
the borders values as the reference field to identify the MDs(the same method previously applied by Tsurutani et al.,1999).
The MD occurrence rates of the two methods of analyses are shown in Fig. 4. The top panel shows the numberof MDs per day from the computer analyses in dashed red,

588

F. L. GUARNIERI et al.: INTERPLANETARY MAGNETIC DECREASE AUTOMATIC DETECTION CODE

and for those from hand analyses in solid black. The reader
should note that the number of events from hand analyses isalways greater or equal to the number from computer analyses. Over the whole interval, there are 118 MDs identified
by hand and 57 events identified by computer.
Each computer-selected event was compared with theevents identified by hand. It is noted that all 57 computer
selected events were also identified by hand analyses.
This result gives confidence to the accuracy of the present
program (and its internal parameters) used for this region of
space, since no false positive MD was detected.
The causes for the code missing MDs were studied. It
was found that the missed events fall into several categories.
The two main causes were: 1) events where the magnetic
field decrease is near the threshold of −0.5B0 , and 2) when
there are rapid oscillations in the magnetic field magnitude(if these oscillations have amplitudes comparable to the MD
decrease, they can change the reference value [B0 ] for thewindow, while hand-analysis is not affected by these structures). In the first category there were 25 cases of “missed
events” and in the second category there were 17 cases.
Moreover, there are two minor causes of misidentificationthat we called “large MD” or “background contamination”.
The “large MD” refers to MDs that are longer than the window size used. These MDs can be selected by hand inspection but they may be missed by the computer since theirdurations are close to the window size. The “backgroundcontamination” usually occurs when there are discontinuities or shocks around the MD that may affect the B0 calculation for the window.
For the first category of “missed events”, the near
“threshold” events, it is noted that the computer and hand
analysis methods of determining the “background” field
were slightly different. The hand analysis method usedhigher field values for the “background”, so this criterion
was less strict than the computer criterion. The computer
method often contains field values in the decreasing slopesof the MDs, lowering the calculated “background” fields,
giving stricter limits than hand analyses. Here the background field on both sides of the MD was estimated bydrawing line “averages” on a data plot. Of the two “background fields”, the higher value was used for the calculation(a more liberal assumption than the IMDAD code). Next,
the minimum field was determined by the same method.
The 1/e value of the difference between the highest background field and minimum field was required to be greaterthan 0.5B0 . As the reader will readily note, although a simple condition of “0.5B0 ” was used, this is a different criterion still. The point that we wish to emphasize is thatslightly different criteria will yield a different set of events.
Thus, the method of implementation of the criterion is important to understand. On the other hand, it is felt that noone method is better than another. All methods will giveequally valuable information.
It should be obvious that the IMDAD “missed events”
are not really “missed”. Since hand-analyses and computer
analyses will never have identical criteria, each is correct.
It should be noted that the type of hand analyses done here
and in Tsurutani and Ho (1999) is not exact and not 100%
reproducible.

4.

Summary and Discussion

A computer program has been written which identifies
heliospheric MDs in the Ulysses magnetic field data at∼5 AU from the sun. The program works well in the slow
solar wind, in the pure high speed stream solar wind, and in
the compression regions at the interface between slow andhigh speed streams (CIRs). The routine was able to identify
57 of the 118 events identified by hand analysis, about 50%of the events (48.3%). However, all the 57 MDs identified
by the program were also identified by hand analyses, giving confidence to the accuracy of the method. The events
that were missed by the code were events that fell into two
main categories: events that were slightly below the handtechnique threshold level of detection and events associatedwith “wave-like” intervals. For the first case, the slightly
more liberal hand analyses method allowed the detectionof these events. “Wave-like” events were generally foundin hand analyses when the magnetic field magnitude waslow. These events could possibly be compressional waves
or small amplitude mirror mode (Tsurutani et al., 1982)
structures. These low field magnitude regions are generally
low plasma beta (the ratio of magnetic pressure to plasma
thermal pressure) regions. Thus they could also be due tomagnetic noise or turbulent structures.
Acknowledgments. Portions of this work were done at the
Jet Propulsion Laboratory, California Institute of Technology,
Pasadena CA under contract with NASA. EE would like tothank to the Brazilian FAPESP (2007/52533-1) and CNPq (PQ300104/2005-7 and 470706/2006-6) agencies for financial supports.

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Winterhalter, D. H., M. Neugebauer, B. E. Goldstein, E. J. Smith, andS. J. Bame, and A. Balogh, Ulysses field and plasma observations ofmagnetic holes in the solar wind and their relation to mirror-mode
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Winterhalter, D., M. Neugebauer, B. E. Goldstein, E. J. Smith, B. T. Tsurutani, S. J. Bame, and A. Balogh, Magnetic holes in the solar wind andtheir relation to mirror-mode structures, Space Sci. Rev., 72, 201, 1995.
F. L. Guarnieri (e-mail: guarnieri@univap.br), B. T. Tsurutani, and E.
Echer

LETTER

Earth Planets Space, 61, 589–594, 2009

Impacts of torus model on studies of geometrical relationships between
interplanetary magnetic clouds and their solar origins
Katsuhide Marubashi1 , Suk-Kyung Sung1 , Kyung-Suk Cho1 , and Ronald P. Lepping2
1 Space Science Division, Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea
2 Space Weather Laboratory, NASA-Goddard Space Flight Center, Greenbelt, MD 20771, USA(Received December 14, 2007; Revised April 17, 2008; Accepted April 18, 2008; Online published May 29, 2009)

Our recent analysis of interplanetary magnetic clouds (MCs) showed that the orientations of MC axes determined by a model fitting with curvature of MCs taken into account (referred to as a torus model, hereafter) can besignificantly different from those obtained from fittings with a straight cylinder model. Motivated by this finding,
we re-examined geometrical relationships between magnetic field structures of MCs and their solar origins. This
paper describes the results of the re-examination with special attention paid to two MC events, for which different
orientations of MC axes were obtained from a torus model and a cylinder model. For both cases, it is shown thatthe torus models give the MC geometries of magnetic field structures in good agreement with those of coronalarcade structures which were formed in association with the launch of MCs along the magnetic field inversion
lines. Summarizing the analysis results for 12 MCs investigated here, we conclude that: (1) the formation ofcoronal arcade structure is a good indication of MC formation; (2) MC geometries can be obtained that are consistent with the coronal arcades with respect to the axis orientation and the magnetic field structure including
chirality, indicating that no significant direction changes occurred during the propagation of MCs through theinterplanetary medium.
Key words: Interplanetary magnetic clouds, magnetic field structures, solar origins, geometrical relationships.

1.

Introduction

The interplanetary magnetic cloud (MC) occupies thewhole body or a significant part of a plasma cloud ejected
into the solar wind in association with the coronal massejection (CME). The internal structure of a MC is characterized by the nested helical fields, which can be described
as a magnetic flux rope (Goldstein, 1983; Marubashi, 1986;
Burlaga, 1988). The geometrical relationship between magnetic structures of MCs and their solar source region is
one of the key issues for understanding the mechanisms involved in the formation of MCs and their possible deformation during their propagation in interplanetary space. Most
previous studies on this subject have shown that the orientations of MCs are roughly aligned with the inversion lines ofphotospheric longitudinal magnetic fields in the associated
CME sites and that the chirality of MCs are of the same sign
as the chirality of solar magnetic fields in the source regions(e.g., Marubashi, 1986, 1997; Bothmer and Schwenn, 1994;
Bothmer and Rust, 1997; Yurchyshyn et al., 2001). Morerecent studies, however, point out several cases in which theorientations of MCs do not agree with those of the associated filaments or solar magnetic inversion lines (Rust et al.,2005; Wang et al., 2006; Yurchyshyn et al., 2007).
The purpose of this study is to re-examine the geometrical relationships between the MC magnetic fields and thesolar magnetic fields with a new technique to determinec The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

the orientations of MCs. In most studies on this subject,
as mentioned above, the MC orientations were determinedby fitting techniques with a straight cylinder model. Recently, Marubashi and Lepping (2007) analyzed the MC geometries using a torus-shaped flux rope model to take into
account the curvature of the global configuration of MCs.
Their comparison of the MC orientations determined fromthe torus and cylinder models revealed that there actually
are such MC events for which observations can be as well
explained by either of the models but that the obtained orientations are significantly different from each other. Thisfinding impacts on our understanding the connection between MCs and CMEs and suggests that it may be possible
to obtain a better agreement between the MC orientations
and the solar magnetic inversion lines if the MC geometries
are determined with a torus model.
The MC database for this study consists of the analysis
results of 17 long-duration MCs (Marubashi and Lepping,2007). We compared the MC geometries obtained from thetorus and cylinder models with the magnetic field structuresin the possible solar source regions of the MCs. We present
here our analysis results, with a focus on two events forwhich the connection between the MC and related solar
phenomena can be seen in a straightforward way. Similar
connections are also seen for other MC events.

2.

Analysis Results

Figure 1 shows the fitting results of the MC encounteredon March 4, 1998, with solid lines for the torus model anddotted lines for the cylinder model, superposed on the ob-

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(a)
0.4
A
0.2
Z

S

S/C

0
-0.2
-0.4
0.4

0.2

0
Y

-0.2 -0.4

0-0.4-0.2

0.2 0.4
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(b)
0.4
S/C

0.2
Z

0
-0.2
-0.4
S
0.4

0.2

0
Y

-0.2 -0.4

A0-0.4-0.2

0.2 0.4
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Fig. 2. Two geometries obtained for the magnetic cloud of March 4, 1998,
from the fittings to the torus model (a) and to the cylinder model (b).
Three directions are indicated: A, axial field; S, toroidal field on thesurface; S/C, spacecraft trajectory relative to the magnetic cloud.

Fig. 1. Results of fitting the torus model (solid curve) and the cylindermodel (dotted curve) to the magnetic cloud encountered on March 4,
1998. The bottom three panels show the projected magnetic field vectors
onto three planes in GSE coordinates.

served variations of solar wind magnetic fields during a 3day interval. Plotted from top to bottom are the magnetic
field intensity, the X , Y , and Z components in GSE (geocentric solar ecliptic) coordinates, the ratio of standard deviations of high-resolution data to the average intensity, thesolar wind speed, the number density ratio of He++ /H+ , theproton number density, the proton temperature, the plasma
beta based on protons, and the magnetic field vectors projected on the X -Y , X -Z , and Y -Z planes of GSE coordinates. The dashed curve drawn along with the proton temperature shows the temperature statistically expected fromthe solar wind speed (Lopez, 1987). Two vertical solidlines indicate the MC boundaries as determined by suchcharacteristics as the magnetic field rotation, the enhanced
He++ /H+ ratio, the relatively small magnetic field fluctuations, and the abnormally low proton temperature (Richardson and Cane, 1993). The vertical dashed line indicates theshock associated with this MC. The observed variations inmagnetic field and solar wind speed are well reproduced byboth the torus and cylinder models, so that the difference
between the two fitted curves can be hardly distinguished inthis presentation. However, the MC orientations obtained
from the two models are substantially different from eachother.
Figure 2 depicts the MC geometry obtained from thetorus model (Fig. 2(a)) and that from the cylinder model(Fig. 2(b)), in which three arrows indicate the directionof the axial field of MC (A), the direction of magnetic
field on the MC surface (S), and the direction of spacecraft
trajectory (S/C). We can see that this MC has the lefthanded magnetic chirality from the two arrows, A and S.
At the location where the spacecraft traversed the MC, theapproximate direction of the torus axial field is given byθ (latitude angle) = 17.4◦ and φ (longitudinal angle) =136.9◦ , whereas the direction of the cylinder axis is givenby θ = 29.3◦ , and φ = 76.7◦ (for details of the fitted values,
including other parameters, see Marubashi and Lepping,2007).
In an attempt to identify the most plausible solar source
event of this MC, we searched the LASCO CME catalog (Yashiro et al., 2004; see also the website http://cdaw.
gsfc.nasa.gov/CME list) for candidate CMEs and related
solar phenomena within a selected time window. For thispurpose, we first estimate the launch time of the CME corresponding to this MC, assuming that the MC propagated at aconstant speed. In accordance with three values for the typical speeds, 340 km/s (from the cylinder fitting), 350 km/s
(from the torus fitting), and 365 km/s (the maximum speed
within the MC), the launch time is estimated to be in theinterval from 15:00 UT, February 27 to 01:00 UT, February
28, 1998. Thus, we select a time window from 03:00 UT,

K. MARUBASHI et al.: IMPACTS OF TORUS MODEL ON MC GEOMETRY

(a)

(b)

(c)

(d)

591

8164
8171

(e)

Fig. 3. Solar observations related to the March 4, 1998 MC: (a) LASCO C2 CME running difference image at 17:27 UT, February 28, 1998; (b)Yohkoh/SXT image at 11:34 UT; (c) SOHO/MDI image 12:48 UT, (d) BBSO Hα image at 19:15 UT, February 27; (e) the torus MC inclination
inferred from a local fit with a torus model.

February 27 to 13:00 UT, February 28, allowing an extra±12 h from the estimated launch time for searching theCME corresponding to the MC. The CME catalog showsthat there were two CMEs with an angular width larger
than 120◦ in this time window. The first one is a full halo
CME which appeared in the LASCO C2 field of view firstat 20:07 UT on February 27, 1998, and the second one is apartial halo CME with angular width of 169◦ that appeared
at 12:48 UT on February 28, 1998. Of these two, the latter was identified as a solar source event of the March 4,
1998 MC by Gopalswamy et al. (2000, 2001), the speed ofwhich is estimated to be approximately 300 km/s at 20 Rs.
We adopt this selection and search for the solar source region of the CME for the purpose of comparing structures
between the MC and solar magnetic fields.
Figure 3 shows images of solar observations relevant togeneration of the MC of March 4, 1998 (a: SOHO/LASCO
C2 image; b: Yohkoh/SXT, c: SOHO/MDI; d: BBSO Hα).
The torus shape corresponding to the MC is also shown in
Fig. 3(e) for the purpose of indicating the tilting angle ofthe fitted model. (It should be noted that the actual MC
shape is just locally approximated by the torus.) During
several hours before this CME (Fig. 2(a)) first appeared in
the LASCO C2, we can see two kinds of prominent activities in the Yohkoh/SXT movie. One consists of small activities repeatedly observed in the AR 8171 (approx. 24◦ S, approx. 1◦ W), and the other is the formation of a soft X-ray arcade possibly associated with a filament eruption (Figs. 3(b,d)) along the neutral line extending from the north of AR
8164 towards the north-east in the region of weaker magnetic fields (see Figs. 3(c, d)), similar to the arcade formation exemplified by Tripathi et al. (2004). Although it is592

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(a)
A

0.4

S
0.2
Z

0
S/C
-0.2
-0.4
0.4

0.2

0
Y

-0.2 -0.4

0-0.4-0.2

0.2 0.4
X

(b)
0.4
S/C

0.2
Z

0
S
-0.2
A
-0.4
0.4

0.2

0
Y

-0.2 -0.4

0-0.4-0.2

0.2 0.4
X

Fig. 5. Two geometries obtained for the magnetic cloud of October 1,
1997, from the fittings to the torus model (a) and to the cylinder model.
Three directions are indicated: A, axial field; S, toroidal field on thesurface; S/C, spacecraft trajectory relative to the magnetic cloud.

Fig. 4. Results of fitting the torus model (solid curve) and the cylindermodel (dotted curve), respectively, to the magnetic cloud encounteredon October 1, 1997. The bottom three panels show the projected magnetic field vectors.

difficult to rule out the association between the CME andsome small activity in AR 8171, the arcade-formation event
seems to be directly connected with the CME in Fig. 3(a).
The latter association is more plausible based on several
supporting pieces of evidence: (1) the orientation of the MC
axis is close to the orientation of the arcade, as is evident
by comparing Figs. 3(b, e); (2) the polarity of the magnetic field on the surface of the MC is consistent with thearcade magnetic field, as inferred from the MDI data; (3)the left-handed magnetic field chirality of MC agrees withthe chirality of the coronal magnetic field expected fromthe inverse-S type sigmoid in this region (Rust and Kumar, 1996); (4) The chirality agrees with general tendency
that the MCs with left-handed (right-handed) chirality areformed in association with the solar events in the northern(southern) hemisphere (Marubashi, 1986, 1997; Bothmer
and Schwenn, 1994; Bothmer and Rust, 1997). Finally, it
is possible to suppose from Fig. 3(a) that this CME waslaunched a little toward south, and that the ACE spacecraft
passed the southern end of the MC loop as indicated by thedark dot in Fig. 3(e).

Figures 4 and 5 show the fitting results for another MC
which was encountered on October 1, 1997, in the sameformat as Figs. 1 and 2. Again, both cylinder and torus
models having the left-handed chirality reproduce the magnetic field variations agreeing well with the observation. Itshould be noted here that the torus parameters used here aredifferent from original values presented in Marubashi andLepping (2007). The orientation of the torus plane determined by the standard fitting method is given by θn = 35.1◦ ,and φn = 65.0◦ , the latitude and longitude angles of a vector normal to the torus plane. This torus plane is tilted too
much compared with the direction of the post-eruption arcade as will be seen later. Since our purpose is to examine a possibility to obtain the orientation of the MC axis
which is close to the orientation of the inversion line ofsolar magnetic fields, we executed a least-squares method
slightly modified from that applied in the previous work.
We tried fitting with fixed φn , using different values aroundφn = 65.0◦ , and searched the parameter set which can reproduce the observed magnetic fields, and give geometries
having the axis orientation as parallel to the inversion line
as possible. Thus, we obtain a result shown in Fig. 4 forθn = 14.6◦ , and φn = 77.5◦ . The point is that we can get
such an MC geometry by using a torus model.
As for the solar source of this MC, the CME catalog
shows that there was only one CME with angular width
greater than 120◦ within the time window from 08:00 UT
on September 27 to 14:00 UT on September 28, 1997, thatis, the halo CME that appeared in the LASCO C2 field of

K. MARUBASHI et al.: IMPACTS OF TORUS MODEL ON MC GEOMETRY

(a)

(b)

(c)

(d)

8087

593

8088

(e)

Fig. 6. Solar observations related to the October 1, 1997 MC: (a) LASCO C2 CME running difference image at 03:53 UT, September 28, 1997; (b)Yohkoh/SXT image at 08:27 UT; (c) SOHO/MDI image 12:51 UT, (d) Meudon Hα image at 06:55 UT, September 27; (e) the torus MC inclination
inferred from a local fit with a torus model.

view at 01:08 UT on September 28, 1997. Though there is a
gap in the Yohkoh/SXT data from 22:39 UT September 27
to 08:23 UT September 28, we can see an arcade-formation
activity which started around 22:12 UT on September 27
and developed rather slowly near the region surrounding themagnetic inversion line in the northern hemisphere. Gopalswamy et al. (2001) identified the solar source of the MCof October 1, 1977 to be this halo CME and associatedit with the disappearing filament at 22◦ N, 05E. Figure 6
presents the images relevant to the generation of the MC,
together with the torus tilt obtained from the fitting. Accepting this association, we see that the relationships between this interplanetary MC and the solar magnetic field
are very much similar to the case of the March 4, 1998 MC.
The MC with left-handed magnetic chirality was formed inassociation with the filament disappearance in the northernhemisphere, where an inverse-S type sigmoid had been observed. The orientation of the MC axis is nearly parallel tothe neutral line or the erupted filament. The CME plasma

was launched slightly southward rather than radially, andhit the Earth with its southern end, as seen in Figs. 5(a)and 6(e).
Thus far we have seen the analysis results for two MC
events with special attention being paid to the geometrical relationships between MCs and the magnetic field structures in their possible solar source regions. Here, we briefly
summarize results of our analysis of the 17 long-duration
MCs. This analysis was carried out for only 12 of theseMCs because solar observation data were insufficient forthe other five MCs (for reference, we present the same event
numbers used in Marubashi and Lepping, 2007; #1, #2, #10,
#16, and #17). We were able to find plausible solar source
event in six cases (#4, #5, #7, #12, #13, and #15), and foreach of these, the magnetic inversion line on the Sun is consistent with the orientation of the MC axis determined by
the torus fitting. We also found a formation of arcade-likestructures along the magnetic inversion line within the solar source regions near the time of CME launch. For one

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case (#14), no prominent solar activity was seen in the time Bothmer, V. and D. M. Rust, The field configuration of magnetic clouds
and the solar cycle, in Coronal Mass Ejections, Geophys. Monogr. Ser.,window estimated by the MC observation. For the remainvol. 99, edited by N. Crooker, J. A. Joselyn, and J. Feynman, 139–146,
ing five cases, more detailed analyses are needed both on
AGU, Washington, D.C., 1997.
the solar events and on the MC structures, although it is not Burlaga, L. F., Magnetic clouds and force-free fields with constant alpha,J. Geophys. Res., 93, 7217–7224, 1988.
impossible to find candidates as the solar sources.

3.

Conclusions and Discussion

By analyzing the geometries of 12 long-duration MCs
and their relationships with their solar origins, we havedrawn the following conclusions.
(1) The arcade formation in the corona is a good indicationof the generation of an MC.
(2) The magnetic field structure of a MC is consistent withthe structure of a flux rope loop formed in the coronalregion above the arcade, as various CME models commonly predict (see Forbes, 2000, for a review).
The above two findings are consistent with the view that
MCs are expanding helical flux ropes formed in association
with CME launch (Marubashi, 1997). The more comprehensive relation between the post-eruption arcades and flux
rope structures in CMEs has been shown by Cremades andBothmer (2004) and Tripathi et al. (2004).
(3) Furthermore, for MCs of which the orientations obtained from cylinder fitting mismatch the above relationship, it is possible to obtain an MC orientation
which is consistent with the above by using a torus.
This suggests that no significant direction change of
MCs is needed during the propagation through the interplanetary medium.
It is desirable to extend this study further to other MC
events of shorter durations because our study is focused
only on the long-duration MCs. Such a study is currently
underway, but we can point out that two MCs analyzed
by Ishibashi and Marubashi (2004) and Crooker and Webb(2006), respectively, are good examples of where good relationships are obtained using a torus model to explain thealignment between the MC axis and the inversion line ofcoronal magnetic fields.
Acknowledgments. We gratefully acknowledge the use of datafrom the WIND SWE instrument, provided by the National Space
Science Center at the Goddard Space Flight Center, and ACE
MAG and SWEPAM instruments provided by the ACE Science
Center (http://www.srl.caltech.edu/ACE/ASC/). We also acknowledge the use of solar data from the SOHO LASCO and MDI instruments, YOHKOH SXT instruments, and Hα images from Big
Bear Solar Observatory and Meudon Observatory. We express ourparticular thanks to the many researchers involved in making andfreeing providing the LASCO CME catalogs. This work was supported by the Development of Korean Space Weather Center, theproject of KASI, and the KASI basic research fund.

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Cremades, H. and V. Bothmer, On the three-dimensional configuration ofcoronal mass ejections, Astron. Astrophys., 422, 307–322, 2004.
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K. Marubashi (e-mail: kmaru@kasi.re.kr), S.-K. Sung, K.-S. Cho, and
R. P. Lepping

LETTER

Earth Planets Space, 61, 595–597, 2009

Halo coronal mass ejections and geomagnetic storms
Nat Gopalswamy
NASA Goddard Space Flight Center, Greenbelt, Maryland, U.S.A.
(Received June 21, 2008; Revised October 27, 2008; Accepted October 27, 2008; Online published May 29, 2009)

In this letter, I show that the discrepancies in the geoeffectiveness of halo coronal mass ejections (CMEs) reported in the literature arise due to the varied definitions of halo CMEs used by different authors. In particular,
I show that the low geoeffectiveness rate is a direct consequence of including partial halo CMEs. The geoeffectiveness of partial halo CMEs is lower because they are of low speed and likely to make a glancing impact on
Earth.
Key words: Coronal mass ejections, geomagnetic storms, geoeffectiveness, halo CMEs.

1.

Introduction

Coronal mass ejections (CMEs) that appear to surroundthe occulting disk of the observing coronagraphs in skyplane projection are known as halo CMEs (Howard et al.,1982). Halo CMEs are fast and wide on the average and areassociated with flares of greater X-ray importance because
only energetic CMEs expand rapidly to appear above theocculting disk early in the event (Gopalswamy et al., 2007).
Extensive observations from the Solar and Heliospheric Observatory (SOHO) mission’s Large Angle and Spectrometric Coronagraphs (LASCO) have shown that full halos constitute ∼3.6% of all CMEs, while CMEs with width ≥120◦
account for ∼11% (Gopalswamy, 2004). Full halos havean apparent width (W ) of 360◦ , while partial halos have120◦ ≤ W < 360◦ . Halo CMEs are said to be frontsided if
the site of eruption (also known as the solar source) can be
identified on the visible disk usually identified as the location of H-alpha flares or filament eruptions. Details on how
to identify the solar sources can be found in Gopalswamy
et al. (2007). Halos with their sources within ±45◦ of thecentral meridian are known as disk halos, while those with acentral meridian distance (CMD) beyond ±45◦ but not beyond ±90◦ are known as limb halos. Disk halos are likely
to arrive at Earth and cause geomagnetic storms, while limb
halos only impact Earth with their flanks and hence are lessgeoeffective (see Gopalswamy et al., 2007).
Since CMEs propagate approximately radially from theSun (except for a small eastward deflection due to solar
rotation—see Gosling et al., 1987), disk halos are likely hit
Earth. Of course, the interplanetary counterpart of CMEs
(ICMEs) must contain southward magnetic field component(Bs ) to be geoeffective. It is well known that the intensityof the resulting magnetic storm depends on the magnitudeof Bs and the speed V with which the CME impacts Earth’s
magnetosphere (see e.g., Gonzalez et al., 1994; Tsurutani
and Gonzalez, 1997). Halo CMEs are more energetic (avc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. No claim is made to original U.S. Government works.

erage speed is ∼1000 km/s compared to ∼470 km/s for ordinary CMEs), so the V part is expected to be high. When
CMEs are aimed directly at Earth, the ICMEs are likely toarrive at Earth as magnetic clouds (MCs), which are a subset
of ICMEs that have flux rope structure. Since Earth passes
through the nose of the MC, the chance of encountering Bs
somewhere within the MC is high (except for unipolar MCs
with north-pointing axis—see Yurchyshyn et al., 2001).
When the ICME is shock-driving, the sheath portion lying
between the shock and the MC may also play a significant
role in producing geomagnetic storms (see e.g., Gosling
et al., 1990). The sheath may have intervals of north andsouth-pointing magnetic fields, in addition to the varying
field orientation in the MC portion. An Earth-directed halo
CME leads to a situation whereby Earth passes through thenose of the shock, where the sheath field is most intense andmay cause intense magnetic storm if south-pointing. Thus
the ability of a halo CME in producing a geomagnetic storm
depends on the structure of its interplanetary counterpart(the ICME event).
Since halos became common place in the SOHO era,
there have been several attempts to characterize their geoeffectiveness (see e.g., Zhao and Webb, 2003; Yermolaev
and Yermolaev, 2003; Kim et al., 2005; Yermolaev et al.,2005; Gopalswamy et al., 2007). Using CMEs from the risephase of solar cycle 23, St. Cyr et al. (2000) concluded that
∼75% of the frontside CMEs are geoeffective. In most of
the works discussed here, the geoeffectiveness is defined as
the ability of a CME or an interplanetary structure to cause
geomagnetic storms with intensity (Dst ) ≤ −50 nT. Whilemost of the intense storms are caused by CMEs, moderate
storms (−100 nT < Dst < −50 nT) may also be causedby other structures such as corotating interaction regions.
Zhao and Webb (2003) found an overall geoeffectivenessrate of ∼64% for frontside halos detected up to the solar
maximum in 2000. Yermolaev and Yermolaev (2003) useddata from the period 1976–2000 and came up with a lower
rate of 40–50%. Michalek et al. (2006) found that ∼56%
of frontside halos are geoeffective, but they did not use all
the halos because of limitations in the method of obtaining

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space speeds. Kim et al. (2005) reported that only about
40% of the frontside halos are geoeffective. Yermolaev etal. (2005) compiled published results and noted that thatthe geoeffectiveness rate varied from <40% to >80%. Recently Gopalswamy et al. (2007) analyzed 378 halo CMEs
covering almost whole of solar cycle 23 and found that
∼71% of frontside halos are geoeffective. Zhao and Webb
(2003) and Gopalswamy et al. (2007) used the same definition of halo CMEs (W = 360◦ ) and obtained similar geoeffectiveness rates. On the other hand, Kim et al. (2005)
and Yermolaev and Yermolaev (2003) defined their halos
as CMEs with W ≥ 120◦ and obtained the lower geoeffectiveness rate. The purpose of this letter is to show thatthe discrepancy in the rate of geoeffectiveness can simply
be explained by the different definition of halo CMEs usedby these authors. We take Kim et al. (2005) and Gopalswamy et al. (2007) representing the low and high geoeffectiveness rates, respectively. Both these works have published their list of events and the study periods have maximum overlap. They also use data from the same instrument(SOHO/LASCO), so the comparison is straightforward. Finally, both works use the same definition of geoeffectiveness: the ability of a CME to produce a geomagnetic storm
with Dst ≤ −50 nT.

2.

Geoeffectiveness of Partial Halo CMEs

Kim et al. (2005) investigated 305 CMEs (1997 to 2003)
that included full (W = 360◦ ) and partial halos (120◦ <W < 360◦ ) and found that 121 of them were geoeffective.
On the other hand Gopalswamy et al. (2007) studied 378
full halos for the period 1996 to 2005. For making a propercomparison, we first separate the full and partial halos in
Kim et al. (2005). We then use the geoeffectiveness of asubset of full halos from Gopalswamy et al. (2007) corresponding to the Kim et al. (2005) study period to estimate
the geoeffectiveness of partial halo CMEs.
Among the 378 full halos reported by Gopalswamy etal. (2007), 168 occurred during the period 1997 to 2003
(the study period of Kim et al., 2005). Many geomagnetic
storms during the study period had multiple CME association, so we eliminate 68 such CMEs in estimating the geoeffectiveness rate. Sixty five of the remaining 100 frontside
full halos (65%) were geoeffective. Note that this rate isclose to the one obtained by Zhao and Webb (2003). Excluding the full halos from the CMEs in Kim et al. (2005),
we get 205 partial halos (305 minus 100), out of which 56(121 minus 65) were geoeffective. Thus we get a geoeffectiveness rate of 27% (56 out of 205) for the partial halos
alone. The 40% geoeffectiveness rate obtained by Kim etal. (2005) is thus a consequence of combining highly geoeffective (65%) full halos and marginally geoeffective (27%)
partial halos.
Note that we used the CME data for the period 1997–
2003 in the above calculation. To extend this result to
the whole study period (1996–2005) considered by Gopalswamy et al. (2007), we need to estimate the faction ofpartial halos that are geoeffective. Since Gopalswamy etal. (2007) did not include partial halos in their study, we
estimate the geoeffectiveness of partial halos by extrapolation. To do this, we make use of the fact that 3.5% of

all CMEs are full halos, while 11% are full + partial halos(Gopalswamy, 2004). Assuming that these fractions apply
equally well to the front and backside CMEs and recalling that 229 full halos were frontsided, one can estimate
the frontside wide CMEs as (11%/3.5%) × 229 = 720.
Therefore, 720 − 229 = 491 is the likely number of partial
halos. At the 27% geoeffectiveness rate estimated above,
134 of the 491 partial halos are expected to be geoeffective. Therefore, out of the 720 wide CMEs, 163 full halos
and 134 partial halos (total of 297 or 41%) are geoeffective. This is virtually the same as the 40% rate obtained byKim et al. (2005) and confirms that inclusion of partial halos lowers the overall geoeffectiveness rate. Note that thegeoeffectiveness of halos varies with the phase of the solar cycle (see Gopalswamy et al., 2007, figure 8; Zhao andWebb, 2003) and the way multiple halos associated with agiven storm are treated. We estimate that these effects canaccount for an additional 10% variation.
2.1 Why are partial halos less geoeffective?
In studying the geoeffectiveness of CMEs as a functionof source latitude, Gopalswamy et al. (2007) found thatthe strongly geoeffective (Dst ≤ −100 nT) and moderately geoeffective (−50 ≥ Dst > −100 nT) CMEs haveaverage longitudes of W10 and E03, respectively. The
non-geoeffective CMEs have an average longitude similar
to the moderately geoeffective CMEs (E02). Furthermore,
the fraction of limb halos steadily increases from 17% forstrongly-geoeffective, to 31% for moderately geoeffective,
and 37% for non-geoeffective CMEs. The average speeds
also decrease in the same order (see figure 9 of Gopalswamy
et al., 2007). From these observations, Gopalswamy etal. (2007) concluded that non-geoeffective CMEs are relatively slower, originate predominantly from the eastern
hemisphere, and have a greater central meridian distance.
Partial halos generally have properties similar to the moderately geoeffective and non-geoeffective halos. Thus partial halos are less energetic and do not expand enough tofully surround the occulting disk within the LASCO fieldof view.
Gopalswamy et al. (2007) also reported that the geoeffectiveness rates of limb and disk halos as 60% and 75%,
respectively. The geoeffectiveness of partial halos originating closer to the limb is expected to be even lower because
they are slower and less likely to impact Earth. Thus, inclusion of partial halos reduces the overall geoeffectivenessrate of halo CMEs and hence correctly explains the lower
geoeffectiveness rates reported in the literature.

3.

Discussion and Conclusions

One of the important aspects of CME geoeffectivenessstudies is to identify the solar source of CMEs. One mightargue that the geoeffectiveness may be overestimated whenfrontsided CMEs are mistakenly classified as backsided
CMEs. This can happen only when frontsided halos haveno disk signature. There may also be cases in which a fortuitous disk activity coincides with a backside CME andhence a backside CME gets classified as a frontside CME.
Sometimes, one observes a full halo, which may be a combination of multiple CMEs occurring at different position
angles. Such occurrences are generally rare and cannot ac-

N. GOPALSWAMY: HALO CORONAL MASS EJECTIONS

count for the large discrepancies in the reported geoeffectiveness rate.
To clarify the identification of solar sources of halo
CMEs, let us consider the association between CMEs andsoft X-ray flares, one of the obvious indicators of disk activity. Whenever the eruption occurs on the frontside (CMDin the range 0 to 90◦ ), we observe a soft X-ray flare. The
halo CME appears asymmetric when the solar source hasa larger CMD, typically beyond 45◦ . When the eruption
is behind the limb, but not too far behind, we usually observe some EUV dimming above the concerned limb, but
no soft X-ray flare is observed because the flare gets occulted by the solar limb. When a flare is partially occulted
by a limb, the soft X-ray light curve tends to be very gradual and we observe the CME above the occulting limb. The
extreme case is a backside CME whose associated flare iscompletely occulted, and we see no disk activity. In someof these cases one can see EUV dimming around most partof the solar disk, indicating a backsided eruption. This kindof relationship between the soft X-ray flare and CMEs canbe easily seen by tracking a large active region (AR) during
its disk passage and eventual disappearance behind the west
limb (e.g., AR 10486 reported in Gopalswamy et al., 2005).
When one starts from geomagnetic storms and relatethem to CMEs near the Sun, occasionally it becomes difficult to identify the CME. Zhang et al. (2007) were notable to identify wide CMEs or their solar sources for ∼10%of large geomagnetic storms. Zhang et al. (2007) started
with large geomagnetic storms and searched for CMEs andtheir solar sources. The solar and geomagnetic events wereseparated by more than a day to a few days. On the other
hand, Gopalswamy et al. (2007) started with halo CMEs
and identified their solar sources. Observations of the halo
CME and the associated disk signature are nearly simultaneous. Halo CMEs are more energetic (see figure 4 ofGopalswamy et al., 2007), so there is usually a prompt (andstrong) disk signature if the halo is frontsided. Thus, thesolar source identification for geomagnetic storms and thatfor halo CMEs do not have the same level of difficulty. Furthermore, geomagnetic storms can also be caused by nonhalo CMEs. If a CME originates close to the disk centerand arrives at Earth with a southward magnetic field component, it will cause a geomagnetic storm. It is known
that some magnetic clouds, which are interplanetary CMEs
(ICMEs) with flux rope structure, are associated with nonhalo CMEs. A recent statistical study (Gopalswamy et al.,2008) finds that only ∼63% of magnetic clouds are associated with full halos. The fraction increases to ∼86% whenfull and partial halos are combined. The remaining 14% ofmagnetic clouds are associated with non-halo CMEs originating from close to the disk center. Since magnetic clouds
constitute the most geoeffective subset of ICMEs, one expects that some magnetic clouds associated with non-halo
CMEs are also geoeffective.
In conclusion, we confirm that the lower rate of geoeffectiveness obtained by some authors is due to the inclusionof partial halos. The reported variation in geoeffectiveness

597

rates can be readily explained by the different definition of
halo CMEs used by different authors. Partial halos are lessenergetic and generally originate far from the disk center, so
most of them behave similar to the nongeoeffective CMEs.
Acknowledgments. Work supported by NASA’s LWS and TR&T
programs.

References
Gonzalez, W. D., J. A. Joselyn, Y. Kamide, H. W. Kroehl, G. Rostoker, B.
T. Tsurutani, and V. M. Vasyliunas, What is a geomagnetic storm?, J.
Geophys. Res., 99, 5771, 1994.
Gopalswamy, N., A global picture of CMEs in the inner heliosphere, in The
Sun and the Heliosphere as an Integrated System, edited by G. Polettoand S. T. Suess, chap. 8, p. 201, Kluwer Acad., Boston, 2004.
Gopalswamy, N., S. Yashiro, Y. Liu, G. Michalek, A. Vourlidas, M. L.
Kaiser, and R. A. Howard, Coronal mass ejections and other extreme
characteristics of the 2003 October–November solar eruptions, J. Geophys. Res., 110, A09S15, doi:10.1029/2004JA010958, 2005.
Gopalswamy, N., S. Yashiro, and S. Akiyama, Geoeffectiveness of
halo coronal mass ejections, J. Geophys. Res., 112, A06112, doi:
10.1029/2006JA012149, 2007.
Gopalswamy, N., S. Akiyama, S. Yashiro, G. Michalek, and R. P. Lepping,Solar sources and geospace consequences of interplanetary magnetic
clouds observed during solar cycle 23, J. Atm. Sol. Terr. Phys., 70, 245,
doi:10.1016/j.jastp.2007.08.070, 2008.
Gosling, J. T., M. F. Thomsen, S. J. Bame, and R. D. Zwickl, The eastward deflection of fast coronal mass ejecta in interplanetary space, J.
Geophys. Res., 92, 12399, 1987.
Gosling, J. T., D. J. McComas, J. L. Phillips, and S. J. Bame, Coronalmass ejections and large geomagnetic storms, Geophys. Res. Lett., 17,901, 1990.
Howard, R. A., D. J. Michels, N. R. Sheeley, Jr., and M. J. Koomen, The
observation of a coronal transient directed at earth, Astrophys. J., 263,
L101, 1982.
Kim, R.-S., K.-S. Cho, Y.-J. Moon, Y.-H. Kim, Y. Yi, M. Dryer, S.-C.
Bong, and Y.-D. Park, Forecast evaluation of the coronal mass ejection (CME) geoeffectiveness using halo CMEs from 1997 to 2003, J.
Geophys. Res., 110, A11104, doi:10.1029/2005JA011218, 2005.
Michalek, G., N. Gopalswamy, A. Lara, and S. Yashiro, Properties
and geoeffectiveness of halo CMEs, Space Weather, 4, S10003,
doi:10.1029/2005SW000218, 2006.
St. Cyr, O. C. et al., Properties of coronal mass ejections: SOHO LASCO
observations from January 1996 to June 1998, J. Geophys. Res., 105,
18,169, 2000.
Tsurutani, B. T. and W. D. Gonzalez, The interplanetary causes of magnetic storms: A review, in Magnetic Storms, edited by B. T. Tsurutani,
W. D. Gonzalez, Y. Kamide, and J. K. Arballo, p. 77, AGU Monograph
98, AGU, Washington DC, 1997.
Yermolaev, Yu. I. and M. Yu. Yermolaev, Statistical relationships between
solar, interplanetary, and geomagnetic disturbances, 1976–2000: 3, Cosmic Res., 41, 539, 2003.
Yermolaev, Yu. I., M. Yu. Yermolaev, G. N. Zastenker, L. M. Zelenyi, A.
A. Petrukovich, and J.-A. Sauvaud, Statistical studies of geomagnetic
storm dependencies on solar and interplanetary events: a review, Planet.
Space Sci., 53(1–3), 189–196, 2005.
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the magnetic fields in interplanetary flux ropes and solar filaments,
Astrophys. J., 563, 381, 2001.
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A10102, doi:10.1029/2007JA012321, 2007.
Zhao, X. P. and D. F. Webb, Source regions and storm effectiveness offrontside full halo coronal mass ejections, J. Geophys. Res., 108(A6),1234, doi:10.1029/2002JA009606, 2003.
N. Gopalswamy (e-mail: Nat.Gopalswamy@nasa.gov)

LETTER

Earth Planets Space, 61, 599–602, 2009

Numerical simulations of the solar corona and Coronal Mass Ejections
Stefaan Poedts, Carla Jacobs, Bart van der Holst, Emmanuel Chané, and Rony Keppens
Centrum voor Plasma-Astrofysica, Katholieke Universiteit Leuven, Belgium(Received October 31, 2007; Revised January 30, 2008; Accepted August 24, 2008; Online published May 29, 2009)

Numerical simulations of Coronal Mass Ejections (CMEs) can provide a deeper insight in the structure andpropagation of these impressive solar events. In this work, we present our latest results of numerical simulationsof the initial evolution of a fast CME. For this purpose, the equations of ideal MagnetoHydroDynamics (MHD)
have been solved on a three-dimensional (3D) mesh by means of an explicit, finite volume solver, where thesimulation domain ranges from the lower solar corona up to 30R . In order to simulate the propagation of a
CME throughout the heliosphere, a magnetic flux rope is superposed on top of a stationary background solar(MHD) wind with extra density added to the flux rope. The flux rope is launched by giving it an extra initial
velocity in order to get a fast CME forming a 3D shock wave. The magnetic field inside the initial flux rope is
described in terms of Bessel functions and possesses a high amount of twist.
Key words: Magnetohydrodynamics, numerical, coronal mass ejections.

1.

Introduction

It is generally accepted that coronal mass ejections(CMEs) originate from the so-called ‘closed’ magnetic regions on the Sun, consisting of thousands of magnetic
loops. Such ‘closed’ magnetic fields can be found in active regions, filaments, and transequatorial interconnection
regions. The latter regions are most likely to appear during solar minimum, when the active regions are located, on
average, much closer to the equator. Cremades and Bothmer (2004) studied 124 structured CME events and analysed the relation between the source region characteristics
at the solar surface and the morphology of the corresponding CME observed with LASCO. They concluded thatstructured CMEs can be interpreted as three-dimensional
magnetic field entities that arise in a self-similar mannerfrom pre-existing small-scale loop systems. Jing et al.
(2004) made a statistical study of more then 100 filament
eruptions and found that 56% of the investigated events corresponded with a CME. Gilbert et al. (2000) performed
also a statistical study of prominence activity and developed
definitions of active and eruptive prominences. These authors came to the conclusion that eruptive prominences are
more strongly associated to CMEs (viz. 94% of the investigated events) than active prominences (only 46%), and thatprobably all CMEs associated with eruptive prominences
possess the three-part front-cavity-core structure. In general, filaments are believed to form in magnetic fields ofthe shape of sheared arcades and that the prominence material is suspended in the corona by concave upward magnetic fields, possibly possessing some twisted topology (e.g.
Kippenhahn and Schlüter, 1957; Kuperus and Raadu, 1974;
Manchester, 2001; Karpen et al., 2001; Low and Zhang,c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

2004).
Axisymmetric (2.5D) MHD models can be used to numerically simulate CME propagation (e.g. Wu et al., 1999).
Chané et al. (2006) demonstrated that 2.5D simulations
with a simple CME model, consisting of a high-density
plasma blob including a magnetic flux rope, can predict theflow variables at 1 AU for a specific CME event reasonably well. Remark that Jacobs et al. (2007) made a detailed
comparison of these 2.5D simulation results to a similar 3D
simulation and showed that the 2.5D simulation yields acceptable results provided the momentum of the initial CME
is chosen in a proper way. However, it is straightforward to
see that the effect of the CME depends on the angular position of the observer and that the assumption of axial symmetry poses severe restrictions to the possible magnetic field
configuration in the magnetic cloud. In the present paper,
the three-dimensional (3D) extension of this 2.5D modelis presented. The strategy followed for simulating a CME
event is the same as in Chané et al. (2006), but in stead oflaunching a spherical plasma blob, a more advanced magnetic flux rope model, with an enhanced density, is flung
into the interplanetary medium by giving it an initial velocity profile. The initial magnetic configuration in the flux
rope is a modification of the Lundquist equilibrium for constant α force-free fields in cylinder geometry and will bepresented in the next section.

2.

Simulation Set-up

The ideal MHD equations have been solved in sphericalcoordinates (r, θ, ϕ) on a three-dimensional spherical mesh,covering a complete sphere, i.e. θ ∈ [0, π ] and ϕ ∈ [0, 2π].
The magnetic field is kept divergence-free by using thevector potential on the nodal points. The computational
domain covers the region between the lower corona and
30R , using a grid resolution of 324 × 95 × 184 cells,
including two ghost cells at each boundary. The grid shows

599

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an accumulation of cells both towards the solar surface andtowards the solar equator, where the grid size varies fromr = 0.02R near the solar surface to r = 0.25R
at the outer boundary and from θ = 4◦ near the polesto θ = 0.8◦ at the equator. The grid was taken to beequidistant in the azimuthal direction. The simulation was
executed on the VIC-cluster of the K.U.Leuven. To reacha time of t = 10 h in the code, 35 382 iterations wereneeded. The run was finalised in about 21.5 h by using
120 processors simultaneously.
In order to construct a background solar wind model, thefull set of (ideal) MHD equations has been solved in a corotating frame along with an extra added gravitational force
as well as an additional heating/cooling source term, very
similar to the term that was used by Groth et al. (2000).
This wind model shows no dependence on the azimuthal direction and provides a good approximation for the roughly
axisymmetric wind occurring at solar minimum.
Romashets and Vandas (2003) present an expression for Fig. 1. Initial magnetic field configuration. The solar surface is coloured
with the radial magnetic field strength. Inside the flux rope the isosurthe magnetic field in toroidal geometry, reading:face of ρ = 2ρ∗ is plotted, with ρ∗ the surface density. The isosurface
R0 − 2r  cos θ J0 (αr  ) sin θ  ,2α R0 (R0 + r  cos θ  )rBϕ  = B0 1 −cos θ J0 (αr  ),2R0
R0 − 2r  cos θ J0 (αr  ) cos θ Bθ  = B0
2α R0 (R0 + r  cos θ  )r−B0 1 −cos θ  J1 (αr  ),2R0
Br  = B0

is coloured with the radial velocity.

(1)
(2)

(3)

where (r  , ϕ  , θ  ) represent the toroidally curved cylindricalcoordinates, J0 and J1 are Bessel functions of the first kind(of order 0 and 1, respectively), and R0 denotes the major
axis of the torus. The minor axis is indicated by r  = r0
and the constant α is determined by J0 (αr0 ) = 0. In thisway, the magnetic field lines are confined within the torus.
This solution for the magnetic field satisfies the solenoidal
constraint and approximates the force-free condition in thelimit of a large aspect ratio, i.e. in the limit R0 /r01.
Next, the Romashets and Vandas solution is subjected tothe transformation r −→ r − a (Gibson and Low, 1998),
stretching space inward, towards the origin. The transformation deforms the shape of the original flux rope, resembling an already rising prominence. The stretch factor a isset to a value of 0.3R and the top of the flux rope is at aheight of 0.7R above the solar surface. The transformed
flux rope solution is then superposed on top of the stationary background wind model discussed above. To keep the
analogy with previous work (e.g. Jacobs et al., 2005; Chané
et al., 2006) some extra density and velocity is added to theflux rope. The additional density and velocity profiles areboth dependent on the toroidal coordinates r  and ϕ  . In
doing so, we have control over the added amount of mass,energy, and momentum, and as such over the propagationof the CME.
Prominences are always observed above photospheric regions where the magnetic field changes sign. Since in theapplied (axisymmetric) background coronal model for solar minimum the only polarity inversion line coincides withthe equator, the flux rope solution is placed above the so-lar equator in the present simulation. From observations
it is known that filaments lie in a highly sheared fashion
over the inversion line, making an angle of ∼20◦ (Leroyet al., 1984). Also according to Leroy et al. (1984), mostquiescent prominences are of inverse polarity. The initialconfiguration of the flux rope was taken such that the observational constraints were satisfied. The magnetic fieldstrength in a quiescent prominence is typically between 5
and 40 Gauss. In the model, the value for the toroidal fieldin the centre of the flux rope was set to B0 = 1.44 Gauss.
This is lower than what is observed, but remember thatthe initial condition represents a prominence that is alreadyerupting. The maximum velocity inside the flux rope was
set to vcme = 4000 km s−1 and the total amount of massadded equals 4 × 1015 g. A visualisation of the initial stateis shown in Fig. 1.

3.

Results

Figure 2 shows contours of the radial velocity at t =15 min after the onset of the CME event. The initiallyhighly twisted magnetic field in the flux rope reconnectswith the overlying magnetic field, but the magnetic fieldlines in the CME remain connected to the solar surface.
Figure 3 illustrates the longitudinal variation in the density and the velocity. This plot shows the density and radial velocity in the cross-section of three meridional planes
and the equatorial plane. The three meridional planes arelocated at a constant azimuthal position of ϕ = 150◦ ,ϕ = 165◦ , and ϕ = 180◦ . The velocity and density profile in the original undisturbed background solar wind are
indicated on the plots with at dashed line. From these plots
it is clear that a strong shock is propagating ahead of the
CME. Since the CME is launched along the negative X axis, the part of the CME in the plane ϕ = 180◦ moves thefastest.
Gopalswamy et al. (2005) studied the arrival times ofseveral historical fast events and these authors argue that

S. POEDTS et al.: SIMULATIONS OF THE SOLAR CORONA AND CMES

601

Fig. 3. Cut along the equator of the radial velocity (top) and the density(bottom) at three azimuthal positions, 2 h 15 min after the launch of the
CME. The dashed line indicates the steady state wind value.
Fig. 2. Snapshot at t = 15 min showing the radial velocity contours(colour) and the magnetic field lines (black). The solar surface iscoloured with the radial magnetic field strength. Top: velocity contours
in the equatorial plane; bottom: velocity contours in the x z-plane.

the maximum initial speed of a CME may not be muchhigher than ∼3000 km s−1 . In the present simulation, theplasma blob was given an initial speed in order to mimic theeruption. Since no initiation mechanism was considered,also the mechanism for accelerating CMEs is not captured
well in this simulation and the plasma cloud will experiencea strong deceleration in the initial phase of the simulation.
Therefore, the vcme parameter is set to a quite high velocityof 4000 km s−1 . However, remark that this high velocity
is only reached in one single point of the flux rope and theaverage amount of extra velocity added corresponds to avalue of only ∼600 km s−1 . The deceleration of the CME
is made clear in Fig. 4, where the position of the CME front
in the equatorial plane is plotted versus time. The figure
shows the height-time plots for the CME front in the three
meridional planes discussed above. The plot shows also theheight-time profile for the centre of mass, being defines asr ρ̄(r) d 3 r
V
rCRM = .
ρ̄(r) d 3 r
VFig. 4. Height-time curves for the position of the CME front along theequator in three meridional planes and for the centre of relative mass(CRM).

The centre of mass is calculated by using the relative density ρ̄, which is a measure for the excess or depletion of thedensity with respect to the background solar wind density.
Since a CME is defined as an outward motion of a new, discrete, bright, white light feature in the coronagraph field ofview, only those locations with an enhancement in density

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S. POEDTS et al.: SIMULATIONS OF THE SOLAR CORONA AND CMES

Table 1. Average velocity and acceleration of the CME front and of thecentre of relative mass (CRM).
v
a

ϕ = 150◦
1059 km s−1−21.3 m s−2

ϕ = 165◦1411 km s−1−48.5 m s−2

ϕ = 180◦
1594 km s−1−78.8 m s−2of at least 10% with respect to the background density weretaken into account in the calculation of the centre of mass.
The height-time curves were fitted with first and second order polynomials to obtain the average velocity andacceleration. The measured quantities for the average velocity and acceleration are summarised in Table 1. The
CME front (in the ϕ = 180◦ -plane) shows a strong deceleration of 79 m s−2 . The extensive statistical study ofYashiro et al. (2004) pointed out that, on average, the acceleration of CMEs with average velocity v ≥ 900 km s−1
is −15 m s−2 . The strong deceleration of 79 m s−2 of the
CME front is rare, but not un-occurring.

4.

Conclusions

locity, density, and magnetic field on the CME evolution.
Acknowledgments. These results were obtained in the framework of the projects GOA/2004/01 (K.U.Leuven), G.0304.07(FWO-Vlaanderen) and C 90203 (ESA Prodex 8). Financial support by the European Commission through the SOLAIRE Network (MTRN-CT-2006-035484) is gratefully acknowledged. The
numerical results were obtained on the HPC cluster VIC of the
K.U.Leuven.

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2004.
Manchester, W., The role of nonlinear Alfvén waves in shear formation
during solar magnetic flux emergence, ApJ, 547, 503–519, 2001.
Manchester, W. B., T. Gombosi, I. Roussev, D. L. De Zeeuw, I. V. Sokolov,
K. G. Powell, G. Tóth, and M. Opher, Three-dimensional MHD simulation of a flux rope driven CME, J. Geophys. Res., 109, A01102, 2004.
Romashets, E. P. and M. Vandas, Interplanetary magnetic clouds oftoroidal shapes, Proc. ISCS 2003 Symposium, 535–540, 2003.
Roussev, I. I., T. G. Forbes, T. I. Gombosi, I. V. Sokolov, D. L. DeZeeuw,
and J. Birn, A three-dimensional flux rope model for coronal massejections based on a loss of equilibrium, ApJ, 588, L45–L48, 2003.
Titov, V. S. and P. Démoulin, Basic topology of twisted magnetic configurations in solar flares, A&A, 351, 707–720, 1999.
Wang, Y.-M. and N. R. Sheeley, Solar wind speed and coronal flux-tube
expansion, ApJ, 355, 726–732, 1990.
Wu, S. T., W. P. Guo, D. J. Michels, and L. F. Burlaga, MHD descriptionof the dynamical relationships between a flux rope, streamer, coronalmass ejection, and magnetic cloud: An analysis of the January 1997
Sun-Earth connection event, J. Geophys. Res., 104, 14789, 1999.
Yashiro, S., N. Gopalswamy, G. Michalek, O. C. St. Cyr, S. P. Plunkett,N. B. Rich, and R. A. Howard, A catalog of white light coronal massejections observed by the SOHO spacecraft, J. Geophys. Res., 109,
A07105, 2004.

A three-dimensional time dependent MHD simulation ofa CME event has been performed, where the simulation
domain ranged from the lower corona up to 30R . The
CME was mimicked by launching a high density flux ropein the solar wind, where the used model for the backgroundwind represents solar minimum conditions. The magnetic
field topology of the flux rope was the Romashets and Vandas (2003) solution in toroidal geometry. By applying thetransformations of Gibson and Low (1998), the flux rope
was stretched towards the solar surface, imitating a risingprominence. The simulation presented in this paper is the3D generalisation of the 2.5D models described in earlier
work (e.g. Jacobs et al., 2005; Chané et al., 2006). Threedimensional CME simulations provide the ability to investigate the three-dimensional nature of CMEs. With the recent
launch of the STEREO mission, it will become possible tocheck the outcome of the models with the multiple view
point observations made by STEREO.
The model presented here is different from the simulations of e.g. Roussev et al. (2003) and Manchester et al.
(2004) in the sense that we add an extra amount of momentum and energy to the flux rope, in order to have more control over its propagation. Roussev et al. (2003) used the flux
rope model of Titov and Démoulin (1999) and by removing
the overlying line current, the flux rope became unstable,causing an eruption. In case no extra density or velocity isadded, the magnetic field of the flux rope in our model simply reconnects with the overlying coronal field, not causing
a violent eruption. This might be due to the low magnetic
field strength inside the flux rope and a higher magnetic
field strength might be desirable. Another weakness of thesimulation is the background wind model. The medium inwhich the CME is propagating influences the evolution of
the CME. A more realistic wind model with input frommagnetograms and/or empirical laws (e.g. Wang and Sheeley, 1990) for the solar wind is then also necessary if themodel wants to be used to simulate specific CME events.
For future studies it might be interesting to investigate theS. Poedts (e-mail: Stefaan.Poedts@wis.kuleuven.be), C. Jacobs, B. vaneffect of the initial parameters like the amount of added ve- der Holst, E. Chané, and R. Keppens

LETTER

Earth Planets Space, 61, 603–606, 2009

Non-thermal electrons at the Earth’s bow shock: A ‘gradual’ event
M. Oka1 , T. Terasawa2 , M. Fujimoto3 , H. Matsui4 , Y. Kasaba5 , Y. Saito3 , H. Kojima6 , H. Matsumoto7 , and T. Mukai8
1 Kwasan Observatory, Kyoto University, Yamashina-ku, Kyoto, Japan
2 Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan
3 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Kanagawa, Japan
4 University of New Hampshire, Durham, New Hampshire, USA
5 Tohoku University, Sendai, Japan
6 Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto, Japan
7 Kyoto University, Sakyo-ku, Kyoto, Japan
8 Japan Aerospace Exploration Agency, Chofu, Tokyo, Japan(Received February 18, 2008; Revised April 6, 2008; Accepted May 19, 2008; Online published May 29, 2009)

The Earth’s bow shock is known to produce non-thermal electrons which are generally observed as a ‘spike’in their flux profile. Here, in this paper, we present an analysis of electron and whistler wave properties for aquasi-perpendicular shock crossing that is supercritical, but subcritical to the so-called whistler critical Mach
number, Mw
crit , above which whistler waves cannot propagate upstream. We have found that the amplitudes ofwhistler waves increased exponentially as a function of time prior to the shock encounter, while the suprathermal(>2 keV) electron flux similarly increased with time, although with differing e-folding time scales. Comparisonof the electron energy spectrum measured within the ramp with predictions from diffusive shock acceleration
theory was poor, but the variation of pitch angle distribution showed scattering of non-thermal electrons in the
upstream region. While not finding a specific mechanism to account for the electron diffusion, we suggest that thewhistlers seen probably account for the differences observed between this ‘gradual’ event and the ‘spike’ events
seen at shocks with no upstream whistlers.
Key words: Particle acceleration, scattering, bow shock, whistlers.

1.

Introduction

Energetic electrons with energies of more than 20 keV
have been observed at and near the Earth’s bow shock (e.g.,
Fan et al., 1964; Frank and Van Allen, 1964; Anderson,
1969; Vandas, 1989). Since larger electron flux can befound on the interplanetary magnetic field (IMF) tangent
to the bow shock (e.g., Anderson et al., 1979; Kasaba
et al., 2000), electrons are considered to be accelerated
in the quasi-perpendicular region where the shock angle
θ Bn is larger than 45◦ . Gosling et al. (1989) were thefirst to carry out comprehensive analysis of suprathermal(<20 keV) electrons across the shock front. In their quasiperpendicular shock events, energetic electron flux was enhanced at the shock transition, and because of the localized feature, they termed their events as ‘spike’ events. Theenergy spectrum showed a power-law form with the spectrum index of 3–4. The pitch angle distribution was almost
isotropic at the transition layer while it was anisotropic inboth the upstream and the downstream regions. More recently, Oka et al. (2006) conducted a statistical analysis of
the power law indices measured in the shock layers. They
reported that the power-law index of electron energy spectra is regulated by the so-called whistler critical Mach number Mw
crit , which is defined as the critical point above whichc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

whistler waves cannot propagate upstream.
In this paper, we report a shock crossing event thatshowed a ‘gradual’ profile of non-thermal electron flux inassociation with an intensification of precursor whistlers.
Contrary to the spike events reported by Gosling et al.
(1989), the electron flux increased exponentially with decreasing distance from the shock. The event has been determined to be subcritical in relation to the whistler critical Mach number Mw
crit . We will describe properties of
the waves and discuss the origin and transport of the nonthermal electrons in this gradual event.

2.

Observation

Our event is observed by Geotail at ∼03:10 UT on 11
February 1995 at an inbound crossing of the bow shock near
the subsolar point, i.e., at (12.2, 4.0, 0.6)RE in the GSE coordinate. Figure 1 shows the overview of main physicalparameters of the gradual crossing event. The shock transition appears as an abrupt change in both the magnetic fielddata (MGF, Kokubun et al., 1994) as well as the plasma data
(LEP, Mukai et al., 1994). The shock normal direction estimated by the Minimum Variance Analysis (Sonnerup and
Cahill, 1967) was (0.94, 0.31, −0.17), consistent with theshock normal derived from the semi-empirical bow shockmodel of Peredo et al. (1995). This model is known to givenormal directions in agreement with those obtained by thetiming method of multi-spacecraft (Horbury et al., 2002).
The upstream parameters, M A and θ Bn , were then estimatedto be ∼6.8 and ∼68◦ , respectively. (For various methods

603

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M. OKA et al.: A GRADUAL ELECTRON EVENT

Fig. 1. From top to bottom are (a) magnitude |B|, (b) azimuthal φ B , and(c) latitudinal θ B component of the magnetic field (MGF) with 3 s (blackline) and 1/16 s (gray line) sampling, and the energy-time (Et) diagramsof (d) solar wind ions (LEP/SWI), (e) omni-directional energetic ions
(LEP/EAI), and (f) omni-directional electrons (LEP/EAE), respectively.

of shock normal determination, see, e.g., Paschmann and
Daly (1998).) Noticeable in the magnetic field data in Fig. 1
are the relatively large fluctuations increasing with time
(03:08–03:10 UT, δ B/B ∼ 20%). Our particular interest
also goes to the time profile of higher energy (>0.5 keV)electrons, as can be seen in the panel (f) as a smooth increase of count rate in the time period of 03:09–03:11 UT.
It is noted that the spacecraft soon exited from the magnetosheath at 03:15 UT.
Figure 2 shows the detailed spectral properties of the
waves. They are dominated by the right-hand polarizedcomponent accompanied by a frequency cut-off at aroundf LH which threshold seems not to have been noted earlier. We speculate that this is because whistler generation
concerns both ion and electron dynamics. There are tensof detailed models for whistler generation, and it is not
the purpose of this letter to discuss the physical meaningof f LH . From the Minimum Variance Analysis as well as
the Means method (Means, 1972), the propagation angle
θk B (the cone angle between the k-vector and backgroundmagnetic field) were estimated to be 20–40◦ . We also removed the 180◦ ambiguity of the estimated k-vector using
one component of electric field (EFD) data (Matsui et al.,1997). As a result, the waves with frequencies lower than
∼10 Hz indicated propagation toward the sun, away fromthe shock front, consistent with a past report (Orlowski etal., 1994). For higher frequencies, we could not obtain reliable results on the propagation direction, probably due tothe low intensities of the waves. Note that the cone angle
between the k-vector and the solar wind VSW , θkV , were
estimated to be 60–90◦ so that the Doppler shift was not
significant. Supportingly, the spectral slope of the highfrequency range is approximately 5, consistent with past ob-

Fig. 2. From top to bottom are (a) the magnetic field magnitude (equivalent with Fig. 1(a)), (b) root mean square of band pass filtered magnetic field, (c) FFT spectra obtained at region A, B, and C indicated by
the shaded regions in panel (b). The root mean square was obtained
from frequency greater than fourfold the ion cyclotron frequency andhas been normalized by the ambient magnetic field magnitude. Arrows in panel (c) show ion cyclotron
frequency ( f ci = 0.19 Hz) and√lower-hybrid frequency ( f LH = f ci f ce = 8.4 Hz), whereas the black
curve shows the background level obtained from 03:07:05–03:07:20 UT(indicated by two vertical lines). The red, green, and blue corresponds to
the R, L, and C component, respectively from the fluxgate magnetometer (MGF/FX, <8 Hz, light colored) and the search coil magnetometer(MGF/SC, <32 Hz, dark colored).

servations of right-hand polarized whistler waves (Orlowski
et al., 1995). While traveling upwind, the waves sufferedconsiderable (exponential) damping, as shown in the lefthand side of Fig. 3, which shows the temporal profiles ofband pass-filtered magnetic field data. The characteristic
time scale of the damping was calculated for each best fit
model shown by the gray curves and found to be 47 s on
average.
All observed features described above are well consistent with those of the so-called ‘1 Hz whistlers’ reported
elsewhere (e.g., Fairfield, 1974; Sentman et al., 1983; Orlowski et al., 1994). From the above arguments, we conclude the observed waves to be the right-hand polarized
whistler waves propagating away from the shock front.
It is to be emphasized that, while thermal electrons had
been studied with respect to whistler wave generation (e.g.,Tokar et al., 1984; Orlowski et al., 1995), non-thermal
electrons, to the best of these authors’ knowledge, had neverbeen observed in association with the upstream whistlers.
Note again that the gradual profile of non-thermal electrons
has not been analyzed in the past in connection with the bow
shock crossing events as we will discuss below.
The right-hand side of Fig. 3 shows the time profiles ofelectron phase space densities (PSDs). The flux increased
exponentially as the spacecraft approached the shock front.
The characteristic time scale of the increase was calculated
for each best fit model, shown by the red curves. Above
2 keV, the typical time scale was 24 s. During the flux increase, a pitch angle distribution also changed, as shownM. OKA et al.: A GRADUAL ELECTRON EVENT

Fig. 3. (left) Temporal distributions of averaged power spectral densities(red, green, and blue for R, L, and C components) and their exponential
fits (gray lines, 03:08:00–03:10:00 UT). Numbers in each panel show
frequency ranges used for averaging. Frequencies are chosen so thatthey correspond to the resonance conditions of electrons with energy
shown to the right. (right) Temporal distributions of electrons (blacklines) and their exponential fits (red lines, 03:08:00–03:10:30 UT).
Numbers in each panel show center energies of each energy channel.

in Fig. 4. Black symbols indicate the far upstream regionof the shock, and they show strong asymmetry (i.e., larger
flux in µ < 0 region, where µ is the cosine of pitch angle α), indicating that electrons were streaming away fromthe shock front. However, substantial amount of electron
counts were detected in the µ > 0 region during the timeinterval from 03:08:30 to 03:10:00 UT, as indicated by red
symbols. By this time, the spacecraft was immersed in the
precursor waves. The distributions were isotropized in theimmediate downstream (green and blue symbols).
Figure 5 shows the electron energy spectra. The grayline shows the spectrum obtained at 03:00 UT in the puresolar wind where there was no contamination from the bow
shock. The open squares show the spectrum at 03:09:45 UT
just prior to the crossing. There was a significant amount ofenergetic (>1 keV) electrons compared to the solar wind.
The spectrum is roughly a power law. The filled squares
show the spectrum at 03:10:26 UT just within the middleof the shock ramp. It now forms a complete power law
above 2 keV. We then applied a chi-square fit above 2 keVwith a power-law f (E) ∝ E − exp (−E/E roll-off ), where
E is the electron energy as variable,  = 4.3(±0.05),
E roll-off = 3.5(±0.6), and the figures in the parenthesis are
the 68% confidence region. The resultant χ 2 /d.o.f. was
28/21, where d.o.f. is the degree of freedom and is equal to
the number of data points minus the number of free parameters. A fit with the kappa distribution covering the wholeenergy range yielded relatively high χ 2 /d.o.f.. A similar

605

Fig. 4. Pitch angle distributions of electrons of energies 1.89, 2.25,
2.69, 3.21, 3.83, and 4.57 keV. The vertical and horizontal axes show
PSDs and µ (the cosine of pitch angle α), respectively. Since themagnetic field was directed toward the sun, µ > 0 corresponds topropagation away from the shock front. We have organized the obtained
three-dimensional distribution function by µ, and the horizontal axis
has been binned into 16 bins. The color code indicates different timeintervals (in UT), as shown in the annotation.

Fig. 5. Energy spectra of electrons during the bow shock transition.

spectrum was observed in the immediate downstream aswell. Note that E roll-off was introduced to better fit the observation, but we have not succeeded in deriving information of maximum attainable energy of electrons (Oka et al.,2006).

3.

Discussion

The ‘gradual’ profile of electron flux, the scattering ofparticles, and the appearance of the power-law energy spec-

606

M. OKA et al.: A GRADUAL ELECTRON EVENT

trum remind us of the diffusive shock acceleration (DSA,
e.g., Blandford and Ostriker, 1978). In this process, particles are continuously scattered and move back and forthacross the shock front to gain a net momentum from the velocity difference between upstream and downstream. However, there are some difficulties in the DSA to fully explain
the observed features. The observed density ratio r ∼ 2.5(N1 = 21/cm3 for the upstream and N2 = 52/cm3 forthe downstream) and the classical DSA formula DSA =3r/2(r − 1) = 2.5 do not reproduce the observed  ∼ 4.3.
The quantitative difference can readily be interpreted by, forinstance, a free escape boundary that allows a significant
number of particles to escape from the acceleration region.
The discrepancy between the e-folding distances derived
from wave measurements (with the resolution of 47 s) andparticle measurements (with the resolution of 24 s) indicatesthat the waves were not generated by the non-thermal electrons and that self-scattering was weak. Therefore, we do
not consider the classic DSA mechanism to be fully responsible for the generation of the observed power-law spectra.
Nevertheless, we still consider there was substantial scattering in the upstream, as is evident from Fig. 4. We haveshown that the whistler waves were propagating along withthe majority of the electrons. Since the direction must
be opposite to that of electron streaming in order to satisfy the cyclotron resonance condition, the cyclotron resonance by the right-hand-polarized whistlers is unlikely
as the physical mechanism of scattering. The observed
whistlers were oblique waves (θk B = 20–40◦ ), and so theleft-hand-polarized component and/or electrostatic component of the waves might have been playing a role in electron
scattering. It should be also mentioned that the amplitudesof the upstream waves were relatively high so that a nonlinear effect should have played a role not only for the scattering but also acceleration. A recent theory indeed points
out the possibility of efficient particle acceleration at a turbulent magnetic field where all scales are larger than theparticle gyroradius (e.g., Giacalone, 2005; Jokipii and Giacalone, 2007). That the spectral index was relatively large
also favors this theory, although the detailed comparison isleft for future work.
We focus on the fact that the gradual profile was found atw
the shock with MA slightly below Mw
crit (MA /Mcrit ∼ 0.65
in this event). Our interpretation is as follows. In a higher
MA shock (MA > Mw
crit ), whistler waves do not propagate
upstream so that any electron that escapes the shock front
cannot interact with the waves and the intense flux can
only be found at the shock front resulting in ‘spike’ events.
On the other hand, in a much lower MA shock (MAMwcrit ), there would be plenty of waves to scatter particles,
but the number of non-thermal electrons that are subject
to scattering is small. Therefore, we expect to find similar
events in the Mach number range slightly below Mw
crit .
Unfortunately, however, the time resolution needs to be
sufficiently high to resolve the decaying profile of nonthermal electrons. In the 78 events of Oka et al. (2006),
there were a few events that seemed to be ‘gradual’, but the
decaying time was of the order of the time resolution of theparticle measurement (12 s), and thus we could not replicate
the analysis presented in this paper. We anticipate that moresophisticated observations of multi-spacecraft mission suchas Cluster, MMS, and SCOPE/CrossScale will reveal thenature of ‘gradual’ events.
Acknowledgments. The authors are grateful to all members of
the Geotail project. This work was partially supported by the
Grant-in-Aid for Creative Scientific Research (17GS0208) from
the MEXT, Japan. MO was supported by the Grant-in-Aid for
JSPS Postdoctoral Fellows for Research Abroad.

References
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shock and upstream in the solar wind, J. Geophys. Res., 74, 95, 1969.
Anderson, K. A. et al., Thin sheets of energetic electrons upstream fromthe Earth’s bow shock, Geophys. Res. Lett., 6, 401, 1979.
Blandford, R. D. and J. P. Ostriker, Particle acceleration by astrophysicalshocks, Astrophys. J., 221, L29–L32, 1978.
Fairfield, D. H., Whistler waves observed upstream from collisionlessshocks, J. Geophys. Res., 79, 1368–1378, 1974.
Fan, C. Y. et al., Evidence for >30keV electrons accelerated in the shocktransition region beyond the Earth’s magnetospheric boundary, Phys.
Rev. Lett., 13, 149, 1964.
Frank, L. A. and J. A. Van Allen, Measurements of energetic electrons in
the vicinity of the sunward magnetospheric boundary with Explorer 14,
J. Geophys. Res., 69, 4923, 1964.
Giacalone, J., Particle acceleration at shocks moving through an irregularmagnetic field, Astrophys. J., 624, 765, 2005.
Gosling et al., Suprathermal electrons at Earth’s bow shock, J. Geophys.
Res., 94, 10,011–10,025, 1989.
Horbury et al., Four spacecraft measurements of the quasiperpendicularterrestrial bow shock: Orientation and motion, J. Geophys. Res., 107,
273, 2002.
Jokipii, J. R. and J. Giacalone, Adiabatic compression acceleration of fast
charged particles, Astrophys. J., 660, 336, 2007.
Kasaba, Y. et al., Statistical studies of plasma waves and backstreaming
electrons in the terrestrial electron foreshock observed by Geotail, J.
Geophys. Res., 105, 79–103, 2000.
Kokubun et al., The GEOTAIL magnetic-field experiment, J. Geomag.
Geoelectr., 46, 7–21, 1994.
Matsui, H. et al., Long-duration whistler waves in the magnetosheath:
Wave characteristics and the possible source region, J. Geophys. Res.,
102, 17,583–17,593, 1997.
Means, J. D., Use of three-dimensional covariance matrix in analyzing thepolarization properties of plane waves, J. Geophys. Res., 77, 5551, 1972.
Mukai, T. et al., The Low Energy Particle (LEP) experiment onboard the
GEOTAIL satellite, J. Geomag. Geoelectr., 46, 669–692, 1994.
Oka, M. et al., Whistler critical Mach number and electron acceleration at
the bow shock: Geotail observation, Geophys. Res. Lett., 33, L24104,
2006.
Orlowski, D. S. et al., On the source of upstream whistlers in the
Venus foreshock, in COSPAR Colloquia, Plasma environments of nonmagnetic Planets, vol. 4, edited by T. I. Gombosi, 217–227, Pergamon
Press, New York, 1994.
Orlowski, D. S. et al., Damping and spectral formation of upstream
whistlers, J. Geophys. Res., 100, 17,117–17,128, 1995.
Paschmann, G. and P. W. Daly, Analysis methods for multi-spacecraft data,
ISSI Scientific Report, SR-001, pp. 536, 1998.
Peredo, M. et al., Three-dimensional position and shape of the bow shockand their variation with Alfvènic, sonic and magnetosonic Mach numbers and interplanetary magnetic field orientation, J. Geophys. Res., 100,
7907–7916, 1995.
Sentman, D. D. et al., The oblique whistler instability in the earths foreshock, J. Geophys. Res., 88, 2048–2056, 1983.
Sonnerup, B. U. Ö. and L. J. Cahill Jr., Magnetopause structure and attitude
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Inst. Czech, 40, 175–188, 1989.
M. Oka (e-mail: mitsuo.oka@uah.edu), T. Terasawa, M. Fujimoto, H.
Matsui, Y. Kasaba, Y. Saito, H. Kojima, H. Matsumoto, and T. Mukai

LETTER

Earth Planets Space, 61, 607–610, 2009

Influence of the foreshock of the Earth’s bow shock on the interplanetaryshock propagation during their mutual interaction
Lubomı́r Přech, Zdeněk Němeček, and Jana Šafránková
Charles University, Faculty of Mathematics and Physics, V Holesovickach 2, 180 00 Praha 8, Czech Republic(Received October 27, 2007; Revised April 13, 2008; Accepted April 14, 2008; Online published May 29, 2009)

Interplanetary shocks have been recognized as a very efficient source of geomagnetic disturbances. We presenta short study of the propagation of one interplanetary (IP) shock observed by five spacecraft located in the solar
wind far upstream of the Earth’s bow shock as well as in its close vicinity. The IP shock normal was highly
inclined from the Sun-Earth line and thus the IP shock-bow shock interaction started at the flank. We havefound a significant evolution of IP shock parameters during its motion along the bow shock. This modification is
discussed and attributed to the presence of strong fluxes of energetic particles in the foreshock.
Key words: Solar wind-magnetosphere interaction, upstream conditions, interplanetary shock, foreshock.

1.

Introduction

Geospace is affected by the solar wind, a supersonicplasma stream emerging from the Sun. Besides large-scale
structures (such as the interplanetary magnetic field sector and solar wind flow regime boundaries), eruptive solar
events of high intensity, predominantly solar flares resulting in halo Coronal Mass Ejections (CMEs) and solar energetic particle emissions, can have a significant impact on
geospace. The majority of the very intense storms were observed to be associated with interplanetary CMEs (ICMEs)
and shocks passing by the Earth (Tsurutani and Gonzalez,1997). They are an interplanetary manifestation of earthward directed CMEs. For example, interplanetary pressure events, like interplanetary (IP) shocks, compress or expand the magnetosphere and increase or decrease the magnetopause and tail currents that result in changes of othernear-Earth current systems (Le et al., 1998). The geoeffectiveness of the solar wind structures and discontinuities isrelated to their 3D geometry and orientation. Since multispacecraft observations are necessary for the determinationof the 3D geometry and structure of shocks (and/or otherstructures in the solar wind) (e.g., Thomsen, 1988), not too
many experimental studies have attempted to address thisproblem.
Several studies have been done in the recent years analyzing the solar wind interplanetary magnetic structuresthat can be geoeffective (e.g., review by Gonzalez et al.,1999). Vennerstroem (2001) examined 30 years of satellite measurements of the solar wind during magnetic storms
and he had estimated the relative importance of the ejection of magnetic structures from the Sun and the stream interaction processes during solar wind propagation in generating intense southward magnetic fields in the interplanc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

etary medium. Echer et al. (2006) presented a statistical
study of the geoeffectiveness of the solar wind magnetic
interplanetary structures including magnetic clouds (MCs),
corotating interaction regions (CIRs) and interplanetary (IP)shocks over a wide observational period. They observedthat magnetic clouds are more efficient than shocks or CIRs
in producing all geomagnetic disturbances and they haveconfirmed that compound structures (shocks and MCs) are
more geoeffective in every type of magnetospheric activity
than isolated structures. However, the application of thesefindings in the space weather models requires a precise forecasting of the structure arrival to the Earth that is generally adifficult tasks (see e.g., Fry et al., 2003 or McKenna-Lawlor
et al., 2006).
A strong correlation between IP shocks impinging on
the magnetosphere and geomagnetic disturbances has beenreported by many authors (e.g., Gonzalez et al., 1999).
The interaction of IP shocks with the Earth’s bow shockand their transmissions through the magnetosheath to theboundary of the magnetosphere has been studied mainly
by a gas dynamic modeling (e.g., Dryer, 1973; Grib et al.,
1979; Spreiter and Stahara, 1994). Generally, it is assumed
that the incoming IP shocks are planar on the scale-size ofthe magnetosphere in the undisturbed solar wind. Russell
et al. (2000) analyzed a single IP shock with four solar
wind spacecraft and found that normals calculated from thedata of three of them were consistent with the planarity
assumption (with the accuracy of the travel time estimates).
On the other hand, a deviation from planarity has also beenreported (e.g., Russell et al., 1983; Safrankova et al., 1998).
Two papers by Koval et al. (2005, 2006) demonstrates
that the shock front in the magnetosheath is inclined andthis inclination results in a delay of the shock arrival to themagnetopause. A non-planar shock propagation throughthe magnetosheath resulting from experimental observations has been confirmed by two numerical MHD simulation results (Koval et al., 2006).

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L. PŘECH et al.: FORESHOCK EFFECTS AND INTERPLANETARY SHOCK

2.

Observation

The IP shock (probably CIR-driven) was first observedby ACE near the L1 point at ∼0007 UT on August 10, 1998
and about 24 minutes later by WIND at the distance about
80RE from the Earth. As can be seen in Fig. 1, both spacecraft observed nearly rectangular jumps of all parameters;
the solar wind speed changed from ∼410 to ∼440 km/s
and the density from ∼4 to ∼9 cm−3 . These jumps suggest a rather weak IP shock but the shock parameters calculated from the WIND magnetic field and plasma data using
Rankine-Hugoniot relations show that its Alfvénic Mach
number is as high as 6.6 (vA = 54 km/s) in the normal incidence frame. The reason is that, although the shock speed isonly 355 km/s in the observer reference frame, it is largely(on ∼50◦ ) declined from the Sun-Earth line because theshock normal vector is n = [−0.53; −0.44; 0.73] and theshock speed in the solar wind frame is 346 km/s. The shock
can be classified as quasiperpendicular, BN = ∼ 63◦ .
The same IP shock was observed later by IMP 8, Geotail, and Interball-1 in front of the bow shock. Since theirlocations are very important for the present study, we arebringing a sketch in Fig. 2. The spacecraft positions wererotated into one plane but it should be noted that all of themwere very close to the ecliptic plane. We have used the timing of the shock observations by ACE, WIND, IMP 8, and
GEOTAIL and estimated the shock parameters. These parameters are given in the captions of Fig. 2 and one can notethat they are very similar to those derived from WIND measurements. This fact confirms that the shock can be considered to be planar on the scale of the spacecraft separation.
The cross-section of the shock plane with the X YGSE planeis shown as a dashed line in the figure.
Taking into account the shock orientation, one would expect that the shock would arrive nearly simultaneously to
IMP 8 and Geotail and with a significant delay to Interball1. We have chosen the magnetic field strength and ion flux
for a comparison of observation in different points that isv [km/s]

WI n [cm-3] Bx, By [nT]

B, Bz [nT]v [km/s]

ACE n [cm2]ACE, WIND 09/10-Aug-1998
10
8
6
4
480
460
440
420
400
10
8
6
4
2
0
-2
10
5
0
-5
-10
9
8
7
6
5
4
500
480
460
440
420

B, Bz [nT]

The short survey has shown that the problem of the interaction of an IP shock with the Earth’s magnetosphere is
not fully explained. Although MHD modeling achieved aparticular success in description of the IP shock interaction with the bow shock (e.g., Zhuang et al., 1981; Grib,
1982; Yan and Lee, 1996; Samsonov et al., 2006), the models have two significant limitations: (1) their present codes
can be applied only to the shocks perpendicular to the solar wind velocity and (2) they cannot account for foreshock
effects.
In the paper, we have identified one IP shock that was
registered by 5 spacecraft in the solar wind. Two of themwere located far upstream and three others in a close vicinity of the bow shock in different positions with respect tothe expected foreshock boundary. Moreover, the shock normal determined either by the 4-spacecraft method or from
Rankine-Hugoniot relations (this method solves the full setof Rankine-Hugoniot equations according to the Vinas and
Scudder (1986) paper) was declined on a large angle fromthe Sun-Earth line. The paper is devoted to a comprehensive study of this event and it is oriented to a preliminary
analysis of the foreshock effects.

10
8
6
4
2
0
-2

Bx, By [nT]

608

5
0
-5
2300

0000

0100
UT

Fig. 1. Fast forward shock observed on August 10, 1998 by ACE andWind upstream of the bow shock (thin dashed and dashed-dotted lines).
From the top to bottom: ACE (first four panels) and Wind (second four
panels) densities, velocities, and IMF strengths and all components.

shown in Fig. 3. The ion flux is computed as a productof the proton speed and density for all spacecraft except
Interball-1 and it cover the energy range of several keV (upto ∼25 keV) depending on a particular spacecraft. Interball1 was equipped with a special set-up of for ion flux measurements without any selection of energies. Since the contribution of high-energy ions to the total ion flux is small,
we assume that the different energy ranges cannot spoil the
results of our qualitative study.
The originally very steep IP shock front underwent a significant evolution. The IMP 8 observation reveals similar
shock features as those observed by WIND but a strong
significant modification of the shock front was observedby Geotail and no similar shock-like discontinuity was detected at the Interball-1 location. Instead, Interball-1 observed short spikes of both depicted parameters approximately at the predicted time of the IP shock arrival. These
spikes are followed by a gradual rise and they reached their
expected post-shock values only after 10–12 minutes.

3.

Discussion and Conclusion

The shock front modification observed by Interball-1
cannot be probably attributed to a temporal evolution because the shock withstood unchanged for ∼35 minutes from
ACE to IMP 8 and the expected time lag between IMP 8

L. PŘECH et al.: FORESHOCK EFFECTS AND INTERPLANETARY SHOCK

I8 B [nT]

GEOTAIL

GE B [nT]

INTERBALL-1

10

10IB B [nT]

WIND, IMP-8, GEOTAIL, INTERBALL 10-Aug-1998

10-Aug-1998

10
8
6
4
2
5
4
3
2
1
0
6
5
4
3
2
1
0

WIND

Fig. 2. Cylindrical projection of the spacecraft locations onto the equatorial plane. Jerab et al. (2005) and Petrinec and Russell (1996) models were applied to determine Earth’s bow shock and magnetopause
positions before the shock. Shock parameters computed from Rankine-Hugenoit relations from the Wind data are: vsh = 355 km/s, andn = [−0, 53; −0, 44; 0, 73] (an arrow at the Wind location). The normal and speed computed from timing of the 4 spacecraft (Wind, ACE,
Geotail, IMP 8) observations (Koval et al., 2005) are: vsh = 319 km/s,
and n = [−0, 55; −0, 29; 0, 77]. The dashed line shows this shock
plane.

and Interball-1 is about 7 minutes, only. On the other hand,
IMP 8 was orbiting in front of the quasiperpendicular bow
shock, whereas Interball-1 was moving in the quasiparallel region and Geotail was probably near the ion foreshockboundary as can be seen from the schematics in Fig. 4 (notethat the ion foreshock boundary lies downstream of that ofelectron foreshock due to a smaller ion speed). Positionsof the spacecraft as well as the magnetic field vectors areprojected onto the X YGSE plane. The estimated location of
the IP shock is shown by thin dashed lines with about twominute spacing, the heavy dashed line stands for the electron foreshock boundary after the IP shock arrival. Bothupstream and downstream IMF orientations are shown by
the heavy arrows.
The main foreshock feature that can influence the propagation of the IP shock is probably a presence of energetic
particles because the amplitude of ULF waves was very low
in our case (see Fig. 3). For this reason, we are showing
the temporal profiles of several energies measured by Geotail and Interball-1 in Fig. 5. The estimated IP shock fronts
are distinguished by dashed vertical lines. The Interball-1
magnetic field profile is shown for the sake of reference.
The measurements of both spacecraft are, in some sense,
similar. Prior the IP shock arrival, both of them observe
gradually increasing particle fluxes at all energies. Theiranisotropy is very low. It is shown in the last panel for Geotail as anisotropy coefficients and it can be estimated from a(lack of) spin modulation in the Fp2 panel of the Interball-1
data (3th panel in Fig. 5). The anisotropy coefficients, a1
and a2, are amplitudes of the first and second harmonics of

IB flux

GE flux

IMP-8

I8 flux

ACE

609

8
6

8
6

5
4
3
2
1
0
0020

0040

0100

0120

UT

Fig. 3. IMP 8, Geotail, and Interball-1 observations of the IP shock
upstream of the bow shock on August 10, 1998. From top bottom: IMF(first three panels) and ion fluxes (in units of 108 [cm−2 s−1 ]) fromIMP 8, Geotail, and Interball-1, respectively. In each panel, the IMF orion flux from Wind (thin lines) are presented for the sake of reference.

Fig. 4. The sketch of projections of spacecraft locations onto the ecliptic
plane that respects their real observations in different distances from theelectron foreshock boundary (heavy dashed line). The orientations of
upstream (Bu ) and downstream (Bd ) IMF are shown by the arrows. The
estimated orientation of the IP shock is depicted by thin dashed lines.

the Fourier fit to the measured ratio of paralell and perpendicular particle fluxes. The increase of the particle flux canbe connected with the approaching IP shock because theflux of particles accelerated there is added to the original
foreshock flux. The rise of the energetic particle flux is terminated not at but about two minutes after IP shock arrivals
to both locations. After this peak, the particle flux drops
down by an order of magnitude and becomes anisotropic at

610

L. PŘECH et al.: FORESHOCK EFFECTS AND INTERPLANETARY SHOCKIB B [nT]IB Fp1

INTERBALL, GEOTAIL 10-Aug-1998
10
8
6
4
2
100

References

IB Fp2

10
1000
100

GE ani

GE Fi

10
100
10
1
1.0
0.8
0.6
0.4
0.2
0.0
0000

a1
a2
0040

0100

0120

UT

Fig. 5. The temporal profiles of energetic particles measured on Interball-1 and Geotail before and after the IP shock transition. Interball-1 (first three panels) show 3 different energies (blue line—115 keV,
red—50 keV, and black—25 keV) in two directions (Fp1 in the sunward and Fp2 near the anti-sunward directions). Geotail panels (twobottom panels) show energetic particle fluxes (4th panel from top to bottom—the energy range from 67 to 414 keV) and anisotropy coefficients(a1 and a2 in the 5th panel).

the Geotail location. This decrease is probably connectedwith the Geotail exit from the ion foreshock because the
IP shock (and the downstream IMF) approached the bow
shock about 2 minutes after it passed Geotail (see Fig. 4).
The drop of the energetic particle flux is associated with a
new rise of the magnetic field toward its post-shock equilibrium value (compare Figs. 3 and 5).
The behavior of the energetic particles at the Interball-1
location is more peculiar because their flux remains nearly
isotropic for about 6 minutes after the IP shock arrival andthen it jumps down and a strong anisotropy appears. An
analysis of pitch angles revealed that the flux at about 90◦
remains nearly on a previous level and only particles withlow and high pitch angles disappeared. This change is accompanied with a new rise of the magnetic field strength.
In this case, the delay of the change of energetic particle
properties cannot be connected with reformation of the foreshock and its source is unclear.
Finally, we have presented a short case study of the IP
shock propagation through the foreshock. We have shownthat the profiles of basic parameters can be substantiallymodified, probably due to presence of energetic particles.
However, the exact mechanism of this modification requires
a further study that would include a modeling of particle
trajectories.
Acknowledgments. The presented work was partly supported by
the Research plan MSM 0021620860 that is financed by the Ministry of Education of the Czech Republic and partly by the Czech
Grant Agency under Contracts 205/07/0694, and 205/06/0875.
Their supports are greatly acknowledged. The authors would liketo thank to teams of all spacecraft involved in this study.

Dryer, M., Bow shock and its interaction with interplanetary shocks, Radio
Sci., 8, 893–901, 1973.
Echer, E., W. D. Gonzalez, and M. V. Alves, On the geomagnetic effects
of solar wind interplanetary magnetic structures, Space Weather, 4,
S06001, doi:10.1029/2005SW000200, 2006.
Fry, C. D., M. Dryer, Z. Smith, W. Sun, C. S. Deehr, and S.I. Akasofu, Forecasting solar wind structures and shock arrival
times using an ensemble of models, J. Geophys. Res., 108, A1070,
doi:10.1029/2002JA009474, 2003.
Gonzalez, W. D., B. T. Tsurutani, and A. L. C. De Gonzalez, Interplanetaryorigin of geomagnetic storms, Space Sci. Rev., 88, 529–562, 1999.
Grib, S. A., Interaction of non-perpendicular/parallel solar wind shockwaves with the Earth’s magnetosphere, Space Sci. Rev., 32, 43–48, 1982.
Grib, S. A., B. E. Brunelli, M. Dryer, and W.-W. Shen, Interaction ofinterplanetary shock waves with the bow shock-magnetopause system,
J. Geophys. Res., 84, 5907–5921, 1979.
Jerab, M., Z. Nemecek, J. Safrankova, K. Jelinek, and J. Merka, A studyof bow shock locations, Planet. Space Sci., 53, 85–94, 2005.
Koval, A., J. Safrankova, Z. Nemecek, and L. Prech, Deformation of interplanetary shock fronts in the magnetosheath, Geophys. Res. Lett., 32,
doi:10.1029/2005GL023009, 2005.
Koval, A., J. Safrankova, Z. Nemecek, A. A. Samsonov, L. Prech, J. D.
Richardson, and M. Hayosh, Interplanetary shock in the magnetosheath:Comparison of experimental data with MHD modeling, Geophys. Res.
Lett., 33, doi:10.1029/2006GL025707, 2006.
Le, G., C. T. Russell, and J. G. Luhmann, Polar magnetic observationsof the low-altitude magnetosphere during the January 1997 coronalmass ejection/magnetic cloud event, Geophys. Res. Lett., 25, 2533–
2536, 1998.
McKenna-Lawlor, S. M. P., M. Dryer, M. D. Kartalev, Z. Smith, C. D. Fry,
W. Sun, C. S. Deehr, K. Kecskemety, and K. Kudela, Near real-time
predictions of the arrival at Earth of flare-related shocks during Solar
Cycle 23, J. Geophys. Res., 111, A11103, doi:10.1029/2005JA011162,
2006.
Petrinec, S. M. and C. T. Russell, Near-Earth magnetopause shape and size
as determined from the magnetopause flaring angle, J. Geophys. Res.,
101, 137–152, 1996.
Russell, C. T., J. T. Gosling, R. D. Zwickl, and E. J. Smith, Multiple spacecraft observations of interplanetary shocks: ISEE three-dimensional
plasma measurements, J. Geophys. Res., 88, 9941–9947, 1983.
Russell, C. T., et al., The interplanetary shock of September 24, 1998:
Arrival at Earth, J. Geophys. Res., 105, 25,143–25,154, 2000.
Safrankova, J., Z. Nemecek, L. Prech, G. Zastenker, N. Nikolaeva, M.
Nozdrachev, A. Skalsky, K. Paularena, and T. Mukai, January 10–11,
1997 magnetic cloud: Multipoint measurements, Geophys. Res. Lett.,
25, 2549–2552, 1998.
Samsonov, A. A., Z. Nemecek, and J. Safrankova, Numerical MHD modeling of propagation of interplanetary shock through the magnetosheath,
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Spreiter, J. R. and S. S. Stahara, Gasdynamic and magnetohydrodynamic
modeling of the magnetosheath—a tutorial, Adv. Space Res., 14(7), 5–
19, 1994.
Thomsen, M. F., Multispacecraft observations of collisionless shocks, Adv.
Space Res., 8(9), 157, 1988.
Tsurutani, B. T. and W. D. Gonzalez, The interplanetary causes of magnetic storms: a review, in Magnetic storms, edited by B. T. Tsurutani,
W. D. Gonzalez, Y. Kamide, and J. K. Arballo, AGU Monograph 98,
Washington, D.C., pp. 77–90, 1997.
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study, J. Geophys. Res., 106, 29,175–29,184, 2001.
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L. Přech (e-mail: lubomir.prech@mff.cuni.cz), Z. Němeček, and J.
Šafránková

LETTER

Earth Planets Space, 61, 611–614, 2009

Three dimensional configuration of earthward fast plasma flowin the near-Earth plasma sheet
Koji Kondoh, Masayuki Ugai, and Tohru Shimizu
Research Center for Space and Cosmic Evolution, Ehime University, Japan(Received November 2, 2007; Accepted August 16, 2008; Online published May 29, 2009)

The earthward short-term (1-min. order) fast flow event (Flow Burst) and the long-term (10-min. order) fast
flow event (Bursty Bulk Flow) observed in the near-Earth plasma sheet are examined using three dimensional
MHD simulations on the basis of spontaneous fast reconnection model. It is well known that these fast flow eventsare closely related to the magnetic substorms. On the other hand, it is considered that these fast flow events arecaused by the magnetic reconnection in the near-Earth magnetotail. The time profiles of plasma quantities in these
events observed by in-situ satellites are quite different in each event. Above Flow Burst and Bursty Bulk Flow
events are often examined separately due to the large difference in time scale. In this paper, these differences areinterpreted by the three-dimensional position of satellite relative to the X-line and the reconnection jet channel,
and the simulation results are directly compared with the results of in-situ satellite observations using the virtual
satellites located in simulation domain.
Key words: Earthward flow, magnetic reconnection, near-Earth plasma sheet, three-dimensional MHD simulation.

1.

Introduction

Earthward fast flows in the near-Earth plasma sheet havebeen observed in association with geomagnetic substorms(Angelopoulos et al., 1992). It is considered that these fast
flows are fast reconnection outflows. In space plasmas ofextremely large magnetic Reynolds number, magnetic reconnection can convert magnetic energy to plasma energies most effectively by slow shocks. A possible fast reconnection configuration, involving standing slow shocks,
was first proposed by Petschek (1964). In this respect, wehave proposed the spontaneous fast reconnection model.
This model predicts that the fast reconnection mechanism
spontaneously develops from inside the system by the selfconsistent interaction between plasma microscopic processes and macroscopic reconnection flows (Ugai, 1984,1986). The previous MHD simulations have demonstrated
that the spontaneous fast reconnection model works quite
effectively even in three dimensional situations (Ugai andKondoh, 2001; Ugai et al., 2004, 2005). Once the fast reconnection builds up, an Alfvénic fast flow is caused, andif the fast flow is obstructed, the reconnected field lines are
piled up, and a magnetic loop is formed. A magnetic loop
in our simulation is allowed to be formed because of a wallboundary assumed at one edge of a current sheet system(Ugai et al., 2003). Sergeev et al. (2000) showed a narrow transient flow jet using five spacecraft measurements.
They showed that the ∼3Re wide fast plasma jet propagatesfrom 40Re in the midtail, and is able to reach the innermagnetosphere at 6.6Re in about 10 minutes. This propertyc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

consists with the previous results of MHD simulations on
the basis of spontaneous fast reconnection model (Ugai etal., 2003).
Earthward fast flow events observed in the near-Earthplasma sheet have the different profiles in each event. For
example, Figs. 1(a) and (b) are the different two events
observed by Geotail satellite. These figures show the time
profiles of the plasma bulk velocity component Vx (toppanel), the magnetic field components Bx (dotted line), Bz(solid line) (middle panel), and the ion density N (bottom
panel). These satellites observed at X = −29.67RE , Y =7.50RE , Z = −1.26RE (a), X = −28.31RE , Y = 2.65RE ,Z = −2.03RE (b) in GSM coordinate, respectively. In
GSM coordinate system, these events were observed at very
near positions. The maximum velocity of Vx is almost
same, 600 km/s. As you can see, however, these two events
are quite different. The duration of the enhancement of flow
velocity in Fig. 1(a) (∼7 min.) is remarkably longer thanthat in Fig. 1(b) (∼1 min.). The variation of the ion density
in the course of fast flow is large in Fig. 1(a), while that islittle in Fig. 1(b). In this paper, we examine the earthward
fast flow using three-dimensional MHD simulations on thebasis of spontaneous fast reconnection model, and whatcauses these differences.

2.

Simulation Model

The earthward fast flow is closely related to the formationof magnetic loop (or magnetic dipolarization), so that thepresent simulation model is similar to the one of the 3D
magnetic loop dynamics (Kondoh and Ugai, 2007).
These previous magnetic loop simulations using the wallboundary showed that the fast magnetic reconnection produces fast reconnection jet, and it flows in plasma sheet and

611

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K. KONDOH et al.: 3D CONFIGURATION OF EARTHWARD FAST FLOW

0 < y < L y , and 0 < z < L z ; also, for simplicity, the conventional symmetry boundary condition is assumed on theouter boundary plane x = L x , and on the other boundary
planes (y = L y and z = L z ) the free boundary conditions
are assumed.
As in the 2D model, a current-driven anomalous resistivity model is assumed in the form,
η(r, t) = kR [Vd (r, t) − VC ]=0

for Vd > VC ,for Vd < VC

(1)

where Vd (r, t) = |J(r, t)/ρ(r, t)| is the relative electronion drift velocity, and VC may be a threshold for micro
instabilities. Here, kR = 0.003 and VC = 12 are taken.
In order to disturb the initial static configuration, a localized resistivity model is assumed around the point (L x , 0, 0)
in the 3D form,
3
η(r) = η0 exp − ((x − L x ) /k x )2 − |y|/k y − (|z|/k z )3(2)
Fig. 1. Geotail observation data showing the plasma bulk velocity component (Vx ), magnetic field components (Bx , Bz ) and ion density (N )(12:15–12:25 UT, 14 February 1998 (a), 20:30–20:40 UT, 27 January
1996 (b)). The variables in parenthesis indicate the corresponding ones
in our coordinate system.

is suddenly braked at the boundary between the dipolar andtail-like magnetic field because of the counterward pressure
force, and the reconnection jet is decelerated. This situation
may be consistent with the earthward fast flow, and these results are in good agreement with the situation inferred fromthe observation results of earthward fast flow (Shiokawa etal., 1997).
2.1 Simulation modeling
As an initial configuration, the one-dimensional antiparallel magnetic field B = [Bx (y), 0, 0] is assumed as:
Bx (y) = sin(π y/2) for 0 < y < 1; Bx (y) = 1 for 1 <y < Y1 ; Bx (y) = cos[(y − Y1 )π/1.2] for Y1 < y < Ym (=Y1 + 0.6); Bx (y) = 0 for Ym < y; also, Bx (y) = −Bx (−y)
for y < 0. The plasma pressure P(y) initially satisfies thepressure-balance condition, P + Bx2 = 1 + β0 , where β0
is the ratio of plasma pressure to the magnetic pressure in
the ambient magnetic field region 1 < y < Y1 , so that
P(y = 0) = 1+β0 initially (in the present study, β0 = 0.15
is taken); Initially, fluid velocity u = (0, 0, 0) and constanttemperature T = P/ρ = 1 + β0 is assumed, so that theplasma density ρ initially satisfies ρ(y) = P(y)/(1 + β0 ).
The normalization of quantities, based on the initial quantities, is self-evident; Distances are normalized by the halfwidth of the current sheet d0 , B by the field strength in2/(2µ0 ), and ρ bythe magnetic field region Bx0 , P by Bx0√
ρi = ρ(y = 0); also, u by V Ax0 (= Bx0 / µ0 ρi ), time t
by d0 /V Ax0 , current density J by J0 = Bx0 /(µ0 d0 ), and soforth.
Here, the conventional symmetry boundary conditions
are assumed on the (x, y), (y, z), and (z, x) planes. Hence,the computational region can be restricted to the first quadrant only and taken to be a rectangular box, 0 < x < L x ,Here, we take k x = k y = 0.8 and η0 = 0.02 in the manner
similar to the previous 2D simulations; also, k z provides
the 3D effects, we take k z = 5 in the present study. The
disturbance (2) is imposed only in the initial time range
0 < t < 4, and the anomalous resistivity model (1) isassumed for t ≥ 4. Hence, the fast reconnection mechanism
may be triggered at x = L x in this model.
It should be noted that sufficiently small mesh sizes
are required for precise computations of the spontaneous
fast reconnection evolution, so that we assume x =0.04, y = 0.015, and z = 0.1. Also, we take themagnetic field region size Y1 = 4, and the whole computational region size is assumed to be L x = 10, L y = 9.6
and L z = 9.8. Here, we should notice that positive x, y, zdirections in this paper correspond to tailward, south-ward,
and east-ward in usual GSM co-ordinate system, respectively.

3.

Results

In this simulation model, initiated by the disturbance (2)given at x = L x in the finite extent |z| < k z = 5, the current sheet thinning occurs near the x = L x , giving rise todistinct enhancement of the current density. Once the drift
velocity Vd exceeds the given threshold (1), fast reconnection drastically grows as nonlinear instability because of thepositive feedback between the anomalous resistivity and thereconnection flow. Ahead of the Alfvénic reconnection jet
flowing to negative x-direction, a large-scale 3D plasmoid
is formed and propagates, and the plasmoid collides withthe x = 0 wall boundary, giving rise to a 3D magnetic loop.
3.1 Virtual observations
In order to directly compare the simulations with thesatellite observations, let us consider such a virtual satellitethat is located at a spatial point (x, y, z) in the plasma sheet.
For simplicity, we assume that the satellite does not move inspite of the progress of time. Then, the virtual satellite canreadily detect the temporal changes of plasma quantities at
its location on the basis of the simulation results. In what
follows, we examine what the virtual satellite observes as
the fast reconnection mechanism builds up and proceeds.

K. KONDOH et al.: 3D CONFIGURATION OF EARTHWARD FAST FLOW

Fig. 2. Time variations of −Vx , Bx , −B y , ρ, and P for the interval oft = 30 to 42 at X = 4.0, Z = 0.0, Y = 0.0 (a) and 0.8 (b).

At first, two virtual satellites are located at the positions(4.0, 0.0, 0.0) and (4.0, 0.8, 0.0) in order to examine the profiles at different y-positions. These positions correspondto them in the central plasma sheet (hereafter, call CPS)
and near the plasma sheet boundary layer (hereafter, callPSBL), respectively. Figure 2 shows the temporal variations of the plasma flow velocity (top panel), magnetic fieldcomponents (middle panel), plasma pressure and plasma
density (bottom panel) detected by the virtual satellites located at (4.0, 0.0, 0.0) (a) and (4.0, 0.8, 0.0) (b). In the CPS(a), the earthward flow velocity Vx reaches Alfvén velocity. The local magnetic field dipolarizes a little. P and ρ
largely decrease in the course of the fast flow, and the temperature becomes high there. On the other hand, near the
PSBL (b), the enhancement of Vx is small and short, Bx
largely decrease in the course of fast flow. The clear dipolarization is also detected. The durations of the variationsin P and ρ are nearly same and short. The temperaturein the course of the fast flow is high as well as that in the
CPS. The peak times of the pressure enhancement TP indicated by the vertical solid lines are almost same t ∼ 37.7.
The vertical dotted lines indicate the peak times of the otherquantities. The earthward flow speed |Vx | at TP are almost
same ∼1.0 at both positions. The earthward flow speed in
the CPS gradually increase from t ∼ 30, whereas it near the
PSBL starts to increase just before TP . The anti-correlation
between the earthward flow speed |Vx | and earthward component of magnetic field Bx is clear in Fig. 2(b). This rapid
increase (decrease) and decrease (increase) of |Vx |(Bx ) near
the PSBL means that the satellite suddenly goes in the fast
flow channel and suddenly goes out there.
Secondly, the other two virtual satellites are located at(4.0, 0.4, 0.0) and (4.0, 0.4, 1.2) in order to examine theprofiles at different z-positions. These positions correspondto the those in the channel of Alfvénic fast flow (hereafter,
call fast flow channel) and outside of the fast flow channel
in the z-direction, respectively. In Fig. 2, the one satellite

613

Fig. 3. Time variations of −Vx , Bx , −B y , ρ, and P for the interval oft = 30 to 42 at X = 4.0, Y = 0.4, Z = 0.0 (a) and 1.2 (b).

was located in the y = 0 plane in order to examine theprofiles of the satellite observations at different y-positions.
However, it is rare case that the actual satellites are locatedin the neutral sheet, that is, they observe no Bx component. Therefore, these two virtual satellites are located in
the y = 0.4 plane. Figure 3 shows the temporal variationsof the plasma flow velocity (top panel), magnetic field components (middle panel), plasma pressure and plasma density (bottom panel) detected by the virtual satellite locatedat (4.0, 0.4, 0.0) (a) and (4.0, 0.4, 1.2) (b). In the fast flow
channel (a), the enhancement of earthward flow speed islarge, but the satellite goes out the fast flow channel in they-direction at t ∼ 40. The plasma pressure and density
decrease is significantly large. On the other hand, the enhancement of earthward flow speed observed outside thefast flow (b) is small, but the duration is very long because
the satellite does not go out the fast flow channel in the ydirection easily due to the calm plasma sheet thinning. The
decrease of plasma pressure and density observed outside
the fast flow channel is not so large.

4.

Summary

In this paper, the earthward fast flow events observed in
the near-Earth plasma sheet were examined using three dimensional magnetohydrodynamics simulations on the basisof the spontaneous fast reconnection model. In particular,
the properties of the variation of physical quantities in eachobservation point relative to the X reconnection line and thenarrow channel of fast reconnection jet were investigated inthree dimensions. The time variations of physical quantities
observed by virtual satellites were quite different between
the satellite positions in central plasma sheet and near theplasma sheet boundary layer. The satellite located in central plasma sheet does not go out the narrow channel of fast
flow, so that the enhancement of earthward fast flow speed
is large, and the decrease of plasma pressure and density
is large. On the other hand, the satellite located near the614

K. KONDOH et al.: 3D CONFIGURATION OF EARTHWARD FAST FLOW

plasma sheet boundary layer suddenly comes in the narrow
channel and suddenly goes out, so that the enhancement ofearthward fast flow speed is small and short, the decreaseof earthward component of magnetic field is large in thecourse of fast flow, and the variations of plasma pressureand density are observed only in the course of fast flow.
The time variations of physical quantities observed by virtual satellites were also quite different between the satellite
positions in the sheet current direction. As mentioned in
Introduction, the Alfvénic earthward fast jet flows in very
narrow channel. In addition to this, relatively slow earthward jet (about 1/3 of Alfvén speed) flows in wider region
in the sheet current direction. In that region, plasma sheet
thinning is also calm, so that the satellite located in that region does not go out that region easily. Therefore, the long
duration enhancement of earthward flow is observed in that
region. Let us interpret the positions of the satellites whichobserved the sample two events shown in Introduction on
the basis of these results. The properties in Fig. 1(a) werelong enhancement of earthward flow speed, small variationof earthward component of magnetic field, small increaseof northward component of magnetic field, and small decrease of plasma density. These properties are same as thatobserved in the region near the central plasma sheet andoutside of the narrow channel of the Alfvénic fast flow. On
the other hand, the properties in Fig. 1(b) were short enhancement of earthward flow speed, very small variationof plasma density, and large variation of earthward component of magnetic field. These were clearly same as theresults observed at the near plasma sheet boundary layer. In
summary, we have demonstrated that the time variation ofplasma quantities in the earthward fast flow event depends
on the satellite position, in particular on the position relative
to narrow channel of Alfvénic fast flow.
Acknowledgments. This work was supported by Grant-in-Aids
for Creative Scientific Research ‘The Basic Study of Space
Weather Prediction’ (17GS0208, Head Investigator: K. Shibata)from the Ministry of Education in Japan, Mitsubishi Foundation,
RISH of Kyoto University, and Solar Terrestrial Environment Laboratory of Nagoya University. The computer program was tested
and run at the Computational Centers of Nagoya and Kyoto University. Geotail magnetic field and plasma data were provided by
T. Nagai and T. Mukai through DARTS at Institute of Space andAstronautical Science, JAXA in Japan.

References
Angelopoulos, V., W. Baumjohann, C. F. Kennel, F. V. Coroniti, M. G.
Kivelson, R. Pellat, R. J. Walker, H. Luhr, and G. Pashmann, Bursty
bulk flows in the inner central plasma sheet, J. Geophys. Res., 97, 4027–
4039, 1992.
Kondoh, K. and M. Ugai, Study of three dimensional structure of the fast
convection flow in the plasma sheet by MHD simulations on the basis of
spontaneous fast reconnection model, Adv. Space Res., 39, 1378–1381,
2007.
Petschek, H. E., Magnetic field annihilation, Magnetic Field Annihilation,
NASA Spec. Publ. SP-50, 425–439, 1964.
Sergeev, V. A., J.-A. Sauvaud, D. Popescu, R. A. Kovrazhkin, K. Liou, P.
T. Newell, M. Brittnacher, G. Parks, R. Nakamura, T. Mukai, and G. D.
Reeves, Multiple-spacecraft observation of a narrow transient plasma jetin the Earth’s plasma sheet, Geophys. Res. Lett., 27, 851–854, 2000.
Shiokawa, K. et al., Braking of high-speed flows in the near-Earth tail,Geophys. Res. Lett., 24, 1179–1182, 1997.
Ugai, M., Self-consistent development of fast magnetic reconnection withanomalous plasma resistivity, Plasma Phys. Controlled Fusion, 26,
1,549–1,563, 1984.
Ugai, M., Global dynamics and rapid collapse of an isolated current-sheet
system enclosed by free boundaries, Phys. Fluids, 29, 3,659–3,667,
1986.
Ugai, M. and K. Kondoh, Computer studies on the spontaneous fast reconnection evolution in various physical situations, Phys. Plasmas, 8,
1,545–1,552, 2001.
Ugai, M., K. Kondoh, and T. Shimizu, Computer simulations on threedimensional magnetic loop dynamics by the spontaneous fast reconnection model, Phys. Plasmas, 10, 357–363, 2003.
Ugai, M., K. Kondoh, and T. Shimizu, Computer studies on the threedimensional spontaneous fast reconnection model as a nonlinear instability, Phys. Plasmas, 11, 1,416–1,423, 2004.
Ugai, M., K. Kondoh, and T. Shimizu, Spontaneous fast reconnection
model in three dimensions, Phys. Plasmas, 12, 042903, 2005.
K. Kondoh (e-mail:Shimizu

kondo@cs.ehime-u.ac.jp), M. Ugai, and T.

LETTER

Earth Planets Space, 61, 615–619, 2009

Timing of substorm related auroral oscillations
P. Martin1 , N. E. Turner1 , and J. Wanliss2
1 Florida Institute of Technology
2 Presbyterian College(Received October 26, 2007; Accepted August 16, 2008; Online published May 29, 2009)

Previous studies have shown that auroral luminosity oscillations are often associated with substorms. Here we
examine photometer data for the magnetospheric substorm on April 1, 2000 (expansive phase onset at 0525 UT)
to study the detailed timing of the auroral oscillations relative to onset. Accurate timing information for theperiodicities in the photometer data were determined using the wavelet transform. We find that the oscillations
occur primarily during the recovery phase.
Key words: Aurora, substorm, wavelet, CANOPUS.

1.

Introduction

Magnetospheric substorms are among the more consequential space weather effects, second in importance only tothe massive and global space storms. Several studies haveconsidered the effects of magnetohydrodynamic (MHD)
waves on particle precipitation in the ionosphere (Berger,
1963; Davidson, 1990; Milan et al., 2001), and a strong linkhas been suggested between discrete auroral arcs and MHD
waves (Samson et al., 1996; Wanliss and Rankin, 2002;
Wanliss et al., 2002). MHD field line resonances (FLRs) areformed through wave coupling of compressional and shear
Alfvén waves. The local compression of the magnetosphereat substorm expansive phase onset generates compressional
MHD waves that encounter positive gradients in the Alfvénvelocity leading to the excitation of shear Alfvén waves on
the magnetic shells distant from the source of the onset. Because of the coupling of energy at spatially different locations, auroral activity is expected to occur at high and low
latitudes. Theory predicts that the high latitude activity willfeature a poleward phase shift of 180 degrees across the beltof auroral oscillation (Hughes, 1983; Liu et al., 1995). Similarly, the low latitude activity should exhibit a 180 degree
equatorward phase shift and a temporarily varying parallel
electric field will be established along the resonant field line
(Block and Fälthammer, 1990; Liu et al., 1995). A consequence of this parallel electric field is the periodicities ofthe precipitating protons and electrons are anti-correlated.
If there were no parallel electric field there should be nosuch phase difference and the precipitation of protons andelectrons would likely be similarly modulated (Liu et al.,1995).
In this study we examine the timing of substorm associated auroral oscillations in order to determine which substorm phase they are associated with. The data are for thesubstorm on April 1, 2000 previously studied in detail by
c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

Wanliss and Rankin (2002). They found 2.2 mHz pulsations
in magnetometer and photometer data. The proton and electron auroras were found to oscillate essentially out of phase,and the variation of phase across the peak in the luminosity resonance followed the pattern expected for the couplingof resonant Alfvén modes by normal compressional modesin the magnetotail. The previous work established accurate frequency information, but here we wish to establish
detailed timing of the oscillations, a task for which the multiple filters of the wavelet transform are best suited.

2.

Data Description

Wanliss and Rankin (2002) used photometer data fromthe Gillam meridian scanning photometer in northern
Canada and found luminosity oscillations associated withmagnetospheric substorms. They examined photometerand magnetometer data of a magnetospheric substorm on
April 1, 2000 which had its expansive phase onset at0525 UT. They examined the proton (486.1 nm) and electron (557.7 nm, 630.0 nm) auroras. The 486.1 nm (Hβ)
emission is caused by precipitation of protons of tens ofkeV, 557.7 nm from hot electrons of several keV, and630.0 nm from warm electrons of a few hundred eV. Thisparticular substorm occurred during a moderate space storm
recovery phase with minimum Dst = −60 nT. Figure 1
shows the 557.7 nm photometer data from the Gillam station (GILL). The data show brightness (Rayleighs) as afunction of latitude and time. Each meridian scan takes one
minute to complete, and data are organized into 17 latitudinal bins. The substorm growth phase is indicated by thesteady equatorward motion of the auroras prior to 0525 UT,
indicative of stretching of the inner magnetotail (Wanliss etal., 2000). At this time the emissions brighten and begin
to move poleward, indicative of dipolarization of the previously stretched field lines.
A Fourier spectrogram of each wavelength revealed
a peak around 2.2 mHz (Wanliss and Rankin, 2002).
The 630.0 nm wavelength also showed peaks at 2.9 and3.8 mHz. Using CANOPUS magnetometer data the Pi2

615

616

P. MARTIN et al.: TIMING OF AURORAL OSCILLATIONS

Fig. 1. Photometer data (557.7 nm) from the Gillam station for April 1, 2000 where substorm onset begins at the 309th minute of the day. The firstvertical line indicates substorm onset and the two other lines indicate an equatorward intensification of the aurora.

pulsation was found to be localized between 67.4 and 69.7
degrees geomagnetic latitude. A phase correlation analysis was performed to determine if the spectral peaks might
be related to field line resonances (FLR). The signals at
66.6, 66.1, and 65.6 degrees magnetic latitude, were anticorrelated which is consistent with a FLR and a parallel
electric field. The phase shift around 2.2 mHz showed a
120 degree phase shift at ∼66 degrees for the 557.7 nm line
which is lower than the theoretically required 180 degrees
expected for a FLR (Chen and Hasegawa, 1974). For the630.0 nm emission there was a 100 degree phase change
which is qualitatively consistent but not quantitatively consistent with the FLR theory.

3.

Wavelet Analysis Method

As with our previous work we produce a spectrogramof the photometer data for the substorm on April, 1 2000.
Spectral analysis yields excellent frequency resolution forthe peaks in the spectrogram, but poor timing information.
In this study we seek good timing and frequency information, thus the wavelet transform is used to identify significant spectral power in frequency/time space. The varying
size of the frequency/time bins makes it easier to identify
wave power in time compared to the fixed size of the frequency/time bins in the windowed Fourier transform. Obviously, good time information results in decreased frequency
resolution.
The output of the wavelet transform is both time and frequency dependent which is similar to the windowed Fouriertransform. However, one obvious difference is the variable

time length of the wavelet which results in a variable scale
size or frequency band. The user does not need to know thefrequency band to be searched for significant waves. The
time span of the wavelet determines the frequency of theband in the spectrum. The wavelet makes multiple passes
through the time series, adjusting its size for each pass. Thisis necessary to guarantee a complete period will fit in the
wavelet and be recognized as a true wave, not a discontinuity. The resulting wave power is distributed in frequency
and time. The highest possible frequency of the wavelet
transform is the Nyquist frequency which is determined by
the sampling rate. The lowest possible frequency is determined by the time length of the time series. The versionof the wavelet transformed used in this study, required aminimum of eight complete wavelets to fit in the time series. The time length of the wavelet determines the lowest
possible frequency. The multiple scale sizes also provide
an advantage, in terms of timing issues, over the windowed
Fourier transform. There is little power leakage along thetime axis.
The power element of the wavelet transform represents
the variance of the original time series at a specific range oftime and frequency. Percival and Walden (1993, 2000) and
Torrence and Compo (1998) showed the distribution of thepower elements of the windowed Fourier and wavelet spectrums are similar to a chi-square distribution with 2 degrees
of freedom. Therefore, analysis of variance (ANOVA) canbe performed on the output to determine an accurate estimate of the frequency/time spectrum of the time series or
the power spectral density (PSD).

P. MARTIN et al.: TIMING OF AURORAL OSCILLATIONS

617

Fig. 2. The wavelet spectrum of the 557.7 nm photometer data measured at 61.6 degrees latitude. The regions outlined highlight significant spectral
power.

-50 to 0 min

64
63
62
61
60
59
58
57
56

Latitude (degrees)

Latitude (degrees)

486.1 nm

0

1

2

3

4

5

0 to 5 min

66
65
64
63
62
61
60
59
58
57
56

6

0

1

5 - 10 min

66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

6

Frequency (mHz)

Latitude (degrees)

2

3

4

5

6

5

6

Frequency (mHz)

Latitude (degrees)

Latitude (degrees)

Frequency (mHz)

10 - 30 min

66
65
64
63
62
61
60
59
58
57
0

1

2

3

4

Frequency (mHz)

30 to 60 min

66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

6

Frequency (mHz)

Fig. 3. The significant peaks in the 486.1 nm photometer spectra based on measurements at different latitudes. The data are divided into time intervals
which represent the phases of the substorm. The vertical dashed lines mark the CMS frequencies greater than 1 mHz.

618

P. MARTIN et al.: TIMING OF AURORAL OSCILLATIONS

557.7 nm0 to 5 min
Latitude (degrees)

Latitude (degrees)-50 to 0 min
66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

66
65
64
63
62
61
60
59
58
57
56

6

0

1

5 to 10 min

66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

2

3

4

5

6

5

6

Frequency (mHz)
10 to 30 min
Latitude (degrees)

Latitude (degrees)

Frequency (mHz)

5

66
65
64
63
62
61
60
59
58
57
56
0

6

1

Frequency (mHz)

2

3

4

Frequency (mHz)

Latitude (degrees)

30 to 60 min
66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

6

Frequency (mHz)

Fig. 4. The significant peaks in the 557.7 nm photometer spectra based on measurements at different latitudes.

630.0 nm0 to 5 min

66
65
64
63
62
61
60
59
58
57
56

Latitude (degrees)

Latitude (degrees)-50 to 0 min

0

1

2

3

4

5

66
65
64
63
62
61
60
59
58
57
56

6

0

1

66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

6

Frequency (mHz)
30 to 60 min
Latitude (degrees)

2

3

4

5

6

5

6

Frequency (mHz)
10 to 30 min
Latitude (degrees)

Latitude (degrees)

Frequency (mHz)
5 to 10 min
66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

Frequency (mHz)

66
65
64
63
62
61
60
59
58
57
56
0

1

2

3

4

5

6

Frequency (mHz)

Fig. 5. The significant peaks in the 630.0 nm photometer spectra based on measurements at different latitudes.

P. MARTIN et al.: TIMING OF AURORAL OSCILLATIONS

The power spectrum is determined from the baseline
power level for each frequency band from which wave
amplitudes can be measured (Percival and Walden, 1993,
2000; Torrence and Compo, 1998). The process of analysis of variance for the wavelet power spectrum assumes
the time series has a mean power spectrum (Torrence andCompo, 1998). If a peak in the spectrum is significantly
above the background then it can be assumed to be a true
feature with a particular percent confidence (Torrence andCompo, 1998). A 90% confidence level was calculated foreach scale which spans the entire length of the time series(256 minutes). Any random power variable with a valueless than the 90% confidence level has a 90% probabilityof being the true mean and was considered to be part ofthe background. A power value greater than the confidence
level is considered extraordinary and therefore significant.
Any significant power value is considered to be a real peakin the spectral estimate.
We have used the complex valued Morlet wavelet over a
256 minute interval (±128 minutes from substorm onset).
The time resolution of the continuous wavelet transform(CWT) increases at higher frequencies where the bandwidth
gets larger (Press et al., 1992; Percival and Walden, 2000).
For this analysis, the transform is set up for 56 scales orfrequency bins; there are 5 subscales for every scale andthere are 11 scales. These scales span 0.47 mHz to 500 mHz
which is the Nyquist frequency. The first 18 scales (0.47 to
5.73 mHz) were used for this analysis. Figure 2 shows the
spectrogram for the 557.7 nm data with the 90% confidence
level indicated.

4.

Results

The significant peaks from the seventeen latitudes foreach of the three auroral wavelengths are combined to create Figs. 3 through 5. The spectra are summarized according to latitude and frequency across the entire 256 minuteinterval around the substorm onset which is marked as timeequal to zero. The error bars indicate the bandwidth of thepeaks. The error bar range marks high and low frequencies
where the signal/noise drops below a value of 1. The vertical dashed lines mark the CMS frequencies greater than
1 mHz as identified by Samson et al. (1991) (1.3, 1.9, 2.7
and 3.3 mHz).
We find that spectral peaks in the 3 observed auroral
wavelengths (486.1, 557.7, and 630.0 nm) have a NorthSouth alignment during the expansion phase of the substorm. The North-South arrangement is a result of thespectral peaks from the 17 different latitudes possessing thesame frequency. In each of the three studied auroral wavelengths no significant wave activity is observed during the
growth and early expansive phases of the substorm (−50 to
0 min, and 0 to 5 min). Figures 3 through 5 show that thepeaks in the spectrum form a North-South arrangement near
one of the CMS frequencies, with most significant activity
occurring from 10 to 30 minutes after substorm onset whenthe expansion phase is well developed.

5.

619

Discussion

The study by Wanliss and Rankin (2002) showed how oscillations in the aurora were tied to substorm initiated, field
line resonances. Here we have considered the timing of the
FLR. Whereas the previous study accurately determined thefrequency of the auroral oscillations, here we have utilized
the wavelet transform to achieve accurate and quantitative
isolation of the timing of significant oscillations. We findthat the auroral oscillations for both electron and proton auroras do not begin at substorm expansion phase onset, butseveral minutes after the identified onset, and at a relatively
localized latitude range. The oscillations intensify throughout the rest of the expansion phase across a wide range oflatitudes, before dying down during the substorm recovery
phase.
Acknowledgments. The Gillam meridian scanning photometer isowned and operated by the Canadian Space Agency. Work on thisproject by PM and NT was supported by NSF grant #0454685.

References
Berger, S., Giant pulsations in the magnetic field and pulsating aurora,
Planet. Space Sci., 11, 867, 1963.
Block, L. and C.-G. Fälthammar, The role of magnetic-field-aligned electric fields in auroral acceleration, J. Geophys. Res., 95(A5), 5877–5888,
1990.
Chen, L. and A. Hasegawa, A theory of long-period magnetic pulsations,1,
Steady excitation of field line resonances, J. Geophys. Res., 79, 1024,
1974.
Davidson, G. T., Pitch-angle diffusion and the origin of temporal andspatial structures in morningside aurorae, Space Sci. Rev., 53, 45, 1990.
Hughes, W., Waves in magnetospheric plasmas: Editorial, Geophys. Res.
Lett., 10(8), 601–602, 1983.
Liu, W. W. et al., Theory and observation of auroral substorms: a magnetohydrodynamic approach, J. Geophys. Res., 100, 79, 1995.
Milan, S. E. et al., Auroral forms and the field-aligned current structureassociated with field line resonances, J. Geophys. Res., 106, 25825,
2001.
Percival, D. B. and A. T. Walden, Spectral Analysis for Physical Applications, pp. 196–258, Cambridge University Press, 1993.
Percival, D. B. and A. T. Walden, Wavelet Methods for Time Series Analysis, pp. 56–145, Cambridge University Press, 2000.
Press, W. H., S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, pp. 496–608, Cambridge University Press, 1992.
Samson, J. C., R. A. Greenwald, J. M. Ruohoniemi, T. J. Hughes, and D. D.
Wallis, Magnetometer and radar observations of magnetohydrodynamic
cavity modes in the Earth’s magnetosphere, Can. J. Phys., 69, 928,1991.
Samson, J. C. et al., Observations of field line resonances, auroral arcs, andauroral vortex structure, J. Geophys. Res., 101, 17373–17383, 1996.
Torrence, C. and G. P. Compo, A practical guide to wavelet analysis, Bull.
Am. Meteor. Soc., 79(1), 61–78, 1998.
Wanliss, J. A. and R. Rankin, Auroral substorm dynamics and field line
resonances, Earth Planets Space, 54, 927, 2002.
Wanliss, J. A., J. C. Samson, and E. Friedrich, On the use of photometerdata to map dynamics of the magnetotail current sheet during substorm
growth phase, J. Geophys. Res., 105, 27673–27684, 2000.
Wanliss, J. A., R. Rankin, J. C. Samson, and V. T. Tikhonchuk,
Field line resonances in a stretched magnetotail: CANOPUS opticaland magnetometer observations, J. Geophys. Res., 107(0), 10.1029/
2001JA000257, 2002.
P. Martin (e-mail: pmartin@fit.edu), N. E. Turner, and J. Wanliss

LETTER

Earth Planets Space, 61, 621–624, 2009

Statistically predicting Dst without satellite data
A. S. Parnowski
Space Research Institute NASU & NSAU, 40 prosp. Akad. Glushkova, Kyiv-187, 03680 MSP, Ukraine(Received August 14, 2007; Revised September 16, 2007; Accepted September 23, 2007; Online published May 29, 2009)

In this paper we construct a regression relationship for predicting Dst 1 hour ahead. Our model uses only
previous Dst values. This regression is totally unbiased and does not rely on any physical model, except for thefact that Dst somehow contains the information on the recurrent geomagnetic storms. This regression has theprediction efficiency of 0.964, linear correlation with official Dst index of 0.982, and RMS of 4.52 nT. These
characteristics are inferior only to our other model, which uses satellite data and provides the prediction efficiencyof 0.975, linear correlation with official Dst index of 0.986, and RMS of 3.76 nT. This makes it quite suitable forprediction purposes when satellite data are not available.
Key words: Space weather, statistical model, Dst prediction.

1.

Introduction

Space weather prediction is one of the main tasks of modern space research. The necessity of such activities waswell understood for a long time (Marubashi, 1989). Space
weather prediction activities divide into two large categories: prediction of space weather directly in space, andprediction of space weather manifestations on the Earth.
The first category is mostly important for planning ofspace missions, predicting and evading hardware failuresof spacecraft due to arcing in electronic components, andassuring astronaut safety with respect to radiation hazard.
These tasks mainly require prediction of energetic particle
fluxes. The second category deals with influence of space
weather on power grid operation, radio communications,and health of people, especially those with cardiovasculardiseases. These tasks mainly require prediction of geomagnetic disturbances. This article will focus on space weather
prediction on the Earth.
There are many quantitative indices of geomagnetic activity. The most widely used of them are storm-time disturbance Dst and planetary geomagnetic activity index Kp. Dst
is more convenient for prediction purposes, because it directly equals the disturbance of H -component on the Earthmeasured in gammas (1γ = 10−4 Gs = 1 nT). It is averaged over several low- and mid-latitude magnetometer stations and is usually associated with the westward ring current, which appears during the storm at 4–8RE , although
this association was strongly criticized by e.g. Campbell(1996). At the same time, Kp is an integral and more artificial characteristic of the overall level of geomagnetic disturbance. In this paper Dst is used for space weather prediction.
Space weather prediction is a challenging and nontrivial
activity (Joselyn, 1995; Li et al., 2003). Since Burton etc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

al. (1975) published their pioneering work, many authors
tried to forecast space weather indices. Papers (Kugblenu
et al., 1999; Watanabe et al., 2002; Wing et al., 2005;
Pallocchia et al., 2006) featured neural network approach;papers (Zhou and Wei, 1998; Balikhin et al., 2001; Harrison
and Drezet, 2001) incorporated adaptive filtering; papers(Rangarajan and Barreto, 1999; Oh and Yi, 2004; Wei et al.,
2004; Johnson and Wing, 2004) applied statistical methods;
papers (Burton et al., 1975; Valdivia et al., 1996; O’Brien
and McPherron, 2000a, b; Temerin and Li, 2002; Ballatore
and Gonzales, 2003; Cid et al., 2005; Siscoe et al., 2005;
Temerin and Li, 2006) used empirical models; and papers(Dryer et al., 1984; Raeder et al., 2001) developed global
MHD simulations.
The best results for 1-hour prediction were achieved by
Temerin and Li (2002, 2006), who used an empirical model.
They achieved the prediction efficiency of 0.91, linear correlation of 0.95 and RMS of 6.4 nT. Neural network approach provides short-term predictions up to 4 hours in thepaper (Wing et al., 2005). It experiences significant difficulties predicting geomagnetic storms with Kp > 5, though.
Adaptive filtering seems more successful being able to provide 8-hour predictions in the paper (Harrison and Drezet,2001). However, in the papers, which incorporate adaptive
filtering, the volume of the dataset usually does not exceed
6 months of data (4380 points), which is not enough to correctly describe long-time variations in geomagnetic activity,
caused, e.g., by 11-year solar cycle. Statistical methods giveinteresting results, but were rarely used for prediction, andmuch more often for developing and constraining empiricalmodels (Johnson and Wing, 2004). Empirical models werethe most often used, and provided some of the best 1-hour
predictions. Most of them are improvements of the empirical relationship proposed in a pioneering paper by Burton
et al. (1975), who analysed the ring current injection anddecay. However, their model suffered from the lack of solar
wind data and poor physical understanding of solar windmagnetosphere interaction at that time. Global MHD simu-

621

622

A. S. PARNOWSKI: STATISTICALLY PREDICTING DST WITHOUT SATELLITE DATA

Fig. 1. Scatter plots of measured Dst versus Dst 1 hour ago (on the left) and versus predicted Dst (on the right).

lations give the longest prediction times but fail to correctly
describe kinetics in boundary layers and ballooning instabilities, which are believed to be responsible for the substorm onset.
Here we use the same method as in our other article(Parnowski, 2008), which combines statistical and empirical approaches. We payed attention mostly to 1-hour prediction, though we obtained a 9-hour prediction as well. We
predicted Dst 1 hour ahead because the temporal resolutionof the dataset was 1 hour, so we just predicted the next value
in the series. Besides, longer prediction times resulted in
predicted value being shifted in time. For prediction we
use only that information, which is available at the moment
when prediction is made, i.e. 1 hour prior to the predictedvalue. We will reference to this value as “1 hour ago”. We
determine the quality of prediction by 3 values: residual
mean square (RMS), prediction efficiency (PE), defined as[1 − (mean squared residual)/(variance of data)] (Temerin
and Li, 2002), and the linear correlation coefficient (LC)between the prediction and Dst. In the article (Parnowski,2008) we constructed a regression relationship, which provides PE = 0.975, LC = 0.986, and RMS = 3.76 nT.
However, this relationship requires satellite data to becontinuous for the previous 20 hours. Thus, when the datacontain a gap for some reason, we are unable to predict Dst
for the next 20 hours. For this reason, we need an ‘emergency’ regression, which would operate without satellite
data. Besides, satellite data are often missing during verystrong geomagnetic storms, which are the most interesting
events. Such a regression will be constructed in this article.

1963), Ci are the regression coefficients, and xi are theregressors, which are functions of input quantities and their
combinations. Values of Ci are determined by the leastsquare method with equal statistical weights of all points,
and the statistical significance of the regressors–by Fisher
test (Fisher, 1954; Hudson, 1964).
The initial number of regressors was deliberately excessive to let Fisher test select the most statistically significantof them. This was done in the following way. After processing the data with the least square method, Fisher significance parameter F was determined for each regressor.
All F values were compared to the values 2.7055, 3.84,
5.02, 6.635, 7.879, 10.83 and 12.1, which correspond tostatistical significance of 90, 95, 97.5, 99, 99.5, 99.9 and99.95% respectively. Then, insignificant regressors were
rejected and the routine was repeated until all the regressors were significant. We chose the minimal significancelevel of 90%. In contrast to empirical models we do not
add fitting parameters and all the regressors have obvious
physical meaning. The described routine was applied to thecomplete 43-year dataset sans rejects. More details on theroutine can be found in the paper (Parnowski, 2008).
First, we determined which previous Dst values are statistically significant. For this purpose, we constructed a regression
Dst( j) = C0 +NCi Dst( j − i),i=1where N is the oldest Dst value; we reached the value N =900. We found that there are statistically significant values
as far as 801 hours ago (33 days and 9 hours). The statistical
2. Data, Routine and Results
We used the OMNI 2 database, available at NSSDC significance of this oldest value is over 99.9%. However, it(http://nssdc.gsfc.nasa.gov/omniweb/). It contains IMF, so- is possible that there are even older statistically significant
lar wind and geomagnetic data, averaged over 1-hour inter- values. A similar situation was reported by Johnson andvals (49 parameters in total, starting from Jan 1, 1963). The Wing (2004) regarding Kp: “the significance is often quite
complete 43-year Dst time series given therein is continu- large for extended periods of time (10–20 days)”. Thisous and features an eye-visible 27-day and 11-year period- might be related in some way to recurrent geomagnetic
storms, but some additional research is required before final
icity, which hints for strong dependence on solar activity.
explanation could be given to this phenomenon. This will
We seek Dst in a regression form
be done in a future article.
Dst( j) =Ci xi ,
After determining which previous Dst values are statistii
cally significant, we added nonlinear terms. We tried differwhere j is the current step (number of hours since Jan 1, ent powers of the most significant terms and their products.

A. S. PARNOWSKI: STATISTICALLY PREDICTING DST WITHOUT SATELLITE DATA

623

Fig. 2. Experimental Dst index data and theoretical predictions from several models. Reprinted from (Cid et al., 2005). “Dst from Kyoto” stands forthe official Dst index from WDC-B.

Fig. 3. Our prediction for the same period of time as on Fig. 2. Satellite data is missing in the left part of the plot.

Thus, we constructed a regression, which consisted only of can be switched to high temporal resolution mode, sensitive
Dst terms and a constant regressor. Its characteristics are: equipment can be turned off, etc.
PE = 0.964, LC = 0.982, RMS = 4.53 nT.
To illustrate predictive capabilities of our model we 4. Summary
present several figures: Fig. 1 shows scatter plots of meaIn this article we obtained the following results:
sured Dst versus Dst 1 hour ago (it is the simplest possible
1. We derived a regression, which relies only on previous
prediction model) on the left and versus prediction on the
Dst values.
right; Fig. 2 shows predictions by Cerrato et al. (2004),
2.
It
allows predicting Dst 1 hour ahead with PE = 0.964,
Fenrich and Luhmann (1998), O’Brien and McPherronLC= 0.982 and RMS = 4.53 nT. Thus, it is very
(2000b), and Burton et al. (1975) for Jul 15–19, 2000; Fig. 3
convenientfor on-line Dst prediction when satellite
shows our prediction for the same period of time.
data
are
not
available.
More comparison with other models can be found in the3.
Previous
Dstvalues are statistically significant up to
paper (Parnowski, 2008).
801 hours ago and possibly more.
4. Nonlinear terms appeared to be very significant.
3. Conclusion
It appeared possible to predict Dst 1 hour ahead using
only its previous values. This hints for recurrent behaviourof geomagnetic activity. In terms of prediction efficiency
and linear correlation with the official Dst index this modelis inferior to the model, which uses satellite solar wind data.
However, satellite data is often missing during strong geomagnetic storms and this model can be used to fill the gap
in predicted Dst time series. Thus, a combination of a regression model using satellite data with the model obtainedin this article can provide accurate on-line operational Dst
forecast.
Of course, larger prediction times are desirable, but 1hour prediction is still useful. For example, magnetometers

Acknowledgments. Author is grateful to the National Space Science Data Center for the OMNI 2 database.

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A. S. Parnowski (e-mail: dyx@ikd.kiev.ua)

LETTER

Earth Planets Space, 61, 625–628, 2009

Properties of dayside nonlinear rising tone chorus emissions at large L
observed by GEOTAIL
Olga P. Verkhoglyadova1,2 , Bruce T. Tsurutani3 , Y. Omura2 , and S. Yagitani4
1 University of California, Riverside, USA
2 RISH, Kyoto University, Uji, Kyoto, Japan
3 Jet Propulsion Laboratory, CalTech, Pasadena, USA
4 Kanazawa University, Kanazawa, Japan(Received September 10, 2007; Revised November 11, 2007; Accepted December 20, 2007; Online published May 29, 2009)This paper studies some wave properties of nonlinear rising tone chorus emissions in the outer regions of thedayside equatorial magnetosphere at ∼(6.3, −4.7, 0.7RE ) in GSE coordinates. We analyze data obtained with
the PWI and WFC receivers on GEOTAIL associated with a substorm on April 29, 1993. Fine structure of thechorus elements and inter-element spacings are shown. Directions of propagation of the chorus elements relative
to the local magnetic field lines are analyzed. Wave polarizations, intensities and spectral properties of chorus in
the equatorial Earth’s magnetosphere are discussed.
Key words: Chorus emissions, wave-particle interactions, electron acceleration.

1.

Introduction

Major chorus statistical properties have been presented in
Tsurutani and Smith (1974, 1977), Nagano et al. (1996) and
Meredith et al. (2001, 2003). Recently, progress has been
made in studies of wave properties in the generation region,such as fine structure and propagation of chorus (Santolik
et al., 2003, 2004) using multipoint Cluster measurements.
We will summarize some relevant chorus characteristics
below.
Chorus ELF waves are observed in the outer magnetosphere at L > 5RE primarily in two latitude regions,and have been classified into equatorial and high-latitude
chorus (Tsurutani and Smith, 1977). Equatorial chorus(MLAT<15◦ ) occurs during substorms with the peak intensity near the magnetic equator. These waves are believed tobe generated by trapped substorm electrons via a cyclotron
resonance instability (see also Lauben et al., 2002). Highlatitude chorus is detected near the magnetopause and has
little apparent connection with substorm activity. Our study
is focused on the near-equatorial dayside chorus waves.
Equatorial chorus is an electromagnetic whistler mode
wave observed as two distinct bands, one above and one
below 0.5 of the local electron gyrofrequency, νce (Tsurutani and Smith, 1974). The wave absence at 0.5νce can be
explained by Landau damping. Chorus is often composedof ∼0.5 sec elements. There are several types of frequencytime chorus structures: rising and falling tones, and narrowband (structureless) chorus. Chorus is a nonlinear emission.
Its elements are composed of sub-elements or wave packets separated by intervals of noise (Santolik et al., 2003).
Chorus plays an important role in wave-particle interacc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

tions in the outer magnetosphere (Tsurutani and Lakhina,
1997; Horne et al., 2005). An up-to-date review of thechorus-driven electron acceleration based on CRRES observations was made by Meredith et al. (2001, 2003). Computer modeling results on relativistic electron interaction
with whistler mode waves were reported by Omura andSummers (2004). In the case of a chorus element, contribution to the pitch-angle diffusion from a nearly monochromatic large-amplitude sub-element(s) can be much larger
than from an average wave field of the whole element. The
main focus of this study is on properties of nonlinear chorus
emissions which could be important for wave-particle interactions, i.e., fine structure of the chorus waves, direction of
propagation, polarization and magnitudes of the magnetic
field disturbances.

2.

Analysis of the GEOTAIL Data

We present first results on four time intervals of wave
activity during a substorm interval starting at ∼2307 UT of
April 29, 1993. A major negative excursion of the AL index
started at ∼2100 UT. Assuming chorus wave generation bygradient-drifting of 10–40 keV electrons, a delay time between the onset of chorus and a substorm is estimated as ∼2 hrs (Tsurutani and Smith, 1974). Equatorial daytime chorus is expected to have maximum intensity at ∼1000 LT due
to the dayside maximum of energetic electron precipitation.
This timing agrees with the beginning of rising tone chorus
observations by GEOTAIL around ∼930 LT. The satellite
was located in the near-equatorial magnetosphere at ∼(6.3,−4.7, 0.7RE ) (in GSE coordinates) and the geocentric distance of 7.9RE at the time of these observations. Intense
chorus emissions were observed with the PWI and WFC
instruments (Matsumoto et al., 1993; Nagano et al., 1996)
onboard GEOTAIL. The PWI (plasma wave instrument)
consists of a 3-component search-coil and 2 wire (elec-

625

626

O. P. VERKHOGLYADOVA et al.: PROPERTIES OF NONLINEAR RISING TONE CHORUS
Table 1. Properties of rising tone elements (see text for details).
Start time2306:55
2306:55
2311:39
2321:072349:312349:31

t, sec
0.3
0.15
0.3
0.68
0.7
0.6

ν1,2 , kHz
0.9, 0.5
0.75, 0.62
0.95, 0.55
1.1, 0.65
1.1, 0.65
1,
0.6

ν, Hz
220
130
400
450
450
400

ν0 , kHz
0.8
0.7
0.75
0.875
0.875
0.8

νce , kHz
3.44
3.44
3.51
3.50
3.03
3.03

Bmax , pT
80
70
200
300
100
100

θ, ◦
11
29
17
42
22
22

θG , ◦
62
66
65
60
55
58

θr , ◦
77
78
78
76
73
75

Fig. 1. Time-frequency power spectra of three magnetic field components in GSM coordinates derived from WFC measurements onboard GEOTAIL.
The beginning of the interval corresponds to 2306:55 UT of April 29, 1993. The left, central and right panels correspond to Bx , B y and Bz components.

tric) antennas with sensitivity of 1.5×10−5 nT/Hz1/2 for themagnetic field and 8.0×10−9 V/(m Hz1/2 ) for the electricfield, respectively. The WFC (wave form capture) receiversamples 8.7 sec snapshots every 5 min between 10 Hz and
4 kHz. For each of the four time intervals of ∼8.7 sec duration we select several distinct rising tone chorus elements.
Properties of 6 such elements are summarized in Table 1.
The following parameters were estimated: t is the duration of a rising tone element, ν1,2 are the maximum and minimum frequencies within the element, ν is the frequency
band (bandwidth at half-maximum), ν0 —average frequencyof the tone, Bmax —the maximum magnitude of magnetic
field disturbance in the chorus, θ —the propagation angle
to the local magnetic field line, θG —the local Gendrin angle calculated for ν0 , and θr is the resonance angle. Averagemagnetic field components measured at ∼2306:55 UT were(26.1, 52.1, 108.2 nT) is GSE coordinate system. An example of chorus is shown in Fig 1.
We process magnetic field waveforms in the principal or
the minimum variance analysis (MVA) frame to find direction of propagation of the waves (Tsurutani and Smith,1977), which corresponds to a direction of minimum variation. As it follows from the chorus generation mechanism,
the most intense elements correspond to waves generated
locally and propagating under small angles θ to the local
magnetic fieldline (see also Goldstein and Tsurutani, 1984).
Whereas waves generated far away have smaller magnitudes (due to Landau damping) and may be propagating
obliquely to the local magnetic field line. Our results inTable 1 show that observed intense chorus emissions propagate under relatively small angles to the local magnetic
field line. We found that chorus sub-elements sometimes
have different directions of propagation relative to the background magnetic field.
The maximum angle of electromagnetic wave propaga-

Fig. 2. A schematic view of the inner magnetosphere distorted by the solar
wind compression obtained with the Tsyganenko model (Tsyganenko,
2002). A projection into noon local time plane is shown. The projectionof the GEOTAIL spacecraft position into the (X Z ) plane is indicated bya small dot. “Minimum B pockets” are shown.

tion relative to the magnetic field line is the resonance angle,
cos(θr ) = ν/νce (Goldstein and Tsurutani, 1984), presented
in the last column of Table 1. The “Gendrin” angle, shownin the next to the last column of Table 1, is defined in linear
plasma theory and corresponds to a minimum value of therefractive index parallel to the magnetic field line and is defined locally as cos(θG ) = 2ν/νce (Gendrin, 1961). At thesame time, the Gendrin angle is the upper limit for the angle θ . The condition for angular region θ = ±θG indicatesa proximity to wave generation region for the lower-band

O. P. VERKHOGLYADOVA et al.: PROPERTIES OF NONLINEAR RISING TONE CHORUS

(a)

627

(b)

Fig. 3. (a) Example of magnetic field waveform of a chorus element shown in the principal frame. B1 , B2 and B3 denote the maxumum, intermediate
and minimum variance directions, respectively. Notice sub-elements separated by intervals of noise. (b) Instantaneous spectrum of the chorus
sub-element at t  2.585 sec obtained by using Morlet wavelet.

chorus (ν0 < 0.5νce ) (Lauben et al., 2002). The estimatedθG in the Table 1 are quite large and are not close to ±θ.
By the definition and given constant wave frequency, θGis larger in the areas of large background magnetic field, B0 ,and smaller in the “minimum B pockets” (Tsurutani andSmith, 1977). What was the Geotail position in the dipole
magnetic field? Figure 2 presents schematic view of thenoon local time cross-section of the inner magnetosphere in
the GSM coordinates. This sketch was produced with the
Tsyganenko model (Tsyganenko, 2002) under undisturbed
conditions. The beginning of the interval of Geotail observations was characterized by a very quiet ring current withminumum SYM-H  −10 nT. For this model application
we choose Dst = 0, IMF Bz = 0 and B y = 0 (in GSM) andthe solar wind dynamical pressure equal to 6 nPa. The magnetic dipole axis is tilted towards the X -axis of the GSM
coordinate system.
A distortion (compression) of the outer dayside magnetosphere field lines as compared to a dipole field is clearlyshown. Areas of minimum B0 are situated at high magnetic
latitudes and at large L (r > 6RE ). This sketch is similar tothat in Tsurutani and Smith (1977). The small dot on theright side of the plot is the GEOTAIL position in the (X Z )plane. The GEOTAIL GSM coordinates were ∼(6.3, −4.4,−1.7RE ). Thus, the satellite at the time of chorus measurements was located at the magnetic equator and away fromthe “minimum B pockets”.
We use FFT and Morlet wavelet analyses to study spectral properties of the chorus. The wavelet analysis is often applied to study spectral characteristics of a signal withvarying time frequencies (Torrence and Compo, 1998). We
use the Morlet wavelet with adjustable resolution in timeand frequency to calculate instantaneous spectra of chorus elements as well as standard wave spectra in the timefrequency variables. Distinct spectral features within chorus elements corresponding to sub-elements or wave packets were detected. Similar analysis was performed by Santolik et al. (2003, 2004) based on Cluster data. The peakfrequency in our study corresponds to about (0.15–0.4)νce(see Table 1). Thus, only the lower-band chorus elements(ν0 < 0.5νce ) were analyzed. Figure 3(a) shows an example
of one chorus element in the MVA frame consisting of wave
packets or sub-elements. One can notice that the wave iscircularly polarized. The spectrum of a chorus sub-element
is a narrow-band signal (Fig. 3(b)). Bandwidths at halfmaxima for the chorus elements are presented in Table 1.
The spectra of wave packets are narrower, and correspondto only a part of the riser element. Wavelet analysis revealed that the wave packet intervals showed small changes
in phase, and noise intervals showed large changes in phase.
The latter can be explained by random character of disturbances in noise intervals and corresponding rotations of thepolarization plane.
We estimate spectral wave intensities for a sub-element
and for the whole element presented in the first line of Table 1. Wave intensity of the wave packet is ∼5.7 10−3 nT2compared to ∼7.4 10−4 nT2 average over the whole element, showing increase by the factor of about 8. The ratioof the wave packet intensity to intensity of the inter-element
spacing (∼6 10−5 nT2 ) is thus about two orders of magnitude.

3.

Conclusions

The study addresses some properties of the rising tone
chorus emissions observed with PWI and WFC instruments
onboard GEOTAIL during a substorm of April 29, 1993.
Most of the chorus waves were found to propagate undersmall angles (∼11◦ –22◦ ) relative to the ambient magnetic
field lines. The waves were not propagating at the Gendrin
angles. GEOTAIL was located near the magnetic equatorand away from the “minimum B pockets” (Tsurutani andSmith, 1977). We use the Tsyganenko model to illustratethat the outer magnetosphere was compressed, even under very quiet conditions. Correct interplanetary data areneeded to map the “minimum B pockets” more accurately.
These waves are nearly parallel propagating and are presumably generated close to the GEOTAIL location at large
L in the vicinity of the near-equatorial magnetopause. Tim-

628

O. P. VERKHOGLYADOVA et al.: PROPERTIES OF NONLINEAR RISING TONE CHORUS

ing of the chorus observation correspond roughly to timedelays of substorm electrons drifting from the midnight sector. There is a possibility that magnetospheric compression
due to the solar wind ram pressure enhances chorus generation at large L-shells (Zhou et al., 2003). Chorus can be intensified by drift-shell splitting. These mechanisms require
further studies.
Chorus emissions show distinct fine structure with wave
packets separated by intervals of noise (Santolik et al.,2003). We apply FFT and Morlet wavelet transforms toestimate spectral wave intensities for a wave packet or subelement and the whole element. It is shown that the chorus
emissions have higher intensities (>10−3 nT2 ) inside subelements compared to the average intensity of the wholeelement by the factor of ∼8.
Acknowledgments. Work of O.V. at RISH, Kyoto University was
supported by JSPS Fellowship.

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1029/2002JA009701, 2003.
O. P. Verkhoglyadova (e-mail: olgav@ucr.edu), B. T. Tsurutani, Y.
Omura, and S. Yagitani

LETTER

Earth Planets Space, 61, 629–631, 2009

Proxy for the ionospheric peak plasma density reducedby the solar zenith angle
T. L. Gulyaeva1,2
1 IZMIRAN, 142190 Troitsk, Moscow Region, Russia
2 Space Research Centre PAS, Bartycka 18-A, 00-716 Warsaw, Poland(Received October 17, 2007; Revised January 25, 2008; Accepted March 19, 2008; Online published May 29, 2009)

The F2 layer peak plasma density Nm F2 is reduced by the factor constructed from the relative changes in the
Sun’s zenith angle χ for a particular local time and the local noon value χ0 . Proposed transformation yields
a proxy for the peak plasma density which coincides with the source observation at noon but apart from thelatter is gradually reduced towards the night. Hourly observations at 8 ground based ionosondes for the solar
maximum (2000) and minimum (2006) are analyzed for inter-stations and inter-seasonal correlation of the peakplasma density and the proxy values. The proxy values show improved correlation between the data at different
locations and improved inter-seasonal correlations for a particular location due to greater homogeneity of results
throughout the year contributing to improved evaluation of the ionospheric weather indices.
Key words: Ionosphere, plasma density, solar zenith angle.

1.

Introduction

Diurnal and seasonal changes of the plasma density andtemperature in the ionosphere depend directly on the illumination of the upper atmosphere by the Sun. The features of the peak plasma density, Nm F2 , m−3 , proportional
to square of the ionospheric critical frequency f o F2 can bemade more uniform if the effect of the solar grazing incidence on the plasma density in the F region could be reduced with a proper transformation.
Earlier, the relevant relations of the noon F2 layer critical frequency have been investigated for the magnetic conjugate locations at the ends of the magnetic line of force
assuming that daytime temperature of the neutral gas is
proportional to the cosine of the Sun’s zenith angle at local noon (Rotwell, 1962). The correction factor deduced
for such relation, so called “M-factor” has been used forconstructing the global model of the noon f o F2 critical frequency from the data of global network of ionosondes (Besprozvannaja, 1970, 1987) and the monthly ionospheric index M F2 (Mikhailov and Mikhailov, 1995). However, thisapproach is valid only for the local noon while relevanttransformation for all times throughout the day is required.
The solar zenith angle determines proportions of daytime
and nighttime conditions in the ionosphere at different altitudes over the Earth (Gulyaev and Gulyaeva, 1984) with
relevant plasma density and temperature controlled by theenergy transmitted from the Sun in the form of an electromagnetic wave radiation in the UV/EUV ranges to the upper atmosphere (Chapman, 1931). The solar zenith angle
dependence as predicted by the Chapman ionization theory
cannot thoroughly explain spatial and temporal variationsc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

of the ion density by the factors such as plasma production due to UV/EUV alone, differential loss due to varying
recombination rate, transport, neutral winds, atmosphericcomposition. The energy input from the magnetosphere in
the form of electric fields and charged particle precipitation due to the solar wind also contributes significantly tothe changes of the peak plasma density (Lal, 1997). If thedominant effect of the solar zenith angle on the ionosphericplasma density could be reduced by a proper transformation, an improved metric of the solar-controlled behaviourof the plasma around the peak of the F2 layer can be obtained.
In the present paper, the variations in the Sun’s zenith
angle are used to produce a proxy for the peak plasma density, Np F2 , by multiplying the observed peak plasma density Nm F2 by a factor related with the solar zenith angle χ ata particular time and the local noon value χ0 . This process
is evaluated with the data of eight ground based ionosondes
at solar minimum (2006) and maximum (2000) to illustrate
the advantages of the reduced peak plasma density as compared with the source observations that will be useful for
applications in the ionosphere modeling and forecasting.

2.

Technique of Inversion of the F2 Layer Critical
Frequency by the Solar Zenith Angle

The solar zenith angle χ reaches peak at the local midnight tending to a minimum at the local noon. Impact of thelocal conditions of the Sun’s illumination can be excluded
by normalizing the peak plasma density Nm F2 by the solar
zenith angle χ in radians. Change of the normalizing factor 1/χ from day to night is shown by the dashed line withtriangles in Fig. 1.
The multiplier 1/χ is larger when the solar zenith angle
gets smaller and in the limit of noon between the north andsouth tropics as χ approaches zero, 1/χ tends to infinity.

629

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T. L. GULYAEVA: PROXY FOR THE PEAK PLASMA DENSITY
Table 1. Geodetic and geomagnetic coordinates (latitude and longitude)of the ionosonde stations providing data used in the present paper.
Station
Sodankyla
Julius-Rugen
ChiltonMoscow
TortosaRome
El Arenosillo
Wakkanai

Geodetic
Lat
Lon
◦N
◦E
67.4
026.6
54.6
013.4
51.6
358.7
55.5
037.3
40.4
000.3
41.8
012.5
37.1
353.3
45.4
141.7

Magnetic
Lat
Lon
◦N
◦E
63.6
120.8
54.3
099.7
54.1
083.2
50.4
123.2
43.6
080.9
42.3
093.2
41.4
072.3
35.5
207.3

Fig. 1. Correction factor deduced from the solar zenith angle.

To avoid this singularity, we introduce the second orderpolynomial approximation of the best least square fit to 1/χ
for the angles of χ > 1 rad. as follows:z(χ ) = γ (x 2 − βx + α)(1)where x = χ ◦ /100, α = 3.8749, β = 3.5402, and γ =0.4444 and z(χ ) is given in solid line in Fig. 1.
Multiplying Nm F2 by the coefficient z(χ) yields reducednighttime and sunrise/sunset values but tends to increase thedaytime values, particularly in summer towards the equatorwhen z  1. To equilibrate such opposite effects for day
and night we replace multiplier in Eq. (1) by the normalizing factor C(χ , χ0 ) equal to the ratio of the coefficient of
Eq. (1) for given local time to the value for local noon:
Fig. 2. Monthly median of observed peak plasma density Nm F2 at Chilton
C(χ , χ0 ) = z(χ )/z(χ0 ).

(2)

and proxy Np F2 reduced by the solar zenith angle for four seasons at thesolar minimum 2006.

With the normalizing factor defined in terms of coefficients α and β we obtain the proxy Np F2 for the peak solar minimum: spring (March), summer (June), autumn
plasma density Nm F2 by multiplying the latter by C(χ , χ0 ): (September) and winter (December) 2006. The source me(3) dian and the proxy median coincide at noon. The diurNp F2 = C(χ , χ0 ) × Nm F2 .
nal curve of Np F2 become rather uniform throughout the
The resultant Np F2 coincides with the source value Nm F2 year gradually reduced from day to night which corresponds
at noon (C0 = 1) but it is essentially reduced towards to reduced income of the ionizing radiation from the Sun
the night when coefficient C(χ , χ0 ) tends to zero depicting (Gulyaev and Gulyaeva, 1984). The sunrise minimum ofa reduced maintenance of nighttime ionization compared Nm F2 is smoothed in the diurnal change of Np F2 . The diwith its noon value. Thus, all regularities of the noon peak urnal variation is particularly improved at summer when it
plasma density Nm F2 (Besprozvannaja, 1987; Williscroft became similar to Np F2 variation for other seasons.
The hourly values of Nm F2 and Np F2 for four seasons are
and Poole, 1996) are valid for Np F2 . However the reduced
used for each pair of stations of Table 1 and the mean of allvalues of Np F2 at other times are significantly changed.
correlation coefficients are computed. In Table 2, the inter3. Validation of the Proxy for the Peak Plasma location correlation coefficient r2 is presented for selected
Density with Ground Based Ionosonde Datamonths at solar maximum (2000) and minimum (2006).
The above transformation is applied to daily-hourly ob- Improved correlation between the stations data is obtained
servations at 8 ionospheric stations listed in Table 1 for the with the proxy values in all cases. The most appreciable
solar maximum (2000) and minimum (2006). The solar improvement of r2 is obtained for the summer solstice when
zenith angle was calculated for given day of year, geode- the dominant is daytime process of the ion production due
tic coordinates of ionosonde site and local time with the to solar illumination during the day.
standard subroutine SOCO (McNamara, 1986) of the InterWhile the improvement in the correlation of the data fromnational Reference Ionosphere code (Bilitza, 2001).
different stations has been the primary goal of implementaFigure 2 shows the monthly median at Chilton for the tion of Eq. (3), the results reveal also an improved the intersource Nm F2 and reduced Np F2 for 4 seasons during the seasonal correlation coefficient r1 for each station in Ta-

T. L. GULYAEVA: PROXY FOR THE PEAK PLASMA DENSITY
Table 2. Mean inter-station correlation coefficient for observed Nm F2
and proxy Np F2 for the peak plasma density at solar maximum andminimum for four seasons/months.
Year
Month
03
06
09
12

2000
Nm F2
0.841
0.521
0.653
0.827

2006
Np F2
0.906
0.834
0.814
0.881

Nm F2
0.801
0.478
0.771
0.756

Np F2
0.888
0.802
0.883
0.856

631

The advantages of the proposed approach proved to be
useful for reconstruction of missed ionosonde observationsof the critical frequency f o F2 with the data of another station using the cloning technique discussed in (Gulyaeva etal., 2008) so that the complete daily/hourly data sets for selected location/season/month are available for derivation of
the ionospheric weather indices.

4.

Conclusion

In this study, a new technique for obtaining a proxy forthe ionospheric peak plasma density is proposed. The corTable 3. Inter-seasonal correlation coefficient averaged for all stations for
Nm F2 and Np F2 at solar maximum (2000) and solar minimum (2006) rection factor depends on ratio of the solar zenith angle atthe time of observation to its local noon value. The noon
for two pairs of months.
values of the normalized peak plasma density coincide with
Year
2000
2006
observations of Nm F2 but Np F2 is gradually reduced fromMonths
Nm F2
Np F2
Nm F2
Np F2
day to night throughout the year for all observations ana03∼12
0.824
0.938
0.641
0.880
lyzed at eight ionospheric stations for the maximum and
06∼09
0.298
0.858
0.528
0.885
minimum of solar activity. The normalization of the peakplasma density improves not only the correlation coefficient
between the data of different stations but also the interseasonal correlation for the data of a particular station.
The proposed technique of inversion of the peak plasma
density by the solar zenith angle presents physically justified replacement of the variable by a proxy value of significantly improved characteristics. The proposed proxy parameter exhibits diurnal/seasonal homogeneity of the peakelectron density which is one of the key parameters of modern ionospheric models.

Fig. 3. Inter-seasonal relation for September versus June 2006 for observed peak plasma density Nm F2 (upper panel) and for proxy Np F2(lower panel) at Wakkanai.

ble 1. The averages of the correlation coefficients r1 are provided in Table 3 for all stations referring to selected monthsof March–December and June–September at the solar maximum and minimum. The proposed technique brings improved inter-seasonal correlations for Np F2 as comparedwith Nm F2 , particularly, for the June–September pair ofmonths due to the most appreciable changes in Np F2 forthe summer solstice.
Figure 3 illustrates inter-seasonal relation for June–
September at Wakkanai between the hourly values of Nm F2(upper panel) and Np F2 (lower panel) at solar minimum,
2006. It is evident that regression between the data for 2
different seasons (summer and equinox) is improved in theproxy data set as compared with the observed Nm F2 . It is
expected that proposed transformation of the F2 layer peakdensity depicting more uniform daily/seasonal variation ascompared with the observations would be helpful for themodelling and forecasting purposes than the more sophisticated day-to-day and hour-to-hour changes of the source
Nm F2 data.

Acknowledgments. The ionospheric data used in the present
study are provided via internet from WDC A for STP, Boulder,
CO, USA; WDC C1, Oxford, UK; IZMIRAN, Moscow, Russia;
SGO, Sodankyla, Finland; WDC for Ionosphere, NICT, Tokyo,
Japan. The author thanks two anonymous referees for useful comments. The author is grateful to Feza Arican for her comments andassistance in improvements to the paper.

References
Besprozvannaja, A. S., On a nature of the seasonal anomaly of the F2 layernoon ionization, Geomagn. Aeronomy, 10, 986–992, 1970.
Besprozvannaja, A. S., Peculiarities of the regular F2 layers, Geomagn.
Aeronomy, 27, 728–734, 1987.
Bilitza, D., International Reference Ionosphere 2000, Radio Sci., 36(2),261–275, 2001.
Chapman, S., Absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth, Proc. Phys. Soc.,
London, 43, 26–45, 1931.
Gulyaev, R. A. and T. L. Gulyaeva, On illuminating the ionosphere by
sunlight during nighttime, Geomagn. Aeronomy, 24, 347–348, 1984.
Gulyaeva, T. L., I. Stanislawska, and M. Tomasik, Ionospheric weather:
Cloning missed foF2 observations for derivation of variability index,
Ann. Geophys., 26, 315–321, 2008.
Lal, C., Contribution to F2 layer ionization due to the solar wind, J. Atmos.
Solar-Terr. Phys., 59(17), 2203–2211, 1997.
McNamara, L., Private communication, 1986.
Mikhailov, A. V. and V. V. Mikhailov, A new ionospheric index MF2, Adv.
Space Res., 15(2), 93–97, 1995.
Rotwell, P., Charged particles in the Earth’s magnetic field and the ionospheric F2-layer, J. Phys. Soc. Japan, 17, Suppl. 1, 263–267, 1962.
Williscroft, L.-A. and A. W. V. Poole, Neural networks, foF2, sunspot
number and magnetic activity, Geophys. Res. Lett., 23(24), 3659–3662,
1996.
T. L. Gulyaeva (e-mail: gulyaeva@izmiran.ru)

LETTER

Earth Planets Space, 61, 633–635, 2009

Investigation of ionospheric gradients for GAGAN application
K. Ravi Chandra, V. Satya Srinivas, and A. D. Sarma
Research and Training Unit for Navigational Electronics, Osmania University, Hyderabad, India(Received October 29, 2007; Revised July 21, 2008; Accepted September 28, 2008; Online published May 29, 2009)

To cater to the needs of aviation applications, GPS Aided GEO Augmented Navigation (GAGAN) system isbeing implemented over the Indian region. The most prominent parameter affecting the navigation accuracy of
GAGAN is ionospheric delay which is a function of TEC. In the equatorial and low latitude regions such as
India, TEC is often quite high with large spatial gradients. Carrier phase data from the GAGAN network ofIndian TEC Stations is used for estimating ionospheric gradients in multiple viewing directions. Rate of TEC(ROT) and Rate of TEC Index (ROTI) are calculated to identify the ionospheric gradients. Among the satellite
signals arriving in multiple directions, the signals which suffer from severe ionospheric gradients are identified
and avoided for improving GAGAN positional accuracy. The outcome of this paper will be helpful for improving
GAGAN system performance.
Key words: GAGAN, ionospheric gradients, ROT, ROTI.

1.

Introduction

The Global Positioning System (GPS) is a navigation
system which provides continuous positioning and timing
information under all weather conditions. As the accuracyof the stand alone GPS is not sufficient for category I (CATI) precision approach, Space Based Augmentation Systems(SBAS) are evolved to cater to the needs of aviation applications. GPS Aided GEO Augmented Navigation (GAGAN)
is one such system planned in India. The most prominenterror affecting the accuracy of GAGAN is the ionosphericdelay. The ionosphere is decorrelated with distance and as
well as with time causing anomalies. For reliable communication, navigation and surveillance systems, ionosphericgradients need to be thoroughly investigated for improving
the performance. The purpose of the gradients is to identify
the satellite signals, which are gradient-free in their direction of propagation. As a result, precise TEC data can beobtained from among the visible satellites in multiple directions. To achieve this objective, initially the satellite signals which do not severely suffer from the gradient effects
are identified. Subsequently, among the identified satellite
signals the best four are considered for accurate positional
information using the Dilution of Precision (DOP) approach(Parkinson et al., 1996). Jean-Marie (2006) referred DOP
as the effect of ‘geometry of satellites’ on measurement accuracy. Gang et al. (2003) have proposed a new method‘Cumulative sum’, which quickly and reliably detects small
but hazardous gradients for Local Area Augmentation System (LAAS) scenario. Walter et al. (2004) reported the effects of large ionospheric gradients on single frequency airborne smoothing filters for Wide Area Augmentation System (WAAS) and LAAS, and also their mitigation techc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

niques. Warnant and Pottiaux (2000) also made an attempt
to identify possible correlations between the ionospheric activity and unidentified problems in GPS data processing by
duly detecting the travelling ionospheric disturbances. In
this paper the estimated ROT and ROTI (TECu/min) of all
visible satellites are used to identify signals which sufferfrom severe ionospheric gradients.

2.

Results and Discussion

In the GAGAN network 20 TEC stations are installed
to monitor the ionospheric behavior. The data from oneof these TEC stations (Lucknow, Lat. 26.76◦ N, Long.
80.88◦ E) is used for this analysis. The processed GPS datacontains 23 parameters. Out of these only seven parameters,
namely user position, PRN number of satellite, GPS weeknumber, GPS seconds of the week, elevation angle, azimuth
angle and TEC are used in the analysis.
Several days of data corresponding to both quiet anddisturbed days are analyzed. However, in this paper the datafrom various visible Satellite Vehicles (SVs) corresponding
to a typical disturbed (7 < K P < 8) day (25th July, 2004)
is processed and analyzed for identifying the ionosphericgradients. The sampling rate of data is 1 minute.
The rate of change of the ionospheric delay (ROT) due tosatellite signals received at the receiver is given as (Warnant
and Pottiaux, 2000)
ROTku (ti ) =TECku (ti ) − TECku (ti−1 )(TECu/ min).
ti − ti−1(1)

Where ROTku (ti ) = Rate of TEC estimated at time epoch ti
by receiver (u) on satellite (k), TECku (ti ) and TECku (ti−1 ) =Total Electron Content measured by receiver (u) on satellite(k) at epoch ti and epoch ti−1 respectively.
ROT is a function of K p , viewing direction and magnetic
activity. Secondly, these ROT values are converted fromslant to vertical using a standard mapping function M(E)

633

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K. RAVI CHANDRA et al.: INVESTIGATION OF IONOSPHERE

(a)

(a)

(b)

(b)

(c)

(c)

Fig. 1. Variation of vertical ionospheric gradient for all visible multiple
viewing satellites based on Lucknow GAGAN network TEC stations(25th July, 2004) over a local time period (17:00–19:00 Hrs).

Fig. 2. Variation of ROTI for all visible multiple viewing satellites basedon Lucknow GAGAN network TEC stations (25th July, 2004) over a
local time period (17:00–19:00 Hrs).

(Guochang, 2003)

ROT. ROTI is standard deviation of ROT and is given
as (Krankowski et al., 2005)

M(E) = 1 −RERE + h1/2

2
cos2 E.

(2)

Where E = Elevation angle at the reference station(in degrees),h = Altitude of the ionospheric shell above thesurface of the Earth (350 Km)
RE = Earth radius (6378 Km).
The slant ROT is averaged over 10 minutes to obtain

ROTI =


ROT2 − ROT2 (TECu/ min)(3)

ROTI measurements can be used to predict the presence ofionospheric scintillation also (Basu et al., 1999). Its values
signify the presence of only temporal gradients. In order
to identify spatial gradients, Jiyun et al. (2006) proposed a‘Time step method’. By considering the distance between
the Ionospheric Pierce Point (IPP) at epoch ti and IPP at
epoch ti−1 , the vertical ionospheric gradient (σVIG ) is esti-

K. RAVI CHANDRA et al.: INVESTIGATION OF IONOSPHERE

mated asσuk VIG (ti ) =TECku (ti ) − TECku (ti−1 )Dti ,ti−1(mm/Km).

(4)

Where Dti ,ti−1 = Distance between the IPPs corresponding
to time epochs ti and ti−1 .
As the delays due to different epochs were considered
and divided by the corresponding separation, the estimatedσVIG is a combination of both temporal and spatial gradients.
The typical data from various visible satellites corresponding to two hours (Local time: 17:00–19:00 Hrs) areprocessed and analyzed. Variations of σVIG with respect
to local time are presented for selected visible satellites(Fig. 1). At 17.08 Hrs, eight satellites are visible. Afterabout 17.74 Hrs, SV 20 and after 17.91 Hrs, SV 16 havegone out of sight and only six satellites are visible. Afterabout 18.24 hours, the SV 8 has come in to line of sight toreference station. Hence, there exists a corresponding traceof ROTI curve after 18.24 hour onwards. From the data, it
is evident that, at any point of time GPS receiver is in line ofsight with a minimum six and a maximum eight satellites.
To investigate the effect due to temporal gradients, variationof ROTI with respect to local time is presented for all visible satellites (Fig. 2). It is shown that for the entire time
period ROTI and σVIG for SVs 1, 13, 16, 19, 20, 23 and 27
has not exceeded the maximum values of 0.085 TECu/min(PRN 16) and 0.177 mm/Km (PRN 27) respectively. Further, there are no abrupt changes in the plots. It signifies that
impact of ionospheric anomalous activity (7 < K p < 8) on
different viewing SVs has the similar effect. Except for a
few epochs, SVs 3 and 8 also show similar trend. At local
time of 18.41 Hrs, both ROTI (0.1238 TECu/min) and σVIG
(0.4047 mm/Km) are identified to be the maximum due to
PRN 8. From both Figs. 1 and 2, it is observed that, the plots
exhibit similar trend. It signifies that even though σVIG is acombination of both temporal and spatial gradients, the roleof temporal gradients seem to be predominant. The reason
for this could be less spatial variation between the successive IPPs. This is in turn based upon the radial movement ofsatellite (angular velocity of approx. 3.9 Km/sec) and user.
On estimation of gradients an attempt is made to improve
the accuracy and integrity of user position. As example estimation, a time epoch of 17.08 Hrs is considered. Out of all
the visible satellites, σVIG values of SV 3 (0.2378 mm/Km)
and SV 27 (0.1777 mm/Km) are found to be relatively
higher than the rest of the SVs. Therefore, the signals fromthese two SVs are avoided. Consequently, among the available SVs, only six will remain. Among these six SVs, thebest four are chosen, based on DOP geometry for accurate
position estimation. Since there are six visible satellites
DOP geometry is to be checked only for 15 combinations

635

of four satellites. In this way we are able to avoid the signals affected by ionospheric gradients and also minimize
the DOP computations from 70 to 15 for selection of thebest 4 SVs.

3.

Conclusions

In order to provide accurate position as well as integrity
information, investigation of ionospheric gradients is necessary for GAGAN applications. The outcome of this work
can be extended for the LAAS system for improving performance of Required Navigation Performance (RNP) parameters viz. accuracy, availability, integrity and continuity toachieve CAT II accuracy requirement of civil aviation applications. This paper emphasizes that, precise estimation andidentification of ionospheric gradients over a low latitude
region is necessary to achieve better accuracies. This will
help to identify relatively gradient-free propagation paths,
among the multiple viewing directions of satellites. Subsequently, among the available satellite signals the best four
can be chosen to achieve best DOP value for improving positional and integrity information.
Acknowledgments. The research work presented in this paper
has been carried out under the project entitled “Analysis and modeling of Indian Ionospheric Electron Content for GPS Applications” funded by ISRO, Bangalore, Vide Order No. CAWSES:05,
Dated: 28th December, 2005.

References
Basu, S., K. M. Groves, J. M. Quinn, and P. Doherty, A comparison of
TEC fluctuation and scintillation at Ascension Island, J. Atmos. Sol.
Terr. Phys., 61, 1219–1226, 1999.
Gang, X., S. Pullen, M. Luo, and P. Enge, Detecting Ionospheric Gradients with Cumulative Sum (CUSUM) Method, American Institute of
Aeronautics and Astronautics, Inc. (AIAA 2003-2415), 2003.
Guochang, Xu., GPS Theory, Algorithms and Applications, SpringerVerlog, Berlin, Germany, 2003.
Jean-Marie, Z., Essentials of Satellite Navigation, Ublox compendium,
GPS-X-02007-C, 2006.
Jiyun, L., S. Pullen, S. Datta-Barua, and P. Enge, Assessment of Nominal
Ionosphere Spatial Decorrelation for LAAS, IEEE/ION PLANS 2006,
pp. 506–514, 2006.
Krankowski, A., I. I. Shagimuratov, Lubomir, W. Baran, and I. I. EphishoV,
Study of TEC fluctuations in Antarctic Ionosphere during storm using
GPS observations, Acta Geophysic Apolonica, 53(2), 205–218, 2005.
Parkinson, B. W., GPS Theory and Applications, pp. 81–114, American
Institute of Aeronautics and Astronautics, Inc, Volume I, Washington,
1996.
Walter, T., S. Datta-Barua, J. Blanch, and P. Enge, The Effects of Large
Ionospheric Gradients on Single Frequency Airborne Smoothing Filters
for WAAS and LAAS, Institute of Navigation’s National Technical Meeting, San Diego CA, January 2004.
Warnant, R. and E. Pottiaux, The increase of the ionospheric activity as
measured by GPS, Earth Planets Space, 52, 1055–1060, 2000.
K. Ravi Chandra, V. Satya Srinivas, and A. D. Sarma (e-mail:ad sarma@yahoo.com)

LETTER

Earth Planets Space, 61, 637–641, 2009

The total failures of GPS functioning caused by the powerful solar radio burst
on December 13, 2006
E. L. Afraimovich, V. V. Demyanov, and G. Ya. Smolkov
Institute of Solar-Terrestrial Physics, the Russian Academy of Sciences, the Siberian Branch, 664033, Irkutsk, Russia(Received October 23, 2007; Revised July 6, 2008; Accepted August 21, 2008; Online published May 29, 2009)

We investigated failures in the GPS performance produced by extremely dense solar radio burst fluxes associated with the intense (X3.4 in GOES classification) solar flare and Halo CME recorded by SOHO/LASCO on
December 13, 2006. According to substantial experimental evidence, high-precision GPS positioning on the entire sunlit side of the Earth was partially disrupted for more than 12–15 min; the high level of GPS slips resulted
from the wideband solar radio noise emission. Our results are in agreement with the data obtained recently for theextreme solar radio burst on December 6, 2006, and provide a sound basis for revising the role of space weather
factors in the functioning of state-of-the-art satellite systems and for taking a more thorough account of thesefactors in their development and operation.
Key words: Solar flares, solar radio emission, GPS, GLONASS, GALILEO.

1.

Introduction

Strong solar activity observed on December 6 and 13,
2006; i.e., during the solar cycle 23 minimum, was absolutely unexpected. Its study and analyses of the consequences for the space environment are not complete yet.
This kind of solar activity is of great interest not only to astronomers and radio astronomers, but to other scientists andengineers, as well. The broadband solar radio emission following the flare exceeded powerful solar radio bursts in all
known flares by at least two orders of magnitude (Cerruti etal., 2006a, b; Carrano et al., 2007; Carrano and Bridgwood,
2008; Gary, 2008).
The powerful solar radio burst (SRB) on December 6,
2006, led to failures in the functioning of wideband satellite
radio systems including the GPS. The functioning failuresand deep damping of GPS signals were registered at certain
standard GPS receivers and specialized monitors of ionospheric scintillations in the L range (Cerruti et al., 2006a, b;
Carrano et al., 2007; Carrano and Bridgwood, 2008; Kintner, 2008). However, worldwide failures of the GPS due toextreme solar activity in December 2006 are still a matterof debate. Meanwhile, this problem is of doubtless scientific and practical interest as regards to the estimation of thespace weather effect on the functioning of one of the mostpowerful and reliable satellite systems considered practically impregnable. Using data from the global network ofdual-frequency GPS receivers, Afraimovich et al. (2007)
found significant evidence that the high-precision GPS positioning on the entire sunlit side of the Earth was paralyzed
for more than 10 minutes on December 6, 2006.
There are many published papers regarding the GPS failc The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

ure during the 2006 December 6 SRB (see References). But
we do not know any publications on the GPS failure during
the 2006 December 13 powerful SRB, although the radio
flux F(t) was strong enough for both bursts. In this study,
we investigate global failures of the GPS performance dueto the 2006 December 13 SRB.

2.

The Solar Radio Bursts on 13 December 2006
(Concise Description)

Complex, and especially large, microwave bursts wererecorded from 02:21 to 04:37 UT, exhibiting weakening
with time. A type II burst (02:27–02:44 UT) was followed
by a type IV radio burst that ended at 10:12 UT (signaturesof wideband solar radio noise emission and disturbances ofthe solar corona). This radio emission is associated with
X-type flare and Halo CME. The latter commenced at
02:18:30 UT (first seen by the LASCO C2 at 02:54 UT andby the LASCO C3 at 03:18 UT; the C3 occulting disk was
fully surrounded by 03:42 UT, the mean plane-of-the-sky
speed was ∼1440–1800 km/sec). The events with MHD
fast-mode shock wave (type II) and plasmoid ejection (HaloCME) are confirmed by observations with the EUV Imaging Spectrometer on-board the Hinode satellite (Asai et al.,2008). Such radio emission was associated with an X-type
flare, proton storms, and Halo CME. The said events started
and developed at different time intervals and stages of theflare and at different heights in the solar atmosphere.
The flare occurred at the apparent collision site between
the large opposite polarities of the umbral magnetic fieldof AR 10930. The polarity inversion line at the collisionsite became very complicated and unsteady due to highly
sheared magnetic fields caused by the rotation and W-to-E
motion of emerging fluxes. The fine structure of magnetic
fields at the flare site changed with time: some parts ofthe complicated polarity inversion line disappeared, andthen the azimuthal angle of the magnetic fields changed

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E. L. AFRAIMOVICH et al.: GPS FUNCTIONING FAILURES CAUSED BY THE POWERFUL SOLAR RADIO BURST

GPS frequencies ( f 1 = 1575.42 MHz and f 2 = 1227.60
MHz) at 2:20–2:28 UT (corresponding to the type II radio burst) and 3:30–3:38 UT (corresponding to the type IV
radio burst). Klobuchar et al. (1999) predicted that solar
radio bursts could affect GPS performance if a solar flux
was sufficiently large in the L band frequency range andhad a RHCP—to which polarization GPS antennas are receptive. Therefore it is important first to know data of solar radio flux with RHCP, especially near the auxiliary GPS
frequency f 2 (see below Section 5.2).
Data from the Nobeyama Radio Polarimeters (http://
solar.nro.nao.ac.jp/norp/html/event/20061213 0247/) showthat the RHCP solar radio emission on December 13, 2006
exceeded 1.47·105 sfu at 1 GHz at 02:28:09 UT, exceeding
2.57·105 sfu at 2 GHz at 03:35:51 UT (Fig. 1(a), thick grayline and black line, respectively). The sharp impulses of thesolar radio flux can be noted in the first interval, 02:20 to
02:28 UT (symbol A), and in the second interval, 03:30 to
03:38 UT (symbol B). The vertical dashed lines correspondto the centre of time intervals A and B.

3.

Fig. 1. The relative number of GPS sites W (t) where the 30-s count omissions were observed during December 13, 2006, solar radio bursts: (a)the flux F(t) of the RHCP radio emission observed by the Nobeyama
Radio Polarimeters at 1 GHz and at 2 GHz; thick gray line and blackline, respectively; logarithmic scale. The vertical dashed lines correspond to the centre of time intervals A and B. About the marks A and
B look in the text. (b) region R3 , Australia; region R0 , GPS world network, and region R1 , Western Asia, gray line, thick gray line and blackline, respectively, all PRN; (c) region R0 , GPS world network, PRN
13 and 28, thick gray line and black line, respectively; (d) region R2 ,GEONET, PRN 13 and 22, thick gray line and black line, respectively;(e) time dependences of elevation angle θ (t) for different PRN and selected GPS sites KARR, ALIC, TOW2, region R3 , Australia (dots);
empty time intervals correspond to the count omissions.

by ∼90◦ in those areas, becoming more spatially uniform
within the collision site (Kubo et al., 2007; Su et al.,2007). In such circumstances the Right Hand Circular
Polarization (RHCP) of microwave bursts can only be
registered in certain intervals of the flare time. This wasclearly confirmed by observations of total fluxes andcircular polarity at the Nobeyama Radio Polarimeters(see Fig. 1(a)) and fixed-frequency observations of total
fluxes in other observatories (RSTN Learmonth, Palehua,
http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarradio.html).
Moreover, the circular polarity of microwave bursts during
the X3.4 flare in December 2006 could also change dueto the reversal of the circular polarity sign when the radio
emission was propagating across a fragmented magnetic
field.
This study is focused on the microwave band of two

Method for GPS Data Processing

We use the GLOBDET software developed at the
ISTP SB RAS to treat GPS data from the global network of dual-frequency receivers (Afraimovich et al.,
2000; Afraimovich, 2000). Our database of the GPS
network’s RINEX files includes data from over 1500
GPS sites (http://sopac.ucsd.edu/other/services.html). We
also complement data from the Japanese GPS network
GEONET (about 1225 sites in all) (ftp://terras.gsi.go.jp/
data/GPS products/). At present, it is the largest regional
GPS network in the world.
Figure 2 presents the geometry of the global networkof GPS receivers in the Earth sunlit side ((a), (b), graycircles) and GEONET geometry ((b), black triangles) on
December 13, 2006. The names of the sites are not given,
for reasons of space. It is clear that the level of solar noiseinterference depends on the Sun zenith angle χ (Carrano
et al., 2007). We have examined this dependence. The
rectangles mark different regions (R0 –R3 ) with different
zenith angles χ . Asterisks show the location of sunlit points
for December 13, 2006, at 02:30 and 03:30 UT. The bold
triangles on Fig. 2 (region R3 , Australia) mark selected GPS
sites KARR, ALIC, TOW2.
In order to estimate the GPS performance we used different methods for processing RINEX files described by
Afraimovich et al. (2002). For all n lines of sight (LOS)
between the GPS world network receivers and satellites wecalculate the relative number of GPS sites W (t)%, where
the 30-s count omission for GPS satellites with their pseudo
random noise (PRN) code number (Hofmann-Wellenhof etal., 1992) was simultaneously observed at two GPS frequencies f 1 and f 2 .
In addition, for all LOSs between GEONET/GPS receivers and PRN, we calculated the relative density Q(t)%of measurement slips of main GPS-signal parameters: L 1 ,L 2 are the phase delay, and P1 , P2 the group delay for f 1
and f 2 , respectively. A measurement slip was registeredwhen the current 30-s count of corresponding GPS parameters equaled zero or the current 30-s count of all parameters

E. L. AFRAIMOVICH et al.: GPS FUNCTIONING FAILURES CAUSED BY THE POWERFUL SOLAR RADIO BURST

639

Fig. 3. The relative density of slips of phase (L) and group (P) GPS delay
measurements Q(t) during the solar radio burst on December 13, 2006;
GEONET, Japan; L 1 , L 2 —(b), (a); and P1 , P2 —(d), (c), respectively.
GPS signal parameters registered by TRIMBLE-5700 receivers (thinblack lines) and by TRS-LEGACY receivers (thick gray lines). For
TRS-LEGACY parameters L 1 and P1 number of slips Q(t) = 0 duringwhole duration of radio burst.

Fig. 2. The geometry of global network of GPS receivers in sunlit sideof the Earth ((a), (b), gray circles) and GEONET geometry in Japan((b), black triangles). The names of the sites are not given for reasonsof space. The rectangles mark different region (R0 –R3 ) with different
Sun zenith angles χ . Stars at Australia map R3 show the location of thesunlit points for December 13, 2006, on 02:30 and 03:30 UT; the bold
triangles mark selected GPS sites KARR, ALIC, TOW2.

was entirely absent. The measurement slip of L 2 and P2
implies an impossibility of precise positioning in the dualfrequency mode; hence an incorrect determination of coordinates is possible in single-frequency mode. However,positioning in general is impossible if the signal at oneof the GPS frequencies is not registered at all (HofmannWellenhof et al., 1992).
We also defined the corresponding maximum values
Wmax % and Q max %. The time resolution of the W (t) dependence, 30 s, allowed us to compare in detail the W (t)and Q(t) values with those of the solar radio emission flux.
We obtained data for all LOSs with an elevation angle θ between the direction along the LOS and terrestrial surface at
the reception site of over 5◦ .

4.

Results

Figure 1(e) illustrates the process of registering the 30-s
count omission for different PRN and selected GPS sites—
KARR, ALIC, TOW2—located near sunlit points corresponding to 02:30 and 03:30 UT (Fig. 2, region R3 , Australia). Each time dependence of the elevation angle θ(t)is labeled with the GPS site and PRN name; empty timeintervals correspond to count omissions.
One can see that for a low elevation angle θ < 30◦
the count omissions coincide with the impulse SRB during
periods A and B (ALIC-01, ALIC-13, ALIC-27, KARR-13,
KARR-27, TOW2-01). There are no count omissions for ahigh elevation angle θ (ALIC-20, KARR-20).
Figure 1 shows the dependence of count omissions in
GPS measurements upon the Sun zenith angle χ during the2006 December 13 SRB. The total count omissions W (t)for all registered PRN are presented in panel (b) for region
R1 (black line, 80◦ > χ > 90◦ ; n = 51), for region R0(thick gray line, 0◦ > χ > 90◦ ; n = 587 GPS sites), andfor region R3 (gray line, 0◦ > χ > 10◦ ; n = 119). The
maximum Wmax values of over 62% and 18% were recorded
for 0◦ > χ > 10◦ , and 80◦ > χ > 90◦ , respectively. There
was a wide range of zenith angles χ for the entire region R0 ,but even for this region the maximum Wmax values exceeded
37%, since the zenith angle χ did not exceed 50◦ for mostof the GPS world network sites.
Figure 1(c) and (d) give the W (t) time-dependences
for satellites with selected PRN registered from 02:15 to
03:45 UT. Maximum Wmax values for region R0 can beas high as 50% (panel (c)) and 48% (PRN28, n = 16; andPRN13, n = 43, respectively). In region R2 (panel (d), χ ∼60◦ ), Wmax is 19% and 8% (PRN22, n = 405; and PRN13,
n = 255, respectively).
A sharp increase in count omissions completely coincides with the impulse SRB not only during periods A andB, but also, to a lesser extent, at 02:45–03:20 UT (Fig. 1).
Comparison of the time dependence of count omissions
W (t) for the high zenith angle 0◦ > χ > 10◦ to that for640

E. L. AFRAIMOVICH et al.: GPS FUNCTIONING FAILURES CAUSED BY THE POWERFUL SOLAR RADIO BURST

the intensity of RHCP radio emission F(t) at frequencies
1 GHz and 2 GHz demonstrate a close similarity between
these dependences (Fig. 1(a, b)). It is also necessary to notethat the threshold ε, at which GPS receiver failures occur athigh zenith angle, does not exceed 20,000 sfu (as indicatedby a horizontal line in panel (a)).
A comparison between different types of GPS receivers’
response to wideband solar radio emission impact is ofgreat interest. The dense network of GEONET GPS receivers, equipped with 1200 TRIMBLE-5700 and 25 TRSLEGACY receivers, is best suited for this purpose. Since
the entire network is expanded over a rather small area, all
the receivers were under similar influence of the solar radio
noise emission during the extreme solar activity on December 13, 2006. Figure 3 presents the relative density Q(t) of
measurement slips for the L 1 , P1 , L 2 , P2 parameters registered by TRIMBLE-5700 (black lines) and TRS-LEGACY
receivers (thick gray lines) on December 13, 2006. It is obvious that significant measurement slips for the main GPS
signal parameters were registered by TRIMBLE-5700 receivers not only at the auxiliary frequency f 2 (L 2 ), but atthe basic GPS frequency f 1 (L 1 ) as well. Nevertheless, significant measurement slips for the main parameters weredetected by TRS-LEGACY receivers at the auxiliary frequency f 2 only. For TRS-LEGACY, the number of L 1 andP1 slips was nil during the entire radio burst.

5.

Discussion

There are some peculiarities in the time dependenciesof count omissions and measurement slips for GPS-signal
parameters we obtained:
5.1. Count omissions in GPS measurements increase as
the line-of-sight elevation angle decreases. A monotonous
reduction in signal level is associated with increasing
satellite-to-receiver distance. Under usual conditions, additive noise in ∼40 dB is below the level of signals, as a resultof correlation processing of broadband signal in the receiver(Hofmann-Wellenhof et al., 1992; ICD-200c). During powerful solar radio bursts, noise level at low elevation is higher
than the signal, which causes failures in phase tracking of
the GPS signal. Besides, according to the said mechanism,
the dependence of density of the maximum count omissions
is not proportional to the maximum radio emission power. It
is likely to be determined by the signal-to-noise ratio threshold that may differ for different GPS receivers.
5.2. The GPS measurement count omissions at the auxiliary frequency f 2 essentially exceed those for the basic GPS
frequency f 1 . A lower signal/noise ratio at f 2 is primarily
due to the fact that the f 2 power at the GPS satellite transmitter output is 6 dB less than that of the basic frequency
f 1 with the C/A code (ICD-200c). Similar correlations of
the effective radiated power of f 1 (30 watt) and f 2 (21 watt)signals are also typical of the Russian GLONASS system(Perov and Kharisov, 2005).
Phase tracking slips of the f 2 GPS signal may also be
caused by lower signal/noise ratio when we use commercial noncoded receivers for f 2 installed at the global GPS
network stations. These receivers have no access to themilitary “Y” code, and have to use the noncoded or seminoncoded mode of reception. As a result, the signal/noise

ratio at f 2 is, at best, 13 dB lower than the mode of fully
coded reception. Thus, the difference in signal powers at f 1
and f 2 for commercial receivers may exceed 10 dB, which
may lead to a slip density increase at f 2 owing to the influence of additive interference, but different types of GPS
receivers respond differently to this interference.
5.3. The maximum values of W (t) for the time interval
A are lower than those for B, while the radio flux F(t)is also strong enough for both. It is quite natural, sincestrong bursts of solar radio emission at two GPS frequencies
occurred simultaneously only during the time interval B,
not A (Fig. 1(a)). Therefore the probability of the GPS
count omissions is higher for the time interval B than for
A (see Section 2).
5.4. The maximum values of Q max % for L 2 and P2 for
TRIMBLE-5700 receivers for the time interval A are higher
than those for B, while the opposite is true for the L 1 andP1 parameters. On the other hand, the maximum values of
L 2 and P2 TRS-LEGACY receivers for the time interval
A are lower than those for B. The main reason for thisdiscrepancy are different characteristics of hardware andsoftware components in different GPS receivers.
5.5. Besides, the maximum values Q max % of all L 1 , P1 ,
L 2 , P2 parameters are higher than those of count omissions
Wmax %. It is quite natural, since W (t) is registered for thecount omission only, whereas Q(t) includes not only thecount omission, but also the measurement slips of each of
the L 1 , P1 , L 2 , P2 parameters (Section 2).

6.

Conclusion

We found that high-precision GPS positioning on the entire sunlit side of the Earth was partially disrupted during the extreme solar-radio burst on December 13, 2006,
for more than 12–15 min; a high level of GPS slips resulted from wideband solar radio noise emission. Our results agree with data obtained recently for the extreme solar
radio burst on December 6, 2006 (Cerruti et al., 2006a, b;
Afraimovich et al., 2007; Carrano et al., 2007; Carrano andBridgwood, 2008; Kintner, 2008).
We confirmed the results obtained by Carrano et al.
(2007) in that GPS failure does depend on Sun zenith angle χ . An increase in count omissions at high zenith angles
χ (Fig. 1) testifies to the solar origin of interference (noise)at two GPS frequencies. A growing number of failures withincreasing zenith angle is caused by an increase in atmospheric losses.
We agree also with the conclusion by Chen et al. (2005).
Direct interference from SRB is not usually considered asa potential threat to GPS signal tracing, since the flux density of most bursts is below the GPS f 1 frequency threat
threshold of 40,000 sfu, proposed by Klobuchar et al.
(1999). However, analysis by Chen et al. (2005) revealed
that a much lower threshold (4,000–12,000 sfu) should be
adopted for codeless or semicodeless dual-frequency GPS
receivers. For SRB on December 13, 2006, the threshold ε,
at which GPS receiver failures occur at high zenith angle,
does not exceed 20,000 sfu (as indicated by a horizontal
line on Fig. 1(a)).
A more detailed analysis of space distribution of GPS
performance slips caused by strong solar radio bursts will

E. L. AFRAIMOVICH et al.: GPS FUNCTIONING FAILURES CAUSED BY THE POWERFUL SOLAR RADIO BURST

be the subject of our future works. There are other dense
GPS networks, for example, the permanent Korean GPS
Network, KGN (Jin and Park, 2007). The accurately unified national GPS network with more than 2500 stations,
named “National 2000’ GPS Control Network”, has been
established by integrating the existing six nationwide GPS
networks of China (Yuanxi et al., 2007). A similar analysis
should be made for GPS failures during the 2006 December
13 powerful solar radio burst in the said regions.
Our results provide a serious basis for revising the role ofspace weather factors in the functioning of modern satellite
systems and for taking a more thorough account of thesefactors, in practice. Similar failures in the functioning ofsatellite navigation systems (GPS, GLONASS, European
system GALILEO) may be fatal to operating safety systems
as a whole, leading to great financial losses. Another important conclusion of our investigation is that continuous calibrated monitoring of the solar radio emission flux level by alarge number of solar radio spectrographs allows solar radio
noise level in the range of GPS-GLONASS-GALILEO frequencies to be estimated. Indeed, strong solar radio bursts
can be applied as a global and free tool for testing satellite
broadband radio systems including GPS. We agree with thisconclusion by Gary (2008): “As our society becomes evermore dependent on wireless technology, the effects of solar
radio bursts can be expected to appear more often. Missioncritical systems should be designed with solar radio emission in mind. A warning system based on an improved setof world-wide instrumentation could be implemented at relatively low cost, taking advantage of new technology thatallows broadband digital signal measurements. Ultimately,such extreme flux density bursts need to be studied at highspatial resolution in order to better understand the conditions leading to their occurrence, and ultimately to be able
to predict such events”.
Acknowledgments. Authors express profound gratitude to Prof.
G. A. Zherebtsov for his support and interest in this investigation; to S. V. Voeykov and A. B. Ishin for their help in data andmanuscript preparation, to Dr. V. V. Grechnev for his help in using the 1 GHz and 2 GHz data of the Nobeyama Radio Polarimeters; to colleagues from the Nobeyama Radio Observatory, forsolar radio emission data on December 13, 2006; the the IGS
center (http://lox.ucsd.edu/cgi-bin/al-lCoords.cgi?) and GEONET(ftp://terras.gsi.go.jp/data/GPS products/) for RINEX data fromGPS receiver networks. The work is supported by the Siberian
Branch of the Russian Academy of Sciences; the Program of basic
research of the Presidium of the Russian Academy of Sciences 30“Solar activity and physical processes in the Sun-Earth system”.
Finally, the authors wish to thank the referees for valuable suggestions which greatly improved the presentation of this paper.

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LETTER

Earth Planets Space, 61, 643–648, 2009

Aeronomic effects of the solar flares in the topside ionosphere
L. A. Leonovich and A. V. Taschilin
Institute of Solar-Terrestrial Physics, Russian Academy of Sciences SB RAS, 664033 p/o box 4026, Irkutsk, Russia(Received October 23, 2007; Revised February 22, 2008; Accepted March 20, 2008; Online published May 29, 2009)

We obtained that according to the GPS data at altitudes of the topside ionosphere (h > 300 km) a flare is able tocause a decrease of the electron content. Using the theoretical model it is shown that the intense transport of O+
ions into the above-situated plasma caused by a sharp increase in the ion production rate and thermal expansionof the ionospheric plasma is a cause of the formation of the negative disturbance in the electron concentration in
the topside ionosphere.
Key words: Solar flares, disturbances, ionosphere, GPS, modeling.

1.

Observations of the TEC Variations during a
Similar decrease in the electron content after the beginning of a solar flare was detected in ionospheric observaPowerful Flare on 14 July 2000

Phase measurements of GPS signals make it possible
to obtain variations of TEC along the receiver-satellite
path, Fitzgerald (1997), Hoffmann-Wellenhof et al. (1992),
Klobuchar (1986). Knowing variations in TEC, one is able
to evaluate the changes in the total electron content abovesome given level, using the method based on the effectsof partial “shadowing” of the atmosphere by the globe,
Leonovich et al. (2002).
Now we consider the results of application of the methodfore-quoted to studies of the ionospheric effects of the powerful solar flare X5.7/3B registered on 14 July 2000 at
1024 UT (N22W07) on the background of quiet geomagnetic situation (Dst = −10 nT). Figure 1(a) shows thetime behavior of the energy flux of the soft X rays in the
0.1–0.8 nm range (the data from the GOES 10 satellite)
for the flare in consideration. Vertical dashed lines show
the beginning of the flare and the time when the X-ray flux
was maximal. The corresponding variations in TEC alongrays directed to the GPS satellites and crossing the shadowboundary at various heights h 0 during the flare are shown in
Figs. 1(b)–1(f).
One can see in Fig. 1(b) that the total electron content
within the entire ionosphere (h 0 = 0) for the IRKT station located in the sunlit hemisphere starts to grow fromthe moment of the flare beginning (1012 UT) and lasts till
1036 UT. At the ray crossing the shadow region at a heightof 240 km (Fig. 1(c)), the TEC grow begins some time after
the flare beginning in the soft X-ray range. Similar picture isseen at other rays satisfying the condition h 0 < 380 km. At
the same time, for the rays with h 0 ≥ 380 km (Figs. 1(d)–1(e)) a decrease in the electron content above the h 0 leveloccurs after the flare beginning (1012 UT) and lasts till1024 UT, i.e., till the moment of the flare maximum in thesoft X-ray range.
c The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Societyof Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.

tions using the incoherent scatter radar at Arecibo, Thomeand Wagner (1981). During two solar flares on 21 and 23
May 1967, negative disturbances of the electron concentration with an amplitude from 3% to 10% were registered
within the height interval 280–600 km. The goal of this paper is studying mechanism of electron concentration negative disturbances in the topside ionosphere caused by solar
flares.

2.

Results of the Model Calculations of the Ionosphere Behavior during a Solar Flare

For studying physical processes governing ionosphericeffects of solar flares, we used the model of the ionosphereplasmasphere interaction, Krinberg and Taschilin (1984).
The model makes it possible to calculate time variations of
the ion composition, temperature, and also of the fluxes ofparticles and heat in the conjugated ionospheres. The modelis based on numerical solution of the nonstationary equations of the balance of particles and energy of the thermal
plasma within closed magnetic field tubes, their bases lying
at a height h = 100 km. It is assumed that the ionosphericplasma consists of electrons and atomic ions H+ and O+ ,+and also of molecular ions NO+ , N+
2 , and O2 . The UVradiation spectrum by Richards et al. (1994) and the X-ray
radiation spectrum by Nusinov (1992) were used for the calculation of the photoionization rates of the thermosphericconstituents O, O2 , and N2 and energetic spectra of the primary photoelectrons in undisturbed conditions (without aflare). The MSIS 86, Hedin et al. (1991), global empiricalmodel of the thermosphere was used for the description of
the spatial-time variations of the atmospheric temperatureand concentrations of the neutral components O, O2 , N2 ,and H.
For studying the flare effects, a disturbed model of thesolar radiation spectrum in the X-ray and UV ranges wascreated. According to the existence of the pulse and slow
phases of a flare, we assumed that the spectrum within the
wavelength interval 0.1–10 nm stays disturbed during 36

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L. A. LEONOVICH AND A. V. TASCHILIN: EFFECTS OF THE SOLAR FLARES IN THE TOPSIDE IONOSPHERE
Table 1. Increase in the solar radiation intensity for particular spectralintervals during the flare.
Intervals, nm
Intensity factor

0.1–0.8
1000

0.8–2
100

2–4
50

4–6
20

6–10
4

10–105
1.3

terval was split to 6 parts. For each part the most typicalvalue of the intensity factor, Avakyan et al. (1994), Horanand Kreplin (1981), Korenkov and Namgaladze (1977), wasfound. The value was determined as the ratio of the energy
flux during the flare to the radiation flux of the quiet Sun.
Table 1 shows values of the flare intensity factors for each
spectral interval.
The reaction of the midlatitude ionosphere to a considered solar flare was simulated by calculating the variationsof plasma parameters within the geomagnetic field tube.
The calculation was performed for the period 10–15 July
2000, using arbitrary initial conditions corresponding to low
content of the thermal plasma in the tube. The consideredtime period was characterized by high level of solar activity(F10.7 ≈ 210). The model calculation results of height-time
variations of the electron concentration for different conditions of solar irradiating intensity are shown in Figs. 2,(2(a)–2(f))—for the terminator area and (2(g)–2(l))—forthe local noon. The moment of a solar flare beginning isshown by vertical dashed lines.
The character of the time behavior of Ne changes principally above the F2 layer. One can see in Figs. 2(d)–2(f)and 2(j)–2(l) that within the height interval 380–600 km instead of the electron concentration increase after the flare
beginning, a trough is formed in the time behavior of Ne .
The value of the Ne decrease amplitude lies within 1–5%.
It should be noted that the obtained in the calculations negative disturbance of the electron concentration in the topside ionosphere agrees well to the presented above TEC
variations obtained as a result of processing of GPS signals and in observations at the Arecibo incoherent scatterradar Thome and Wagner (1981). Thus, one can conclude
that the conditions during a solar flare could be such that anincrease of the electron concentration occurs in the lower
ionosphere, but in the topside ionosphere Ne decreases.

3.

Fig. 1. Results of the TEC response according to the GPS measurements.
Time profiles of the soft X-ray radiation within the 1–8 Å range (thedata of the GOES 10 satellite) during the solar flare on 14 July 2000(a). Examples of the TEC responses to the solar flare measured at
the rays (between ground-based stations and GPS satellite) crossing theboundary of the Earth’s shadow cone at different altitudes h 0 (b–f).

minutes (the slow phase), whereas the pulse phase (for the
10–105 nm interval) lasts during 15 minutes. We also assumed that the spectrum is disturbed instantly and stays
constant during the above indicated time intervals, switching off instantly after that. To give the value of the disturbance of the solar energy flux, the entire wavelength in-

Discussion of the Modeling Results

In order to find the causes of formation of the electron concentration negative disturbance in the topside ionosphere, we assumed that the Ne decrease is related to inhomogeneous variations of the ultraviolet radiation in various
parts of the spectrum during a flare. On the basis of this assumption, the UV-radiation spectrum within the 10–105 nm
range was split to 19 equal intervals. Then, for each interval in turn, the factor of flare radiation intensity was varied from 1.3 to 10, whereas for the other intervals it stayed
equal to 1.3. The calculations showed that the effect of Ne
decrease after the beginning of a flare is pronounced best at
the increase of the intensity factor in three following spectral intervals: 15–20 nm, 30–35 nm, and 35–40 nm.
In order to understand the physical causes of the electron concentration depletion at altitudes of the topside ionosphere, we consider the continuity equation for the iono-

L. A. LEONOVICH AND A. V. TASCHILIN: EFFECTS OF THE SOLAR FLARES IN THE TOPSIDE IONOSPHERE

645

Fig. 2. The model calculation results of the height-time variations of the electron concentration for different conditions of solar irradiating intensity,(2(a)–2(f))—for the terminator area and (2(g)–2(l))—for the local noon. The dashed lines show variations of the electron concentration when solar
flare misses. The moment of a solar flare beginning is shown by vertical dashed lines.

spheric plasma written in the form:

total balance of the terms in the right-hand side and thata negative disturbance to be formed the right-hand side∂ Ne
= q − ln − div(W),(1) of (1) should be negative during the flare. The results of∂tthe modeling make it possible to determine the processes
where q is the ion production rate; ln is the loss rate of providing realization of such situation.
Figure 3 shows the time variations of the electron concenelectron-ion pairs in chemical reactions; and W is the total
ion flux along a geomagnetic field line. It follows from tration and particular terms of the right-hand side of Eq. (1)(1) that the sign of the Ne changes is determined by the at a height of the F2 layer (300 km) and in the topside iono-

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L. A. LEONOVICH AND A. V. TASCHILIN: EFFECTS OF THE SOLAR FLARES IN THE TOPSIDE IONOSPHERE

Fig. 3. Analysis of the effect of the decrease in the electron concentration during the solar flare. Thick lines show the time variations of the electron
concentration during a solar flare at heights of 300 km (a) and 500 km (c), diamonds show the time variations of the electron concentration in theabsence of the flare. The time variations of the terms in the continuity equation calculated for height 300 km (b) where the effect of the electron
concentration depletion during the flare is not observed and 500 km (d) where the effect is clearly pronounced are also shown in the bottom panels.

sphere (500 km). It should be noted that within this heightinterval ions of the atomic oxygen prevail and so Eq. (1)actually describe the balance of O+ ions. It follows from
Fig. 3(b) that at a level of 300 km the value of ion production rate exceeds considerably the loss of charged particles due to the recombination ln and transport of O+ ionsalong the field lines (divW > 0). As a result, there occurs
a monotonous increase in Ne during a flare. After the endof the flare, the photoionization rate decreases sharply. Dueto that, the electron concentration at first decreases sharply
and then is stabilized at some level, the latter being determined by the balance between the photoionization, inputof the O+ ions from the above-located plasmasphere, andchemical loss.
At altitudes of the topside ionosphere (500 km), the relation between particular terms of the right-hand side of (1)changes. First, a decrease with height in the absolute values of the ion production rates and recombination occurs,
and, second, the role of the diffuse transport of ions in theionization balance grows. Figure 3(d) shows that the valuesof the divergence of ion flux rapidly increases on an absolute value with the beginning of the flare and becomes a

predominating term in the right-hand side of Eq. (1). This
happens due to the reformation of the vertical profile of theion flux above the F2 -layer maximum with the beginningof the flare. After the sharp increase in the initial momentof the flare, the absolute value of the flux divergence decreases reaching the pre-flare value at the end of the pulse
phase (Fig. 3(d)). Then a reversal of the flux divergencesign to the opposite one occurs accompanied by an increaseof the electron concentration.
Figure 4 shows the vertical profiles of the ion flux before
the flare and in the maximal phase of the flare. One can seethat under undisturbed conditions ions O+ are transported
from the topside ionosphere through the F2 layer into thelower ionosphere. During the maximal phase of the flare,
the plasma pressure in the F2 layer increases sharply andabove ∼380 km an intense upward flux of O+ ions into
the plasmasphere is formed. As a result, at altitudes above∼380 km the divergence of the ion flux is positive andconsiderable on quantity, that specifies on essential upwardof plasma from the ionosphere to the plasmasphere.
Thus, one can conclude that the decrease of the electron
concentration in the topside ionosphere is due to the bring-L. A. LEONOVICH AND A. V. TASCHILIN: EFFECTS OF THE SOLAR FLARES IN THE TOPSIDE IONOSPHERE

647

can not any more support the upward flux of O+ ions, andthe ionosphere relaxes to the undisturbed state.
Now we consider the problem of length of the height interval in which the conditions needed to formation of thenegative disturbance in Ne are fulfilled. Figure 5 shows
the vertical profiles of the particular terms in the right-handside of Eq. (1) before a flare (Fig. 5(a)) and during the flare(Fig. 5(b)). In the same figures, the summated profile of allterms in the right-hand side of Eq. (1) is shown by triangles. One can see that in the absence of a solar flare in thedaytime the resulting curve is positive at h < 400 km andis close to zero above 400 km, that is, in the topside ionosphere the condition ∂ Ne /∂t ≥ 0 is fulfilled everywhere.
During a flare the right-hand side of Eq. (1) takes negativevalues in the 380–600 km altitude range (is shown by horizontal dashed lines in Fig. 5). So it follows that a negative
disturbance of the electron concentration during a flare cancover almost the entire topside ionosphere.

4.

Conclusions

The response of the ionosphere to a solar flare is studied
on the basis of the observational data and results of theoretical modeling. The analysis of the results obtained made it
possible to draw the following conclusions:Fig. 4. Vertical profile of the flux W. Thin line shows the flux behavior
before the flare. Thick line shows the flux behavior during the flare.

ing out to the plasmasphere of O+ ions. After “switchingoff” the flare, the plasma pressure in the F2 layer decreases
quickly down to the level at which the difference in the pressure between the upper and lower parts of the ionosphere1. According to the observations of the variations in TEC
and electron concentration at the GPS receivers network and at the IS installation at Arecibo, negative disturbances of the electron concentration can be formedin the topside ionosphere during solar flares.
2. It is found in the model simulations that the mostsignificant effect of the Ne depletion is seen during
the flares with a strong increase in the solar radiation
within the following spectral intervals: 15–20 nm and
30–40 nm.
3. The intense transporting of O+ ions up into the abovelocated plasmasphere is a cause of the formation of theFig. 5. Analysis of the continuity equation. Vertical profiles of the terms of the continuity equation before the flare (a) and during the flare (b). Thincurves show the electron formation rate q; dashed curves show the electron loss rate ln ; thick lines show the flux divergence div(W). The data for theloss rate and flux divergence are shown with negative signs as they enter to the considered equation. The curve with triangles is a resulting curve.

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L. A. LEONOVICH AND A. V. TASCHILIN: EFFECTS OF THE SOLAR FLARES IN THE TOPSIDE IONOSPHERE
1007/BF00151295, 1981.
negative disturbance in Ne in the topside ionosphere.
The transporting is caused by the sharp increase in the Klobuchar, J. A., Ionospheric time-delay algorithm for single-frequency
GPS users, IEEE Trans. Aero. Electron. Sys., 23(3), 325, 1986.
ion production rate and in the thermal expansion of the Korenkov, Yu. N. and A. A. Namgaladze, Modelling of the ionosphericionospheric plasma.
effects of the solar flares, in Ionospheric disturbances and forecast

Acknowledgments. The GPS data on the 14 July 2000 flare
were kindly provided by E. L. Afraimovich and S. V. Voeikov.
E. B. Romanova helped considerably in model simulations. We
sincerely thank them all.

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L. A. Leonovich (e-mail: lal@iszf.irk.ru) and A. V. Taschilin