**RELATION BETWEEN CORONAL MASS EJECTIONS AND THEIR INTERPLANTARY
COUNTERPARTS**

N. Gopalswamy

*Center for Solar Physics and Space Weather, Department of Physics, The
Catholic University of America, Washington DC 20064, USA and NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA*

**ABSTRACT**

Our current knowledge on coronal mass ejections (CMEs) comes from two
spatial domains: the near-Sun (up to 30 solar radii) region
remote-sensed by coronagraphs and the geospace and beyond where *in
situ* observations are made by spacecraft. Comparing observations from
these two domains has helped us understand the propagation and evolution
of CMEs through the interplanetary (IP) medium and develop an empirical
model to predict the 1-AU arrival of CMEs. In this paper, we review the
available information on the relation between CMEs and their IP
counterparts. In particular, we concentrate on issues related to the
prediction of the arrival of ICMEs in the geospace. We discuss the solar
sources of the three largest geomagnetic storms of year 2000 and compare
the predicted and observed arrival times of the associated CMEs.

1.  **INTRODUCTION**

Coronal Mass ejections (CMEs) are large-scale magnetized plasma
structures that erupt from the Sun and are transported in to the
heliosphere (Tousey, 1973). They exhibit various observational
signatures depending on their age and location of observation in the
heliosphere. Billions of tons of material are dumped into the solar wind
during each ejection; several CMEs can take place on a single day during
the maximum of solar activity cycle. CMEs are multithermal structures in
general, carrying coronal (\~2 MK) material in the front followed by
cool prominence (\~8000 K) material in some cases and hot flare-material
(\~10 MK) in others. When a CME erupts, it leaves behind hot
post-eruption arcades or flare loops that mark the location of the
eruption on the Sun. CMEs drive powerful interplanetary (IP) shocks,
which in turn accelerate electrons and ions over extended periods of
time. The accelerated electrons produce type II radio bursts in the IP
medium. While the protons and heavier ions accelerated by the shock near
the Sun reach 1 AU in a few tens of minutes, the shock arrives carrying
locally accelerated energetic storm particles (ESPs).

Spacecraft instruments can directly sample the CMEs. Since CMEs
propagate long distances before reaching the spacecraft, they are
considerably evolved and hence it is difficult to relate the *in situ*
observations to the CME substructures observed near the Sun. The generic
term used for CMEs in the solar wind is \'ejecta\'. Interplanetary CME
(ICME) is another general term used to describe the CME-like disturbance
in the solar wind. When the ejecta contains ordered magnetic field it is
known as a magnetic cloud (Burlaga *et al.*, 1981). Disordered magnetic
fields are also commonly observed in the ejecta (e.g., Hundhausen,
1972); magnetic clouds constitute only a small fraction (\~1/3) of the
IP ejecta. *In situ* observations of CMEs can be used to infer the
magnetic field topology of the IP CMEs (ICMEs) and the physical
conditions of their birthplace near the Sun (see, e.g., Henke *et al.*,
1998; Lepri *et al.*, 2001). Most often, the spacecraft in the solar
wind detect the following sequence of structures: IP shock, sheath, and
ejecta. On rare occasions, one observes cool dense material towards the
end of the ejecta that resemble the prominence resting at the bottom of
the coronal cavity in the pre-eruption phase of CMEs (Gopalswamy *et
al.*, 1998). As a working hypothesis, one can relate CMEs and ICMEs as
follows: CME shock  IP shock, CME front  sheath, CME void  ejecta,
and CME core  pressure pulse.

CMEs are relevant for two aspects of space weather: 1. Geomagnetic
storms and the consequent geoeffects, and 2. solar energetic particles
(SEPs and ESPs). When a CME impinges up on the Earth's magnetosphere, it
causes geomagnetic storms provided the IP magnetic field carried by it
has a southward component. The earliest disturbance that arrives at 1 AU
is the shock ahead of the CME, and marks the onset of the storm, usually
referred to as "storm sudden commencement" or SSC. However, not all
geomagnetic storms are preceded by SSCs. The shock arrival is also
important as they bring the ESPs with them. In this review, we will
concentrate on the arrival of CMEs at 1 AU. The arrival of shocks ahead
of the CMEs can be inferred from the CME arrival using the standard
piston-shock relationship. We also discuss how the speed with which CMEs
arrive at 1 AU could be predicted form their initial speed.

**2. THE EMPIRICAL CME ARRIVAL MODEL**

Availability of simultaneous data on CMEs and ICMEs has made it possible
to estimate the influence of solar wind on CMEs as they propagate away
from the Sun. Gopalswamy *et al.* (2000a) selected about two dozen IP
ejecta observed by the Wind spacecraft and identified the corresponding
frontside CME events observed by the Solar and Heliospheric Observatory
(SOHO) mission's Large Angle and Spectrometric Coronagraph (LASCO).
Assuming that the same object remote-sensed by the coronagraph
propagates to the spacecraft in the solar wind, they found that CMEs are
subjected to an IP acceleration (*a*) that depends linearly on the CME
initial speed (*u*): *a = α -- βu.* Here *α* and *β* are positive
constants determined from the scatter plot of *a* and *u*. The IP
acceleration was obtained from the CME speed, ICME speed and the transit
time of the CME to 1 AU. The critical speed given by *u~c~ = α/β* was
identified as the solar wind speed. The acceleration was positive *u \>
u~c~* and negative for *u \< u~c~* otherwise, consistent with the
observed distribution of CME speeds near the Sun and at 1 AU. Assuming
that all the CMEs undergo the same acceleration given above, one can
solve the kinematic equation *S = ut + ½ at^2^* to get the time (*t*)
taken by any CME to reach the distance *S* = 1 AU. The solution *t* as a
function of *u* is the prediction model.

Gopalswamy *et al.* (2001a) considered two of the limitations of the
above empirical model: 1. Projection effects in determining the space
speed of Earth-directed CMEs, and 2. the spatial extent over which the
IP acceleration operates. To avoid the projection effects, they
considered data from remote- and local-sensing spacecraft that had
orthogonal views. Helios-1 and the Pioneer Venus Orbiter (PVO) were in
quadrature with the P78-1 satellite in the 1970s and 1980s (Sheeley *et
al.*, 1985; Lindsay *et al.*, 1999). Limb CMEs detected by Solwind
coronagraph on board P78-1 that headed towards either Helios-1 or PVO
were identified to get the *a* versus *u* relationship, thus minimizing
the projection effects. This resulted in *α* = 2.193 and *β = 0.0054*.
The constants *α* and *β* are adjusted such that the units of *a* and
*u* are m.s^-1^ and km.s^-1^, respectively. The acceleration cessation
distance depends on both the CME speed and the background solar wind
speed. Gopalswamy *et al.* (2001a) crudely estimated this distance to be
about 0.76 AU. Solving the above kinematic equation for *S* = 0.76 AU
and assuming that the CME propagates freely beyond 0.76 AU, they
obtained the prediction curve labeled G in Figure 1. In order to test
the validity of this model, they used 47 new events observed by SOHO and
Wind (diamond symbols in Figure 1). The prediction agrees with the
observation within about 11 hours. While the agreement is very good for
the fast CMEs, there is considerable scatter for the low CMEs. In the
next subsection, we compare this model with other works related to the
prediction of CME arrival.

![](media/image1.wmf)

Fig. 1. Travel time of CMEs as a function of their initial speed. The
solid curve (G) is the prediction model of Gopalswamy *et al.* (2001a).
The two straight lines (V-slow, V-fast) are from Vandas *et al.* (1996)
for the propagation of a flux rope through slow and fast background
solar winds, respectively. The diamonds represent the measured travel
time for a set of 47 events for which CME and ICME observations were
available from SOHO and Wind, respectively (see Gopalswamy *et al.*,
2001a for details on these events).

[2.1 Comparison with Other Models]{.underline}

Brueckner *et al.* (1998) compared the timings of 8 solar-minimum CMEs
observed by LASCO with the onset of geomagnetic storms identified from
the Kp index. They concluded that 6 of the events had an average travel
time of \~80 hours. The thick solid line (B) in Figure 1 represents this
80-hour rule. The CMEs were either halo or semi-halo events. Clearly
some data points lie close to this line, but most of them lie above the
line. We did not extend the line beyond 1000 km/s because they have
stated that their rule may not apply to higher speed CMEs. It must me
pointed out that Brueckner *et al.* (1998) estimated the travel time to
be the interval between CME onset at the Sun and the time when Kp
reaches its maximum value. The latter is not the same as the CME arrival
at 1 AU, but not too different from it.

Vandas *et al.* (1996) performed a parametric study of magnetic cloud
propagation with a computational boundary starting at 18 solar radii
(Rs) from the Sun. They considered a slow (250 km/s) and a fast (750
km/s) solar wind flows into which the magnetic cloud was injected. They
obtained a travel time, which depends linearly on the initial speed of
the cloud, as shown in Figure 1 (straight lines marked V-slow and
V-fast). The lowest speed of the cloud used in the slow-wind (fast-wind)
model was 500 km/s (1500 km/s) so V-fast and V-slow lines have different
starting points. Both the fast- and slow-wind models of Vandas *et al.*
(1996) predict a travel time much larger than that of Gopalswamy *et
al.* (2001a). Note that the Vandas *et al.* curves correspond to a
starting distance of 18 Rs, which will slightly increase the propagation
time. Their travel-time curves also deviate considerably from the data
points.

Recently, Gonzalez-Esparza *et al.* (2002) performed another parametric
study, by simulating CME-like disturbances in the solar wind using a one
dimensional, hydrodynamic single fluid model. Simulated CMEs were
allowed to propagate through a variable ambient solar wind and their
1-AU characteristics were derived. The study showed that the simulated
CME pulses suffered a very strong acceleration/deceleration just after
their injection against the ambient wind before \~ 0.4 AU and afterwards
the magnitude of the acceleration was similar to the interplanetary
acceleration proposed by Gopalswamy *et al.* (2000b). The simulation was
able to reproduce the general characteristics of the Gopalswamy *et al.*
(2001a) prediction model.

[2.2 Predicting Final CME Speed]{.underline}

The ICME speed is an important factor in deciding their
geoeffectiveness. Therefore, it is useful to predict it from the CME
speed measured remotely. The IP acceleration obtained above can be used
in another kinematic relation, *v^2^ = u^2^ + 2aS* to get the speed of
the CME at a distance *S*. Figure 2 shows the plots of the final speeds
obtained for two different values of *S*. The solid parabolic curve
represents the final speed for *S* = 0.76 AU (the distance at which the
interplanetary acceleration *a* is assumed to cease). The dot-dashed
parabolic curve represents the final speed for *S* = 1 AU as used in the
original work by Gopalswamy *et al.* (2000b). The parabolic curves are
not fitted curves to the data points; they are simply the graphic forms
of the kinematic equation *v^2^ = u^2^ + 2aS*, with different values of
*a* and *S.* We have also plotted two sets of data points in Figure 2:
(1) the measured final speeds corresponding to the CME-ICME pairs
(diamonds) from archival observations obtained by spacecraft in
quadrature, and (2) recent data obtained by SOHO and Wind (crosses).
Note that for *u* \> 600 km/s, the solid curve fits the data very well.
The agreement is not so good for the low-speed events: the predicted
speed at 0.76 AU is larger than the observed values. This is expected
because the slow CMEs should have stopped accelerating much before
reaching 0.76 AU. In fact, we expect a flat profile for all initial
speeds less than the solar wind speed, as the observations indicate. We
have also plotted two straight lines that relate the final speed to the
initial speed based on the method of Lindsay *et al.* (1999). These
authors used a scatter plot between the CME speeds (*u*) and the
corresponding ICME speeds (*v*) and obtained the relation, *v = 0.25u +
360*, where *v* and *u* are in units of km/s. The Lindsay *et al.*
(1999) relation (dotted straight line) seems reasonable for the
low-speed (u \< 500 km/s) CMEs, but not for the higher speed ones. This
line was obtained from a set of 32 CME-ICME pairs collected from
Helios-1, PVO, P78-1 and Solar Maximum missions. Gopalswamy *et al.*
(2001a) revised this list and came up with a subset of 19 events
(diamonds in Figure 2) for which the *in situ* measurements were made at
heliocentric distances \> 0.7 AU. The dashed straight line is a fit to
these 19 data points. We do appreciate the fact that different CMEs stop
decelerating at different heliocentric distances, so we expect
considerable scatter when predictions are made based on an average
cessation distance.

![](media/image2.png){width="3.6875in" height="3.1173611111111112in"}

Fig. 2. ICME speed as a function of CME initial speed. The parabolic
curves are based on the empirical CME arrival models: dot-dashed curve
represents the original model (Gopalswamy *et al.*, 2000) and the solid
curve represents the improved model (Gopalswamy *et al.*, 2001a). The
dashed line is from Lindsay *et al.* (1999) using a set of 32 events
from quadrature observations. The dotted line was obtained in a similar
way, but with a subset of 19 events with improved association between
CMEs and ICMEs (the diamonds represent this data set). The crosses
represent CME-ICME pairs observed recently by SOHO and Wind. The last
point corresponds to the fast (1675 km/s) 'Bastille Day' event.

[2.3 Comment on Projection effects]{.underline}

![](media/image3.png){width="4.625in" height="2.6395833333333334in"}When
CME speeds were plotted against their source longitudes, Gopalswamy *et
al.*, (2000b) found a weak correlation suggesting that disk CMEs are
generally of lower speed and that one has to correct for projection
effects to obtain the space speed of CMEs. The SOHO-Wind data points
used in Figure 2 were not corrected for projection effects, yet Figures
1 and 2 show that predictions based on the initial sky-plane speeds of
CMEs are quite reasonable. In fact our attempt to correct the initial
speed for projection effects based on the solar-source location of CMEs
made the prediction worse. The projection effects depend not only on the
source longitude, but also on the cone angle of the CME (see, e.g.,
Leblanc *et al.*, 2001). Since limb CMEs show a variety of cone angles,
one would expect a similar distribution for Earth-directed CMEs. Thus
different Earth-directed CMEs are expected to have different widths, so
the use of an average width for all the CMEs may not be justified, and
might result in a large uncertainty in the correction factor. Another
factor to be considered is the variation of the cone angle with time.
Gopalswamy *et al.* (2001a) pointed out that the projection effects
might partly be compensated for by the initial expansion of the CME.
This means the sky-plane speed may not differ from the space speed by a
great deal. This does not mean projection effects are unimportant. In
fact, the improved estimate of the IP acceleration is a direct result of
minimizing projection effects using quadrature observations. The
orthogonal viewpoints of the spacecraft in quadrature directly reduce
the projection effects, without involving CME widths.

Fig.3. Height-time plots of three representative CMEs observed by
SOHO/LASCO. (a) the accelerating CME of June 21, 1998. The propelling
forces are most dominant in this case. (b) The constant speed CME of
February 17, 2000. In this case, the retarding and propelling forces may
balance each other. (c) The decelerating CME of May 11, 1998 where the
retarding force seem to be dominant. The plots are normalized to the
time the CMEs reach 2.5 Rs.

[2.4 Other Effects]{.underline}

In estimating the IP acceleration, we used an average speed obtained
from a linear fit to the height-time measurements of the CMEs. In Figure
3 we show three representative height-time plots of CMEs commonly found.
Obviously, linear fits will not be appropriate for all the CMEs. When we
used quadratic fits, curves (a) and (c) yield positive and negative
acceleration, respectively. Plot (c) will result in zero acceleration,
and hence linear fit will be appropriate only for such events. Moreover,
faster CMEs predominantly decelerate within the coronagraph field of
view and the magnitude of the acceleration depends quadratically on the
CME speed (Gopalswamy *et al.*, 2001b). The magnitude of the
acceleration is generally larger the average IP acceleration. Some slow
CMEs may attain higher speeds than what we used because of continued
acceleration beyond the coronagraph field of view. This is the likely
reason for the slightly earlier arrival of low-speed CMEs than predicted
(see Figure 1). Other phenomena which might significantly affect the
propagation of CMEs and hence the ability of the prediction model are
the CME-CME interactions (Gopalswamy *et al.* 2001c) and the presence of
large coronal holes in the vicinity of the eruption region.

[2.5 Solar Source]{.underline}

The empirical CME model described above requires the identification of
Earth-directed CMEs (Howard et al., 1982). Those CMEs originating closer
to the disk center have a better chance of hitting the Earth's
magnetosphere. Figure 4 shows the distributions of source longitudes and
latitudes of geoeffective during 1996-2000. The bimodal distribution of
latitudes simply reflect the location of the sources in the active
region belt on either side of the equator. The longitudinal distribution
peaks close to the disk center.

![](media/image4.png){width="4.5625in" height="4.229166666666667in"}Fig.
4: Latitude (top) and longitude of geoeffective solar CMEs during
1996-2000. Note that most of the CMEs originated from close to the disk
center.

Let us consider the largest geomagnetic storms of year 2000 and discuss
their solar sources and how they compare with the prediction model.
There were three storms with Dst \< -200 nT, as listed in Table 1 along
with the properties of the associated CMEs. All the three CMEs are halo
events. The April 4, 2000 CME resulted in the most intense storm of the
year, although the CME was close to the west limb (W66). The storm was
of short duration (\~1 day) and immediately followed the shock arrival
(see Fig. 5a). The LASCO image at 16:43 UT shows that the CME was
clearly directed westwards and has the appearance of a central bright
structure surrounded by an extended diffuse structure (see Fig. 5b). The
latter may be the white-light manifestation of the shock. The ACE
spacecraft, which detected the shock at 1 AU must have passed through
this shock and its sheath. Iron charge state data indicate a quiet solar
wind most of the time except for a short interval roughly coinciding
with the duration of the storm (see Fig. 5a). The predicted time of the
CME arrival at 1 AU was close to the shock arrival. The "Bastille Day"
CME (July 14, 2000) was perfect: it originated from the disk center with
very high speed and arrived at 1 AU as predicted by the model
(prediction: July 15, 21:00 UT, actual arrival was two hours earlier).
The Aug 11, 2000 event was very unusual in that it was relatively slow
(\~700 km/s) but arrived more than a day ahead of our prediction. Even
though it was a western hemisphere event, there was no solar energetic
particle event associated with this CME. The white light CME itself was
a perfectly concentric halo CME. When we examined the solar source, we
found that it was associated with a C2.3 flare from active region just
to the north of the equator. The eruption was accompanied by the
disappearance of transequatorial X-ray structures known as coronal
dimming. Figure 6 shows two soft X-ray images from Yohkoh/SXT one before
and one after the eruption. The X-ray images indicate that there were
weak extended coronal holes around the erupting region. The faster wind
in the coronal holes might have aided the CME in keeping higher speed so
that it reached earlier than expected. Thus, one has to consider not
only the properties of the CMEs, but also the environment into which a
CME is launched.

  ----------------- ----------------- ----------------- -----------------
  **Solar Event**   **04/04 16:32**   **07/14 10:54**   **08/09 16:30**

  Dst               -321 nT           -300 nT           -237 nT

  CME speed         1188 km/s         1675 km/s         702 km/s

  Solar source      N16 W66           N22 W07           N11 W11

  SEP               55 pfu            24000 pfu         None

  IP type II        Yes               Yes               No

  Shock Arrival     04/06 16:02 UT    07/15 14:02       08/11 18:19 UT

  Ejecta Arrival    ? (04/06 16:30)   07/15 19:00       08/12 06:00
  (predicted)                         (21:00)           (08/13 09:00)

  SW speed          375 km/s          450 km/s          410 km/s

  Flare             C 9.7/2F          X5.7/3B           C2.3/SF
  ----------------- ----------------- ----------------- -----------------

Table 1: Solar events associated with the three largest geomagnetic
storms of 2000.

![](media/image6.png){width="4.375in" height="3.5in"}

Fig. 5a (left) The geomagnetic storm of April 04, 2000 (as shown by the
Dst index) along with the solar wind disturbance represented by the "Fe
Ratio," which is the fraction of high-charge state (≥ 16) Fe ion density
relative to the total Fe density in all charge states (the ratio was
multiplied by a factor of 200 to show on the same plot as the Dst). The
thick vertical line around 16 UT on April 16, 2000 represents the IP
shock detected *in situ* by ACE (see also Table 1). The elevated Fe
ratio behind the shock is the sheath material, which contained a
southward magnetic field component and hence resulted in the geomagnetic
storm. Fig. 5b (right) SOHO/LASCO C3 difference image showing that the
2000 April 04 event was ejected westward. The solar source was at N16
W66. The CME was geoeffective and produced the most intense geomagnetic
storm (-321 nT) in 2000.

![](media/image7.png){width="3.1875in" height="3.1875in"}

Fig.7: Soft X-ray images from the Yohkoh mission's soft X-ray telescope
(SXT) before (left) and after (right) the 2000 August 09 eruption. Some
of the transequatorial structures (pointed by the arrow) can be seen
missing. The structures in the active region complex are simplified in
the post-eruption image.

**3. DISCUSSION AND CONCLUSIONS**

The primary focus of this review has been the connection between
near-Sun and near-Earth relationship between CMEs, especially those
aspects relevant to the prediction of CME arrival at 1 AU for space
weather purposes. We took the simplest approach of treating the CME as a
single body without worrying about the internal structure.

This approach has been useful to understand the gross propagation of
CMEs through the IP medium. In reality, the internal structure may
contribute to the continued propulsion of CMEs (see e.g. Yeh, 1995;
Chen, 1997). The constant IP acceleration is a crude approximation to
the actual acceleration profile. The primary reason is we have only two
measurements of the CME speed one near the Sun and the other near the
Earth. The planned STEREO mission will have the capability to track CMEs
throughout the Sun-Earth connected space, which will help us create a
complete radial profile of the CME acceleration. Space speeds of
Earth-directed CMEs can also be measured accurately because of the
capability for quadrature observations. Two other capabilities exist at
present that use radio observations. The IP scintillation (IPS) of
distant radio sources (Tokumaru *et al.*, 2000) observed through CME
structures can be used to get the acceleration profiles of CMEs. The IPS
signal depends crucially on the presence of enhanced turbulence in the
vicinity of CMEs. The current understanding is that such turbulence is
associated with the sheath of the CME-driven shock. The IPS observations
need to be exploited to get a realistic profile of the IP acceleration.
The other capability is the IP type II radio bursts which are due to
shocks driven by fast and wide CMEs (Bougeret *et al.*, 1995; Reiner and
Kaiser, 1999; Gopalswamy *et al.*, 2001b). Of course tracking the shock
is not the same as tracking the CME, but one can always use the
piston-shock relationship to connect them. Both these radio techniques
are useful mainly for fast CMEs that can drive shocks.

The result that the measured sky-plane speed of geoeffective CMEs is a
good representation of the space speed needs further exploration. These
CMEs may expand uniformly with a speed comparable to the radial speed.
Recall that most of the CMEs that had 1 AU counterparts are halo events,
consistent with the idea that these CMEs expand rapidly so they can be
detected as halos. We conclude that CMEs accelerate and expand inside
0.7 AU to an extent more than the empirical model supposes.

**ACKNOWLEDGMENTS**

This work was supported by NASA, Air Force Office of Scientific
Research, and NSF.

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