Astronomy&
Astrophysics

A&A 494, 1107–1118 (2009)
DOI: 10.1051/0004-6361:200809551
c ESO 2009

Forbush decreases and turbulence levels
at coronal mass ejection fronts
P. Subramanian1 , H. M. Antia2 , S. R. Dugad2 , U. D. Goswami2 , S. K. Gupta2 , Y. Hayashi3 , N. Ito3 , S. Kawakami3 ,H. Kojima4 , P. K. Mohanty2 , P. K. Nayak2 , T. Nonaka3 , A. Oshima3 , K. Sivaprasad2 , H. Tanaka2 , and S. C. Tonwar2(The GRAPES-3 collaboration)
1

Indian Institute of Science Education and Research, Sai Trinity Building, Pashan, Pune 411021, India
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, Indiae-mail: gupta@grapes.tifr.res.in
3
Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
4
Nagoya Women’s University, Nagoya 467-8610, Japan
2

Received 11 February 2008 / Accepted 25 October 2008
ABSTRACT

Aims. We seek to estimate the average level of MHD turbulence near coronal mass ejection (CME) fronts as they propagate from the
Sun to the Earth.
Methods. We examined the cosmic ray data from the GRAPES-3 tracking muon telescope at Ooty, together with the data from othersources for three closely observed Forbush decrease events. Each of these event is associated with frontside halo coronal mass ejections(CMEs) and near-Earth magnetic clouds. The associated Forbush decreases are therefore expected to have significant contributions
from the cosmic-ray depressions inside the CMEs/ejecta. In each case, we estimate the magnitude of the Forbush decrease using
a simple model for the diffusion of high-energy protons through the largely closed field lines enclosing the CME as it expands
and propagates from the Sun to the Earth. The diffusion of high-energy protons is inhibited by the smooth, large-scale magnetic
field enclosing the CME and aided by the turbulent fluctuations near the CME front. We use estimates of the cross-field diffusion
coefficient D⊥ derived from the published results of extensive Monte Carlo simulations of cosmic rays propagating through turbulent
magnetic fields. We then compare our estimates with the magnitudes of the observed Forbush decreases.
Results. Our method helps constrain the ratio of energy density in the turbulent magnetic fields to that in the mean magnetic fields
near the CME fronts. This ratio is found to be ∼2% for the 2001 April 11 Forbush decrease event, ∼6% for the 2003 November 20
Forbush decrease event and ∼249% for the much more energetic event of 2003 October 29.
Key words. ISM: cosmic rays – Sun: coronal mass ejections (CMEs) – Sun: solar-terrestrial relations

1. Introduction
Forbush decreases are short-term depressions in the cosmic ray
flux reaching the Earth, and they are caused by the effects of theinterplanetary counterparts of coronal mass ejections (CMEs)
from the Sun (and the shocks they drive) and also the corotating interaction regions originating from the Sun. They havebeen studied closely since their initial discovery in the 1930s(see, e.g., comprehensive observational reviews by Cane 2000;
Venkatesan & Badruddin 1990). With the recent upsurge of interest in space weather effects due to solar transients, the complementary information provided by the cosmic ray signaturesof these effects has assumed increased significance.
In this work, we have examined the data from the
GRAPES-3 tracking muon telescope at Ooty for three wellobserved events. Earlier, we had analysed the Forbush decrease data from this experiment during the period 2001–2004
and searched for events that can be associated with a nearEarth magnetic cloud and a corresponding halo CME from theSun. We start from lists of magnetic cloud events given on
the WIND webpage, http://lepmfi.gsfc.nasa.gov/mfi/
mag_cloud_pub1.html, Lynch et al. (2003) and Huttunen et al.
(2005). We shortlist Forbush decrease events that occurred ina reasonable time window around the time of entry of themagnetic clouds. Of these shortlisted events, we have selected
the three events shown in Fig. 8. Two of these events (2001
April 11 and 2003 October 29) have especially clean decrease
profiles. Even though the decrease profile for the third event on
2003 November 20 is not nearly as clear-cut, we still selected it,
because of its association with a very closely observed magnetic
cloud, and also because it illustrates the diversity of the events
observed with the GRAPES-3 experiment. We estimate the contribution of the depressed cosmic ray density inside the CME to
the total Forbush decrease seen in these datasets, and use it to derive conclusions regarding the level of turbulence near the CME
front.
The events discussed in this work were very closely observed, and they have their origins in full halo CMEs that originated close to the centre of the solar disc. This means that thecorresponding interplanetary CMEs (ICMEs) would have beenintercepted at the Earth as ejecta/magnetic clouds, and the observed cosmic ray depressions corresponding to these eventswould have had contributions from the shock ahead of the
ICME, as well as from the ejecta/magnetic cloud itself (Caneet al. 1994, 1995; Cane & Richardson 1997). Theoretical treatments of Forbush decreases model the effect as arising due toa general propagating region of enhanced turbulence/scattering

Article published by EDP Sciences

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P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

and decreased diffusion (e.g., Nishida 1983; le Roux & Potgieter
1991) and do not distinguish between the shock and the ejecta,
or implicitly assume that the decrease is only due to the shock(e.g., Chih & Lee 1986). It is fairly well known that magnetic
clouds are well-correlated with Forbush decreases (e.g., Zhang& Burlaga 1988; Badruddin et al. 1986; Badruddin et al. 1991;
Venkatesan & Badruddin 1990; Sanderson et al. 1990; see, however, Lockwood et al. 1991, for the opposite viewpoint).
The relationship between the decrease due to the shock andthe one due to the magnetic cloud has been investigated (Caneet al. 1995, 1997; Wibberenz et al. 1997, 1998), and there issome evidence that they can contribute in roughly equal proportions, to the overall magnitude of the decrease, although the individual time profiles of the decrease due to these two effects canbe quite different (Wibberenz et al. 1997). It is worth mentioning that the contributions of the shock and the magnetic cloudto the overall decrease can be discerned relatively easily fromthe spacecraft observations (e.g., Cane et al. 1995, 1997; Cane2000), since the temporal boundaries of the magnetic cloud canbe readily ascertained by using the data from the same source.
These data typically exhibit two steps in the decrease phase, one
corresponding to the shock passage and the second to the entryof the magnetic cloud. The two-step signature, however, need not
be a necessary condition for the Forbush decreases arising fromthe combination of a magnetic cloud and the associated shock.
Even for events where there is clear evidence that both the shockand the following magnetic cloud have intercepted the Earth (asis the case with the three events presented in this paper), theprecise decrease profile will depend upon the standoff distance
between the magnetic cloud and the shock and on the energiesof the protons detected. If the protons are energetic enough that
their mean free path is comparable to the magnetic cloud-shock
standoff distance, the distinct identities of the steps corresponding to the shock and the cloud may not be clear. We attribute 50%of the total decrease to the magnetic cloud (α = 0.5, see Sect. 3),
following the general logic outlined by Wibberenz et al. (1997).
We discuss the sensitivity of our final results to variations in α
in Sect. 7. In our quantitative work, we estimate the magnitudeof the Forbush decrease using filtered data (see Sect. 2.1 for a
description of the filtering method) averaged over 1 h.
The high muon counting rate measured by the GRAPES-3
experiment results in extremely small statistical errors, allowing small changes in the intensity of the cosmic ray flux to bemeasured with high precision. Thus a small drop (∼0.2%) in thecosmic ray flux, during a Forbush decrease event can be reliably detected. This is possible even in the presence of the diurnal anisotropy of much larger magnitude (∼1.0%), through asuitable filtering technique described subsequently.
Before we proceed further, it is worth discussing the terminology we use. The term CME is generally used to denotethe blob of plasma ejected from the solar corona as viewed bycoronographs near the Sun (typically from 1 to 30 R⊙ ). The CME
can be thought of as a largely closed, magnetic flux rope-likemagnetic structure (see, however, Bothmer et al. 1996, 1997,
for evidence of CMEs possessing closed, as well as some open
field lines) whose cross-section expands as it travels through the
heliosphere. There are practically no high-energy cosmic rays
inside it when it starts out from near the Sun, and the ambient cosmic rays diffuse into it via cross-field diffusion acrossthe closed magnetic field lines as it travels through the heliosphere. The term “ICME” is a broad one used to denote the interplanetary counterpart of a CME (see, e.g., Forsyth et al. 2006;
Wimmer-Schweingruber et al. 2006, and references therein),while the term “magnetic cloud” is reserved for ICMEs detected

Fig. 1. A schematic layout the GRAPES-3 air shower array shown
here with 217 detectors (circles). Each of the 16 squares represent a
35 m2 area tracking muon detector with Eµ ≥ 1 GeV used in the present
work.

near the Earth, possessing certain well-defined criteria such asplasma temperature depressions and smooth magnetic field rotations (see, e.g., Burlaga et al. 1981; Bothmer & Schwenn 1998).
Other CME/ICME related ejecta detected near the Earth are
merely called “ejecta”.
The rest of this paper is organised as follows, We briefly
describe the GRAPES-3 experiment in Sect. 2. We describe
the model we used to calculate the magnitude of the expected
Forbush decreases in Sect. 3. The three Forbush decrease events
we analysed are described in Sects. 4–6. We describe our resultsin Sect. 7 and summarise them in Sect. 8.

2. GRAPES-3 experimental system
The GRAPES-3 experiment is located at Ooty (11.4◦N latitude,
76.7◦ E longitude, and 2200 m altitude), in southern India. The
GRAPES-3 air shower experiment was designed to have a compact configuration of a conventional type array, with a separation of only 8 m between the adjacent detectors, which are deployed in a symmetric hexagonal geometry. A schematic layoutof the GRAPES-3 array is shown in Fig. 1. The observations
were started in 2000 with 217 detectors, located within the inner
8 rings (see Fig. 1 Gupta et al. 2005).
A very large-area tracking muon telescope operating as a partof the GRAPES-3 experiment (Gupta et al. 2005; Hayashi et al.
2005), is a unique instrument, to search for the high-energy protons emitted during the active phase of a solar flare or a coronalmass ejection (CME). The muon telescope is capable of providing a high-statistics, directional study of muons. The GRAPES-3
muon telescope covers an area of 560 m2 , consisting of a totalof 16 modules, each 35 m2 in area. These modules are locatedclose to each other as shown in Fig. 1. A cluster of four 35 m2
area neighbouring modules, located inside a common hall, constitutes one supermodule with a total area of 140 m2 . The energy threshold of the telescope is 1 GeV for the muons arriving

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

1109

600

σ = 0.103%

500

Fig. 2. A schematic display of the 4-layer tracking muon telescope
module with 58 PRCs per layer. The four layers of the PRCs labelled
Layer-0, Layer-1, etc. are embedded in concrete blocks. Inclined lines
represent a set of parallel muon tracks.

400
Frequency

Layer−3
Layer−2
Layer−1
Layer−0

300
200
100

along the vertical direction. The cutoff rigidity due to the magnetic field of the Earth at Ooty is 17 GV in the vertical direction
and varies from 12 to 42 GV across the field of view of the muon
telescope as shown later in Fig. 6.
The basic detector element of the muon telescope is a rugged
proportional counter (PRC) made from a 600 cm long steel pipewith 2.3 mm wall thickness and a square cross-sectional area of
10 × 10 cm2 . A muon telescope module with a sensitive areaof 35 m2 consists of a total of 232 PRCs arranged in four layers of 58 PRCs each, with alternate layers placed in orthogonal
directions. Two successive layers of the PRCs are separated by
a 15 cm thick concrete layer, consisting of 60 × 60 × 15 cm3blocks as shown in Fig. 2. The four-layer PRC configuration of
the muon modules allows a 3-D reconstruction of the muon track
direction to an accuracy of ∼6◦ . It is worth noting that the accuracy gradually increases with increasing zenith angle due to thegreater separation of the triggered PRCs.
To achieve an energy threshold of 1 GeV for vertical muons,an absorber of total thickness ∼550 g cm−2 in the form of concrete blocks is employed. This was done by placing a total of
15 layers of concrete blocks above Layer-1, as shown schematically in Fig. 2. A unique feature of the GRAPES-3 muon module is the robust structure of the PRCs, which supports the hugeload of 2.4 m thick concrete in a self-supporting manner. The
concrete blocks are arranged in the shape of an inverted pyramid
to shield the PRCs, with coverage up to 45◦ around the verticaldirection for the incident muons. The threshold energy changes
to sec θ GeV for the muons incident at a zenith angle of θ. The
cross section of a muon telescope module is shown schematically in Fig. 2. A cluster of four such modules, separated by ahorizontal distance of 130 cm at the base constitutes one supermodule. The GRAPES-3 muon telescope contains a total of four
supermodules (Hayashi et al. 2005).
Because of the sensitivity of the PRCs to low-energy γ rays,from the radioactivity present in the concrete absorber, individual PRCs display sizable counting rates of ∼200 Hz. An output
is generated, if any one of the 58 PRCs produces a signal. A
logical “OR” of outputs from all 58 PRCs in a layer is generated, after suitable amplification and shaping to form the layer
OR output. A coincidence of the four OR outputs from the four
layers in a module is used to generate the 4-layer trigger. Despitehigh counting rates of individual PRCs, the 4-layer coincidence
trigger is relatively free of the contribution from the backgroundradioactivity and it is caused only by the passage of a muon. The
observed 4-layer muon counting rate of ∼3200 Hz per module
yields a total counting rate ∼3 × 106 min−1 for all 16 modules.
This high rate permits small changes of .0.1% in the muon flux,
to be detected on a timescale of ∼5 min, after appropriate correction to the variation in the atmospheric pressure with time.

0
-0.4

-0.2

0

0.2

0.4

Fig. 3. Distribution of the relative variation in %, for the 4-layer muoncounting rate for the 35 m2 area modules for time intervals of 6 min.
Also shown is a Gaussian fit to the data. The standard deviation of the
fit is 0.103% as against an expected value of 0.095% based on statistics.

Most of the detected muons are generated by &20 GeV
galactic cosmic rays, and form a stable and dominant background to the variation in their flux produced by the CME/solar
flare. The muon data is grouped online every 10 s, into solidangle bins of ∼0.05 sr, consistent with the angular resolution of
the muon telescope as described below. Since >1 GeV muons aresecondaries produced by the primary protons of energy &20 GeV
in the atmosphere, therefore these observations can be used toprobe the effect of the Sun on cosmic rays.
The data recorded during 2003 October, from 15 out of
16 working modules were used in the statistical analysis described below. The muon rate for each 35 m2 area module wasrecorded for 770 time intervals, each 6 min in duration spreadover a total of about 3.5 days. During this period of 3.5 days, thedata could not be recorded for 70 out of 840 intervals, due to thefailure of the recording system in the first supermodule. Next,
the mean muon rate of the module for the entire duration wascomputed. Then the percent deviation from the mean module
rate was calculated, separately for each module. Finally, the rms
spread in the percent deviation called “relative variation” wascalculated for each module for all 6-min intervals. In Fig. 3, thedistribution of the relative variation in the 4-layer muon rate inpercent, as recorded by the muon modules is shown. Also shownin Fig. 3, is a Gaussian fit to this distribution, which yields a
standard deviation of 0.103%. This value may be compared withan expectation of 0.095%, based on a 6-min muon statistic of
1.1 × 106 per module. This tiny statistical error in muon rate allows a high-precision study of various solar phenomena to be
carried out (Nonaka et al. 2006).
2.1. Data analysis

In all four supermodules, the direction of muons is recorded
into 225 solid-angle bins. This was done by using a dedicateddirection-sensitive trigger with an independent data acquisition
system for each of the four supermodules. As shown in Fig. 4,
the muon angle is determined for each PRC in the lower layer
and binned into 15 angular bins based on the specific location of
the PRC triggered in the upper layer from among the 15 PRCs,
one directly above (central PRC) and 7 each on either side of the1110

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts
17 GV

Fig. 4. A schematic view of muon arrival angle selection based on the
PRC triggered in the lower and 15 PRCs in the upper layer. The triggered PRCs are shown as filled squares.

27 GV

32 GV 37 GV 42 GV

14 GV

40

NW

N

NE

W

V

E

SW

S

SE

20
0

12 GV

-20
-40
-60
-60

225 bins

7

Projected Angle in N-S Plane

60

22 GV

-20
0
20
40
-40
Projected Angle in E-W Plane60

6Fig. 6. The 9 coarse solid-angle bins are shown along with the contours of constant geomagnetic cutoff rigidity in the field of view (FOV).
Cutoff rigidity varies from 12 to 42 GV in the FOV of GRAPES-3.

5

NW

4

N

NE

3
2
1
0

W

V

E

SW

S

SE

−1
−2
−3
−4
−5
−6
−7
−7

−6 −5 −4 −3 −2 −1

0

1

2

3

4

5

6

7

Fig. 5. A schematic of the nine muon arrival direction bins; 3×3 verticalbin V, and four 3 × 5 central bins N, E, W, S, and four 5 × 5 outer bins
NE, SE, SW, NW.

central PRC. This angular binning is carried out in each of thetwo orthogonal projections (XZ and YZ; Z is vertical direction),
thereby generating a 2-dimensional 15 × 15 = 225 solid-angle
map of muon directions. The contents of the 225 solid-angle bins
are recorded, once every 10 s, thus providing a continuous monitoring of the directional flux of muons in the sky.
The variation in the muon rate may be studied in any of the
225 solid angle bins. However, it is expected that the influenceof a solar flare and/or CME would be spread over several bins.
This directional spread could arise from the influence of the terrestrial, solar, and interplanetary magnetic fields, etc. Therefore,
the detected muons have been regrouped into 3 × 3 = 9 coarse
solid-angle bins, as shown schematically in Fig. 5. This regrouping of the data was done by combining either a set of 3 × 5 or
5 × 5 fine solid-angle bins. The exception being the vertical direction where 3 × 3 bins have been combined. This choice of angular segmentation was dictated by the fact that the muon flux iscomparatively larger for the near central directions (N, E, W, S)

than for the outer directions (NE, SE, NW, SW). This choice
results in a relatively similar solid-angle coverage for the ninecoarse bins. Thus the solid-angle of acceptance includes only
13 × 13 = 169 out of original 225 bins, restricting the maximum zenith angle to 50◦ . This still exceeds the shielding coverage of 45◦ , for the PRCs at the outer edge, but such events
constitute <1% of the data. This regrouping also results in muon
statistics for various bins that are not too dissimilar.
At the energies (&20 GeV) of interest here, the propagationof charged particles near the Earth (<20RE , where RE is the radius of the Earth) is strongly influenced by the geomagnetic
field. The access by a charged particle to a given geographicallocation depends on the momentum per unit charge of the particle called rigidity. The threshold value of the rigidity is termed“geomagnetic cutoff rigidity”, which depends on the geographical location on the Earth and the direction of the arriving particle. The geomagnetic cutoff rigidity can be calculated using
a detailed model of the geomagnetic field (Cooke et al. 1991).
The geomagnetic cutoff rigidity for the field of view (FOV) of
the GRAPES-3 muon telescope varies significantly for the ninecoarse, solid-angle bins. We first calculate the cutoff rigidity forthe centre of each of the 169 fine solid-angle bins, which constitute the 9 elements of the FOV, using the IGRF2000 geomagnetic field model. Subsequently, a weighted mean of the cutoff
rigidities of the fine bins constituting a coarse bin is calculated
for each of the 9 coarse bins. These weights are the muon counting rates for a given fine bin. Here, it needs to be emphasised thatthe knowledge of the geomagnetic field at any particular momentin time is imperfect, and it is virtually impossible to determine
the cutoff to a high degree of accuracy. However, the calculated
values of the geomagnetic cutoff represent a very useful approximation to the true values at the time of the observations. In Fig. 6
the contours of constant geomagnetic cutoff rigidity in the FOV
are superimposed over a schematic of the 9 solid-angle bins ofmuon arrival directions. The geomagnetic cutoff rigidity varies
from 12 GV in the west to 42 GV in the east, within the FOV of
the GRAPES-3 tracking muon telescope.
In this study we used the GRAPES-3 data summed over atime interval of one hour for each of the nine bins, which areP. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

Fig. 7. The power spectrum of 28 day data covering the period from
26 March to 22 April 2001. The solid lines show the results for all
9 directions used in the study while the dashed line shows the functionthat is used for filtering out the high-frequency components. The Fouriertransform is multiplied by this function before taking the inverse Fouriertransform to get filtered time series.

identified as NW, N, NE, W, V, E, SW, S, and SE. The calculated cutoff rigidities for these nine bins are 15.5, 18.7, 24.0,
14.3, 17.2, 22.4, 14.4, 17.6, and 22.4 GV, respectively, as seenfrom Fig. 6. The summing over an interval of 1 h improves thesignal-to-noise ratio, but the diurnal variations in the muon flux
are still present. To filter out these oscillations we applied a lowpass filter, removing all frequencies higher than 1 day−1 . In Fig. 7
we show the Fourier transform of the data covering a period of
28 days that includes the event of 2001 April 11. The peaks corresponding to diurnal variation and its first harmonic are visible.
The Fourier transform is multiplied by the function shown by
a dashed line to remove the high-frequency components. Thisfilter is found to be effective in removing high-frequency oscillations, including the diurnal variations and their harmonics. The
Forbush decrease events are also clearer in the filtered data.
The smoothing may tend to change the amplitude of the decrease and possibly shift the onset time for the Forbush decreaseby a few hours in some cases. However, it is often difficult to determine if these differences are artifacts of smoothing or whether
the unfiltered data showed different amplitude because a diurnal
oscillation happened to have the right phase, so as to enhanceor reduce the amplitude of the Forbush decrease. Some fluctuations in muon flux could be due to Forbush decrease and associated events, but it is unlikely that these will be periodic innature, hence are not likely to be affected by the filter. Since
the differences in amplitude caused by filter are not substantial, it would not affect our results significantly. Thus in thiswork, we used the filtered data to study the characteristics ofForbush decrease events, although the unfiltered data are also
shown in corresponding figures for direct comparison. Further,
we repeated the calculations using unfiltered data and find thatthe final results are not significantly different. There can also be
anisotropies intrinsic to the CME/magnetic cloud itself, arising1111

from a B×∇ N drift, where B is the interplanetary magnetic fieldand ∇ N denotes the cosmic-ray density gradient inside the CME(Bieber & Evenson 1998; Munakata et al. 2003, 2005; Kuwabara
et al. 2004). Such anisotropies can potentially be “mixed” withthe diurnal anisotropy, and it is possible that there will still besome residual anisotropy after the filter is applied. This is thecase with one of the weaker events that we have studied here;
namely 2003 November 20.
To determine the properties of Forbush decrease, we divided
the time interval in three parts, the first part before the onset; thesecond part includes the decrease, while the third part includes
the recovery phase. We fit straight lines to the first two parts andan exponential profile for the third part. The point of intersectionof the two straight lines defines the onset time for the Forbush
decrease, while the intersection of the last two fits determines
the minimum of the profile. The difference in the flux between
these two points determines the magnitude M of the decrease(Sect. 3), which is measured in term of percentage change in
steady flux. The fits for all events used in this work are shown in
the respective sections.
In the subsequent analysis we discuss in detail three
Forbush decrease events, namely those on 2001 April 11, 2003
October 29, and 2003 November 20, which were associated with
CME/magnetic clouds. The GRAPES-3 data is recorded alongnine directions as described earlier. However, in Fig. 8 the datafor only the vertical direction is shown for these three events
along with measurements from the Tibet neutron monitor at
Yangbajing (Muraki et al. 2007) as obtained from http://cr0.
izmiran.rssi.ru/tibt/main.htm. The Tibet neutron monitor has a wide solid-angle of acceptance with the dominant contribution coming from the vertical direction; for that reason, we
selected the GRAPES-3 data along the vertical direction for acomparison as shown in Fig. 8. The Tibet neutron monitor waschosen, as Yangbajing (90.5◦E) is located at a similar longitude
as Ooty (76.7◦E), and the geomagnetic cutoff rigidities are also
not too dissimilar (Ooty = 17 GV, and Yangbajing = 14 GV).
The neutron monitor data was scaled down by a factor of 3 tofit the same scale. Here, it needs to be emphasised that both setsof data were subjected to the same low pass filter to remove frequencies higher than 1 day−1 . The detailed features in the Tibet
neutron monitor data follow the GRAPES-3 muon data rather
closely for all three Forbush decrease events as seen from Fig. 8.

3. Proton diffusion into CME/magnetic cloud
We are concerned here with the component of the Forbush decrease produced by the difference between the proton density
inside and outside the magnetic cloud that intercepts the Earth.
To do this, we obtain an estimate of the proton density inside the CME/magnetic cloud produced by the cumulative effect of protons diffusing into the closed magnetic structure of
the CME/magnetic cloud as it propagates towards the Earth. We
use cross-field diffusion coefficients derived from recent numerical treatments of cosmic ray propagation through turbulent magnetic fields.
Before doing so, it is worth taking a brief look at the typical
proton gyro-radius in relation to the overall size of the ejecta to
see how far such a picture involving cross-field diffusion would
be valid. This is especially pertinent here, since the protons detected by the GRAPES-3 experiment are typically very energetic. The GRAPES-3 experiment can detect muons produced

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P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

Fig. 8. Data from Tibet neutron monitor(dashed lines) is compared with GRAPES-3
data (solid line) for vertical direction for the
3 events studied in this work. Both the time series are filtered by applying a low pass filter toremove high frequency components. In order to
fit in the same scale the neutron monitor data is
scaled down by a factor of 3.

by protons of rigidities above 12–42 GV, where the rigidity Rg
is defined by
Pc= 300 B (Gauss) rL (cm),(1)
Zewhere P is the proton momentum, c the speed of light, Z
the charge state (=1 for a proton), e the charge of an electron, B the magnetic field in Gauss, and rL the proton gyroradius in cm. The magnetic field of a typical near-Earth magnetic cloud is ∼10−4 G, while its radius is ∼0.2 AU, or∼3 × 1012 cm (http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_Avg.html). The gyro-radius of a 30 GV proton in thefield of a typical near-Earth magnetic cloud is ∼1012 cm (fromEq. (1)), or 0.3 times the magnetic cloud radius. Estimates of themagnetic field of a CME near the Sun are notoriously hard tocome by, but the rough lower bound of ∼0.1 G given by Bastian
et al. (2001) can be taken as a working number. The gyro-radiusof a 30 GV proton in such a magnetic field is ∼3 × 108 cm,
which is around 3 orders of magnitude smaller than the typical size of a CME at such heights, which is a few solar radii (afew times 1011 cm). Thus the gyro-radius of the typical highenergy proton whose signature is detected by the GRAPES-3
array ranges from 10−3 to 0.3 times the macroscopic size of thestructure into which it penetrates, and the picture of cross-field
diffusion is generally valid.
The flux of protons entering the CME/magnetic cloud at agiven time isRg (volts) =F (cm−2 s−1 ) = D⊥

∂Na
,
∂r

(2)

where F is in units of number per cm2 per sec, D⊥ is the
cross-field diffusion coefficient, and Na the ambient density ofhigh-energy protons. This diffusion takes place throughout thecross-section of the expanding CME, so the total number ofhigh-energy protons that will have diffused into the CME after atime T is
Z T
Z T
∂Na
Ui =
A(t) F(t) dt =D⊥ A(t)
dt,
(3)
∂r
0
0
where A(t) is the cross-sectional area of the CME at time t. The
integration extends from the time the CME is first observed in
the LASCO field of view (t = 0) through the time (t = T ) when
it arrives at the Earth as a magnetic cloud. A reasonable estimate
for ∂Na /∂r would be
Na
∂Na
≃
,
∂r
R(t)

(4)

where R(t) is the CME cross-sectional radius at time t. Assuming
the CME to be an expanding “flux-rope” whose length increases

with time as its cross-sectional area expands (see http://
lepmfi.gsfc.nasa.gov/mfi/Mag_Cloud_Model.html fora cartoon), we can use
A(t) = 2π R(t) L(t),(5)

where L(t) is the length of the flux-rope cylinder at time t, andcan be related to the “height” H of the CME above the solar
limb via
L(t) = 2 π H(t).

(6)

The height above the solar limb H is the most commonly measured quantity for limb CMEs, but it is not clear how well it canbe estimated for the halo CMEs we are considering. We consider
this aspect further in Sect. 4 below. Using Eqs. (5), (6), and (4)in Eq. (3), we have
Z T
2
Ui = 4π Na
D⊥ H(t) dt.
(7)0

The density inside the near-Earth magnetic cloud would be
Ni =

Ui
,
π R(T )2 L(T )(8)and it can be related to the magnitude M of the Forbush decrease
viaRT
4 π 0 D⊥ H(t) dt
Na − Ni ∆N
αM =
=
=1−
,
(9)
Na
Na
R2 (T ) L(T )where L(T ) and R(T ) denote the length and cross-sectional radius at time T , when the ejecta has reached the Earth. The quantity α denotes the fraction of the total decrease that can be attributed to the CME/magnetic cloud. As mentioned earlier, thisfraction is typically around 50% (Wibberenz et al. 1997), so weadopt α = 0.5 in our calculations. We discuss the effect of variations in α on our final result in Sect. 7.
3.1. Cross-field diffusion coefficient

We now turn our attention to the cross-field diffusion coefficient D⊥ , which governs the diffusion of the ambient highenergy protons into the CME across the magnetic fields that enclose it. Protons can travel perpendicular to the direction of theaverage magnetic field as a result of normal transport of particles due to scattering or drift, as well as the braiding/mixing of
the magnetic field itself. The extent of cross-field diffusion depends on several parameters, such as the proton rigidity (whichindicates how tightly the proton is bound to the magnetic field)

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

1113

Table 1. Derived parameters for Forbush decrease for the 2001 April 11 event.
Quantity
FD magnitude
FD onsetFD end1σ2 (Kolmogorov)
1

NW
2.51
15:36
15:07
0.02

N
2.51
17:31
13:55
0.02

NE
1.87
19:26
12:43
0.02

W
2.92
10:05
12:57
0.02

V
2.71
11:45
12:43
0.02

E
2.04
16:19
11:45
0.02

SW
2.58
06:58
09:36
0.02

S
2.37
09:22
11:02
0.02

SE
1.79
12:45
11:17
0.02

The FD end times refer to 2001 April 12.

and the level of turbulence, which can contribute to field linetransport, as well as proton scattering.
The issue of the cross-field diffusion coefficient is a subjectof intensive ongoing research, and a good way to proceed for our
purposes is to use the convenient parametrisation of the resultsof extensive Monte Carlo simulations of cosmic rays propagating through tangled magnetic fields given by Candia & Roulet(2004). Their results can be regarded as a superset of similar
work (e.g., Giacalone & Jokipii 1999; Casse et al. 2002); it contains all the preceding results and also extends the parameter
regime of the simulations. They give the following fit for the“parallel” diffusion coefficient Dk (which is due to scattering of
the particles back and forth along the mean field, as the field issubject to random turbulent fluctuations):s!2(1−γ)!2NkρρDk = c Lmax ρ 2
+
,
(10)
ρk
ρk
σ
where c is the speed of light and the quantities Nk , γ and ρkare constants specific to different kinds of turbulence whose
values are given in Table 1 of Candia & Roulet (2004). The
quantity Lmax is the maximum length scale of the turbulence.
Matthaeus et al. (2005) quote a value of Lmax = 106 km, basedon multi-spacecraft measurements of solar wind turbulence near
the Earth. This is similar to values quoted by other authors (e.g.,
Manoharan et al. 1994) who use very different methods. We takethe quantity Lmax to be a fixed number from near the Sun to
the Earth. Candia & Roulet (2004) call ρ the “rigidity”, but itis somewhat different from our usual definition. It is related tothe usual rigidity Rg by
Rg
rL
=
,
ρ=
Lmax
B0 Lmax(11)

where B0 is the mean magnetic field. The quantity σ2 is the turbulence level, and is defined as
σ2 ≡hB2r iB20(12)where Br is the turbulent magnetic field and the angular braces
denote an ensemble average. The cross-field diffusion coefficient(D⊥ ) is related to the parallel one (Dk ) byN⊥ (σ2 )a⊥ ,ρ ≤ 0.2


D⊥ 
!−2

(13)
=
ρ
2 a

Dk 

, ρ > 0.2.
 N⊥ (σ ) ⊥0.2

The quantities N⊥ and a⊥ are constants specific to different kindsof turbulent spectra, and are given in Table 1 of Candia & Roulet(2004). For concreteness, we assume a Kolmogorov turbulence
spectrum in our calculations. Equations (10) and (13) jointly define the cross-field diffusion coefficient. The magnetic field B0of the CME changes (weakens) as it propagates from the Sun

to the Earth, which means that ρ varies with time. We do notknow how B0 varies with heliocentric distance, but we can assume that the flux is frozen into the CME as it propagates fromthe Sun to the Earth. It may be argued that some of the magnetic
flux will be dissipated in driving the CME. However, on average,
even the flux detected by near-Earth magnetic clouds is enoughto account for some 74% of what is required to drive the CMEfrom the Sun to the Earth (Subramanian & Vourlidas 2007). The
frozen-flux assumption is therefore fairly accurate. This meansthat the product of the magnetic field and the cross-sectional areaof the CME remains approximately constant, i.e.,
#2
R(T )
,
B0 (t) = BMC
R(t)
"

(14)

where BMC is the magnetic field inside the magnetic cloud. The
quantity R(t) is related to the measured expansion velocity Vexp
and the starting radius R0 of the halo CME by
R(t) = Vexp t + R0 .

(15)

We note that the measured quantities R0 and R(t) are the lateralextents of the halo CME measured in the plane of the sky, andare thus representative of the lateral expansion of the CME crosssection.
3.2. Constraining σ2

For a given Forbush decrease event, we measure the quantity
M, and Eqs. (15), (14), (13), (11), and (10) jointly define thecross-field diffusion coefficient D⊥ , which can be used in Eq. (9).
Unfortunately, there is not much simplification possible in theexpression for D⊥ ; the quantity ρ typically straddles regimes
such that both the terms under the square root in Eq. (10) andboth the branches of Eq. (13) need to be retained, and whenD⊥ is finally substituted into Eq. (9) the integral needs to beevaluated numerically. As we see below, we have concrete observational values for all the quantities used in Eq. (9) except
the turbulence level σ2 (Eq. (12)), and it is this quantity that
we seek to constrain. Owing to the different cutoff rigidities indifferent bins and remaining anisotropies, the magnitude M of
the Forbush decrease (for a given event) differs from bin to bin.
Consequently, we obtain slightly different estimates for σ2 fora given event, which can be regarded as a scatter (Tables 1–3).
For a given bin, we adopt a single number for the proton rigidity,
which is equal to the cutoff rigidity for that bin. For instance, we
adopt Rg = 17 GV for the vertical bin, and the values of Rg forthe other bins correspond to the respective cutoff rigidities listed
in Sect. 2.1. We note that this is a simplifying assumption, for amuon detected in a given bin can in fact be produced by protons
possessing a range of energies. We next describe the characteristics of the three events we have selected for our study.

1114

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

Table 2. Derived parameters for Forbush decrease for 2003 October 29 event.
Quantity
FD magnitude
FD onsetFD endσ2 (Kolmogorov)
∗

NW
6.81
00:58
18:00
2.48

N
6.78
23:46∗
17:16
2.49

NE
5.21
22:34∗
16:19
2.55

W
7.76
00:58
19:12
2.45

V
7.76
00:00
18:14
2.45

E
5.85
23:17∗
16:19
2.52

SW
6.92
00:53
18:43
2.48

S
6.82
00:14
17:16
2.49

SE
5.26
23:31∗
15:07
2.55

V
1.24
05:02
04:54
0.06

E
1.04
21:07
05:00
0.06

SW
1.24
06:29
04:16
0.06

S
1.24
11:02
04:12
0.06

SE
0.88
21:07
02:54
0.06

These times refer to 2003 October 28.

Table 3. Derived parameters for Forbush decrease for 2003 November 20 event.
Quantity
FD magnitude
FD onsetFD end1σ2 (Kolmogorov)
∗
1

NW
0.90
13:12∗
04:57
0.06

N
0.91
11:46∗
04:26
0.06

NE
0.89
02:10∗
02:32
0.06

W
1.26
01:26
06:00
0.06

These times refer to 2003 November 21.
The times for FD end refer to 2003 November 24.

4. 2001 April 11 event
4.1. Magnetic cloudThis event had its genesis in a halo CME that started at
05:30 UT on 2001 April 10 (http://cdaw.gsfc.nasa.gov/
CME_list/). The starting radius was R0 = 2.84 R⊙, and the lateral (plane-of-sky) expansion speed was Vexp = 2411 km s−1 .
Based on an examination of several halo CMEs, Schwenn et al.
(2005) conclude that the radial speed V is typically 0.88 times
the expansion speed Vexp of a halo CME. This gives V =0.88 Vexp = 2121 km s−1. The corresponding magnetic cloud was
detected by the ACE spacecraft at 04:00 UT on 2001 April 12,
while the shock reached the Earth at 15:18 UT on 2001 April 11(Lynch et al. 2003). Munakata et al. (2003, 2005) have modelled the magnetic cloud associated with this event as a cylinder
with a Gaussian cross-sectional profile for the cosmic-ray density depletion inside it. They analysed the cosmic-ray directional
anisotropy from muon detector measurements from several stations. Assuming that this anisotropy arises from a diamagnetic
drift due to the interplanetary magnetic field and the density gradient inside the magnetic cloud, they have derived best-fit parameters for the 3D cylindrical model of the magnetic cloud as
it passes across the Earth. The length of the flux rope at time t is
L(t) = 2 π H(t) = 2 π(V t + R0 ).

(16)

The length L at time T is simply
L(T ) = 2π 1 AU.

(17)

It may be noted that we are using the value R0 for the initialvalue of the observed height H above the solar limb. This is notquite right for full halo CMEs, since R0 is really the observed
lateral extent of the CME. However, this is the only concreteobservational quantity available, and the error is not expected tocontribute significantly to our final result for σ2 (see Sect. 7).
The time elapsed between the first observation of the halo CME
and the detection of the magnetic cloud by the ACE spacecraft
is 46.5 h. The average speed of the magnetic cloud by the time itreaches the ACE spacecraft is 640.6 km s−1 (Lynch et al. 2003),
and the spacecraft is located around 1.5 × 106 km from the Earth.
We therefore estimate that the magnetic cloud would have taken∼0.6 h to traverse the distance between ACE and the Earth. The
total time T = 46.5 + 0.6 = 47.1 h. The radius of the magnetic
cloud is R(T ) = 0.106 AU, and magnetic field at the centre of thecloud is estimated to be (Lynch et al. 2003) BMC = 17.8 nT.

Fig. 9. The muon flux in the nine directions is shown for the Forbush
decrease on 2001 April 11. The fluxes are shown as percentage deviation from mean values. The dashed red lines show the unfiltered data,
while solid black lines show the data after applying a low-pass filter.
The dotted blue lines show the fits to filtered data. The vertical lines ineach panel mark the arrival times of shock and magnetic cloud at the
Earth.

4.2. Forbush decrease

Table 1 gives the start and end times and magnitudes of the
Forbush decrease in different bins for this event, as well as thecomputed values of the turbulence level σ2 (Eq. (12)). The shockassociated with this event impacted the Earth at 15:18 UT, 2001
April 11 (Huttunen et al. 2005) and the magnetic cloud first intercepted the ACE spacecraft at 04:00 UT, 2001 April 12 (Lynch
et al. 2003). Evidently, the magnetic cloud was observed on the
Earth after the start of the Forbush decrease and well before its
end in all the directional bins. It therefore stands to reason that
it will have contributed substantially to the overall Forbush decrease. As discussed in Sect. 3, we adopt a value of α = 0.5,

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

Fig. 10. The muon flux in each of the nine directions for the Forbush
decrease on 2003 October 29. The line-styles and markings are the sameas Fig. 9.

which means that the magnetic cloud contributes to 50% of theoverall Forbush decrease.

5. 2003 October 29 event
5.1. Magnetic cloudThis was an exceptional event associated with an X17 flare close
to the central meridian, together with a very fast halo CME. This
full halo CME was first observed at a starting radius of R0 =5.84 R⊙ at 11:30 UT on 2003 October 28 (http://cdaw.gsfc.
nasa.gov/CME_list/). As with the other events, the quantity
R0 really represents the first observed lateral extent of the halo
CME. The quantity L(T ) can be taken to be the same as definedin Eq. (17). The lateral expansion speed of the CME as discerned
from coronograph data is Vexp = 2459 km s−1 , and the radial
expansion speed is related to Vexp by V = 0.88 Vexp as before.
The length of the flux rope at a given time t is given as before by
Eq. (16).
Kuwabara et al. (2004) have derived best-fit parameters forthe 3D cylindrical model of the magnetic cloud as it passes
across the Earth using the methods described in Munakata et al.
(2003, 2005). They estimate the radius of the magnetic cloud tobe R(T ) = 0.14 AU, the magnetic field at the centre of the cloud
to be BMC = 44 nT, and the time of closest approach of the cloudaxis to be 16:27 UT on 2003 October 29. The ACE observations(Huttunen et al. 2005) reveal that the magnetic cloud made its entry at 12:00 UT, 2003 October 29. The time elapsed between thefirst observation of the halo CME (11:30 UT, 2003 October 28)
and the time it was intercepted at the ACE spacecraft (12:00 UT,
2003 October 29) is 24.5 h.
We could not find data for the magnetic cloud speed as measured by the ACE spacecraft. We therefore used the estimateof ∼1400 km s−1 from Kuwabara et al. (2004) for the magnetic
cloud speed. At this speed, the magnetic cloud would take only
∼0.3 h to traverse the distance of 1.5 × 106 km between the1115

Fig. 11. The muon flux in each of the nine directions is shown for the
Forbush decrease on 2003 November 20. The linestyles and markings
are the same as those for Fig. 9.

ACE spacecraft and the Earth. The total time T is therefore
T ≃ 24.8 h. It may be noted that the CME liftoff speeds for thisevent and one previously discussed (2001 April 11) are similar.
However, the event of 2001 April 11 decelerates significantly enroute to the Earth, as a result of which the total travel time T is
almost twice as long as for this event.
5.2. Forbush decrease

The Forbush decrease on 2003 October 29 was among the largest
observed by the GRAPES-3 muon telescope, and it is describedin detail in Nonaka et al. (2006). The time profiles of the decrease as observed by the different modules is shown in Fig. 10of that paper. The derived parameters from the Forbush decrease
profiles in the different directional bins are given in Table 2,
where the magnitude of Forbush decrease derived here from thefit to the filtered data are systematically lower than those observed in the raw data, which were reported earlier (Nonaka et al.
2006). The onset and recovery times in the 2003 October 29 FD
event were relatively faster and thus the reduction in magnitudeis largely caused by the removal of a higher frequency component due to the use of a low-pass filter to remove the diurnal
variations. The shock ahead of the ejecta impacted the Earth at
05:58 UT, 2003 October 29 (Dryer et al. 2004), and the magnetic cloud was detected by the ACE spacecraft at 12:00 UT,
2003 October 29. We noted earlier that it takes around 0.3 h forthe cloud to travel the distance between ACE and the Earth ata speed of 1400 km s−1; in addition to this, if one accounts forthe travel time between the leading edge of the cloud and thecentre using the same speed (and a cloud radius of 0.14 AU),
it results in an additional time of 4 h and 21 min. When added
to 12:00 UT, the final result agrees very well with the intercept
time of 16:27 UT quoted by Kuwabara et al. (2004) for the centre of the cloud. As with the 2001 April 11 event, the magnetic
cloud intercepts the Earth after the start of the Forbush decrease
and well before its end in all the directional bins. The density

1116

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection fronts

Table 4. Summary of various observationally derived parameters for the three events we consider, leading to σ2 (Eq. (12)) as our final result.
Event2001 April 11
2003 October 29
2003 November 20

R0
(R⊙ )
2.84
5.84
6.3

Vexp
(km s−1 )
2411
2459
1660

T
(h)
47.1
24.8
49.4

depletion inside the magnetic cloud will therefore account fora substantial part of the overall Forbush decrease. This justifies
our use of α = 0.5 (Sect. 3) to account for the fraction of theoverall Forbush decrease related to the CME/magnetic cloud.

6. 2003 November 20 event
6.1. Magnetic cloud data

This magnetic cloud event was associated with an erupting filament and a halo CME, and was observed very well (Wang et al.
2006; Huttunen et al. 2005) by the WIND and ACE spacecraft.
Wang et al. (2006) have modelled this cloud as a cylindrical,
force-free flux rope to determine its radius and other parameters.
As we shall see, the Forbush decrease associated with this eventis less than those for the other two events studied in this paper.
However, it illustrates the diversity of events observed with the
GRAPES-3 experiment, and is associated with the best-studied
magnetic cloud of the three events considered in this paper.
The radius of the magnetic cloud as measured by the ACE
spacecraft is (Wang et al. 2006) R(T ) = T (7 h) × Vmax =7×3600×(750 km s−1) = 1.89×107 km, where we have assumed
that magnetic cloud moves with the maximum in-situ speed of
the ambient solar wind behind the shock Vmax = 750 km s−1 .
The magnetic field at the centre of the cloud is estimated to be(Wang et al. 2006) BMC = 50 nT. The most likely solar origin of this magnetic cloud is a full halo CME that was firstrecorded at 08:50 UT on 2003 November 18 at a height of R0 =6.3 R⊙ = 2.76 × 1012 cm (http://cdaw.gsfc.nasa.gov/
CME_list/). The plane-of-sky expansion speed Vexp of the halo
CME as recorded in the CME catalogue is Vexp = 1660 km s−1 .
Following Schwenn et al. (2005), we computed the radial speed
V = 0.88 Vexp = 1460 km s−1. The total time elapsed between
08:50 UT, 2003 November 18 (the time the CME was observed
at 6.3 R⊙ ) and 10.1 UT, 2003 November 20 (the time the mag
cloud was intercepted by ACE, Wang et al. 2006) is 1.76 × 105 s.
Since the ACE satellite is at a distance of ∼1.5×106 km from the
Earth, we estimate that it takes ∼2000 s for the magnetic cloud toarrive at the Earth at the solar wind velocity Vmax = 750 km s−1 .
Therefore, T = 1.76 × 105 + 2000 = 1.78 × 105 s.
6.2. Forbush decrease data

Table 3 gives the data derived from the Forbush decrease observed on 2003 November 20. This is a comparatively smaller
event, and there is considerable variation in start times for thedifferent bins. This variation is most probably due to uncertainty
caused by oscillations in the fluxes before the decrease (mainlyin the NE and N bins), some of which even remain in the filtered data. In this case since the magnitude of Forbush decreaseis comparatively small, the diurnal variations are comparable tothe decrease, and it is not possible to fit the unfiltered data to obtain any meaningful estimates for the parameters of the Forbush

R(T )
(AU)
0.10
0.14
0.12

BMC
(nT)
17.8
44
50

Average σ2 (Kolmogorov)
2%
249%
6%

decrease; hence, it is necessary to only use the filtered data forthis purpose. Furthermore, it is very likely that there is some
CME-related anisotropy remaining in the data, and removing it
requires the technique used by Munakata et al. (2003, 2005) andKuwabara et al. (2004), which is outside the scope of the current
paper.
The shock driven by the CME arrived at the ACE spacecraftat 07:27 UT (Huttunen et al. 2005). Since the average shock
speed from the sun to the Earth is 1020 km s−1 (Wang et al.
2006), it would take around 1470 s to traverse the ∼1.5 million km between the ACE satellite and the Earth, and it would
have reached the Earth at around 07:51 UT, 2003 November 20.
On the other hand, the ACE spacecraft first intercepts the magnetic cloud at 10:06 UT (Wang et al. 2006), and the cloud would
have reached the Earth at around 10:36 UT on 2003 November
20, taking some 2000 s to traverse the distance between ACE
and the Earth at the solar wind velocity of Vmax = 750 km s−1.
Comparing these times with the start times of the Forbush decrease given in Table 3, it is evident that the magnetic cloud start
time is before the start time in most of the bins, and after it ina few of them. However, the end of the Forbush decrease takes
place well after the entry of the magnetic cloud. Thus the overall
decrease should have contributions from both the shock and theejecta/magnetic cloud, and we assume that the CME/magnetic
cloud-related component of the decrease accounts for 50% of
the total decrease, as discussed earlier in Sect. 3. The estimate of
the turbulence level σ2 (Eq. (12)) given in Table 3 was computed
according to the procedure discussed in Sect. 3.

7. Results
We use the observational parameters for each event summarisedin Tables 1–3 using the procedure outlined in Sect. 3.2 to constrain the turbulence level σ2 (Eq. (12)) for each event. Thisquantity represents the ratio of the energy density in the turbulent
magnetic fields to that in the mean magnetic field. We computed
σ2 separately for each directional bins, and the results are listed
in the last row of Tables 1–3. The average value of σ2 for each
event is quoted in Table 4.
We note that the turbulence levels near the CME/ejecta front
for the 2001 April 11 and 2003 November 20 events are fairly
small (around 2% and 6% respectively). These numbers arecommensurate with what would be expected in the general quiescent solar wind at a few tens of R⊙ (e.g., Spangler 2002). The
turbulence level near the CME/ejecta front of 2003 October 29,
on the other hand, is significantly higher (around 249%) and isrepresentative of fairly strong turbulence. This is not surprising,since this event was a much stronger one, and was associatedwith a significantly faster shock. It is conceivable that strong turbulence associated with the shock front can affect the vicinity of
the CME/ejecta behind it.
Our final result regarding the turbulence level σ2 is not very
sensitive to the precise value of α (Eq. (9)). A change of a factor

P. Subramanian et al.: Forbush decreases and turbulence levels at coronal mass ejection frontsof 2 in α changes σ2 by 2 to 4%. We also pointed out earlier thatthe estimate for the initial height of the full halo CMEs is madefrom the first observation of the lateral extent of the CME, R0 .
This is the only concrete observable quantity for halo CMEs, andwe have verified that an error of 1 R⊙ in R0 will result in an errorof around 2% in the estimate of the turbulence level σ2 . The decrease magnitudes vary somewhat from one direction to the next,
as noted earlier. We have verified that these differences in the estimate of the Forbush decrease magnitude contribute a scatter of
only around 2% to our final result for the turbulence level σ2 .
The parameters that influence our final result most strongly are
the average propagation speed V and the total time T elapsed
between the time when the CME was first observed and when it
was intercepted as a magnetic cloud by the ACE spacecraft.

8. Summary
We have focused on the contribution of the CME/ejecta in producing Forbush decreases observable from the Earth, using data
for three events observed with the GRAPES-3 tracking muon
telescope at Ooty. We selected events that clearly have their origins in full-halo CMEs that originate close to the centre of thesolar disc. The Forbush decreases produced by these events will
therefore be due to the shock, as well as to the CME/ejecta.
While it is somewhat difficult to precisely separate out the shockassociated and CME/ejecta-associated contributions, it is reasonable to assume that the CME/ejecta effects accounts for 50%of the overall Forbush decrease. We used CME measurementsfrom LASCO and magnetic cloud measurements from WIND
and ACE to obtain various geometrical parameters of the CME
and its near-Earth manifestation. The CME is a substantiallyclosed magnetic structure that starts out with a negligible number of high-energy protons inside it. We consider the diffusionof high-energy cosmic-ray protons into the CME as it propagates and expands on its way from the Sun to the Earth. Since
the diffusion primarily takes place across the magnetic fields that
enclose the CME, we use an expression from the literature forthe cross-field diffusion coefficient that is derived from extensive simulations of cosmic rays propagating through turbulent
magnetic fields. The diffusion coefficient depends upon several
quantities like the ratio of the proton Larmor radius to the maximum scale length of the turbulence ρ (Eq. (11)) and the levelof turbulence σ2 (Eq. (12)). The turbulence near the CME is
expected to result in a magnetic-field line random walk, leading to scattering of protons and contributing to their cross-field
diffusion.
We constrained the magnitude of σ2 (which is the ratio of theenergy density in the random magnetic fields to that in the largescale magnetic field) in the vicinity of the CME front for eachof the events we analysed. We find that the turbulence level σ2near the CME front for the 2001 April 11 Forbush decrease eventis ∼2% and ∼6% for the event of 2003 November 20, while it is∼249% for the much more energetic event of 2003 October 29.
These estimates may be regarded as an average over the journey of the CME from the Sun to the Earth, for we do not take its
possible radial evolution into account. The radial evolution of σ2
is unlikely to be appreciable, at least in the outer corona, as we
discuss below. If we take turbulent magnetic field fluctuations
to be representative of those in the electron density (Spangler
2002), we note that the power-law index for electron density
fluctuations ∆Ne as a function of heliocentric distance ranges
from −2.2 (Manoharan 1993) to −1.7 (Fallows et al. 2002). Thisis fairly close to the power law index of the background electron density Ne , which is around −2 in the outer corona (e.g.,

1117

Leblanc et al. 1998). In other words, the quantity ∆Ne /Ne does
not vary appreciably with distance from the Sun, and we cansurmise that σ2 behaves similarly.
To the best of our knowledge, these are the first quantitative
estimates of the turbulence levels near CME fronts. Manoharan
et al. (2000) have noted that the turbulent density spectra of
the plasma near CMEs are significantly flatter than what is observed in the slow and fast solar wind, and are similar to what
exists in the near-Sun solar wind acceleration region. However,they were unable to comment on the level of the turbulence.
Badruddin (2002) suggests that the level of turbulence near
the CME/magnetic cloud might influence the magnitude of the
Forbush decrease. However, he only considered the local effectof the turbulence, while our treatment takes into account the cumulative effect of the turbulence near the CME on the crossfield diffusion of protons into it. Wibberenz et al. (1998) quote
the results of Vanhoefer (1996) who makes a simple estimate of
the cross-field diffusion coefficient by calculating the “filling in”
timescale of the CME by energetic protons. This method results
in a rather low estimate for the diffusion coefficient, and theyspeculate that this might be due to the smooth magnetic fields
enclosing the CME. Our treatment considers this aspect in detail, incorporating the expansion of the CME, as well as results
for the cross-field diffusion coefficient adopted from extensive
numerical simulations.

Acknowledgements. We thank D. B. Arjunan, A. Jain, the late S. Karthikeyan,
K. Manjunath, S. Murugapandian, S. D. Morris, B. Rajesh, B. S. Rao, C.
Ravindran, K. C. Ravindran, and R. Sureshkumar for their help in the testing,installation, and operating the proportional counters and the associated electronics and during data acquisition. We acknowledge the administrative services of V.
Viswanathan. We thank A. A. Basha, G. P. Francis, I. M. Haroon, V. Jeyakumar,and K. Ramadass for their help in the fabrication, assembly, and installation ofvarious mechanical components and detectors. The Japanese members of the
GRAPES-3 collaboration acknowledge the partial financial support from the
Ministry of Education and Science of the Government of Japan for the GRAPES3 experiment. Part of this work was carried out when P. Subramanian was at the
Indian Institute of Astrophysics. We are grateful to the Tibet neutron monitor
group for the use of their data. We thank the referee, M. Duldig, for several comments and suggestions that have significantly improved the content of the paper.
This paper is dedicated to the memory of S. Karthikeyan who passed away recently.

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