On the Deceleration of CMEs in the Corona and
Interplanetary Medium deduced from Radio and
White-Light Observations
M. J. Reiner , M. L. Kaisery and J.-L. Bougeret
Catholic University and NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
yNASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Observatoire de Paris, Meudon, France
Abstract. It is generally acknowledged that CMEs, especially the faster ones, must deceleration somewhere between the
high corona and interplanetary medium. However, the detailed characteristics and spatial region over which this deceleration
occurs is still largely unknown. Simultaneous radio and white-light observations can provide information on the speed profiles
of the CME or CME/shock in the high corona and/or interplanetary medium. These observations are consistent with constant
deceleration for most CMEs. From the theoretical or modelling point of view, it is usually assumed that the deceleration of
CMEs is due to a drag term, which is usually taken to be proportional to the relative speed of the CME compared to that of
the solar wind or to this relative speed squared. We point out that such a form for the drag force on the CME inevitably leads
to speed profiles that are inconsistent with both the radio and white-light observations.
above 2R, the fits to the height-time data are generally consistent with constant deceleration [6]. Modellers,
on the other hand, argue that once the CME is released
from the sun it is subject to a drag force as it propagates
through the interplanetary plasma. The analytical form of
this drag force is unknown. However, modellers generally assume that, in analogy with objects falling through
the atmosphere, it is proportional to the density and the
relative speed squared. In this paper we demonstrate that
such a form for the drag force on the CME is not consistent with the observed radio and white-light data.
INTRODUCTION
It is well known that CME speeds measured in the coronagraph are generally significantly higher than the speeds
implied either by their transit times to spacecraft far
from the sun or by the in-situ measured shock speeds
[19, 18, 5]. However, the spatial regime over which the
deceleration occurs and the detailed characterization of
the corresponding speed profiles are not well established,
due in part to the fact that the coronagraph measurements
extend only out to 30R .
Many CMEs, generally the faster ones, can drive
shocks that, in turn, can generate low-frequency radio
emissions [3, 1]. Since the density in the corona and interplanetary medium falls off with increasing heliocentric distance, these type II radio emissions will decrease
in frequency as the CME/shock moves farther from the
sun. Thus these frequency-drifting radio emissions can
provide an alternative method of measuring CME dynamics. Such radio measurements have the advantage
that they measure the radial speed or ’true" speed of
the shock. Therefore, they can be particularly useful for
deducing the dynamics for halo, Earth-directed CMEs,
where projection effects are important [7]. Furthermore,
the low-frequency radio observations can extend the distance range to well beyond 30R [8, 2, 10].
In those cases where there is significant deceleration
implied by the time-sequence of white-light coronagraph
images, it is generally found that, at least for most CMEs
RADIO AND WHITE-LIGHT
OBSERVATIONS OF A CME/SHOCK
In order to describe and understand the dynamics of
CMEs, it is necessary to make time sequenced, remote
observations of signatures of the CME as it propagates
through the solar corona and/or interplanetary medium.
One way of doing this is to analyze the time sequence
of images made by white-light coronagraphs. An alternative way of measuring the dynamics of CMEs is to use
the observed frequency drift of the radio emissions generated by the shock driven ahead of the CME [12, 17].
Both these methods are complementary. The white-light
observations are more direct but have the difficulty that
they are only plane-of-sky observations (which require
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
152
Radio observation for the January 14, 2002
CME
unknown projection effect corrections) and that they only
extend out to 30R . The radio observations, on the other
hand, measure the radial motion and can extend all the
way to 1 AU and beyond, but are less direct in that the observations are made in the frequency domain and therefore require a density model in order to convert to the
spatial regime. The limitations of each of these methods suggest that the best approach therefore is to use the
combined radio and white-light data and to determine the
CME dynamics by requiring consistency between the simultaneous radio and white-light observations [16].
The frequency-drifting type II emissions generated by
this January 14 CME are shown in dynamic spectrum in
Figure 2. A GOES M4.4 LDE X-ray, with peak intensity at 06:27 UT, was associated with this radio event.
As is usually the case, this CME associated flare was
accompanied by a very intense and complex type IIIlike radio burst [11, 14], which is the dominant (overexposed) feature shown in Figure 2. The weaker, much
more slowly drifting, diffuse radio emissions in Figure 2,
observed from 07 : 30 to 10 : 00 UT, are the type II
radio emissions that were generated as the CME/shock
propagated through the high corona and interplanetary
medium. To more readily discern the relationship between these frequency-drifting radio emissions and the
CME dynamics, we have plotted the dynamic spectrum
as inverse frequency versus time [9, 10]. The reason for
doing this is that in the interplanetary medium the plasma
density falls off as 1=R2, where R is the heliocentric distance, so that the observed radio frequency must scale
as 1/R. Thus plotting the radio dynamic spectrum as 1/f
versus time is essentially equivalent to plotting it as R
versus time. The dashed black straight lines in Figure 2
then correspond to the CME/shock moving through the
interplanetary medium at a constant speed. We get two
straight lines, one with half the slope of the other, corresponding to radio emissions at either the fundamental
or harmonic of the plasma frequency (as labelled). We
assumed that the diffuse type II emissions were at the
harmonic. The solid black curves in Figure 2, which provide a somewhat better fit to the observed frequency drift
of the type II emissions, corresponds to the shock moving with a constant deceleration of 14 m s;2 (see below). The height-time and velocity-time relation corresponding to this fit is shown by the solid curves in Figure
1. These curves are clearly consistent with the observed
white-light LASCO data for this near-limb CME.
White-light observation for the January 14,
2002 CME
On January 14, 2002 the SOHO/LASCO coronagraph
observed a white-light CME propagating outward from
SW solar limb. It first appeared in LASCO C2 at 05:40
UT at a height of 2:7R; it was visible in C3 at least to
09:00 UT, when it was at 26R. We estimated the leading edge height of the CME in each LASCO image and
display the corresponding height-time data by the dots
in Figure 1a. The CME initially accelerated until about
06:15 UT. However, after 06:15 UT the height-time data
can be fit either with a straight line (corresponding to a
constant speed of 1463 km/s) or with a modest deceleration (see below). The solar origin of this CME is not
known (there were no SOHO/EIT images), however the
SOHO/MDI images suggest a possible active site near
the western limb. Hence this height-time data may be
close to the true height-time relationship for this CME.
R (Rs)
(a)
(b)
v(km/s)
Speed profile for the January 14, 2002 CME
Possible speed profiles for the CME/shock can be
determined from the measured parameters of the shock
when it was observed in-situ. We then try to select the
"true" speed profile by requiring that the corresponding
height-time profile simultanouesly fit both the whitelight CME height-time data and the frequency-drifting
radio data [15].
The CME-driven shock for this event was observed at
Wind at 05:25 UT on January 17, 2002, corresponding to
a transit time to Earth of 71 hours, and therefore a transit
speed of 587 km s;1 . From the values of the plasma
Time (UT)
FIGURE 1. (a) Height-time plot for the CME observed on
January 14, 2002. (b) Corresponding velocity-time profile (see
text)
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January 14, 2002
1/frequency (kHz)
Type II Emissions
H
Type III Burst
F
06:00
07:00
08:00
09:00
10:00
11:00
Time (UT)
FIGURE 2. Dynamic spectrum of the Wind/WAVES radio emissions observed from 06:00 to 11:00 UT on January 14, 2002 in
the frequency band from 100 kHz to 14 MHz. This is a plot of the intensity of the radio emissions as a function of inverse frequency
(vertical axis) and time (horizontal axis).
parameters on either side of the shock, assuming a gas
hydrodynamic shock, we estimated a shock speed of 403
km s;1 . The fact that this shock speed is significantly
lower than the transit speed suggests that the CME/shock
must have decelerated between the sun and Earth. Some
of this discrepancy could also be due to the fact that
at Earth we observed the flank of this western-directed
shock. However, we ignore this additional complication
here; it is not critical to our argument.
Consistent with the low-frequency type II radio data
[12], we assume that the CME/shock accelerated at a
constant rate, a, until time, ta , i.e., v = vo + at, after
which it moved at a constant speed, v1AU , to 1 AU.
The determination of the acceleration profile, i.e., a and
ta , then depends on the initial speed vo , the measured
shock speed v1AU at 1 AU, and the transit time to 1
AU. Since in the present case the transit time to 1 AU
and the shock speed at 1 AU are known, for any given
initial CME speed, vo , we get a unique solution for the
CME speed profile from the sun to 1 AU. Specifically,
for the January 14, 2002 event, if we assume an initial
CME speed of 1500 km s;1 at 06:15 UT, when the
CME/shock was at 5:3R, then the known transit time
(71 hours) and the speed of the CME shock at 1 AU (403
km s;1 ) requires an acceleration of a = ;14 m s;2 and
a deceleration time of ta = 22 hours. The corresponding
speed profile, as a function of time (to 100 R), is
shown by the solid curve in Figure 1b and, as a function
of heliocentric distance (to 1 AU), by the solid curve in
Figure 3a. The height-time relationship calculated from
this speed profile is shown by the solid curve in Figure
1a and the acceleration relationship, in Figure 3b. The
height-time profile is clearly consistent with the LASCO
height-time data measured for this CME.
Now, in order to compare this CME speed profile with
the frequency-drifting type II emissions in Figure 2, we
next need to convert the corresponding height-time relationship in Figure 1a to a frequency-time relationship.
To do this we assumed a 1=R2 falloff of the plasma density in the interplanetary medium. Then, we adjusted the
value of the density at 1 AU in order that this corresponding frequency versus time curve provide a "best fit" to the
type II frequency drift over the entire frequency range of
the type II emissions shown in Figure 2. This procedure
gave the solid black curves in Figure 2. This fit, which
corresponds to the best overall simultaneous fit to the radio and white-light data, corresponded to a density, normalized at 1 AU, of 15 cm;3.
This procedure can be repeated for other assumed
initial speeds for the CME, in each case solving for the
deceleration and deceleration time, given the contraints
imposed by the known transit time and the shock speed
at 1 AU. In each case, we determined the "best fit" to the
frequency drifting type II data by adjusting the density
at 1 AU. Each case will yield a somewhat different
curve on the 1=f versus time dynamic spectrum. For
example, an initial speed of 1800 km/s, would require
an acceleration of a = ;23 m s;2 and a deceleration
time, ta = 6.25 hours, with density at 1 AU of 24 cm ;3.
However, this solution (not shown) does not provide as
good a simultaneous fit to the white-light and radio data.
CME DECELERATION VIA A DRAG
FORCE
In the above example we have shown that the speed
profile of the CME or CME/shock deduced from the
frequency drift of the type II radio emissions and the
CME height-time measurements is consistent with con-
154
stant deceleration for a finite time period. On the other
hand, modellers typically assume that the deceleration
of CMEs in the solar corona and interplanetary medium
is caused by a drag force [4]. This drag force, FD , is
commonly assumed to be proportional to v 2 , i.e., FD /
Av2 , where is the plasma density of the medium
(corona or interplanetary medium), A is the effective
area, and v is the speed relative to the medium. If this
drag force is the primary cause of CME deceleration,
then it is clear that this will lead to a CME deceleration
that is not constant in time. To illustrate this we suppose
that, after the initial ejection of the CME, this drag force
and gravity (which gives only a small contribution) are
the only forces acting on the CME. Then we have,
ent. There is no way that we can adjust the parameters so
that the solution would provide a reasonable fit either to
the white-light height-time data or to the frequency drift
of the type II radio emissions. These results then suggest
that the commonly assumed analytical expression for the
drag force is inconsistent with the CME dynamics implied by both the observed radio and white-light observations, i.e. it will lead to a CME velocity profile that is
inconsistent with the data. Either this is not the correct
form for the actual drag force acting on the CME or the
drag force is not what causes the CME to decelerate. It is
also clear that using a drag term proportional to the velocity will also yield a nonconstant deceleration, which
is inconsistent with observations.
2
m ddtR2 = G MR2m ; CD 2o Ao (v ; vsw )2
CONCLUSION
(1)
where CD is the drag coefficient, m is the CME mass,
vsw is the solar wind speed, G is the gravitational constant and M is the solar mass. In writing Eq. (1) we assumed that = o =R2 and that A = Ao R2. Eq. (1) was
then solved for the speed profile. We did this by starting
with the known shock speed at 1 AU and then integrating
Eq. (1) inward towards the sun. The values of the various parameters for this CME are unknown, so we simply started with typical values, which were then adjusted
until the solution approached 1R after 71 hours. As
typical values we have taken o = 50 10;20 kg m;3,
CD = 0:5, m = 1:0 1012 kg, A = 0:6 1021 m2 ,
vsw = 3:5 105 m s;1 , v = 4:0 105 m s;1 ,
The solution to Eq. (1) is shown by the dashed curves
in Figures 1 and 3 and by the dot-dashed white curves
in Figure 2. In comparing this solution with the velocity
profile determined from the fits to the white-light and radio data, we see that this solution is fundamentally differ-
In this paper, we have demonstrated that quite reasonable
fits to the dynamics of CMEs, implied by simultaneous
white-light and radio data, are obtained by assuming constant deceleration in the high corona and interplanetary
medium. We have further demonstrated that the commonly used analytical form for the drag force can not
account for the observed CME deceleration as implied
by the white-light and radio data. Therefore, in the spirit
of Galileo Galilei, it is proposed here that a number of
CMEs be dropped from La Torre di Pisa and that their
drag forces be directly measured.
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v(km/s)
(a)
a(m/s2)
(b)
R (Rs)
FIGURE 3. (a) Velocity-distance relationship for the January
14, 2002 CME. (b) Acceleration-distance relationship.
155