A Numerical Study on the Evolution of CMEs and Shocks in
the Interplanetary Medium
J. A. González-Esparza, A. Lara, A. Santillán† and N. Gopalswamy
Instituto de Geofísica, UNAM, México
DGSCA-Cómputo Aplicado, UNAM, México
The Catholic University of America, Washington DC
†
Abstract. We studied the evolution in the solar wind of four CMEs detected by SOHO-LASCO which were associated with
ICMEs and interplanetary (IP) shocks detected afterward by Wind at 1 AU. The study is based on a 1-D hydrodynamic single
fluid model using the ZEUS code. These simple numerical simulations of CME like pulses illuminate several aspects of the
heliocentric evolution of the ICME front and its associated IP shock and we were able to reproduce some characteristics of
the IP shocks and ICMEs inferred from the two-point measurements from spacecraft. The simulation shows that ICMEs and
IP shocks follow different evolutions in the interplanetary medium both having phases of about constant speed propagation
followed by an exponential deceleration with heliocentric distance. IP shocks always propagate faster than their associated
ICME drivers and the former began to decelerate well before the IP shock. The results indicate that, in general, although an
IP shock is driven by its ICME in the inner heliosphere in most of the cases this is not true any more when they approach to
1 AU.
TABLE 1. Four CMEs detected by LASCO and their
associated transient shocks and ICME detected posteriorly by Wind at 1 AU.
INTRODUCTION
Coronal mass ejections (CME) and interplanetary (IP)
shocks play a predominant role in solar-terrestrial relations. We study the dynamics between the Interplanetary counterpart of a CME (ICME) and its associated IP
shock to answer the following question: how far from
the Sun does an IP shock is driven by its ICME? We
simulated four events which were observed by a coronograph near the Sun and afterward in-situ by an spacecraft at 1 AU, employing the numerical code ZEUS-3D
(version 4.2). This code solves the system of ideal MHD
equations (non-resistive, non-viscous) by finite differences on an Eulerian mesh [1]. In order to simplify the
calculations, we neglected all magnetic effects and assume spherical symmetry. These simplified 1-D hydrodynamic numerical simulations of interplanetary disturbances have proved to be very useful in understanding
the basic physical aspects of the injection and heliospheric evolution of solar disturbances [2, 3, 4, 5, 6, 7, 8].
Since the dynamics of an IP shock and its ICME driver
have important 2-D and 3-D effects (e.g., the shock
strength varies along the shock front, the shock-ICME
separation is greater at the shock wings than at the shock
nose, the IP shock has a larger angular extent that its
driver, etc.), our 1-D results are limited to the direction
of the nose of the IP shock and its ICME driver.
A
B
C
D
†
LASCO
CME time
Wind
shock time†
Wind
ICME time
1/06/97 15:10
2/07/97 00:30
4/07/97 14:27
5/12/97 06:30
1/10/97 00:52
2/09/97 12:50
4/10/97 12:55
5/15/97 01:15
1/10/97 05:00
2/10/97 03:00
4/11/97 06:00
5/15/97 10:00
taken from [9]
taken from [10]
NUMERIC SIMULATIONS
The study is based on four halo CMEs (referred as A,
B, C and D) observed by SOHO-LASCO, which were
related to ICME signatures and IP shocks detected afterward by the magnetic and plasma experiments on board
Wind spacecraft. Table 1 shows the times of the four
CMEs near the Sun and their interplanetary counterparts
at 1 AU.
Following a technique similar to that of Gosling and
Riley [1996], we produced the ambient solar wind by
specifying the fluid speed, density and temperature at
an inner boundary located beyond the critical point
(Ro =0.08 AU), and then allowing the code to evolve and
reach an equilibrium state that mimics the observed val-
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
206
CME A (GAMA=1.5)
550
velocity (km/sec)
500
75h
35h
5h
450
400
350
300
density
1000
100
FIGURE 2. Speed evolution of the front of ICME A and its
associated IP shock with heliocentric distance.
10
temperature (K)
1
bitrarily as small jumps with respect to the ambient wind
ahead. We should keep in mind that there is a large uncertainty in estimating the physical characteristics of a
halo CME based on coronograph observations [11].
105
104
0.2
0.4
0.6
0.8
1.0
Heliocentric distance (AU)
RESULTS
FIGURE 1. Propagation of ICME A (solid case) and its
associated IP shock (arrow) at three different times after the
CME injection. The continuous line in the background is the
undistorted ambient wind.
The four events correspond to CMEs propagating with
speeds faster than their ambient winds ahead. Figure 1
shows the evolution of ICME A and its associated IP
shock as they propagate in the interplanetary medium.
This event corresponds to the CME with the lowest increase of speed with respect to the ambient wind and
shortest injection time (Table 2). The figure shows the
plots of velocity, density and temperature at three different times after the CME initiation. At each time step the
code tracks the leading and trailing edges of the ICME
as well as the position of the IP shock and estimates
the shock parameters by solving the Rankine-Hugoniot
equations. The ICME expands radially as propagates outward from the Sun, while the IP shock separates from the
ICME.
Figure 2 shows the speed evolution of the ICME front
and its associated IP shock against heliocentric distance
for event A. The ICME front speed and the IP shock
speed have different evolution. The CME front suffers
a clear deceleration at 0.37 AU, at about 27 hours after
the CME injection, however, the IP shock propagates at
a constant speed until 0.7 AU (47 hours after the CME
injection) after which begins to decelerate. When the
ICME front and the IP shock propagate at about constant speeds, the shock-ICME radial separation increases
linearly with heliocentric distance; however, when the
ICME reaches the critical distance and begins to decelerate this radial separation increases exponentially with
heliocentric distance.
Figure 3 shows a similar plot that the previous figure
but for event C. The ICME front has a clear deceleration
from about 0.4 AU, 21 hours after the CME injection,
whereas its associated IP shock began to decelerate be-
ues of the solar wind at 1 AU. After the ambient solar wind has been established we injected a perturbation from the inner boundary to simulate the propagation
of a CME into the interplanetary medium. These CMElike perturbations were square pulses with a given initial
speed characterized by small increments in density and
temperature, over a finite extent of time [8]. We included
the solar gravity and assumed that the solar wind is an
ideal fluid with a ratio of specific heats, γ = 1.5. All numerical runs have a resolution of .0005 AU/zone with an
in-flow condition at the inner-boundary and an out-flow
condition at the outer-boundary.
Table 2 shows the initial conditions for the four simulations. At the left side there are the input parameters to
produce the numeric ambient wind and the ambient wind
(upstream of the IP shock) observed by Wind. Note that
by defining arbitrary conditions at the inner boundary we
are able to reproduce all the parameters of the ambient
wind measured by Wind for each event. In Table 2, the
events C and D presented an ambient wind with unusuallly very high densities (Nwind > 15 cm 3 ), whereas in
event B the solar wind speed (Vwind > 518 km/s) and
temperature (Twind 10 5 K) were relatively high compared to mean slow wind values. At the right side of Table 2 we have given the characteristics of the four CME
pulses. The values of the CME velocities and the time durations were inferred from analyzing the SOHO-LASCO
movies whereas the other CME values were assumed ar-
207
TABLE 2. Initial conditions for the four simulations. ( Left) Physical characteristics (velocity, density and temperature) of the
numeric ambient wind at the inner boundary (Ro=0.08 AU), the numeric wind at 1 AU and the ambient wind measured by Wind.
(Right) Physical characteristics of the CME-like pulses: initial speed, jumps in density and temperature with respect to the ambient
wind and CME temporal duration.
A
B
C
D
Vo
[km/s]
V 1AU
[km/s]
Vwind
[km/s]
373
380
270
308
377
521
307
322
378
518
306
321
Ambient solar wind
No
N1AU
Nwind
[cm 3 ] [cm 3 ] [cm 3 ]
990
880
2280
2800
6.8
4.4
13.9
18.6
6.5
4.4
15.2
19.5
To
[K]
T 1AU
[K]
Twind
[K]
2.5e5
1.6e6
4.5e5
3.1e5
2.8e4
1.5e5
4.6e4
3.4e4
2.6e4
1.6e5
4.6e4
3.2e4
CME like pulse
Vcme
∆N ∆T dtcme
[km/s]
[h]
473
480
880
700
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
4.4
7.5
5.6
10.4
FIGURE 3. Speed evolution of the front of ICME C and its
associated IP shock with heliocentric distance.
FIGURE 4. Speed evolution of the front of ICME D and its
associated IP shock with heliocentric distance.
yond 0.6 AU at about 31 hours after the CME injection.
Figure 4 shows the plot of the velocity versus heliocentric distance for event D. In this case the ICME front begins to decelerate at about 0.58 AU, 40 hours after the
CME injection, while the IP shock begins a clear deceleration at about 0.85 AU, 61 hours after the CME injection. Note that this longer distance for which the front
propagates at a constant speed is related to the long injection duration of this event. The results show that an
ICME begins to decelerate well before its associated IP
shock, indicating that, in general, most IP shocks are not
driven any more by the time they reach to 1 AU.
Table 3 compares the numerical results with the Wind
observations at 1 AU. The first three columns show the
ICME front speed observed by Wind, the corresponding
simulated results and their difference. In the case of event
A we obtained a poor agreement between the ICME
speed observation and the simulation with a difference
of about -78 km/s. However, for the other three events
the agreement is better and the difference is less than
ten percent. The next three columns in Table 3 show the
IP shock transit time. In this case there is an excellent
agreement between observation and simulation for all
four events, with the maximum difference being less
than two hours. The next three columns show the ICME
transit time. In this case there is a good agreement in 3 of
the four events, but in event C the ICME arrival time was
predicted about 17 hours before the Wind observation.
This might be a geometrical effect (e.g., the shock wing
passed by Wind instead of the shock nose), which cannot
be studied with this 1-D model. Finally the last three
columns show the temporal lag between the IP shock
and the ICME passing at 1 AU. In this case there is a
good agreement in event A and D, however in events B
and C the model predicts that the shock and the ICME
were a few hours closer than their corresponding Wind
observation. Again this may be a geometrical effect.
In summary these simple simulations reproduced most
of the features inferred from the observations.
DISCUSSION AND CONCLUSIONS
The ambient solar wind has a strong influence on the
propagation of ICMEs in the interplanetary medium:
Fast ICMEs decelerate as a consequence of interchange
of momentum with the solar wind ahead. CME C was
initiated about two times faster than CME B (Table 2),
however both events resulted in the same transit times
to 1 AU (Table 3). In the simulations the evolution of
the front of the ICME shows three different phases with
heliocentric distance [8]. After the initial injection, the
ICME suffers a strong deceleration during a couple of
hours reaching an intermediate speed with respect to the
208
TABLE 3. Comparison between Wind in-situ observations at 1 AU and the simulation results: ICME
front speed at 1 AU, interplanetary shock transit time, ICME transit time and shock-ICME temporal
lag.
ICME
speed at 1AU
wind
sim.
dif.
[km/s] [km/s] [km/s]
A
B
C
D
470
515
470
440
392
551
453
466
-78
+36
-17
+26
IP shock
transit time
wind sim. dif.
[h]
[h]
[h]
82
60
60
67
84
60
61
68
+2
-0
+1
+1
ambient wind1 , then it propagates at this approximately
constant speed until at certain point (0.35-0.6 AU), at
which it exponentially decelerates. This heliocentric evolution is consistent with results based on interplanetary
scintillation (IPS) observations of ICMEs [12, 13]. On
the other hand, the IP shock associated with a fast ICME
has a different evolution with two main phases, one having a small and quasi-constant deceleration until at certain point (0.5 - 0.84 AU) at which its deceleration increases exponentially with increasing heliocentric distance. An IP shock always propagates faster than its
ICME driver and the lateer began to decelerate well before the shock. In general, the simulations show that most
transient shocks are not driven any more by their ICMEs
when they reach 1 AU.
Finally, it is remarkable that the 1-D simulation is able
to capture most of the dynamic behavior of CMEs in the
interplanetary medium, consistent with the observations.
Problems such as the neglect of magnetic fields, assumptions of spherical symmetry and homogeneity of the ambient solar wind, and the inner computational boundary
conditions being too far from the Sun need to be considered in future simulations.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
ACKNOWLEDGMENTS
We are grateful to Pete Riley for providing the trace
subroutine and many useful discussions. This project was
partially supported by CONACyT project J33127-E.
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