Radial dependence of propagation speed of solar wind
disturbance
Masahiro Yamashita∗ , Munetoshi Tokumaru∗ and Masayoshi Kojima∗
∗
Solar-Terrestrial Environment Laboratory, Nagoya University, Japan.
Abstract. We studied the propagation of interplanetary counterpart of coronal mass ejections (ICMEs) by using interplanetary
scintillation (IPS) measurements of the Solar-Terrestrial Environment Laboratory at 327MHz. In this study, we analyzed
data of the solar wind disturbance factor, so-called g-value, derived from our IPS measurements. We analyzed two ICME
events observed in 1997 and 2000. We assumed a shell-shape ICME model, defined by six parameters (location, propagation
directions, radial thickness, angular width, and enhancement factor). We determined the most suitable set of those parameters
by matching the model calculations of g-value to IPS observations. Then, we determined the radial variation of the propagation
speed of CME or ICME by comparing our IPS data with coronagraph data and in-situ data. As result, it is found that the
propagation speed of ICME decelerated as V ∝ r−1.05 for the 2000 event and V ∝ r−0.55 the 1997 event.
INTRODUCTION
IPS G-VALUE
Coronal mass ejections (CMEs) are important phenomena because of their large influence on the magnetosphere of the Earth. Therefore, a lot of studies of the dynamics of CMEs near the Sun have made by using coronagraph observations. The knowledge on dynamics of interplanetary counterpart of CMEs (ICMEs) is important,
particularly from the viewpoint of the space weather prediction. However, dynamics of ICMEs are little understood, because ICME observations depend on a limited
number of spacecraft. From the study using in-situ data
near the earth, ICMEs are found to propagate at around
the ambient solar wind speed which ranges from 400 to
800 km/s [1]. On the other hand, it has been reported
from the coronagraph measurements that the propagation
speeds of CMEs range from less than 50 to greater than
2000 km/s [2]. These facts suggest that the radial evolution of the ICME propagation speed takes place between
the corona and 1AU through the interaction with the ambient solar wind.
Interplanetary scintillation (IPS) measurements conducted by the Solar-Terrestrial Environment Laboratory
(STEL), Nagoya University, at 327 MHz [3] allows us
to map the global structure of ICMEs at radial range between 0.2 and 1 AU [4, 5]. In the present paper, we investigated the three-dimensional (3-D) structure of ICMEs
by using our IPS observations and studied radial dependence of the propagation speed of the ICME by combining our data with coronagraph and in-situ observations.
Radio waves from a cosmic radio source are scattered
by the solar wind. As a result, intensity fluctuations are
observed as IPS on the ground. An amplitude of the IPS
depends on the solar wind density fluctuations along the
line-of-sight (Los). The scintillation index m, which is
defined by
< ∆I >
(1)
I
represent the strength of IPS. Here, I is an observed
source intensity, and ∆I is an intensity fluctuation. For
weak scattering, the m-index is related to the solar wind
fluctuations via the following formula
m=
m2 =
ω (z)[∆Ne ]2 dz
(2)
where ω (z) is the weighting function, ∆N e is the level
of solar wind density fluctuations, and z is the distance
from the observer to the radio source along the Los.
The m-index decreases with the radial distance from the
Sun, because solar wind density fluctuations decrease
approximately as r −2 . In addition, the m-index depends
on the apparent size of radio source.
To correct these dependences, we have calculated a
normalized factor, g-value [6], which is given by
m
(3)
m
where m is the mean level of IPS for a given distance.
If we observe the quiet solar wind, the g-value becomes
around an unity. If density enhancements due to ICME
g=
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
754
pass across the Los, the g-value enhances abruptly to
g > 1.
Density enhancement ratio
Angular width
ICME MODEL AND FITTING ANALYSIS
Distance
The g-value obtained form IPS observations corresponds
to an integration of density fluctuations along the Los.
(Equation (2)) Therefore, we have to remove the effect
of the Los integration in order to extract 3-D information
on ICMEs from the g-value data. Although we have removed the effect of the Los integration from IPS observations successfully by using the computer assisted tomography (CAT) method [7, 8, 9], the CAT method is only
applicable to the analysis of a quasi-stationary structure
in the solar wind, therefore we can’t use the CAT method
for a transient component such as ICMEs.
In this study, we have performed the model fitting
analysis to obtain unbiased estimates of the ICME structure from g-value data. If the spatial distribution of ∆N e
is given by a appropriate model, the g-value can be calculated by using Equation (2). This means that we can
determine the ∆Ne distribution by optimizing the model
calculations to observed g-value data. We assume here
that the disturbance has a shell-shape and an isotropic
expansion speed in the radial direction. In this model,
density fluctuations ∆Ne are given as follows.
Latitude
Sun
Longitude
Radial thickness
Earth
FIGURE 1. Shell-shape ICME model defined by six parameters (location, propagation directions, radial thickness, angular
width, and enhancement factor). We made the g-value calculation using this model and determined the best fit parameters.
Event on July 12, 2000
A large active region NOAA 9077 generated some large
flares accompanied by CMEs on July 2000. An ICME
was observed by our IPS measurements on July 12, 2000,
and this is considered to be associated with the M5.7/2B
flare occurred at 21:05 UT on July 10, 2000. A CME was
observed by the LASCO coronagraph in association with
r − r0 2
θ − θ0 2
1
) )+1) this flare. The associated shock arrival was reported from
∆Ne (r, θ ) = 2 ( fenh exp(−(
) )exp(−(
r
dr
dθ
(4)
in-situ measurements of SOHO/Proton Monitor at 9 UT
where f enh is the enhancement factor of ∆N e at the center,
on July 13, 2000.
dr is the radial thickness, d θ is the angular width of
Event on November 8, 1997
the disturbance, r 0 is the distance from the Sun to the
disturbance, r is the distance to a given point, and θ − θ 0
An ICME observed by our IPS observation on Nov. 8
is the angle between the propagation direction and the
1997 is considered to be associated with the X9.4/2B
direction of a given point. Figure 1 illustrates the ∆N e
flare occurred at 11:55 UT on Nov. 6, 1997 and this flare
model. In order to determine the best fit parameters, we
was accompanied with a CME. This CME had a high
calculated the rms deviation χ 2 between observed and
speed, and showed deceleration in the field of view of
calculated g-values. We searched a set of parameters that
LASCO coronagraph. No shock arrival was observed for
2
minimize χ by adjusting model parameters ;
this ICME event.
χ 2 [gobs,i , gcal,i (r0 , θ , dr, d θ , f enh ); (i = 1, n)] ⇒ min (5)
CME SPEED MEASUREMENTS FROM
LASCO DATA
where n is the number of the Los.
ANALYZED EVENTS
We estimated the CME speed in the field of view of
LASCO coronagraph by using C2 and C3 images for two
events analyzed here. We calculate CME speeds from
the location of the leading part of the CME along the
propagation direction of the ICME determined by the
model fitting analysis of IPS data.
In this study, we analyzed ICME events observed by IPS
measurement on July 12, 2000 and November 8, 1997.
755
FIGURE 2. (left) The observed all-sky map of g-value on July 12, 2000 and (right) the result of the model calculations using
the best fit parameters. The dotted circles are constant r contours drawn every 0.3 AU. A center of open circles corresponds to the
location of radio source and a diameter of them represents a level of the g-value.
RESULTS
Event on July 12, 2000
Table 1 shows the best fit parameters obtained by the
model fitting analysis. Figure 2 shows observed g-values
(left) and the result of model calculations using the best
fit parameters (right).
The propagation speeds of the CME derived from
LASCO C2 and C3 images are plotted diamonds and
stars respectively in Figure 3. Here, a mid point between
two adjacent LASCO observations is used as a reference
point for CME speed data, and horizontal bars denote the
distance interval. By comparing coronagraph data taken
at the largest distance with the result of IPS analysis, we
calculated a mean propagation speed between the corona
and the inter planetary (IP) space. This value is plotted by
a square in the figure. By combining the IP shock data at
1AU with the result of IPS analysis, we also calculated
a mean speed between the IP space and the earth orbit.
This speed is shown by a circle in Figure 3. As shown in
Figure 3, the CME accelerated rapidly within 10 Rs, and
then decelerated with increasing distance. In this study,
we focused on the deceleration of ICME. To evaluate
a strength of the ICME deceleration, we fitted speed
data by a function of V = α r −β , where V is an ICME
FIGURE 3. The propagation speed of CME and ICME for
July 12, 2000 event. Speed data from C2 and C3 images,
LASCO - IPS and IPS - in-situ are denoted by diamonds, stars,
a square and a circle symbols respectively. The solid curve
corresponds to the deceleration curve V ∝ r−β with β = 1.05.
speed relative to the ambient solar wind speed, and r is
the distance from the Sun. For the ambient solar wind
speed, we used the proton speed of 500 km/s observed
by SOHO/Proton Monitor just before the shock arrival.
As a result, we obtained β = 1.05.
Event on November 8, 1997
The best fit parameters obtained from the model fitting analysis are shown in Table 2. The radial variation
of propagation speeds of CME or ICME are shown in
Figure 4. The figure suggests that the CME decelerated
slowly in the corona, and also suggests that the ICME
decelerated rapidly as moving from the Sun. A solid line
corresponds to the deceleration curve V ∝ r −β with the
TABLE 1. Obtained the best fit parameters for observation
on Jul. 12, 2000
Distance
Long.
Lat.
Thickness
Angular
width
Density
enhancement
0.56
-36
15
0.12
33
7.2
756
TABLE 2. Obtained the best fit parameters for observation
on Nov. 8, 1997
Distance
Long.
Lat.
Thickness
Angular
width
Density
enhancement
0.60
-50
11
0.13
30
7.4
consistent with this expectation. We need further study
to examine the effect of ambient solar wind on the ICME
propagation in more detail.
SUMMARY
In this study, we made the g-value calculations using a
shell-shape ICME model, and determined six parameters
of the model by matching observed g-value with model
calculations. By combining this result with coronagraph
data and in-situ observations, we clarified the radial evolution of ICME speeds between the corona and the Earth
orbit. We analyzed the ICME events occurred on Jul. 12,
2000 and Nov. 8, 1997. As a result, the ICMEs were
found to decelerate rapidly as they propagated from the
Sun. We compared the strength of deceleration between
those events. As a result, it is found that the propagation
speed of ICME decelerated as V ∝ r −1.05 for the 2000
event and V ∝ r −0.55 the 1997 event.
FIGURE 4. The propagation speed of CME and ICME for
July 8, 1997 event. The solid curve corresponds to the deceleration curve V ∝ r−β with β = 0.55.
ACKNOWLEDGMENTS
best fit parameter of β = 0.55. Here, we used the speed
of 400 km/s obtained from the CAT analysis of our IPS
observations for the ambient solar wind speed.
We used CME images taken by the SOHO/LASCO coronagraph and in-situ data taken by the SOHO/Proton
Monitor. We would like to thank engineering support
from Y. Ishida and N. Yoshimi.
DISCUSSION
REFERENCES
Smart and Shea [10] reported that the blast wave shock
front speed should vary as r −0.5 when the solar wind density decrease as 1/r 2 . We obtained r −0.55 speed dependence for the Nov. 8, 1997 event. This result agrees with
the Smart and Shea model. On the other hand, the Jul.
12, 2000 event showed a radial deceleration of r −1.05 .
This value is steeper than that in the result by Smart and
Shea [10], i.e. Vs ∝ r−0.5 . Thus, our result suggest that
the deceleration profile of IP shock does not necessarily
follow the r −0.5 dependence, and that it depends on the
condition of the ambient solar wind.
Vršnak and Gopalswamy [11] reported the aerodynamic drag force in the interplanetary space acts dominantly as a controlling factor of the ICME propagation.
An amplitude of this force is determined by the density
of ambient solar wind and the speed difference between
ICME and ambient solar wind. In the solar maximum,
the slow speed component of the solar wind becomes
dominant in the entire space of the heliosphere, so that
more intense drag force effect is expected to take place
for the solar maximum ICME event, since the ICME has
to penetrate into a dense slow wind. The fact that the
event Jul. 12, 2000 event showed a steep deceleration is
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