A disturbance or coronal mass ejection being advected by the solar wind will expand at the fastest local characteristic speed - typically approximately the fast-mode speed. To estimate this characteristic wave speed and the velocity field in the ambient corona, it is necessary to know the magnetic field, temperature, and density. Only the density is known from coronal observations. The temperature, magnetic field, and velocity are not yet directly measured in the outer corona and must be estimated from a model. In this study, it is estimated that the magnetic field, solar wind velocity, and characteristic speeds use the MHD model of coronal expansion between 1 and 5 solar radii (R solar radii) with a dipole magnetic field at the base. This model, for a field strength of about 2 gauss at the base, gives flow speeds at low latitudes (near the heliospheric current sheet) of  250 km/s at 5 R solar radii and,  50 km/s at 2 solar radii, and fast-mode speeds to 400 to 500 km/s everywhere between 2 and 5 solar radii. This suggests that the outer edge of a velocity of mass ejection reported by MacQueen and Fisher (1983) and implies that the acceleration mechanism for coronal mass ejections is other than simple entrainment in the solar wind

Moore, R. L.

Suess, S. T.

English

NASA Technical Reports Server

WAVE SPEEDS IN THE CORONA AND THE DYNAMICS OF MASS EJECTIONS
Steven T. Suess and Ronald L. Moore
Space Science Laboratory, NASA Marshall Space Flight Center
Huntsville, Alabama 35812
ABSTRACT
A disturbance or coronal mass ejection being advected by the solar wind will expand at
the fastest local characteristic speed - typically approximately the fast-mode speed. To estimate
this characteristic wave speed and the velocity field in the ambient corona, it is necessary to know
the magnetic field, temperature, and density. Only the density is known from coronal observa-
tions. The temperature, magnetic field, and velocity are not yet directly measured in the outer
corona and must be estimated from a model.
In this study, we estimate the magnetic field, solar wind velocity, and characteristic speeds
using an MHD model of coronal expansion between 1 and 5 solar radii (Ro) with a dipole mag-
netic field at the base. This model, for a field strength of about 2 gauss at the base, gives flow
speeds at low latitudes (near the heliospheric current sheet) of <250 km/s at 5 R o and, <50 km/s
at 2 R o, and fast-mode speeds to 400 to 500 km/s everywhere between 2 and 5 R o. This
suggests that the outer edge of a mass ejection will appear to move at a nearly constant rate of
400 to 500 km/s between 2 and 5 R o. This result is in agreement with the observed velocity of
mass ejections reported by MacQueen and Fisher (1983) and implies that the acceleration mechan-
ism for coronal mass ejections is other than simple entrainment in the solar wind.
INTRODUCTION
The kinematics of coronal transients have been well described elsewhere. It is not our
intent to review this research or to put forth a new or original hypothesis for the origin of
coronal mass ejections. Rather, what we propose is to offer a deeper physical insight into the
dynamics of coronal transients in a way that relates to physical parameters of the corona. The
motivation for our study comes from the velocity data reported by MacQueen and Fisher (1983).
They examined the kinematic properties of several "loop-like" coronal transients over the range
1.2 to 2.4 Ro from Sun center. Their results are partially summarized in Figure l(a). In this
figure, velocity profiles for all of the transients analyzed are reproduced. In Figures l(c) and
l(d), the results are split into transients observed in the inner corona with the Mauna Loa K-
coronameter system and transients observed in the outer corona with the coronagraphs on Skylab
and the SMM. Radial expansion speeds are seen to range from 60 to 900 km/s - except for the
anomalous 6 September 1973 event. Flare-associated events were found to exhibit high speeds
and little acceleration with height. Eruptive-associated events exhibited large accelerations.
MacQueen and Fisher conjectured that the pressure gradient forces responsible for the generation
of the solar wind may play an important role in accelerating the eruptive-associated events.
Here, we examine the behavior of an isolated blob of gas riding upon the background solar
wind and suggest that this behavior is very much like the behavior of coronal mass ejections. The
distinction between the hypothesis made by MacQueen and Fisher and what we are describing is
that rather than riding passively on the solar wind, the expansion of the mass ejection into the
ambient medium is the main cause of the observed motion of the leading edge of the mass
ejection.
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https://ntrs.nasa.gov/search.jsp?R=19860015166 2020-03-20T15:24:43+00:00Z
RESULTS
The model that we use for our computation of characteristic wave speeds in and near
streamers is that published by Steinolfson, Suess, and Wu (1982) (hereafter referred to as SSW).
In that calculation, a model was developed for the formation of a steady coronal streamer through
numerical solution for the time-dependent, dissipationless MHD equations of motion in a
meridional phase, for axisymmetric flow. The flow is polytropic and the atmosphere is stationary
in magnetically closed regions and flowing outward in open regions. The solution is found
through a relaxation in time in a domain extending from 1 to 5 Ro and from pole to pole. The
flow and magnetic fields, density, and temperature are thus known everywhere in the corona.
CMEs never occur in coronal holes. Therefore, in using the results of SSW, we limit our-
selves to results in the neighborhood of the global streamer - polar angles of 90 degrees to 140
degrees (the equator lies at 90 degrees and the polar hole is centered at 180 degrees). The region
of interest is shown in Figure 2, modified from SSW. The closed field lines near 90 degrees are in
magnetostatic equilibrium - the flow speed there is effectively zero. In Figure 2, the shaded
portion is coronal hole-like and therefore excluded from consideration; three radial cuts through
the topology are indicated at 100, 120, and 140 degrees. Figure 3 shows the flow speed, sound
speed, and Alfv_n speed along these radii. A profile is not given for 90 degrees because that is
the magnetic neutral sheet, the field strength is zero there, and hence the Alfv_n speed is also
zero.
Also shown in Figure 3 is the flow + fast-mode speed, where we have used the term
"fast-mode" for the sum of the sound speed and the Alfv6n speed - strictly only a correct
terminology for propagation perpendicular to the magnetic field. We will ignore this distinction
because the propagation of a transient through the corona seems to strongly deform the ambient
field and hence almost certainly have its motion dominated by the Alfv_n speed.
Figure 3 shows that the flow speed is never very large in the vicinity of the streamer, that
the Alfvdn speed is quite large near the Sun, and - most striking of all - the sum of fast mode
and flow speed is both nearly constant in radius and on the order of 400 km/s. The sound speed
between 1 and 5 R o is so small as to be unimportant in this sum.
These results apply only to the streamer vicinity. The Alfv_n speed is quite different in
coronal holes and will be the subject of a separate study. However, near streamers, we feel the
tendency shown in Figure 3, for the flow speed + Alfv_n speed sum to be nearly constant in
radius, is representative of the corona in the vicinity of real streamers. The difference between
individual streamers will be dominated by field strength and density - the sum will be larger
for higher field strength streamers because the density does not rise as fast as the field strength
(SSW). For geometrically more compact streamers, there should be no qualitative difference -
the characteristic speeds will still be of the same order of magnitude.
DISCUSSION
The results shown in Figure 3 are relevant to mass ejections because the front edge of a
disturbance moving through the corona will always move at the fastest local characteristic speed
(Steinolfson, 1985). Thus, if we imagine a blob of plasma injected into the corona and having a
finite overpressure, then its center of mass will move upwards with the solar wind expansion
speed. In addition, its front edge (and back edge as well) will expand outwards away from the
center of mass with the fastest local characteristic speed in the solar wind moving frame of
reference.
263
An obvious question is why should the front edge necessarily be the same as the visible
front edge of a transient. It is true that it does not necessarily have to be the visible front edge.
However, if the front edge is initially visible at the beginning of the transient, then under normal
circumstances, we believe it will only get more visible. This is because a compressive disturbance
in the corona always steepens (Steinolfson, 1985; Zel'dovich and Razier, 1966; Montgomery,
1959; Cohen and Kulsrud, 1974; Steinolfson, 1981; Kantrowitz and Petschek, 1966).
It is also obvious that the sum of speeds shown in Figure 3(d) is a lower bound. After
a shock is formed, the front edge of the disturbance moves at the shock speed. Thus, no freely
expanding CME can move less rapidly through the corona than with the sum of speeds shown
here - about 400 km/s. This is the reason for the result quoted in a study of the numerical
simulation transients by Steinolfson (1982). There, he used the steamer model shown in Figure 2
and introduced a perturbation in pressure at the base. He found that, depending on the magni-
tude and character of the perturbation, he could generate a variety of propagating disturbances,
but that these disturbances never traveled outward more slowly than about 400 km/s in the
neighborhood of the streamer.
By the time a CME reaches a height of 2.0 solar radii, it should be almost free of whatever
initiated the transient or restrained it from freely moving outwards. Thus, on the order of the
time it would take for information to propagate across the transient with the local characteristic
speed, the front edge of CME will appear to be moving at the sum of the solar wind flow speed +
fast-mode speed.
Returning to the data shown in Figure 1, we also offer a hypothesis for why some CMEs
are moving slowly at heights of 2.0 R o and accelerating rapidly. Since the time for information
to propagate across the CME is short with respect to the time it takes the CME to reach these
heights, the CME cannot be moving outwards freely. Apparently the CMEs are being restrained
from moving outwards and the rapid acceleration reflects the release of this restraint. These con-
siderations suggest that the restraint is due to the linkage of the magnetic field in a CME back to the
surface and that this connection is not completely broken at distances below about 2 R o. These
events may therefore more accurately be called "coronal mass releases" rather than mass ejections.
REFERENCES
Cohen, R. H. and Kulsrud, R. M., 1974, Phys. Fluids, 17, 2215.
Kantrowitz, A. R. and Petschek, H. E., 1966, in Plasma Physics in Theory and Application (W. B.
Kunkel, ed.), McGraw-Hill, New York.
MacQueen, R. M. and Fisher, R. R., 1983, Solar Phys., 89, 89.
Montgomery, D., 1959, Phys. Rev. Letters, 2, 36.
Steinolfson, R. S., 1981, J. Geophys. Res., 86, 535.
Steinolfson, R. A., 1982, Astron. Astrophys., 115, 39.
Steinolfson, R. S., 1985, in the proceedings of the AGU Chapman Conference on Collisionless
Shock Waves in the Heliosphere, Napa Valley, California, 20-24 February 1984, in press.
Steinolfson, R. S., Suess, S. T., and Wu, S. T., 1982, Astrophys. J., 255, 730.
Zel'dovich, Ya. B. and Razier, Yu. P., 1966, Physics of Shock Waves and High Temperature
Hydrodynamic Phenomena, Academic Press, New York.
264
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RADIUS (SOLAR RADII)
Figure 1. (a) Radial speed of transients, including measurements from the Mauna Loa
K-coronameter, Skylab coronagraph, and the SMM coronagraph/polarimeter. (From
MacQueen and Fisher, 1983.) (b) Sum of flow speed and fast-mode speed for three positions
in and near an MHD model coronal streamer. (From Steinolfson, Suess, and Wu, 1982.)
(c) Data from panel (a) that were taken only with the Mauna Loa K-coronameter, with the
date the observations were made. (d) Data from panel (a) that were taken only from the
Skylab coronagraph and SMM coronagraph/polarimeter, with the date the observations
were made.
265
STREAMER
VICINITY
100°
90°
5 120°
t /
I /
,,, t t I
t / // 14oo
/ / /
3 t / /
f f /
/
f / /
2
180 °
1 2 3 4 5
Figure 2. Magnetic field lines and flow speed vectors for the MHD streamer model of Steinolfson,
Suess, and Wu (1982). The three radial cuts marked at 100, 120, and 140 degrees are where
the data shown in Figure 1(b) and Figure 3 were taken from.
266
(a) (b)
800
FLOW SPEED SOUND SPEED
w
-- 120o
I lOOO140°120 °E 0 1 5 5
o (c) (d)LLI
800
u_ ALFVEN SPEED FLOW + FAST MODE SPEED
o I o I
1 5 5
RADIUS (SOLAR RADII)
Figure 3. (a) Flow speed, (b) sound speed, (c) Alfv_n speed, and (d) sum of the flow speed, Alfve'n ("fast-mode") speed,
and sound speed along the three radial cuts through the streamer model shown in Figure 2.


Wave speeds in the corona and the dynamics of mass ejections

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