Initiation and Acceleration of a Flareassociated Coronal Mass Ejection

1
Initiation and Acceleration of a Flare-associated
Coronal Mass Ejection

• Peter T. Gallagher1,3, Gareth R. Lawrence2,3, and
  Brian R. Dennis3
• 1L-3 Communications EER Systems, Inc, 2Catholic
  University of America, 3NASA Goddard Space Flight
  Center

Introduction
A high-velocity (2500 km s-1) coronal mass
ejection (CME) associated with the 2002 April 21
X1.5 flare is studied using a unique set of
observations from the Ramaty High Energy Solar
Spectroscopic Imager (RHESSI), the Transition
Region and Coronal Explorer (TRACE), and the
Ultraviolet Coronagraph Spectrometer (UVCS) and
Large Angle and Spectroscopic Coronagraph (LASCO)
instruments on board SOHO (see Figure 1). The
images in Figure 2 show that the event was first
observed as a rapid rise in RHESSI X-rays,
followed by two simultaneous brightenings that
appear to be connected by an ascending loop-like
feature in TRACE (Figure 3). While expanding, the
appearance of the feature remains remarkably
constant as it passes through the TRACE 19.5 nm
passband and LASCO fields of view, allowing its
height-time behavior to be accurately determined
(Figures 4 and 5). The acceleration is consistent
with an exponential rise with an e-folding time
of 138 s and peaks at 1500 m s-2 when the
leading edge is at 1.7 R from Sun center. The
acceleration subsequently falls off with an
e-folding time of over 1000 s. At distances
beyond 3.4 R , the height-time profile is
approximately linear with a constant velocity of
2500 km s-1. Figure 6 shows multiple hard X-ray
(gt25 keV) bursts detected by RHESSI during the
peak acceleration phase of the CME, while Figure
7 shows the gradual rise of the soft X-ray
source, presumed to be below the energy release
site. These results are briefly discussed in
light of recent kinematic models of
flare-associated CMEs (see Figure 8).
RHESSI 12-25 keV
RHESSI 12-25 keV RHESSI 50-100 keV
Figure 3 Top panels TRACE 19.5 nm difference
images created by subtracting each image from a
frame taken at 004230 UT. Bottom panels LASCO
C2 and C3 images showing the similar morphology
of the eruption as it propagates away from the
solar surface.
Figure 1 The 2002 April 21 X-class flare and
CME in RESSI, TRACE, EIT, and LASCO.
Figure 4 Height-time evolution of the 2002 April
21 CME from TRACE, UVCS, and LASCO C2. The data
are shown with 5 pixel error bars. Also given
are best fits for a constant and an exponentially
increasing acceleration.
Figure 7 The height-time evolution of the soft
X-ray source observed with RHESSI and the
post-flare loop tops seen in the TRACE 19.5 nm
images. The presumed rising energy release site
results in the formation of hot loops that cool
and appear sequentially in the different
passbands of the two instruments. After 0300
UT, the cooling time from the 15 MK temperatures
seen by RHESSI to the 1.5 MK seen in the TRACE
19.5 nm bandpass is 4-hours.
Figure 2 TRACE 19.5 nm and RHESSI 12-25 and
50-100 keV images at four times during the flare.
The RHESSI contour levels are at 25, 50 and 75
of the peak flux for each energy band.
Figure 5 (a) The height-time profile for 0047
- 0320 UT. (b) and (c) give the velocity and
acceleration profiles obtained by taking the
first and second numerical derivatives,
respectively. The first-difference values are
given as filled circles, while the three-point
difference values are given using the same symbol
scheme as in (a). The solid lines give the best
fit to the data using Equation 4 for an
exponentially rising acceleration followed by an
exponentially falling acceleration. (d) The
GOES-10 soft X-ray flux for the corresponding
time period.
Coronal Mass Ejection Models
Coronal Mass Ejection Dynamics
To quantify the height-time profile, we consider
three acceleration models. The first assumes
constant acceleration, the second a simple
exponential rise, while the third includes an
exponential rise followed by an exponential
decay. Each acceleration model can be numerically
integrated to obtain the height-time profile as
follows                                      
                             where t is the
time after initiation (taken to be 0047 UT), h0
and v0 are the initial height and velocity,
respectively, and a(t) is the acceleration.
RHESSI 12-25 keV
TRACE 19.5 nm
RHESSI 50-100 keV
  Following Alexander et al. (2002), the simple
case of constant acceleration (a) that might
apply early in the time history is considered.
The best-fit to the data points up to 0106 UT
gives h0 24 3 Mm, v0 13 13 km s-1, and a
117 24 m s-2. As can be seen from Figure 4,
the fit does not well represent the UVCS and
LASCO C2 data points but is acceptable for
heights within the TRACE field of view. A
best-fit of an exponentially varying acceleration
of the form a0 exp(t/?) is also given in Figure
4. As can be seen, this function, with h0 12
3 Mm, v0 0 13 km s-1, a0 48 2 m s-2, and
? 486 8 s, provides an acceptable fit to the
TRACE, UVCS, and LASCO C2 points.
Figure 8 The Flux-Rope Model of Forbes Priest
(1995). (a) The height (h) above the solar
surface of a two-dimensional flux rope as a
function of footpoint separation, ?. (b) and (c)
The flux-rope initially moves closer to the solar
surface as the footpoints converge. A critical
point is then reached which results in flux-rope
ejection. (d) Subsequent current-sheet formation
below the erupting flux-rope.
Further Information Alexander, D., Metcalf, T.
R., Nitta, N., GRL, 29(10), 1403,
2002. Gallagher, P. T., Lawrence, G. R., Dennis,
B. R., ApJ, L53, 588, 2003. Gallagher, P. T.,
Dennis, B. R., Krucker, S., Schwartz, R. A.,
Tolbert, A. K., Sol. Phys., 210, 341,
2002. Forbes, T. G., Priest, E. R., ApJ, 446,
377, 1995. Images, Movies, and Reprints can be
found at http//hesperia.gsfc.nasa.gov/ptg/hess
i/20020421/
Figure 6 RHESSI lightcurves for 0040 0140
UT. The flare is first seen in the 3 - 6 and 6
12 keV energy ranges, starting at 0040 UT.
After a gradual rise at soft X-ray energies, a
rising loop-like feature is observed in the TRACE
field-of-view, which moves away from the surface
with an exponential acceleration profile. Hard
X-ray impulses with energies gt25 keV are only
observed close to the peak of the CME
acceleration profile.
The acceleration time data in Figure 5(c)
suggests an exponential rise, followed by an
exponential decay. A function that shows this
behavior is                                   
                                    where ar
and ad are the initial accelerations and ? r and
?d give the e-folding times for the rise and
decay phases. A best fit to the height, velocity,
and acceleration data was obtained with h0 25
2 Mm, v0 40 4 km s-1, ar 1 1 m s-2, ? r
138 26 s, ad 4950 926 m s-2, and ? d 1249
122 s and is shown in Figure 5.
v