Correlative Analysis of hard and Soft X-rays in Solar Flares using CGRO/BATSE and YOHKOH

9 Pages·1996·0.4 MB·English

by  Zarro, Dominic M

C:.qrelm;ive Analysis of Hard and Soft X-rays
i.n Solar F_ares using CGRO/BATSE _ld YOHKOtI
FINAL REPORT
NAS5-32791
S-_ ,4
Submitted to:
NASA/GSFC Greenbelt, MD 20771
Submitted by:
Dominic M. Zarro
Applied Research Corporation,
8201 Corporate Dr. Landover, MD 20785.
Date:
September 20, 1996
1. INTRODUCTION
Thisreport
describes research performed under the Phase 4 Compto,_ Ga:l..._.a-Ray Observatory (CGRO) Guest
Investigator Program. The objective of this work is to sludy, differer.t mechanisms of solar flare heating by comparing
their predictions with simultaneous hard and soft X-ray observ_ttions. The datase_s used in this work consist of hard
X-ray observations from the CGRO Burst and Transient Source Experiment (BATSE) and soft X-ray observations
.from the Bragg Crystal Spectrometer (BCS) and Soft X-ray telescope (SXT) on the Japanese Yohkoh spacecraft.
2. WORK PERFORMED
(a) Assembling of Datasets
Hard X-ray data necessary for the proposed study were obtained by searching the CGRO/BATSE archive at the
Solar Data Analysis Center (SDAC). The search focussed on impulsive single-loop solar flares for which BATSE
Large Area Detector (LAD) Continuous Data (CONT) were available during tile hard X-ray rise phase. The CONT
data consist of 2.048 second time resolution hard X-ray spectra in 16 channels spanning the range 20 keV to above
300 keV. The high signal-to-noise CONT spectra provide._mation on the energy spectrum of accelerated electrons
on a timescale comparable with simultaneous soft X-ray observations (_ 3 sees).
Soft X-ray data were obtained by searching the SXT and BCS archives at the SDAC, the Institute of Space and
Astronautical Science (ISAS) in Japan, and the Naval Research Laboratory (NRL). The SXT data consist of full-Sun
and partial frame filter images in the 2-10 /_soft X-ray range at approximately 2 arcsec spatial resolution. The
images provide loop geometry information during and pre- and main flare phases. The BCS data consist of Ca XIX
spectra in the 3.16-3.2/_ soft X-ray range and provide diagnostics of the flare temperature and density. A total of
100 flares were found for which simultaneous CGRO and Yohkoh were available.
(b) Data Reduction
Reduction of BATSE/CONT data required convolving a model photon spectrum with the detector response matrix
(DRM) and comparing it with the measured count spectrum at various intervals during the hard X-ray impulsive
phase. The model spectrum consisted of thermal bremsstrahhmg emission plus a power-law component I = ac-7.
The parameters of the model spectrum were adjusted to minimize X2. This analysis was performed using the SPEX
IDL package developed by R. Schwartz at the SDAC. Figure 1 shows a model power-law fit for one of the flares in
the sample.
The power-law fit parameters were used to derive the number flux of accelerated electrons, assuming a thick-target
model for producing hard X-rays. The number flux is given by (Lin and Hudson 1976):
Nob, _--3 x 1033a(7 - 1)2B('r - 1/2, 1/2)E_ -_ (1),
where B(x, y) is the beta function and Ec is the low-energy cutoff in the power-law energy spectrum of the electrons.
The cutoff energy is a free parameter that is determined from the data analysis.
Reduction of the BCS Ca XIX spectra involved fitting synthetic resonance and dielectronic satellite line spectra to
the Ca XIX profiles to determine the characteristic temperature T and emission measure EM = f n_'dV of the soft
X-ray emitting plasma. This analysis was performed using software developed by the Principal Investigator. Figure 2
shows a model spectrum fit for one of the flares in the sample. The derived emission measures were combined with
geometry information from simultaneous Yohkoh Soft X-ray Telescope images to compute the electron density n
I_I':__,,,"t°_::;t--. LAD/CONi- D[=-i , 3 ()f:_-S_:_p-92
100.000
10.000
"7,
--R
1.000
E
¢.}
"7.
¢/1
{D 0.100
O
O
¢.-
Q.
0.010
0.001
10 ._'1.,00 1000
Energy (keV)
Interval 12
09:03:52.45- 09:04:00.64
f_vth_bpow parameters: 1.000e-05, 1.000, 0.5843, 4.444, 400.0, 1.930
Figure 1. Power-law fit to the BATSE LAD CONT spectrum at the time of the rust hard X-ray burst for a flare observed on
6 September 1992
of the flare plasma. The latter is given by n __ k/EM/2fAL, where A and L denote the cross-sectional area and
half-length, respectively, of the flare loop. The parameter f is the loop filling factor which is determined from the
data analysis.
(c) Data Analysis _.
The simultaneous hard and soft X-ray data were analyzed using a flare heating model in which plasma is Joule
heated by magnetic field-aligned coronal currents, and electrons are runaway-accelerated simultaneously by DC-
electric fields (I-Iolman 1985, Tsuneta 1985). A novel analysis technique was developed in which the DC-electric field
strength could be derived by solving a simplified equation of energy balance. The energy balance equation (integrated
over the loop volume) is given by:
VdU/dt = VcQ¢_ - VP_ (2),
where U = 3nkT is the total thermal energy of the flare loop, Qcurr is the current heating rate (assumed uniform
along the loop), and Prad = 2.2 x lO-19n2T -1/2 is the energy loss due to radiation. The parameters n and T refer to
the density and temperature within the loop, respectively. The latter parameters are expected to become spatially
uniform after approximately a hydrodynamic timescale (-_ 30 - 60 s). The volume of the current-heated region Vc is
assumed to be less than the total volume V of the loop. From the ratio of these two volumes, the loop filling factor
f = 14/V is defined.
For a loop that is heated uniformly by current-dissipation, the Joule heating rate is given by:
Chan 3: Ca XlX 6-SEP-92 09:03.",.1"c., " E (3.0 s)
1.4"106
1.2"106
1.0,106 Te6 = !7.1 + 1.4 MK(2)
Vturb= 162.80 + 21.05
"7, EM48= 1.502 + 0.,531 (2)
_O
VEL =-169.0+ 32.3 km
8.0,105
U
t- Wshift=10.25 + 0.12 mA
O
6.0,105 Chi2/n = 1.630
FiLLev= 3
n
v
4.0,105
Lt.
2.0°105
0
3.170 3.180 3.190 3.200
WAVELENGTH (Ang)
Figure 2. Spectral fittoBCS Ca XIX spectrum for a flareobserved on 6 September 1992 showing two-component temperature fit
to line profile.
Qcurr = nkTv,(E/Eo) 2 ergs cm -s s-i (3),
where _e _ 3.2 x lO:nT -3/_ s-1 is the thermal collision frequency (for classical resistivity), E is the electric field
strength (assumed uniform along the loop length), and Ez) = 7 x 10-SnT -i volts cm -i is the Dreicer field. The
Dreicer field is the field strength at which all the electrons in the plasma undergo thermal runaway.
Given T and n from soft X-ray observations, the energy balance equation is reduced to the two unknowns: E and
f. Two different methods were developed and applied for solving the energy equation assuming different constraints
on the unknown parameters.
Method (1): Constant Filling Factor
It is expected that the observed plasma will be filamented into numerous unresolved structures. Electrodynamic
arguments indicate that filamentation is necessary to ensure a stable current system in which the overall self-induction
magnetic field of current-carrying electrons is less than the ambient magnetic field strength. Substituting Qc,,,r into
equation (2), the following dependence of E on the filling factor f was derived:
./(r) + Pr.,)
(4).
E= Eo v ]_-_.
The parameter f was assumed to be constant in time and a grid of solutions for E as a function of time was

the observed flux. In this case, the densi:;> _'¢ithin the current-heaz, ed region w&s too low to provide a large enough
population of thermal e]ectrons to undergo runaway. For f < .001, runaway acceleration also failed to match the
observed number flux. gx_nination of equation-(5), shows that /_un "_ exp(-gD/E). Since Eo-"- n, the runaway
zate drops exponentially with increasing densi;,y. Physically, the runaway electrons become thermalized by collisions
when the density in the current-heated region becomes very large.
Method (2): Constant Low-energy Electron Cutoff
The assumption of a filling fa,ctor that is constant in time is likely to become invalid as the flare energy is distributed
.throughout the loop system and.the heating process extends to possibly multiple loops. The,following method was
developed to avoid this assumption.
Combination of the observed nonthermal thick-target flux [equation (1)] with the predicted runaway electron
flux [equation (5)] gives an expression for the current:heating and acceleration volume Ve. Elimination of V_
from the energy-balance ¢Cluation- reduces it to a function of the unknowns, e = E/ED and E¢_it. Substitution
of E, rit= me(ED/E)v,2/2 further reduces energy-balance to an equation in the single unknown E.
Using the soft X-ray inferred values of n and T, no.t_ysically plausible solutions for E could be derived to
satisfy this equation. In general, it was found that for the typical range of soft X-ray electron temperatures of
10 - 25 x 106 K during the flare, the predicted number flux of runaway electrons was 2-3 orders of magnitude
below that required to explain the observed nonthermal electron flux implied by BATSE observations. One possible
resolution of the discrepancy is to invoke some form of anomalous resistivity that increases the effective collision
frequency and, thereby, increase the runaway flux (Holman 1985). This solution is considered somewhat adhoc given
that the physical parameters defining anomalous resistivity are not well understood. A second means for increasing
the number of nonthermal electrons in the current channels is to invoke the existence of a hotter plasma component in
the acceleration region. The higher-temperature would raise the population of thermal electrons available to undergo
runaway and produce nonthermal hard X-rays.
The temperature in the acceleration region can be expressed in terms of the critical energy,
Tho_ = 2(EcriJk)(E/ED). A family of solutions to the energy balance equation was constructed for different values
of E,_it that were assumed to be constant in time. Figure 4 shows the resulting solutions for two flares observed
on 17 February 1992, and 13 January 1992 (the Masuda flare). In both flares, discrete values of E_ in the range of
40-55 keV were chosen. The resulting values of Thor varied in the range of 30 - 45 x 106 K. These temperatures
are consistent with typical super-hot values reported from high-spectral resolution germanium detector observations
(Lin e* al. 1981). As a further consistency check, the values of Thor were compared with the thermal temperatures
derived from ratio of the Yohkoh Hard X-ray Telescope (HXT) L (19-24 keV) and M1 (24-35 keV) energy channels.
Remarkably, the HXT temperatures fall well-within the range and variation of Thor.
3. SUMMARY
BATSE hard X-ray observations of solar flares have provided useful diagnostics for studying heating and accelera-
tion processes in solar flares. The present study has utilized high signal-to-noise BATSE spectral observations above
20 keV to determine the energization properties of accelerated electrons and to explore the effects of these electrons
on the thermal and nonthermal responses of loop plasma in solar flares. The analysis was strengthed by combining
BATSE hard X-ray data with simultaneous _bhkoh soft X-ray observations which provided additional constraints on
various model parameters.
5.0-107 _
r
k
4.0,107_ -
L 40 keY
35 keY
30 k©V
}-- 3.0"107 I-
2.0-10 7 i
F BCS Ca XIX
1.0"107 , I , , i , , I , , l , , I , , z , ,
17:27:00 17:27:30 17:28:00 17:28:30 17:29:00 17:29:30 17:30:00
Start Time=(t3-Jan-92 17:26:40)
6.0ol 07 _
i I
:HXT
_- 55 keV
4.0-10 7 _-- _t', " _-"....'_,,,_
I-- ; "_ "".... " '..
3.0.107 ;c-
2.0_107_
BCS Ca XlX
1.0.10 7
I , • p ,
I
15:40:00
15:41:00 15:42:00 15:43:00 15:44:00
Start Time (17-Feb-92 15:40:00)
Figure 4. Temporal variations of the the high-temperature component deduced from solving energy-balance in a loop with a DC-
electric field component. Shown are different temperature vaxiations in two flares (observed by CGRO/BATSE and Yohkoh) for
different values of the critical energy above which electrons axe accelerated by electron runaway. The computed temperatures are
compared with the temperatures inferred from Yohkoh HXT and BCS. The computed temperatures are more consistent with the
super-hot temperatures implied by HXT than the cooler soft X-ray temperature implied by BCS.
The main thrust of the analysis was to investigate how coronal currents and their associated DC-eleetric fields
can be used to self-consistently explain thermal and nonthermal emissions in solar flares. The analysis technique
involved the solution of a simplified ene.-gy-balance equntion in a q,:a.si-static loop that was uniformly heated by
field-aligned currents. The energy-ha.lance equation was rash:ted to the three unknowns: electric field strength" E,
filamentation factor f, an,] elecZrou low-energy cutoff E=. h family of so!utions for E was derived using two different
methods. In the first h-aethodr f was assumed constant in time and de:rived by matching-the predicted runaway
.electron flux with the BATSE-computed nouthetmai flu::. In this case, the energy-balance solutions required that
the filamented subregior_-occupy a volume that is _ 10-a of the-total loop volume. Such filamentation is necessary
to ensure a sufficiently high density of thermal electrons to undergo runaway acceleration. Strong fllamentation of
current--heated plasma is consistent with electrodynamic constraints that require a stable current system. In the
second method, the acceleration region was assumed to be at a different temperature from the thermM soft X-ray
emitting.plasma. In this case, the energy-balance solutions required th.at the acceleration region have temperatures
that are characteristically superhot.
Based on the joint analysis of CGRO and Yohkoh data, it is concluded that current heating and runaway accel-
eration mechanisms provide a viable means of explaining and understanding thermal and nonthermal processes in
solar flares. The above results have been presented at several meetings, including the "High Energy Solar Physics
Workshop" held in August 1995 at GSFC, Maryland, andS., workshop on "Observations of Magnetic Reconnection
in the Solar Atmosphere" held in Bath, England in March, 1996. These results are being prepared for publication in
the Astrophysical Journal.
REFERENCES
Holman, G.D. 1985, ApJ, 293,584
Holman, G.D., Kundu, M., and Kane, S. 1989, ApJ, 345, 1050
Lin, R.P.. and Hudson, H.S. 1976, Solar Phys., 50, 153
Lin, R.P., Schwartz, R.A., Pelling, R.M., and Hurley, K.C. 1981, 251, L109
Tsuneta, S. 1985, ApJ, 290, 353
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4. TITLE ANDSUBTITLE 5. FUNDING NUMBERS
Correlative Analysis of Hard and Soft X-rays in Solar Flares Using
CGRO/BATSE and YOHKOH Code 661
Contract: NAS5-32791
6. AUTHOR(S)
Dr. Dominic Zarro
7. PERFORMING ORGANIZATION NAME(S) ANDADDRESS(ES) 8. PERFORMING ORGANIZATION
REPORT NUMBER
Applied Research Corporation
8201 Corporate Drive, Suite I120
Landover, MD 20785 R96-254
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AGENCY REPORT NUMBER
NASA Aeronautics and Space Administration
CR-199886
Washington, D.C, 20546-0001
11. SUPPLEMENTARY NOTES
Technical Monitor: J. Norris, Code 661
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13. ABSTRACT (Maximum 200 words)
We propose to continue a study that we have commenced under the Cycle 2 and 3 Guest Investigator programs. Our
broad aim is to test the validity of different flare models by comparing their predictions with simultaneous CGRO BATSE
hard X-ray and Yohkoh soft X-ray observations. For the Cycle 4 program, we will locus on current heating and electric field
acceleration models. We will use BATSE spectral observations in the 20-300 keV provided by the Large Area and Spectros-
copy detectors to determine the nontherma[ hard X-ray emission component that is related to the rate 1_of accelerated
electrons. We will use Yohhok soft X-ray observations to deduce the temperature T, densityn, and associated thermal
heating rate Q in the flare plasma. We have developed an analysis technique that combines N and Q in a novel way to
determine the strength and variation of the De-electric field in solar flares.
14. SUBJECT TERMS 15. NUMBER OF PAGES
Sun, Flares, Corona 9.
16. PRICE CODE
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