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Statistical Properties of Hot Thermal Plasmas in M/X Flares Using
RHESSI Fe & Fe/Ni Line* and Continuum Observations
Amir Caspi†1,2, Sam Krucker2, Robert P. Lin1,2
† [email protected]; http://sprg.ssl.berkeley.edu/~cepheid/spd2007/ 1 Department of Physics, University of California, Berkeley, CA 94720
2 Space Sciences Laboratory, University of California, Berkeley, CA 94720
* (Fe & Fe/Ni line analysis not shown here)
IntroductionHard X-ray emission from “super-hot” thermal plasma (T > 30MK)
was first observed in solar flares by Lin et al. (1981), and has since been observed in a handful of large flares. The origins of such hot plasma remain poorly understood. We present the first results from a study investigating the following questions:
• What is the highest temperature achieved during flares, and when does it occur?
• Is there an intrinsic limit to the maximum flare temperature, and if so, on what does it depend?
• Does “super-hot” imply “super-energetic?”• Do “super-hot” flares behave differently than
merely “hot” flares?
Flare SelectionSince 2002, RHESSI has observed over 500 flares of GOES class M
and X, which are the most likely candidates for “super-hot” temperatures (GOES class is often used as a proxy for flare temperature). For analysis, we selected flares as follows:
• Flare occurred during 2002 to 2005• Good coverage of X-ray peak (currently defined as uninterrupted
observation over the full 10 minutes prior to GOES SXR peak)• Imageable with grid 3 (~7 arcsec FWHM) using CLEAN• Clearly identifiable HXR (25-50 keV) and SXR (6-12 keV)
peaks, occurring before the GOES SXR peak (in order: HXR, SXR [RHESSI], SXR [GOES])
• Time-series spectra are fit reasonably well by the model (below)
260 analyzable flares (234 M-class, 26 X-class)
Selected Flares
Heliocentric positions of the selected flares are shown; flares already processed
(results at right) are highlighted in red.
Sam
ple
Imag
e/S
pect
rum
Top
: a s
ampl
e C
LE
AN
imag
e us
ing
grid
s 3-
9 (e
x. 7
); th
e co
ntou
r (a
t 50%
of
peak
pix
el f
lux)
is u
sed
to
appr
oxim
ate
the
sour
ce v
olum
eB
otto
m: a
sam
ple
spec
trum
with
the
mod
el f
it; th
e in
stru
men
tal a
rtif
act i
s in
clud
ed f
or a
ttenu
ator
sta
te A
3
MethodologyFor each selected flare, we perform the following analysis:• Image [CLEAN] w/ grids 3-9 (excl. 7) in 6-15 keV energy band
(thermally-dominated), 40-sec duration at GOES SXR peak time• Approximate flare volume based on area enclosed by 50%
CLEAN contour* (contour at 50% of peak pixel flux)• Obtain spectra (all grids excl. 2 & 7) in 20-sec intervals for the
10 minutes prior to GOES SXR peak; identify HXR/SXR peaks• Fit each interval between the HXR/SXR peak times with:
isothermal continuum, power-law non-thermal continuum, 2 Gaussian lines (Fe & Fe/Ni complexes)†
• Compute source density, thermal energy from fit parametersA sample image and spectrum are shown for reference.
* This approximation is fairly crude but gives a first-order estimate; we will improve this estimate by using visibility-based imaging algorithms and forward-modeling of the source.
† In the A3 shutter state, a 3rd Gaussian is added to model an instrumental artifact which is not yet accounted for in the spectral response matrix.
First ResultsPreliminary analysis has been completed for 37 flares from the
initial set of 260 (~14% of the sample set), and first results are given below. The results will likely change somewhat as we improve the analytical method and continue analysis on the entire sample set.
Max
. Tem
p. v
s. G
OE
S c
lass
The
max
imum
isot
herm
al p
lasm
a te
mpe
ratu
re o
ccur
ring
dur
ing
the
flar
e (f
rom
spe
ctra
l fitt
ing)
ver
sus
GO
ES
cla
ss.
The
re
appe
ars
to b
e a
(ver
y) r
ough
pow
er-l
aw c
orre
latio
n.
Den
sity
/Vol
. vs.
GO
ES
cla
ss
The
den
sity
(at
the
tim
e of
max
imum
tem
pera
ture
) an
d es
tim
ated
sou
rce
volu
me
vs. G
OE
S c
lass
. Den
siti
es a
re d
eriv
ed f
rom
the
emis
sion
mea
sure
& e
stim
ated
so
urce
vol
ume,
ass
umin
g a
unit
y fi
llin
g fa
ctor
. The
re a
ppea
rs to
be
no
corr
elat
ion
for
eith
er q
uant
ity,
alt
houg
h th
is m
ay c
hang
e as
we
impr
ove
the
volu
me
esti
mat
ion
tech
niqu
e.
Ene
rgy
vs. G
OE
S c
lass
Tot
al th
erm
al e
nerg
y an
d th
erm
al e
nerg
y de
nsit
y (a
t tim
e of
max
imum
te
mpe
ratu
re)
vs. G
OE
S c
lass
. Ene
rgie
s ar
e de
rive
d fr
om th
e em
issi
on
mea
sure
and
est
imat
ed s
ourc
e vo
lum
e, a
ssum
ing
a un
ity
fill
ing
fact
or a
nd
ion/
elec
tron
ther
mal
equ
ilib
rium
. The
re a
ppea
rs to
be
a (v
ery)
rou
gh p
ower
-la
w c
orre
lati
on f
or e
nerg
y, a
nd p
ossi
bly
(loo
se)
uppe
r/lo
wer
lim
its
for
ener
gy d
ensi
ty. M
agne
tic
ener
gy d
ensi
ties
for
var
ious
fie
ld s
tren
gths
are
sh
own
for
refe
renc
e; f
or la
rge
flar
es, t
his
sugg
ests
the
fiel
d st
reng
th a
t the
lo
opto
p (t
he lo
cati
on o
f th
e th
erm
al e
mis
sion
) m
ust b
e ~2
00G
or
high
er in
or
der
to c
onfi
ne th
e th
erm
al p
lasm
a w
ithi
n th
e lo
op.
Em
issi
on M
easu
re v
s. M
ax T
The
isot
herm
al e
mis
sion
mea
sure
at t
he ti
me
of (
and
plot
ted
agai
nst)
the
max
imum
tem
pera
ture
obs
erve
d by
RH
ESS
I. N
o co
rrel
atio
n ca
n be
in
ferr
ed, b
ut th
ere
may
be
loos
e up
per/
low
er li
mit
s on
the
EM
at
max
imum
tem
pera
ture
.
Den
sity
/Vol
. vs.
Max
. T
The
den
sity
(at
the
tim
e of
max
imum
tem
pera
ture
) an
d es
tim
ated
sou
rce
volu
me
vs. t
he m
axim
um te
mpe
ratu
re o
bser
ved
by R
HE
SSI.
D
enst
ies
are
deri
ved
as b
efor
e (s
ee le
ft).
The
re a
ppea
rs to
be
no
corr
elat
ion
for
eith
er q
uant
ity,
alt
houg
h th
is m
ay c
hang
e as
we
impr
ove
the
volu
me
esti
mat
ion
tech
niqu
e.
Ene
rgy
vs. M
ax. T
Tot
al th
erm
al e
nerg
y an
d th
erm
al e
nerg
y de
nsit
y (a
t tim
e of
max
imum
te
mpe
ratu
re)
vs. m
axim
um te
mpe
ratu
re o
bser
ved
by R
HE
SI.
Ene
rgie
s ar
e de
rive
d as
bef
ore
(see
left
). N
o co
rrel
atio
n ca
n be
infe
rred
, but
ther
e m
ay b
e lo
ose
uppe
r/lo
wer
lim
its
for
the
ener
gy a
nd e
nerg
y de
nsit
y fo
r a
give
n m
axim
um te
mpe
ratu
re.
SummaryWe selected 260 M/X-class flares for analysis to characterize thermal flare plasmas
and investigate the properties of “super-hot” flares. Preliminary analysis has been completed on 37 flares:
• “Super-hot” plasma temperatures appear to be a common feature of X-class flares, but may be uncommon for M-class flares.
• Maximum flare temperature and thermal energy may be power-law correlated with GOES class (a proxy for lower bulk plasma temperature), while energy density may show upper/lower limits
• Emission measure is not clearly correlated with maximum temperature, but upper/lower limits may exist; similarly for energy density
• Density and source volume do not appear to show any correlation or limits vs. GOES class or maximum temperature; however, this may change as we improve the imaging method and volume estimation technique.
We anticipate that these results will change as we analyze the rest of the sample set and improve our analytical method.
Ongoing/Future WorkThese are only first results - there remains a lot more to be done. We plan to:• Complete analysis on the remaining 223 selected flares• Utilize visibility-based imaging algorithms and forward-modeling of source
sizes to improve the estimates of source volume• Improve the criteria for flare selection and time-interval selection (for spectral
fitting) to reduce possible selection bias• Separate occulted from on-disk flares to explore characteristics as a function
of population• Use the Fe & Fe/Ni line complex ratio (already being fit) as another
diagnostic of maximum flare temperature and analyze its behavior alongside the continuum temperature measurements
• Explore differential emission measure fitting to examine the behavior of temperature distributions with GOES class, etc.
• Use imaging spectroscopy on spatially-separate sources to reduce spectral ambiguity (of source-integrated spectra) and examine the behaviors of multiple spatial locations within flares
RHESSI data is vast, rich, and flexible - there are many ways to analyze it…this is just the tip of the proverbial iceberg!
