Statistical Properties of Super-Hot Solar Flares
description
Transcript of Statistical Properties of Super-Hot Solar Flares
Statistical Properties ofSuper-Hot Solar Flares
Amir Caspi†1*, Säm Krucker2,3, Robert P. Lin2,4,5
† [email protected]; http://sprg.ssl.berkeley.edu/~cepheid/agu2011/ 1 Laboratory for Atmospheric and Space Physics, Univ. of Colorado, Boulder, CO 80303
* Formerly at: 2 Space Sciences Laboratory, Univ. of California, Berkeley, CA 947203 Inst. of 4D Technologies, School of Engineering, Univ. of Applied Sciences Northwestern Switzerland, Windisch, CH
* Formerly at: 4 Department of Physics, Univ. of California, Berkeley, CA 947205 School of Space Research, Kyung Hee University, Republic of Korea
SH13B-1942
2
IntroductionRHESSI has shown that “super-hot” (T > 30 MK) thermal plasma
appears common in intense, M- & X-class flares. Recent studies of individual X-class events (Caspi & Lin 2010, ApJ 725, L161; Longcope et al. 2010, SolPhys 267, 107) showed that the super-hot component is spectrally & spatially distinct from the ~10-20 MK plasma observed by GOES, suggesting that the two populations are heated by different physical mechanisms. However, it remains unknown why only some flares achieve super-hot temperatures and on what this depends; the origins of super-hot plasma remain poorly understood.
We present a survey of 37 M/X flares to investigate: • What is the highest temperature achieved during flares? • Is there an intrinsic limit to the maximum flare temperature?• Does “super-hot” imply “super-energetic?”• Do “hot” and “super-hot” flares behave differently?
3
Flare SelectionAnalysis was restricted to only M- and X-class flares – those most
likely to produce super-hot plasma. We required:
• Good RHESSI coverage of X-ray peak (defined as uninterrupted observation over the full 10 minutes prior to GOES SXR peak)
• Clearly identifiable HXR (25-50 keV) and SXR (6-12 keV) peaks, occurring in order before the GOES SXR peak
• Time-series spectra fit reasonably well by the model (below)• Imageable with grid 3 (~7 arcsec FWHM) using CLEAN
260 analyzable flares during 2002-2005 (234 M, 26 X)
37 flares chosen in simple chronological order (25 M [from 2002], 12 X [from 2002-2004]) – see Table 1
4
Sel
ecte
d F
lare
s
5
AnalysisFor each selected flare, we:• Accumulate spectra (all detectors excl. 2 & 7) in 20-sec
intervals, 1/3-keV energy bins for 10 minutes prior to GOES SXR peak
• Fit spectrum at each interval with photon model: isothermal continuum, power-law non-thermal continuum, and 2 Gaussian lines (Fe & Fe/Ni complexes)†; identify max. temperature
• Image [CLEAN] w/ grids 3-9 (excl. 7) in 6-15 keV energy band (thermally-dominated), 40-sec duration around time of max T
• Approximate flare volume from area within 50% intensity contour* as V = (4/3)π (A/π)3/2
• Compute source density, thermal energy from fit parametersA sample spectrum (right) and image (inset) are shown for reference.
* Area is corrected for point-spread function broadening; volume estimate is good to 1 st order and simulations show it to be a reasonable approximation, within a ~23% uncertainty.
† In the A3 shutter state, a 3rd Gaussian is added to approximately correct for a small miscalibration of the thick attenuator response. Spot-check shows correction good to within ~4%.
6
Sam
ple
Spe
ctru
m/I
mag
e
Exa
mpl
e ph
oton
spe
ctru
m a
nd m
odel
fit
; the
fit
was
app
lied
at e
ach
inte
rval
and
th
e m
axim
um-t
empe
ratu
re a
nd m
axim
um-e
nerg
y in
terv
als
wer
e id
enti
fied
. In
the
A3
(thi
ck+
thin
) st
ate,
the
thir
d G
auss
ian
feat
ure
is a
dded
to
appr
oxim
atel
y co
rrec
t for
a s
mal
l mis
cali
brat
ion
of th
e th
ick
atte
nuat
or
resp
onse
. (I
nset
) E
xam
ple
imag
e at
the
tim
e of
max
imum
tem
pera
ture
; the
so
urce
vol
ume
is a
ppro
xim
ated
fro
m th
e ar
ea o
f >
50%
inte
nsit
y.
7
Max
. T v
s. G
OE
S c
lass
Max
imum
isot
herm
al c
onti
nuum
tem
pera
ture
mea
sure
d by
RH
ESS
I (d
iam
onds
) an
d G
OE
S (c
ross
es)
vers
us G
OE
S c
lass
for
the
37
anal
yzed
fla
res,
wit
h fi
t cor
rela
tion
s. T
he R
HE
SSI
corr
elat
ion
is
sign
ific
antl
y (>
7σ)
stee
per
than
the
GO
ES
corr
elat
ion.
Spe
ctra
l fit
s w
ith
a re
duce
d χ2 >
2 (
open
dia
mon
ds)
are
dist
ribu
ted
even
ly in
G
OE
S cl
ass
and
do n
ot s
igni
fica
ntly
ske
w th
e co
rrel
atio
n.
8
Vol
ume
vs. m
ax T
Est
imat
ed v
olum
e de
rive
d fr
om th
e 6-
15 k
eV im
ages
cot
empo
ral w
ith,
an
d ve
rsus
, the
max
imum
RH
ESS
I te
mpe
ratu
re. T
he d
istr
ibut
ion
is
roug
hly
unif
orm
. In
a fe
w c
ases
(sq
uare
sym
bols
), th
e im
ages
sho
w
a co
mpl
ex m
orph
olog
y an
d su
gges
t mul
tipl
e so
urce
s, s
kew
ing
the
volu
me
mea
sure
men
t whi
ch a
ssum
es o
nly
a si
ngle
sou
rce;
not
e th
at
the
larg
est v
olum
es a
ll s
uffe
r fr
om th
is is
sue,
and
mos
t of
thes
e al
so
exhi
bit p
oor
chi-
squa
red
valu
es (
open
sym
bols
) fo
r th
e sp
ectr
al f
it.
9
Den
sity
vs.
max
T
RH
ES
SI
ther
mal
ele
ctro
n de
nsity
cot
empo
ral w
ith, a
nd v
ersu
s, th
e m
axim
um R
HE
SS
I te
mpe
ratu
re. 1
2 of
14
supe
r-ho
t fla
res
have
den
sity
≳3.2×
1010
cm
-3. T
he o
utlie
rs a
re a
ssoc
iate
d w
ith th
e un
cert
ain
“mul
tiple
so
urce
” vo
lum
e m
easu
rem
ents
. H
igh
dens
ities
app
ear
nece
ssar
y (b
ut n
ot
suff
icie
nt)
for
supe
r-ho
t tem
pera
ture
s, c
onsi
sten
t with
for
mat
ion
due
to
com
pres
sion
(e.
g. C
aspi
& L
in 2
010;
Lon
gcop
e et
al.
2010
), o
r th
ick-
targ
et c
ollis
iona
l ene
rgy
loss
by
non-
ther
mal
par
ticle
s.
10
Ene
rgy
vs. m
ax T
Tot
al e
nerg
y (a
ssum
ing
T i = T
e) o
f th
e R
HE
SSI
ther
mal
pla
sma
cote
mpo
ral w
ith,
and
ver
sus,
the
max
imum
RH
ES
SI te
mpe
ratu
re. 1
3 of
14
supe
r-ho
t fla
res
exce
ed ~
2.4×
1029
erg
at t
he ti
me
of th
e m
axim
um te
mpe
ratu
re, v
ersu
s a
sign
ific
ant s
catt
er a
mon
g co
oler
fl
ares
. (T
he o
ne s
uper
-hot
out
lier
is th
e “f
aile
d er
upti
on”
of 2
002
May
27
(cf.
Ji e
t al.
2003
, ApJ
, 595
, L13
5).
11
Ene
rgy
dens
ity
vs. m
ax T
The
rmal
ene
rgy
dens
ity
of th
e R
HE
SS
I th
erm
al p
lasm
a co
tem
pora
l wit
h, a
nd v
ersu
s, th
e m
axim
um R
HE
SS
I te
mpe
ratu
re. M
agne
tic
fiel
d st
reng
ths
for
sele
cted
val
ues
of e
quiv
alen
t m
agne
tic
ener
gy d
ensi
ty (
B2 /
8π)
are
show
n fo
r re
fere
nce;
thes
e ar
e th
e m
inim
um f
ield
st
reng
ths
requ
ired
to c
onta
in th
e th
erm
al p
lasm
a (i
.e. β
< 1
). 1
3 of
14
supe
r-ho
t fla
res
requ
ire
B
100
G in
the
coro
na, w
here
the
supe
r-ho
t pla
sma
is lo
cate
d.≳
12Max
. Ene
rgy
vs. G
OE
S c
lass
Max
imum
tota
l the
rmal
ene
rgy
(ass
umin
g T
i = T
e) o
f th
e R
HE
SS
I pl
asm
a ac
hiev
ed d
urin
g th
e fl
are
vers
us G
OE
S c
lass
, wit
h fi
t cor
rela
tion
. T
hese
are
inst
anta
neou
s en
ergi
es a
nd d
o no
t re
flec
t los
ses
(rad
iati
ve, c
ondu
ctiv
e, e
tc.)
, thu
s th
e tr
ue m
axim
um e
nerg
y is
like
ly h
ighe
r.
The
pow
er-l
aw r
elat
ions
hip
sugg
ests
that
GO
ES
cla
ss is
a g
ood
prox
y fo
r pe
ak th
erm
al
ener
gy, a
nd th
us p
ossi
bly
for
tota
l ene
rgy
rele
ase.
13Max
. ene
rgy
dens
ity
vs. m
ax T
The
rmal
ene
rgy
dens
ity
corr
espo
ndin
g to
the
max
imum
ene
rgy
vers
us m
axim
um R
HE
SSI
tem
pera
ture
, wit
h re
fere
nce
mag
neti
c fi
eld
stre
ngth
s. S
uper
-hot
fla
res
have
sig
nifi
cant
ly h
ighe
r m
axim
um e
nerg
y de
nsit
y, w
ith
13 o
f 14
exc
eedi
ng ~
970
erg
cm-3, e
quiv
alen
t to
B
160
G;
excl
udin
g th
e “p
ossi
ble
mul
ti-s
ourc
e” o
utli
ers
≳(s
quar
es)
high
ligh
ts th
is a
ssoc
iati
on m
ore
stro
ngly
. St
rong
mag
neti
c fi
elds
app
ear
to b
e st
rict
ly n
eces
sary
(b
ut n
ot s
uffi
cien
t) f
or th
e fo
rmat
ion
of s
uper
-hot
pla
sma,
con
sist
ent w
ith
heat
ing
by c
ompr
essi
on o
f th
e m
agne
tic
fiel
d (C
aspi
& L
in 2
010)
.
15
Discussion• Both RHESSI and GOES maximum temperatures show a strong correlation
with GOES class. Since the temperature responses of the two instruments are significantly different, this simultaneous correlation suggests that the entire temperature distribution (and underlying physics) may scale with GOES class.
• The RHESSI correlation is significantly steeper than the GOES correlation, consistent with different formation mechanisms for the two populations (since similar formation would imply similar correlation). The two correlations cross at GOES class of ~C2; if RHESSI plasma is formed directly in the corona (e.g. Caspi & Lin 2010; Longcope et al. 2010), this suggests that the coronal formation mechanism is present in all flares of at least moderate intensity, even those that do not reach super-hot temperatures. This and the above bullet together suggest that the temperature distribution above ~5 MK may be strongly bimodal for all >C flares, not just super-hot/X-class flares.
• Thermal plasma volume is completely uncorrelated with temperature or GOES class, but high densities (≳3×1010 cm-3) appear necessary for formation of super-hot plasma. The high density may be either a result of formation (e.g. by the same compression that would heat the plasma) or the cause of it (e.g. a thick target for collisional energy loss by low-energy non-thermal particles, which would not have sufficient energy to reach the chromospheric footpoints).
16
Discussion• Strong coronal magnetic fields, exceeding ~200 G, appear necessary (though
not sufficient) for the formation of super-hot plasma. This inference is supported by coronal fields inferred from µ-waves during X-class flares (e.g. Asai et al. 2006, PASJ, 58, L1), and is consistent with formation in the corona by compression of reconnected loops (Caspi & Lin 2010), though other explanations are, of course, also possible.
• The inferred magnetic field strength B β∝ 1/2 is a strict lower limit since β < 1 (else the magnetic field could not contain the thermal plasma, and it would expand and cool). Since B cannot exceed the photospheric value (no more than 1000-3000 G even in the most intense active regions), this also provides a lower limit on the coronal/super-hot β of >0.01, and µ-wave observations (per above) suggest that β ≈ 1.
17
SummaryOur analysis of 37 M- and X-class flares has shown that:
• Maximum RHESSI and GOES temperatures are strongly correlated with GOES class, but the RHESSI correlation is significantly steeper; the (bimodal) temperature distribution likely also scales with GOES class
• Maximum thermal energy is strongly correlated with GOES class;• Super-hot flares are strongly associated with a high electron number
density and a high maximum thermal energy density, and thus with strong coronal magnetic fields; super-hot plasma may thus reflect not only higher temperatures, but a higher energy input into the plasma;
• β ≈ 1 in the super-hot region, suggesting that the plasma is efficiently heated to its physical maximum
These correlations and associations that distinguish super-hot and non-super-hot flares may help to constrain models of flare reconnection and subsequent plasma heating.