Statistical Properties ofSuper-Hot Solar Flares

Amir Caspi†1*, Säm Krucker2,3, Robert P. Lin2,4,5

† amir.caspi@lasp.colorado.edu; 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.