RESULTS OF THE LEBAN DIAGNOSTIC PROCEDURE APPLIED TO TWO SMM - OBSERVED FLARES

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RESULTS OF THE LEBAN DIAGNOSTIC PROCEDURE APPLIED TO TWO SMM -

OBSERVED FLARES

B. Sylwester, J. Sylwester, J. Jakimiec

To cite this version:

B. Sylwester, J. Sylwester, J. Jakimiec. RESULTS OF THE LEBAN DIAGNOSTIC PROCEDURE

APPLIED TO TWO SMM - OBSERVED FLARES. Journal de Physique Colloques, 1988, 49 (C1),

pp.C1-309-C1-314. �10.1051/jphyscol:1988165�. �jpa-00227579�

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JOURNAL DE PHYSIQUE

Colloque C1, Suppl6ment au n03, Tome 49, Mars 1988

RESULTS OF THE LEBAN DIAGNOSTIC PROCEDURE APPLIED TO TWO SMM -

OBSERVED FLARES

B. SYLWESTER, J. SYLWESTER and J. JAKIMIEC'

Space Research Centre, Polish Acadamy of Sciences, Wroclaw, Pol and

*~stronomical Institute, Wroclaw University. Wroclaw, Poland

ABSTRACT

In a previous paper <B. Sylwester e t al., 1986) we proposed a new procedure called LEBAN <Loop Energy Balance Analvsis> f o r deriving the basic geometrical p a r a l n e t e r s of f l a r i n g loops. In a subsequent paper <B. Sylwester e t al., 1987> t h e Palermo Code r e s u l t s of hydrodynamic f l a r e loop modelling have been used t o confirm t h e validity of t h e LEBAN procedure f o r t h i s purpose. In t h e p r e s e n t i n v e s t i g a t i o n t h e LEBAN procedure has been applied t o analyse two SMM-observed f l a r e s Con 12 Nov. 1980. -17:OO UT and on 18 Nov. 1980, -15:OO UT>. Estimated f l a r e loop l e n g t h s and c r o s s - s e c t i o n s have been compared with t h o s e derived f r o m deconvolved H M S images a n d / o r e s t i m a t e d i n d i f f e r e n t way by o t h e r a u t h o r s . If t h e loop semi-length L is known from o t h e r o b s e r v a t i o n s , t h i s allows t o e s t i m a t e t h e p o r t i o n r ) of t h e loop which w a s heated. Time v a r i a t i o n s of o t h e r i m p o r t a n t p a r a m e t e r s c h a r a c t e r i z i n g t h e f l a r e plasma < t h e heating rate, t h e mean density. t h e t o t a l energy c o n t e n t ) are a l s o discussed.

INTRODUCTION

Recently (Sylwester e t al., 1986>, we have proposed a new diagnostic procedure called LEBAN f o r deriving basic geometrical p a r a m e t e r s of a f l a r i n g loop. Based on t h e t i m e v a r i a t i o n s of t h r e e easily measured p a r a m e t e r s , i.e.: t h e maxilnum and t h e mean t e m p e r a t u r e of t h e plasma, and t h e t o t a l emission measure, LEBAN allows t o estimate t h e e f f e c t i v e length and t h e c r o s s - s e c t i o n of t h e f l a r i n g loop. Since Last year w e have improved t h e method and t e s t e d i t s r e l i a b i l i t y using r e s u l t s of t h e hydrodynamic f l a r e loop modelling CPalermo Code Modelling

-

PCM>. R e s u l t s of t h e s e tests have been described i n Paper I <Sylwester e t al., 1987>. I t t u r n e d o u t t h a t it is possible t o e s t i m a t e t h e equivalent p a r t

<@> of t h e f l a r i n g loop which is h e a t e d

,

i f i n addition t o t h e

time h i s t o r y of t h e t h r e e basic p a r a m e t e r s t h e measured loop l e n g t h Cas derived, f o r i n s t a n c e , f r o m t h e X-ray f l a r e images> is known. Consequently, w e are able t o determine t h e amount of t h e thermally deposited f l a r e energy and o t h e r components of f l a r e energy balance. In t h e p r e s e n t paper w e apply t h e LEBAN method t o two well observed s o l a r f l a r e s .

DATA USED I N THE ANALYSIS

Accurate values of t h e t h r e e p a r a m e t e r s c h a r a c t e r i z i n g t h e f l a r i n g loop a t any time during t h e f l a r e are needed t o make possible t h e LEBAN diagnostic: t h e maximum and t h e mean t e m p e r a t u r e of t h e plasma <Tm and T respectively>, and t h e t o t a l

-

plasma emission measure E . In o r d e r t o e s t i m a t e values o f t h e s e p a r a m e t e r s , i n t h e p r e s e n t paper w e have used t h e X-ray fluxes measured by t h e

BCS

and

HXIS

i n s t r u m e n t s aboard t h e SMM

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988165

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C1-310

JOURNAL D E PHYSIQUE

s a t e l l i t e . R a t i o s o f t h e i n t e g r a t e d flare f l u x e s measured by

HXIS

i n s t r u m e n t i n channels 3 <8

-

11.5 keV> and 1 (3.5

-

5.5 keV>

have been used t o d e r i v e t h e maximum t e m p e r a t u r e o f t h e f l a r i n g plasma. R a t i o s o f t h e satellite t o t h e resonarace line f l u x e s <Ca k and w l i n e s in t h e n o t a t i o n o f Uabriel, 1972> o b s e r v e d i n BCS channel 1 have been used t o estimate t h e a v e r a g e plasma t e m p e r a t u r e . The value o f t h e a b s o l u t e f l u x o b s e r v e d i n t h e w Une has provided t h e t o t a l emission measure. R e l a t i o n s between t h e o b s e r v a t i o n a l l y derived <TS/*, Tca, sCa> and r e q u i r e d <Tm, T,

-

E > p a r a m e t e r s a r e as follows:

where. T9/* is t h e i s o t h e r m a l t e m p e r a t u r e f r o m HXIS channel 3 t o 1 r a t i o < i n MK>, Tca <MK> and eCa ax-e t h e t e m p e r a t u r e and emission m e a s u r e d e r i v e d by f i t t i n g a s y n t h e t i c s p e c t r u m t o t h e o b s e r v e d BCS channel 1 s p e c t r u m <see Lemen e t al., 1984).

Relations <I>, < 2 > and <3> have been o b t a i n e d by means o f d e t a i l e d modelling using t h e PCM r e s u l t s and will b e d i s c u s s e d i n a s e p a r a t e paper. In deriving t h e s e r e l a t i o n s w e have assumed that the BCS and H X I S f l u x e s used are formed i n the f l a r e plasma a t t e m p e r a t u r e s T

>

Tmin, where Tmin

-

¹⁰

^MK.

THE 1 8 t h NOVEMBER 1980 FLARE

This limb f l a r e occured i n t h e NOAA a c t i v e r e g i o n 2779 a t 14:51

UT

and w a s c l a s s i f i e d as M 3 b a s e d on UOES s o f t X-ray data. H a p a t r o l s r e p o r t e d no f l a r e a t t h i s time. The f l a r e has been a l r e a d y e x t e n s i v e l y analysed by Simr.ett and S t r o n g . (1984) i n X-rays and by Schmahl e t al.. (1986) i n microwaves. A s recommended i n t h e method, a t f i r s t w e check whether. t h e q u a s i - s t e a d y - s t a t e <QSS> p h a s e is p r e s e n t f o r t h e i n v e s t i g a t e d f l a r e . In Figure 1 w e p r e s e n t t h e t i m e h i s t o r y o f t h e p a r a m e t e r C defined as:

A s is s e e n i n Figure 1, t h e QSS phase can b e f i n d in t h e period f r o m 15:OO t o 15:08

U T

with t h e a v e r a g e value of C indicated. The value o f C is r e l a t e d t o t h e g e o m e t r i c a l p a r a m e t e r s o f t h e loop i n t h e following way:

where L is t h e semilength o f flaring7 loop, A is t h e loop c r o s s - s e c t i o n area, and W

=

7.16 . l o - <cgs> is a c o n s t a n t r e l a t e d t o t h e scaling l a w f o r t h e QSS phase <c.f. Equation < I >

i n Paper I>. From C value one c a n o b t a i n L/A r a t i o f r o m Equation

<5>.

In t h e a n a l y s i s o f t h e f l a r e i n i t i a l phase, w e i n v e s t i g a t e t h e e n e r g y balance e q u a t i o n f o r t h e whole loop i n t h e i n t e g r a l form.

This l e a d s t o t h e following r e l a t i o n <c.f. Equation <16> i n Paper I>:

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where:

C *

=

K ) <AA>'" < 3 k ~ > - '

Time from 1451 UT (mln)

r 1 1 I I

Fig. 1. Plot of t h e time h i s t o r y of t h e p a r a m e t e r C <see t e x t f o r definition>. Time period when C is c o n s t a n t a t t h e lowest level correspond t o t h e Quasi-Steady-State phase of f l a r e evolution when classical s c e n g Law f o r loops is applicable. The constancy of C means a l s o t h a t t h e f l a r i n g loop geometry does n o t vary during t h e f l a r e decay.

Here: K ^I 9 - l o - ? , f

=

3.30, a

=

0.7'0 Cc.f. Paper I>, k is t h e Boltzman c o n s t a n t . 13 i s t h e f r a c t i o n of t h e f l a r i n g loop which is e f f e c t i v e l y h e a t e d , a i s t h e f r a c t i o n o f t h e enersgy conducted o u t which r e t u r n s back t o t h e high t e m p e r a t u r e region with t h e ififlowing s t r e a m of matter and Pr<T> is t h e r a d i a t i v e l o s s

18 Nov 1980 C = 9.50.10'~~

f u n c t i o n f o r t h e optically t h i n plasnia. Initially w e performed calculations by taking y

=

ycr

=

0.9 in Equation ( 7 ) . A s can be

-

- -

I I I I I

s e e n from Figure 2. during t h e i n i t i a l f l a r e phase, t h e observed behaviour of % ' ' 2 ~ s can be described by a c o n s t a n t value of C

.

By f i t t i n g a s t r a i g h t line t o t h e r i s i n g p o r t i o n o f t h e graph we obtained t h e Ci value. Using t h e C * . and L/A one can o b t a i n t h e upper l i n t i t s of t h e loop semilength

L+

and n e x t t h e c r o s s s e c t i o n A_. For t h e considered f l a r e , t h e corresponding

7

values a r e L

-

^6.3.10' ^{cm. and} ^A* ⁼ 2 . 1 0 ' ~ cm2.From Figure 4 of S i m n e t t and S t r o n g . <1984>, <deconvolved channel 1 HXIS images of t h e f l a r e > , we have e$timated semilength of t h e main f l a r i n g s t r u c t u r e as L

=

2.10 on. So t h e upper limit derived i n o u r analysis is i n agreement with t h i s observation. From $he VLA o b s e r v a t i a n s Sclmahl e t al.. (1985) found A 6 . 1 0 ~ ~ cm

,

^which

is above our upper limit. b u t is a t t h e level o f t h e b e s t i n s t r u m e n t a l resolution.

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JOURNAL

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PHYSIQUE

I I

18 Nov 1980

,

-15 00 UT flare

& 1 I

Fig. 2. Dependence of

%"2

( c h a r a c t e r i z i n g t h e thermal energy>

v s t h e S ~ ~ < c h a r a c t e r i z i n g t h e t o t a l energy deposited ~ ~ d t f r o m t h e fLare o n s e t > . The r i s i n g p o r t i o n of t h e plot can be w e l l approximated by a s t r a i g h t line with a slope c o e f f i c i e n t C*. Constant Ci means a l s o t h a t t h e f l a r i n g loop geometry does n o t change during t h e initial heating.

When we made use of t h e observed value of L

,

and treat it as a n additional d a t a , t h e n we followed a n o t h e r path: from C and L values we derived

A =

^6.3-lo'* cm2. This value i s much below t h e V L A resolution. N e x t , based on t h e measured C1 value, indicated i n Figure 2, w e calculated ). from Equation C7> and t h e corresponding I) from Equatio~> (8). For 18 Nov 1980 f l a r e t h e e s t i m a t e d 13 value w a s r )

=

0.42.

Now w e could proceed t o i v e s t i g a t e t h e evolution of individual t e r m s in t h e energy balance equation Cc.f. Equation C5> in Paper I>. With a known value of 0 w e have calculated each of t h e terms and p l o t t e d t h e values i n Figure 3. I t is s e e n from t h e Figure, t h a t in t h e i n i t i a l phase t h e energy deposited i n t o t h e loop tH is nearly fully t r a n s f e r r e d i n t o t h e thermal energy lth of t h e h e a t e d plasma. During t h e decay phase, t h e radiatively l o s t energy I r becomes more Important, being comparable with t h e energy l o s t by conduction 18 which r e p r e s e n t s t h e t r u e l o s s e s of

c'

t h e energy o u t of t h e i n v e s t i g a t e d region <plasma with t h e t e m p e r a t u r e above 10 MK>. Derived e l e c t r o n density in t h e fl-ing loop is n_

- =

8.0.10'~ cm-a a t t h e beginning of t h e heatirrg, and i n c r e a s e s t o 3.0.

loii

cm-a a t t h e end of t h e impulsive phase of t h i s f l a r e . L9;er on t h e d e n s i t y slowly d e c r e a s e s , being s t i l l above 10" cm half a n hour a f t e ~ t h e maximum. The e s t i m a t e d value of t h e energy deposition r a t e is a t maximum 50 e r g cm ^-3 s -1

.

In t h e Q S S phase t h e heating of t h e plasma still takes place b u t a t t h e level 20 t i m e s smaller.

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18 Nov 1980.

Time from 1451 UT (rnin)

Fig. 3. Time N s t o r v of t h e energy balance devided i n t o main components. XH s t a n d s f o r t h e t o t a l energy deposited from t h e f l a r e o n s e t . Sth is t h e thermal energy c o n t e n t a t a given time,

lr

i s t h e energy r a d i a t e d away and 15 is t h e

C

energy l o s t from t h e i n v e s t i g a t e d high t e m p e r a t u r e f l a r e by conduction.

THE 12 NOVEMBER FLARE

This f l a r e occured n e a r t h e disc c e n t e r a t 17:OO

UT

and was c l a s s i f i e d as a n Ha e v e n t of importance 1B. For t h i s f l a r e a s e t of ground-based as well as X-ray o b s e ~ v a t i o n s were available. The f l a r e was extensivelv studied by Mac Neice e t al., C1985> as a typical example of a compact f l a r e . The comparison of t h e Palermo Code hydrodynamic models with t h e S M M o b s e r v a t i o n s f o r t h i s f l a r e w a s made by P e r e s e t al.. (1987). Based on combined analvsis of t h e Ha and s o f t X-ray o b s e r v a t i o n s , t h e y i n f e r r e d t h a t t h e se8niiengt.h of t h e main f l a r i n g loop s t r u c t u r e w a s 2 . 1 0 ~ cm and t h e c r o s s - s e c t i o n 2 . 5 ~ 1 0 ' ~ c m ~ .

A s in t h e previous c a s e , f i r s t w e e s t i m a t e d t h e upper &imits - f o r t h e length and t h e c r o s s - s e c t i o n based on t h e

Tm,

T, and s

. .

v a r i a t i o n s only. In this c a s e

L+ =

5 . 1 . 1 0 ~ cm and A+ = 5 . loid cm2. Next we adopted d i f f e r e n t value f o r t h e loop semilength L

=

3 . 8 . 1 0 ~ cm. which we derived from deconvolved HXIS images in t h e energy bmd 3.5

-

8 keV, and obtained t h e following values f o r t h e p a r a m e t e r s : A

=

3.8.l0'*cm2, (3 = 0.74.. In t h i s f l a r e r e l a t i v e l y l a r g e r p o r t i o n of t h e loop was heated. In c o n t r a r y t o t h e previous c a s e , t h i s f l a r e w a s of very s h o r t dur'ation

-

^{6 min}

only. During t h e main p a r t of t h e f l a r e evolution t h e d e n s i t y w a s n o t changing s u b s t a n t i a l l y , being in t h e r a n g e 1.2

-

1.6~!0"cm-~. The maximum r a t e of energy d $ p e ~ i t i o n w a s 0.4 e r g cm s -i and during t h e Q S S phase 1.4 e r g c m - s .

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JOURNAL

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Cross-sections obtained in LEBAN a r e based on e s t i m a t e s of t h e loop length f r o m HXIS d a t a . These loop l e n g t h s are n o t c o r r e c t e d f o r t h e p r o j e c t i o n e f f e c t s , t h e r e f o r e derived c r o s s - s e c t i o n s should be understand as lower limits. Nevertheless t h e calculated values of c r o s s - s e c t i o n f o r b o t h f l a r e s are much l e s s t h a n t h e r e s o l u t i o n of e x i s t i n g radio o r X-pay o b s e r v a t i o n s .

I n d i r e c t information on t h e c r o s s - s e c t i o n may be obtained by e s t i m a t i n g t h e measured axen of Ha kernels

.

Mac Neice e t al.,

<1985> found t h e kernel a r e a as 5 . 1 0 ' ~ c m ~ < f o r t h e 12 November f l a r e > which is i n a good agreement with o u r value. These e s t i m a t e d c r o s s - s e c t i o n s provide a typical r a d l u s of t h e loop r

=

1

-

2 a r c s e c , and consequently t h e loop a s p e c t r a t i o L/r -20.

T h e r e f o r e f o r a f l a r e loops similar t o t h o s e d y s e d , t h e filling f a c t o r f o r t h e SUM i n s t r u m e n t s can be -0.05, which is comparable t o t h e filling f a c t o r s e s t i m a t e d by Wolfson e t al., (1983) and de Jager e t al., (1983).

Derived (3 values correspond t o t h e c a s e when s i g n i f i c a n t p o r t i o n of t h e = f l a r i n g loop volume is heated, of t h e o r d e r o f 50 % <2

lo2*

cm i n a b s o l u t e terms>. I t is possible t o understand t k i s l a r g e volumes h e a t e d within t h e hypothesis t h a t MHD turbulence a c t s as i m p o r t a n t f a c t o r in t h e p r o c e s s of magnetic field energy d i s s i p a t i o n Ccf. Jakimiec e t al., 1986).

ACKNOWLEDGEMENTS

This work w a s p a r t l y funded by Polish Academy of Sciences Program CPBP 01.20

-

Development and Exploatation o f Space Research.

The BCS is p a r t of t h e X-ray Poiychromator built by a consortium involving Lockheed Palo Alto Research Laboratory, Mullard Space Science l a b o r a t o r y , and Rutherford Appleton Laboratory. HXIS i n s t r u m e n t is built by t h e Laboratory f o r Space Research, U t r e c h t , and t h e University of Bimingham.

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de Jager C., Machado M.E., Schade A., S t r o n g K.T., S v a s t k a Z., Woodgate B.E., van Tend W.: 1983, Solar Phys., 84, 205.

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Mac Neice P., Pallavicini R., Mason H.E., S i m n e t t G.M. Antonucci A., Shine R.A., Rust D.M., Jordan C., Dennis B.R.: 1985, Solar Phys., 99, 167.

P e r e s U., Reale F., S e r i o S., Pallavicini R.: 1987, Astrophys.

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Simnett Q.M., S t r o n g K.T.: 1984, Astrophys. J., 284, ,839.

Sylwester, B.. Farnik, F., Sylwester,

J.,

Jakimiec,

J.,

Valnlcek, B.: 1986, Adv. Space Res, 6, 233.

Sylwester B., Sylwester J., Jakimiec J., Fludra A., Peres. U., S e r i o S.: 1987, Proceedings of t h e IAU 10th European Regional Astronomy Meeting

.

Prague, <Paper I>.

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