Small-scale reconnection in solar flares

A& Space Rex Vol. 29, No. 7, pp. 1101-l 106.2002 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273- 1 I77/02 $22.00 + 0.00 PII: SO273-1177(02)00028-5

Pergamon www.elsevier.com/locate/asr

SMALL-SCALE

RECONNECTION

IN SOLAR FLARES

J. Jakimiec Astronomical

Institute

of Wroctaw University, PL-51-622

Wrochw,

Poland

ABSTRACT Observations indicate that X-ray flare kernels, situated near the tops of flaring loops are turbulent regions where the flare energy is released. It is shown that the kernels can be developed by multiple reconnections in a confined volume. Such a turbulent model of flare kernels very well explains quick heating of large plasma volumes. It is also suggested how such a model can explain basic properties of the flare impulsive phase. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION Yohkoh X-ray images show that a significant part of the hot flare plasma is contained in X-ray kernels which are situated near the tops of flaring loops (loop-top flare kernels). In a pervious paper (Jakimiec et al. 1998) it was argued that the kernels are turbulent regions where the flare energy is released. FORMATION OF TURBULENT KERNELS In previous papers (Jakimiec 1998, 1999) a simple scheme was presented showing that the flare kernels can develop by a chain of multiple reconnections in a magneticaly confined volume. This scheme is shown in Fig. 1. Magnetic lines BP and PC represent two magnetic flux tubes which reconnect at P. Magnetic field p is the result of the reconnection and it moves to the right. Assume that the tubes BP and PC are somewhat twisted. Then the “ends” of the lines p cannot freely move along BP and PC, so that the lines p change their curvature during their motion to the right (see the right arrow p in Fig. la). Next assume that the moving field p meets a neighbouring field R with which it can reconnect. Magnetic fields ri and r2 are the result of the reconnection at R. They move away from R and can reconnect with the magnetic fields PC and PB at Si and S2. Magnetic fields resulting from these reconnections will, in turn, reconnect with the magnetic field p and R, etc. This process of multiple reconnection and tangling of the magnetic lines of force will proceed further, since each new magnetic field appearing as a result of a reconnection will meet an appropriate field with which in can reconnect. Each reconnection site produces two new reconnection sites, so that in a next step we have two times more reconnection sites than in the pervious step. Hence, after k steps it may be 2(k-1) reconnection sites. For example, after 31 steps we may have lo9 small-scale reconnection sites. And this process of the magnetic field fragmentation and tangling proceeds very quickly. Let 1 be a free path of a magnetic line of force between two successive reconnection it undergoes. (in Fig. 1, Zi = PR, The mean free path, &, decreases with the progress of the fragmentation l2 = RS, etc.). Let lk decrease by a factor 9 in a next step: &+i =q&. Than the time of the magnetic field fragmentation is:

1101

J. Jakimiec

Fig. 1. Schematic diagram showing development of the chain of reconnections BPC: (a) beginning of the chain; (b) its continuation.

2=

-1 V

ca

=-4

E lk k=l

V

in the confined volume

1

(l-’

velocity of the reconnection flows. By way of example we have taken (f rom non-thermal line broadening in the X-ray spectra) and Ii = 5000 km (the diameter of a medium-size flare kernel). This gives z = 100 set for the time of turbulence development in the kernel which is in agreement with the observed time-delay (l-3 min) between the beginning of the flare heating and beginning of the flare impulsive phase. In is important to note that actual magnetic configuration is three-dimensional rather than planar: the magnetic flux tubes do not lie in the plane of the figure, the lines R, PB and PC represent their projections on the plane. A turbulent kernel will develop in the volume PBC, with many transient current sheets (reconnection sites), where the magnetic energy will be dissipated very efficiently. This model of flare kernel well explains fast heating of large plasma volumes. It is important to note that the turbulence will continuously interact with the surrounding magnetic field and dissipate it which will allow to release a large amount of energy and explains long duration of big flares. The turbulence which develops in the kernel is a special kind of MHD turbulence. It is driven by multiple reconnections.- The magnetic energy is transformed into kinetic energy and heat at all scales 1, but the main magnetic field dissipation occurs in many transient current sheets, at small 1. For the developed MHD turbulence the turbulent magnetic diffusivity can be estimated from the formula (see Parker 1979, Chapter 7): where v is the mean

q = 0.5, v = 100 km/s

qlt

=$i ,

(1)

Small-Scale

Reconnection

in Solar Flares

1103

where i and i are the mean velocity and mean free path of the magnetic lines of force at the range of turbulent motions which is most efficient in the magnetic field dissipation. DISCUSSION OF THE THERMAL ENERGY RELEASE In a previous paper (Jakimiec 1990) it was shown that the large amount of flare plasma cannot be heated to high temperature by laminar current sheets. This is because of very efficient cooling by thermal conduction along the magnetic lines of force. In the course of turbulence development the magnetic lines become tangled which decreases the energy outflow by thermal conduction. The temperature excess, AT, of an investigated volume of enhanced heating, over its surroundings, increases. But simultaneously increases cooling by turbulent plasma motions due to the increase of the density in the kernel, which is the result of plasma flows during flare development (“chromospheric evaporation”) The energy flux transferred by the turbulence is:

F-__K< t- ’ dr ’ where dT/dr is the temperature

gradient

(2)

and: pep

vi

(3)

Kt =-

2

’

where p is the density, cp is the specific heat at constant pressure, $ and 1 are the mean velocity and mean free path of plasma elements which are most efficient in the heat transfer. We assumed (i I) for magnetic field and plasma motions are approximately equal (cf. Parker 1979, Chapter 7). The temperature excess, AT, ceases to increase, i.e. it reaches its maximum value, (AT)-, when the balance between the energy release and outflow is achieved:

(4)

where radiative

Ek = E, -E, losses

is the efficient

E, = N2@(T)).

heating

rate, per unit volume

(i.e. heating

rate EH minus

From (2) and (4) we obtain:

(3 Consider a spherical region of radius r, inside a turbulent flare kernel where enhanced in the kernel. Integration of Eq. energy release occurs, i.e., this is a hot region (inhomogeneity) (5) from r = 0 to r = r, gives:

(AT),,=$K

.

(6)

Kt

Mean values of Ei

for flare kernels

tions show that typically

Ei

can be estimated

are significantly

from X-ray observations.

higher than radiative

Those investiga-

Jakimiec 1losses ER _. (see \

et al.

1104

1. Jakimiec

2001). Hence we can neglect

ER in EL and write Eq. (6) in the form:

(7)

The heating function

EH canbe evaluated as follows: E, =-

where z is the characteristic

time of the magnetic

H2 (87tz) ’

(8)

field dissipation:

(9) Using Eqs. (l), (3), (8) and (9), we obtain from Eq. (7):

It is very important that the temperature excess (AT),, does not depend on the size of -inhomogeneities, rO, nor on the local values of the turbulence characteristics (v 1). This explains why very different flare kernels achieve similar values of the temperature, T = (2-3)x107 K (see Jakimiec et al. 1998). The physical reason of this is that in the turbulent regime the energy release is very closely coupled with the cooling. Analysis of soft X-ray images of flare kernels shows that the electron density, N, is typically (2-3)x10” cme3 when the temperature reaches its maximum value. Taking H = 300 Gs, we obtain (AT)- = (2-3)x107 K which is in a good agreement with the observational estimates for the hot component of flare kernels (see Jakimiec et al. 1998). IMPULSIVE OR NON-THERMAL COMPONENT OF A FLARE During the impulsive phase of a flare the HXR emission is spiky (see Fig. 2) which is interpreted as being due to the fact that non-thermal electrons are accelerated erratically. Analysis of the HXR emission shows that: 1. A huge amount of electrons

is accelerated

in a very short time (t - 1 set).

2. The accelerated electrons easily escape from the acceleration region into the magnetic field which is evidenced by intense HXR emission from flare footpoints.

external

To be in agreement with the point (2) we should admit that the non-thermal electron are accelerated mainly near the kernel boundaries to be able to easily escape into the external magnetic field. Thus, the boundary layer of the kernel where the high-speed turbulence collides with the external magnetic field should be a very dynamic, “boiling” layer (see Fig. 3). The BATSE spectrometer on the Compton Gamma Ray Observatory was a very sensitive instrument, so that the counting rates in the flare HXR records are high (see Fig. 2) and even the

Small-Scale

Reconnection

GRO/BATSE 4.ox104c’

’ ’ ’ ’ I ’

-1.0x104 .

I

#

#

I

I

21:50

DISCLA Rates

’ ’ ’ I ’ 3 ’ ’

e

I

I

I

in Solar Flares

I

I

*

I

I

1105

set

(1.024

overages)

I ’ ’ ’ ’ ’ 1 ’ ’ ’ ’ ’ 1 ’ ’ * ’ ’ 1 ’ ’ s

*

I

.

.

.

8 .

I

*

I

n

.

*

I a .

22:04 22:06 22:oo 22:02 Start Time (14~Moy-93 21:56:06)

Fig. 2. Time-variation of the hard X-rays (E 2 30 keV) Gamma Ray Observatory BATSE spectrometer.

for the

flare

of

.

-

0

1 * .

.

* .

22:08

14 May

1993

recorded

by the

smallest peaks in the records are real peaks of the solar emission. Using the thick-target model of the HXR emission (Brown 1971) we have estimated that -1O33 non-thermal electrons are needed to produce the smallest peaks seen in Fig. 2. It is known from the analysis of soft X-ray images that the electron density in flare kernels are N - 10” cmm3 during the impulsive phase. Taking Nd3 = 1O33 we can estimate the size, d, of a magnetic structure at the kernel boundary (see Fig. 3) which is responsible for one acceleration episode, i.e. a small peak in Fig. 2. We obtain d = 200 km which means that the structures, in which the acceleration occurs, are not very small. An appropriate mechanism of the electron acceleration will be presented in a next paper. DISCUSSION AND CONCLUSIONS Our scheme of the flare development is quite different from that proposed by LaRosa and Moore (1993). The main point of their scheme is the development of “classical” eddy turbulence in the reconnection flows. This requires to overcome a significant magnetic-field resistance to the formation of the eddies and it is difficult to overcome this resistance. In our scheme the chain of reconnections develops spontaneously as the result of topological instability of the magnetic field configuration. The magnetic lines of force are tangled by multiple reconnections and not by their twisting by eddy motions, so that the magnetic field does not significantly resist to the tangling. The main conclusions of the present paper are the following: 1. The turbulent kernels a confined volume.

can develop

2. The turbulent

very well explain

kernels

by a chain of multiple

magnetic

field reconnections

in

fast heating of large plasma volumes.

3. The kernel boundaries, where the high-speed turbulence collides magnetic field, should be most efficient in particle acceleration.

with

the

surrounding

1106

J. Jakimiec

Fig. 3. Schematic diagram showing the interaction of the turbulent magnetic field of a flare kernel with the external field.

ACKNOWLEDGMENTS This research has been supported of Scientific Research.

by the grant No. 2 P03D 016 14 of the Polish Committee

REFERENCES Brown, J .C., Solar Phys., 18, 489, 1971 Jakimiec, J., Adv. Space Res., Vol. 10, No. 9, 109, 1990 Jakimiec, J., Publ. Czech Astr. Znstit., 88, 124, 1998 Jakimiec, J., Tomczak, M., Falewicz, R., Phillips, K. J. H., Fludra, A., A&A, 334, 1112, 1998 Jakimiec, J., ETA, SP-448, 729, 1999 Jakimiec, J., Falewicz, R., Tomczak, M., Adv. Space Rex, this issue, 2001 LaRosa, T. N., Moore, R. L., ApJ, 418, 912, 1993 LaRosa, T. N., Moore, R. L., Miller, J. A., Shore, S. N., ApJ, 467, 454, 1996 Parker, E. N., Cosmical Magnetic Fields, Charendon Press, Oxford 1979