Adv. Space Res. Vol. 13, No.9, pp. (9)307—(9)310, 1993 0273—1177/93 $24.00
Printed in Great Britain. All rights reserved. Copyright © 1993 COSPAR
ESTIMATION OF EQUIVALENT FLARING
LOOP GEOMETRY BASED ON
BROADBAND SOFT X-RAY
OBSERVATIONS
J. Sy1wester,~ B. Sylwester,* J. Jakimiec,** H. A. Garcia,***
S. Seriot and F. Realet
* Space Research Centre, Polish Academy of Sciences, Wroclaw, Poland
** Institute of Astronomy, Wroclaw University, Poland
*** Space Environment Laboratoiy, Boulder, CO, U.S.A.
~j’ Osservatorio Astronomico, Palermo, Italy
ABS1’RACT
Hydrodynamic models of a simple flaring loop, obtained using the Palermo-Harvard code have been used to
consider the flare global energy balance. During the heating phase the time variations of the total thermal energy
contained in the coronal portion of the loop is well represented by a simple analytical formula with parameters
depending on the flaring loop geometry. The loop geometry parameters are the loop semi-length and the cross-
sectional area. A method is introduced which allows to estimate values of these parameters from a fit to the
measurements. We have applied this method to the interpretation of GOES soft X-ray data for the flare on 11
September 1989, for which high-resolution XUV images were available from the NIXT experiment.
INTRODUCTION
High resolution X-ray images of the Sun, such as those obtained from SKYLAB /1/, NIXT /2/ and YOHKOH
/3/, reveal that for a number of flares the bulk of the soft X-ray emission comes from a single loop-like structure
of nearly constant cross-section (including a few events observed as two-ribbon flares in Ha). For large two-
ribbon flares several flaring loops are sometimes observed to be bright at the same time. h~ most cases the lengths
of individual loops are similar. To simplify the description of the flaring region’s geometry, we introduce two
representative parameters, i.e. loop semi-length L, (along the magnetic field line) and cross-sectional area A, (not
necessarily circular). L corresponds to the high temperature (T> 1MK) portion of the loop; A may represent the
sum of several sub-areas, each corresponding to an individual component. We shall assume that L and A are
constant throughout the duration of the flare, which is consistent with some of the observed flares. In the
following sections, we consider how the total thermal energy, E, contained in the coronal portion of the flaring
loop, may vary with time and how this variation depends on L and A. This is based on the results of
hydrodynamic (HD) modelling of simple flares performed using Palermo-Harvard code /4/. Next the actual flare
measurements are analysed. We have selected time varying GOES ion-chamber currents in two broad-bands (0.5
- 4 A and 1 - 8 A) as our primary data set. Using present method of analysis we have derived equivalent L and A
values for a single flare, on 11 September 1989 16:30 UT, for which independent observations of flaring loop
parameters were available from NIXT /2/. Finally, derived equivalent values of L and A are compared with the
directly observed values.
TIME VARIATIONS OF FLARE THERMAL ENERGY
The energy balance equation of flaring plasma can be written in the following simplified form /5/:
clE/dt = - - - (1)
where eH e~ and ~ are the total rates of heating, radiative and conductive losses respectively; ~ is the
energy gain rate related to the convective flow of the plasma into the loop. The heating and radiative loss terms
are integrated along the loop length, while the conductive losses are the net flux conducted away through the
transition region. In this equation we assume that all transient forms of energy such as the energy contained in
turbulence or accelerated particles are dissipated into thermal energy in time scales less than that of the variation
of the heating rate, eM. It has been suggested that the effective rate of conductive losses is less than ~ due to
energy carried into the loop by convection /5/, i.e:
= (2)
This result has also been reaffirmed by additional HD model calculations.
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