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Astron. Astrophys. 318, L17-L20 (1997)

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2. Numerical Method

2.1. General Procedure

A fully consistent and accurate treatment of the flare hydrodynamics together with its radiative transfer is extremely difficult and has not yet been achieved. Canfield & Gayley (1987) computed the H [FORMULA] emission from dynamic atmospheres by use of the probabilistic radiative transfer method. As the authors indicated, such a method loses accuracy in the presence of large velocity gradients. The present work, however, will not treat the flare dynamics in detail but use a better code of the radiative transfer.

We employ the same program as that used by Fang et al. (1993) to compute the line profiles from an atmosphere with a prescribed temperature versus column mass density relation and a velocity field. The program solves the equations of statistical equilibrium and radiative transfer iteratively until a convergence is reached. A four-level-plus-continuum atomic model for hydrogen is adopted here. The line broadening mechanisms include the Doppler effect, Stark effect, radiative damping, and resonance broadening.

In particular, the non-thermal excitation and ionization transition rates caused by a possible precipitating electron beam have been included in the statistical equations, i.e., these rates are added to the radiative and thermal collisional rates which are normally considered. To do so, we first calculate the energy deposit rates at different atmospheric layers by an electron beam with given flux and power index values. The non-thermal transition rates are then evaluated according to their relative collisional cross-sections. All formulae related to this problem can be found in Fang et al. (1993).

2.2. Description of the Velocity Field

The existence of a velocity field makes the local atomic absorption (emission) profile Doppler shifted, thus changing the radiative transition rates and ultimately the line source function. In some special cases when the non-thermal collisional transition rates dominate over the radiative rates, the statistical equilibrium will keep relatively stable against the variation of the velocity field. Thus the effect of the velocity field is mainly concentrated on producing an asymmetric line profile, whose asymmetry property depends on whether the moving layer is absorptive or emissive relative to the underlying intensity irradiated on it (Ding & Fang 1996).

Supposing that the chromospheric mass motion is caused by the downward propagation of a condensation, the moving region should be located lower and lower with time elapsing. Numerical simulations of the gas dynamics in the flare loop show that the condensation is restricted in a very narrow region when it is primarily formed (e.g., Fisher et al. 1985) and is expected to expand somewhat during its downward propagation and dissipation. To simplify this problem, we will consider in the following only the case of an atmosphere purely superimposed by an arbitrary velocity field, which is assumed to be confined to different heights but occupy a small vertical space (i.e., only 2-3 grid points of the atmosphere have a non-zero velocity value). Of course, such simple kinetic descriptions represent no real situations of flare dynamics and the following results can only be taken as suggestive.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998