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Astron. Astrophys. 354, 714-724 (2000)

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1. Introduction

Observations of the linear polarisation of spectral lines in solar flares provide unique information on the modes of energy transport from the corona to deeper layers during these dynamic events. The [FORMULA]-line is the emission most frequently observed in solar flares, and significant properties of the energy transfer process can be derived from measurements of its polarisation vector.

Many [FORMULA]-line observations reported an existance of linear polarisation with a degree of polarisation normally in the range of [FORMULA], in some cases exceeding [FORMULA] (Chambe & Hénoux 1979; Hénoux & Semel 1981; Hénoux & Chambe 1990a; Hénoux 1991; Firstova & Boulatov 1996). In most cases the highest degree of polarisation does not correspond to the brightest areas of flares. In the observations by Hénoux et al. (1990b) the direction of plane of polarisation coincides with the flare-to-disk centre direction, whereas some observations by Firstova & Bulatov (1996) show the plane of polarisation to be perpendicular to this direction.

The first interpretation of [FORMULA]-line polarisation was made in the approximation of optically thin plasma, using the Born cross-sections for line excitation by charged particles or external radiation (Hénoux & Semel 1981). The observed polarisation was assigned to impact polarisation or to polarisation by high energy radiation (UV and EUV) as the Zeeman or Stark effects produce a polarisation degree of about [FORMULA] (Hénoux & Semel 1981; Chambe & Hénoux 1979). The authors have also shown that highly energetic particles (electron or protons) produce negative polarisation with the plane of polarisation being mainly perpendicular to the solar centre direction. On the other hand, a directed heat flux can produce positive polarisation with the plane of polarisation being parallel to the solar centre.

In order to explain observed positive polarisation in the [FORMULA]-line, low energy proton beams ([FORMULA] keV) were used as the source of slow directed fluxes (Hénoux & Chambe 1990a; Hénoux et al. 1993). Their simulations gave a reasonable degree of polarisation. However, they did not take into account the collective effects of proton beams on the ambient plasma which can excite kinetic Alfven waves simultaneously with the [FORMULA]-line emission (Voitenko 1998).

Recently, simulations of impact polarisation in [FORMULA]-line emission were performed for proton beams precipitating into a flaring atmosphere and causing a redistribution in population between the Zeeman excited states using the density matrix formalism (Vogt et al. 1997). The collisional mechanisms by proton beams and by the ambient plasma electrons, as well as the radiative ones were taken into account for incident and diffusive fields in [FORMULA], [FORMULA] and [FORMULA] lines. The calculated [FORMULA]-line polarisation was found to be lower by up to an order of magnitude than the ones observed during a flare. The simulations only fit observations for a very weak emission at the very beginning of a flare onset although the best fit is found for the quiet Sun or plage models (Vogt et al. 1997). Therefore, in order to get a better fit of polarimetric observations in flares other agents producing [FORMULA]- line polarisation should be considered.

As such agents, electron beams were suggested for propagation in the fully ionised plasma of solar flares (Fletcher & Brown 1995). Their simulations gave a degree of polarisation of about [FORMULA], but required electron beams with very high initial energy fluxes of [FORMULA]. They are three orders of magnitude higher than typical fluxes deduced from the X-ray observations in solar flares.

In many flares the [FORMULA]-line emission is very bright and wide, so it is likely to be optically thick. Moreover, at chromospheric depths, where magnetic field can reach 1000 Gs (Lozitskii & Baranovskii 1993; Silva et al. 1996), the hydrogen atom levels are likely to be split. Therefore, for the interpretation of [FORMULA]-line polarisation it is necessary to include these two effects. This can be done using the density matrix approach. It has been applied earlier to the [FORMULA] line in solar prominences (Bommier 1980; Landi Degl'Innocenti 1982) and for Hydrogen lines in flares (Vogt et al. 1997). Recently, the transfer of polarised radiation of two-level hydrogen atoms embedded in an optically thick magnetised medium was generalised for weak, intermediate and strong magnetic fields (Landi Degl'Innocenti et al. 1990, 1991b; Bommier et al. 1991; Bommier et al. 1996; Landi Degl'Innocenti 1996).

In the present paper, the effect of electron beam injection on the [FORMULA]-line polarisation during the impulsive phase of flares is investigated in a magnetised plasma loop using the approach similar to those of Vogt et al. (1997). Firstly, the solutions of the time-dependent Boltzman equation were used for beam electrons with anisotropic scattering in presence of the return current electric and converging magnetic field (Zharkova et al. 1995). Secondly, the diffusive [FORMULA] radiation field for a 5 level hydrogen model atom without fine structure was calculated in the full non-LTE approach as described by Zharkova & Kobylinsky (1989, 1991, 1993). And, thirdly, the density matrix technique was applied for the solution of a steady state equation in a flaring atmosphere with angular anisotropy caused by electron beam impacts and external radiation by the method of Landi Degl'Innocenti (1985).

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© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000