Astron. Astrophys. 333, 1069-1081 (1998)

1. Introduction

The elemental abundances vary from the photosphere of the sun to the interplanetary space. A comparison of spectroscopic observations in the photosphere with in-situ measurements in the solar wind or spectroscopic observations in the corona clearly show, that elements with a first ionization potential (FIP) below 10 eV are enriched in relation to those with higher FIP. The factor of enhancement varies from 2 (fast wind) over 4 (slow wind) up to 10 (polar plumes) depending on the respectively observed structure. See Anders & Grevesse (1989), von Steiger et al. (1995), Hénoux & Somov (1992), Hénoux (1995) and Meyer (1996) for collections of the measurements and a review of different attempts to describe this so-called FIP-effect theoretically.

It is now widely accepted that the basic mechanism for fractionation of elements is driven by an ion-neutral separation in the chromosphere, well above the temperature minimum and near but below K (Geiss 1982). For this the recent fractionation models, which allowed for the first time a detailed quantitative comparison with the measurements, assumed the trace gases to diffuse on a background of hydrogen and to be ionized by the UV-photons coming from the higher layers of the chromosphere and transition region: von Steiger & Geiss (1989) and Marsch et al. (1995) were able to explain the fractionation in the slow wind, while recently Peter (1996) found a velocity-dependence of the fractionation, which leads to the understanding of the FIP-effect in the slow and the fast wind within the same model.

For a more advanced fractionation model, capable of explaining also other phenomena like the strong enrichments of magnesium in polar plumes (observations e. g. of Widing & Feldman 1992) or the "absolute" fractionation, i. e. the fractionation in relation to hydrogen (measurements of von Steiger et al. 1995), a sophisticated model for the main gas, i. e. the background, is needed. This paper offers just such a model.

The aim is to define the background for a fractionation model, which can describe the abundance variation from the photosphere to the solar wind or corona. There are two major constraints for such a main gas model: on the one hand the flow of the material has to be treated self-consistently, because the fractionation connects the abundances on solar surface with those in the solar wind. Since the fractionation processes are located in the chromosphere one has to describe the source region of the solar wind including the plasma flow.

On the other hand such a main gas model has to be also the model atmosphere for the chromosphere. In the last two decades many comprehensive atmospheric models were published, e. g. the continuum atmosphere by Gingerich & de Jager (1968), the semi-empirical model of Vernazza et al. (1981) or the one of Fontenla et al. (1990) including ambipolar diffusion. But all these models assume a static atmosphere and do not include a self-consistent treatment of the flow.

Of course, a complete model combining the source region of the solar wind with the upper atmospheric layers, would be the ultimate goal. Yet, it is very complicated to combine an exact treatment of the radiative transport with the plasma dynamics and thermodynamics, and therefore one has to simplify the problem. Because the aim of this paper is to offer a main gas model for the description of a solar-wind-related phenomenon, the main emphasis will be on the flows. Radiative transport will not be included, but special attention will be paid on the ionization of the material. Thus the present model is not a full atmospheric model for the chromosphere, but it may serve well as a background for the minor ion fractionation.

Another aim of this paper is to elucidate the special role of helium: its abundance, which is about 10% in the photosphere, varies from some percent in the "quiet" solar wind (Schwenn 1990) to up to 40% in the driver gas of flare-induced interplanetary shocks (Hirschberg et al. 1970, Borrini et al. 1982). With an abundance of 10% and an atomic weight four times higher than hydrogen, helium contributes about one fourth to the total mass and can thus not be treated as a trace gas, i. e. as test particles, but must be included in the main gas, with collisional coupling to the hydrogen. As it turns out, the wide variations of the helium abundances cannot be understood on the basis of an ionization-diffusion model for a thin layer in the chromosphere.

The models presented in this paper are an extension of the main gas model of Marsch et al. (1995), who only considered diffusion and (photo-) ionization. In the present models also the effects of e. g. the absorption of the ionizing radiation, the recombination and the gravitation are considered. This will remove the problems of their simple main gas model, like the infinite proton speed at the bottom. Additionally an energy equation is solved to determine the temperature structure. This makes possible to study the influence of the flows on the temperature profile.

In the next section at first the assumed geometry and the basic assumptions as used in the model are presented, before in Sect. 3 the model equations are established. This section also describes the ionization and elastic collisions as well as heating, radiative cooling and heat flux. Before discussing the results for a pure hydrogen gas in Sect. 5 an analytical approximation for this case will be presented in Sect. 4. At least the effects of helium will be considered in Sect. 6 and the resulting abundance variations will be discussed. Sect. 7 summarizes the results of the paper.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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