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Astron. Astrophys. 357, 767-776 (2000)

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1. Introduction

The effects of opacity in solar spectral lines have been studied on a number of occasions (Jordan 1967; Doschek et al. 1976; Doyle & McWhirter 1980). Jordan (1967) established the technique of using branching ratios of lines arising from a common upper level to extract information on opacities from spectral observations. Doyle & McWhirter subsequently developed this same technique to study opacity at the solar limb and their work included a simple model of predicted line ratios from the region on-disk up to the limb. Escape probability and escape factor expressions originated with the work of Holstein, 1947 (see also McWhirter 1965; Irons 1979). More recently Kastner & Kastner (1990), Kastner & Bhatia (1989) and Kastner & Bhatia (1992) have reworked escape probability expressions and have used them for predicting emergent intensities and optically thick population structures. The latter paper contained predicted limb brightening curves and ratio variations for a number of C III lines.

In Paper I of this series (Brooks et al. 2000) the observational approach of Doyle & McWhirter was extended and used in an analysis of spectral data from the SOHO spectrometers CDS and SUMER with three objectives in mind: firstly to present some systematics of the incidence of opacity along iso-electronic sequences; secondly to extend the Doyle & McWhirter analysis to the case of lines with optical thicknesses significantly greater than unity on the solar disk and thirdly to judge the suitability of lines observed by CDS and SUMER for differential emission measure analysis (DEM).

In the present paper this approach is developed further in order to assess the escape probability as a modelling tool within dynamic and detailed structural atmospheric models. The escape probability approach for dealing with opacity has the advantage that it is relatively simple, avoiding the need for a full solution of the radiative transfer equation. Since the chromosphere and transition-zone represent regions of non-negligible opacity from which the spectral emission is dominated by atmospheric structure, such techniques are potentially very useful. The theory is developed to include consistent modification to the population structure within the atmosphere models considered and the effects of line blending on the emergent intensities and population structure. We seek also to take better account of the geometric extension of the line of sight at the limb to predict both limb brightening and branching ratio variations on crossing the limb for selected lines of C II and C III. As in Paper  these predictions are compared with observational data from SUMER. In Paper  it was shown that off-limb the branching ratio characteristics are dominated by the presence of instrumentally scattered light. This effect is also accounted for within the new models.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000