1 Introduction

Scattered light emerging from a stellar atmosphere is expected to be partially linearly polarized. This effect should be greatest at the limb of the star, with a pure electron scattering atmosphere giving a limb polarization of 11.7% (Chandrasekhar 1946, 1950). Less idealised calculations (Collins & Buergher 1974) suggest a lower degree of limb polarization, around 2% for early-type stars, though this figure is rather sensitive to the ionization state of the outermost atmospheric layers. Clearly a spherically symmetric star will exhibit no net polarization, but if the symmetry is broken by an eclipse the limb polarization should in principle be detectable. Theoretical polarimetric light curves for this situation have been calculated by Landi Degl'Innocenti et al. (1988).

The first detection of this "Chandrasekhar effect'' was in the Algol system (Kemp et al. 1983). This data was analysed by Wilson & Liou (1993), but the complexity of the system and the amount of modelling involved in the analysis prevented them from making any reliable estimate of the limb polarization.

The inversion of polarimetric light curves from eclipsing binary stars should allow the limb polarization of the eclipsed star to be measured (and the photometric light curve should similarly give the limb darkening). In fact this inverse problem is highly ill-conditioned, and relating observations to stellar atmosphere models is therefore far from straightforward. In this paper we investigate the practical feasibility of determining of limb polarization by this method.

This allows us to address three closely related issues:

1.

We develop a method of obtaining the polarization at a point on the stellar disc, and of estimating the error on this value. This is based on the Backus-Gilbert inversion technique.

2.

We determine the maximium accuracy possible in determining limb polarization, given a number of data points and a noise level.

3.

Thus, we are able to put forward an observational strategy which should allow the best measurement of limb polarization.

In Sect. 2 we give a brief overview of the problem. We set out the formalism of the Backus-Gilbert method in Sect. 3, and discuss its suitability for the problem at hand. Section 4 contains the calculations for the specific case of eclipsing binary stars, and Sect. 5 presents the results of the inversion scheme when applied to simulated data, and the conclusions that can be drawn from these. Section 6 considers a simplified analogue of the Algol system, comparing the theoretical polarization profile with the best resolution current measurements can achieve.