6 Conclusions

Our studies of simulated data show the fundamental limitations on the determination of limb polarization in eclipsing binary stars. In particular, Fig. 4 indicates that limb polarizations of order a few percent are only just above the threshold of detectability, even in perfectly spherically symmetric, non-interacting binary systems. The situation will be worse in more complex systems.

It is important to appreciate that the Backus-Gilbert method does not strictly estimate the polarization at a point on the stellar disc, but rather the polarization convolved with the resolution function. To relate the results of the inversion to a particular model, it is necessary to calculate the theoretical value of this convolution, which should be consistent with the $\lambda$ we have chosen and with all higher values of $\lambda$ - these represent coarser averages over the stellar disc.

The bottom line is that one must take care in drawing conclusions about limb polarization from studies of eclipsing binaries. It is clearly not possible to distinguish between stellar atmosphere models on this basis if their predicted limb polarizations differ by less than the maximum accuracy achievable. On the other hand, an appreciation of the issues raised in this paper will allow a meaningful determination of limb polarization, with reliable error estimates.

Formally, the eclipsing binary problem is very similar to the gravitational microlensing problem. Indeed, part of the initial motivation for this work sprang from studies of the microlensing of extended sources. A future paper (Coleman et al. in preparation) will apply the inverse problem approach outlined in this paper to the use of microlensing as a probe of stellar atmospheres.

Acknowledgements

We would like to thank Dr. Richard K. Barrett for enlightening discussions of the Backus-Gilbert method. IJC was supported by a PPARC studentship.