6 Conclusion

This paper aimed at designing instrumental and observational constrains of interfero- polarimetry for studying matter distribution inside scattering environments. Adding a polarimetric mode to an interferometer extends its capacities to explore extended atmospheres in which intrinsic polarization becomes a non negligible observable. This implies to observe at small spatial frequencies (i.e. ${B/\lambda}\approx 1/(10\ R^*)$) and with a specific focal instrumentation separating the polarized interferograms and enabling an accurate calibration of the instrumental polarization. For spherical or ellipsoidal hot envelopes, an accuracy of 1% on the visibility is enough to put a lower limit to the exponent of the matter distribution, which is obviously compatible with existing instruments. Moreover this leads to limiting magnitudes $M_v\approx 4$ in a monospeckle mode and $M_v\approx 8-10$ in multispeckle modes, which permits to foresee the observation of many hot stars by this technique.

Our accuracy on the angular diameter is not enough to detect its variations with polarization. Thus the envelope dimensions can be determined by High Angular Resolution observations in natural light. Using Earth-rotation synthesis allows to constrain the envelope flattening.

We have limited our study to pure single Thomson scattering and to an equatorial observation, which constitutes the most favorable case. Now, we should obviously integrate in our general formalism more realistic source functions (including opacities) and take into account multiple scattering or polarization inside emission lines (Be stars, ...) to provide a more detailed analysis of physical conditions in the envelope. For this purpose and to strongly constrain the geometry and the density of the envelope, interfero-polarimetry has to be used in conjunction with others techniques such as spectroscopic ones especially for Be stars (Waters 1986).

Of course interfero-polarimetry can be applied to future imaging arrays (Aime & Roddier 1976; Rousselet-Perraut et al. 1997b) for which a polarimetric instrumentation must be advocated since it greatly reduces the instrumental bias. Moreover providing quasi instantaneous polarized images of the intensity maps, these future arrays (NPOI - Armstrong 1994, OVLA) would enable to detect local structures at the stellar surfaces or throughout circumstellar environments. As such, they would contribute to a better understanding of the mass-loss mechanisms and the stellar evolution theories.

Finally we can obviously foresee to extend this technique to other objects such as contact or semi-contact binaries where mutual reflection effect is at play, evolved red supergiants for studying grains and dusts scattering or absorption in molecular bands, magnetic stars for obtaining magnetograms and constraining the models of oblique rotators, ... But for these objects, limiting magnitudes can be constraining and besides adapted astrophysical models have to be developed to compute the flux contributions.

Acknowledgements

The author wants to greatly thank F. Perraut, F. Vakili, D. Mourard, Ph. Stee and F. Ménard for the discussions and their fruitful comments. The author is grateful to K. Wood who refereed this paper and

whose suggestions were very helpful. This work has been supported by the Collège de France.