Interferometric-Doppler imaging of stellar surface structure

In this paper we discuss the combination of two basic approaches which should potentially generate images of spatially unresolved stars: differential interferometry and classical spectroscopy. Doppler Imaging provides indirect observational information on stellar surface structures by modeling the rotational modulation of the observed flux distribution across spectral lines. Similarly, differential interferometry makes it possible to measure the disturbances of photocentroid location of an unresolved star as a function of wavelength and to deduce the corresponding stellar map. We present the general formalism to reconstruct images from spectroscopy and differential interferometry data for sources with spatially unresolved structures, and we discuss how their combination improves the image reconstructions. This technique, that we call Interferometric-Doppler Imaging (IDI), leads to significant progress in solving some long-standing problems of Doppler Imaging, such as latitude smearing and bias as well as the non-uniqueness of the solution in the special case of an equator-on star. We treat explicitly the most delicate case of non-radial stellar pulsations, for which the cancellation of opposite sign temperature or velocity fields introduces additional difficulties. The performance of the method is demonstrated, using the indirect imaging code built on the basis of the developed approach to reconstruct an input image from a series of generated noisy spectra. The problem of image reconstruction from two-aperture interferometry data has been particularly addressed since it represents the case of most presently operating interferometers.