On the invertibility of Doppler imaging: an approach based on generalized tomography

Mapping star surface structures helps to constrain astrophysical models and to understand their properties better. As telescopes do not have sufficien t resolution, indirect methods such as Doppler imaging are used. Surface te mperature inhomogeneities are reconstructed from time series evolution. In Doppler imaging the measure is the integral of the star intensity on manifo lds defined by an angular and a shift variable just as in classical tomogra phy. To begin we briefly explain the Doppler imaging principle, then the me asure is reduced to a block system of two by two generalized Radon transfor ms. Following the approach of Quinto for the rotation invariant Radon trans form, the invertibility of this operator is studied. The major result of th is work is that non-trivial surface temperature distributions (even smooth ones) are invisible from Doppler imaging. More precisely, a family of radia l functions (axial symmetric functions according to the rotation axis of th e star) are shown to belong to the kernel of the considered operator.