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

摘要

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