Multiple scattering Sunyaev-Zeldovich signal I: lowest order effect

Future high-resolution, high-sensitivity Sunyaev-Zeldovich (SZ) observations of individual clusters will allow us to study the dynamical state of the intra cluster medium (ICM). To exploit the full potential of this new observational window, it is crucial to understand the different contributions to the total SZ signal. Here, we investigate the signature caused by multiple scatterings at lowest order of the electron temperature. Previous analytic discussions of this problem used the isotropic scattering approximation (ISA), which even for the simplest cluster geometries is rather rough. We take a step forward and consistently treat the anisotropy of the ambient radiation field caused by the first scattering. We show that the multiple scattering SZ signal directly probes line of sight anisotropies of the ICM, thereby delivering a new set of SZ observables which could be used for 3D cluster-profile reconstruction. The multiple scattering signal should furthermore correlate spatially with the cluster's X-ray and SZ polarization signals, an effect that could allow enhancing the detectability of this contribution.