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.
