Sunyaev–Zel'dovich polarization as a probe of the intracluster medium

We present high‐resolution hydrodynamical simulations of the degree and direction of polarization imprinted on the cosmic microwave background (CMB) by the Sunyaev–Zel'dovich effect in the line of sight of massive galaxy clusters. We focus on two contributions to the electron rest‐frame radiation quadrupole anisotropy in addition to the intrinsic CMB quadrupole that contributes most of the induced CMB polarization: the radiation quadrupole seen by electrons due to their own velocity in the plane normal to the line of sight and the radiation quadrupole due to the thermal Sunyaev–Zel'dovich effect, which is generated by a previous scattering elsewhere in the cores of the local and nearby clusters. We show that inside the virial radius of a massive cluster, this latter effect, although being of second order in the optical depth, can reach the nK level of the former effect. These two effects can, respectively, constrain the projected tangential velocity and inner density profile of the gas, if they can be separated with multifrequency observations. As the information on the direction and magnitude of the tangential velocity of the intracluster medium (ICM) gas is combined with the temperature Sunyaev–Zel'dovich effect probing the projected radial velocity it will be possible to improve our understanding of the dynamics of the ICM. In particular, future polarization observations may be able to trace out the filamentary structure of the cooler and less dense ionized gas that has not yet been incorporated into massive clusters. We also discuss how the collapse of a cluster should produce a peculiar ring‐like polarization pattern which would open a new window to detect protoclusters at high redshift.