Polarization of the Sunyaev-Zel'dovich effect: relativistic imprint of thermal and non-thermal plasma

[Abridged] Inverse Compton scattering of CMB fluctuations off cosmic electron plasma generates a polarization of the associated Sunyaev-Zel'dovich (SZ) effect. This signal has been studied so far mostly in the non-relativistic regime and for a thermal electron population and, as such, has limited astrophysical applications. Partial attempts to extend this calculation for a thermal electron plasma in the relativistic regime have been done but cannot be applied to a general relativistic electron distribution. Here we derive a general form of the SZ effect polarization valid in the full relativistic approach for both thermal and non-thermal electron plasmas, as well as for a generic combination of various electron population co-spatially distributed in the environments of galaxy clusters or radiogalaxy lobes. We derive the spectral shape of the Stokes parameters induced by the IC scattering of every CMB multipole, focusing on the CMB quadrupole and octupole that provide the largest detectable signals in galaxy clusters. We found that the CMB quadrupole induced Stoke parameter Q is always positive with a maximum amplitude at 216 GHz which increases slightly with increasing cluster temperature. The CMB octupole induced Q spectrum shows, instead, a cross-over frequency which depends on the cluster electron temperature, or on the minimum momentum p_1 as well as on the power-law spectral index of a non-thermal electron population. We discuss some possibilities to disentangle the quadrupole-induced Q spectrum from the octupole-induced one which allow to measure these quantities through the SZ effect polarization. We finally apply our model to the realistic case of the Bullet cluster and derive the visibility windows of the total, quandrupole-induced and octupole-induced Stoke parameter Q in the frequency ranges accessible to SKA, ALMA, MILLIMETRON and CORE++ experiments.Comment: 31 pages, 11 figures, submitted to JCA

Multi-frequency constraints on the non-thermal pressure in galaxy clusters

The origin of radio halos in galaxy clusters is still unknown and is the subject of a vibrant debate both from the observational and theoretical point of view. In particular the amount and the nature of non-thermal plasma and of the magnetic field energy density in clusters hosting radio halos is still unclear. The aim of this paper is to derive an estimate of the pressure ratio X between the non-thermal and thermal plasma in radio halo clusters that have combined radio, X-ray and SZ effect observations. From the simultaneous P_{1.4}-L_X and P_{1.4}-Y_{SZ} correlations for a sample of clusters observed with Planck, we derive a correlation between Y_{SZ} and L_X that we use to derive a value for X. This is possible since the Compton parameter Y_{SZ} is proportional to the total plasma pressure in the cluster (that we characterize as the sum of the thermal and non-thermal pressure) while the X-ray luminosity L_X is proportional only to the thermal pressure of the intracluster plasma. Our results indicate that the average (best fit) value of the pressure ratio in a self-similar cluster formation model is X =0.55 \pm 0.05 in the case of an isothermal beta-model with beta=2/3 and a core radius r_c = 0.3 R_{500} holding on average for the cluster sample. We also show that the theoretical prediction for the Y_{SZ}-L_X correlation in this model has a slope that is steeper than the best fit value for the available data. The agreement with the data can be recovered if the pressure ratio X decreases with increasing X-ray luminosity as L_X^{-0.96}. We conclude that the available data on radio halo clusters indicate a substantial amount of non-thermal pressure in cluster atmospheres whose value must decrease with increasing X-ray luminosity, or increasing cluster mass (temperature). (abridged)Comment: A&A, in press; 10 pages; 10 figure