Kinetic Sunyaev--Zel'dovich effect in rotating galaxy clusters from MUSIC simulations

The masses of galaxy clusters are a key tool to constrain cosmology through the physics of large-scale structure formation and accretion. Mass estimates based on X-ray and Sunyaev--Zel'dovich measurements have been found to be affected by the contribution of non-thermal pressure components, due e.g. to kinetic gas energy. The characterization of possible ordered motions (e.g. rotation) of the intra-cluster medium could be important to recover cluster masses accurately. We update the study of gas rotation in clusters through the maps of the kinetic Sunyaev--Zel'dovich effect, using a large sample of massive synthetic galaxy clusters ($ M_{vir} > 5\times 10^{14} h^{-1}$M$_\odot$ at $z~=~0 $) from MUSIC high-resolution simulations. We select few relaxed objects showing peculiar rotational features, as outlined in a companion work. To verify whether it is possible to reconstruct the expected radial profile of the rotational velocity, we fit the maps to a theoretical model accounting for a specific rotational law, referred as the vp2b model. We find that our procedure allows to recover the parameters describing the gas rotational velocity profile within two standard deviations, both with and without accounting for the bulk velocity of the cluster. The amplitude of the temperature distortion produced by the rotation is consistent with theoretical estimates found in the literature, and it is of the order of 23 per cent of the maximum signal produced by the cluster bulk motion. We also recover the bulk velocity projected on the line of sight consistently with the simulation true value.