Gas rotation and dark matter halo shape in cool-core clusters of galaxies

In the context of the study of galaxy clusters it is usual to assume that the intracluster medium (ICM) is static into a spherical dark matter (DM) halo. However, there are observational (and theoretical) pieces of evidence that the estimates of mass under the assumption of hydrostatic equilibrium are biased low with respect to the "true" mass as traced, e.g., by gravitational lensing. Moreover, on the basis of the cosmological N-body DM-only and hydrodynamical simulations there is a clear evidence that the assumptions of spherically symmetric halo and of hydrostatic equilibrium of the ICM are not always justified. One way to detect these departures from hydrostatic equilibrium in the ICM is through the detection of bulk motions. However, the low energy resolution of available X-ray instruments does not allow for this detection via the Doppler shift of the emission lines centroids in the X-ray spectra. In this work, we build polytropic models of the ICM in cool-core clusters: we explore different kinematic conditions of the ICM (in particular, the rotation) and/or different shapes of halos, while preserving the predicted regularity of internal structure of halos (the Navarro-Frenk-White profile and mass-concentration relation) and the universality of observed thermodynamic profiles of the ICM. Then, from these models, we reconstruct the main photometric and spectroscopic observables to test the current photometric upper limits on the rotation speed and to probe the future perspectives via mock observations with the spectrometer RESOLVE on board of XRISM. We conclude that our models predict rotation of 400-500 km/s that do not violate the available observational proxies (i.e. the thermodynamic profiles, shape of iso-surface brightness contours and broadening of X-ray emitting lines), leaving some room in real clusters for possible rotation within 500 km/s, which could be detected with future facilities.