Self-Similar Shocks and Winds in Galaxy Clusters
  A theoretical model framework of spherical symmetry is presented for a composite astrophysical system of two polytropic fluids coupled together by gravity to explore large-scale shocks and flow dynamics in clusters of galaxies or in globular clusters. The existence of such large-scale shocks in clusters of galaxies as inferred by high-resolution X-ray and radio imaging observations implies large-scale systematic flows that are beyond usual static models for clusters of galaxies. Here, we explore self-similar two-fluid flow solutions with shocks for a hot polytropic gas flow in a cluster of galaxies in the presence of a massive dark matter (DM) flow after the initiation of a gravitational core collapse or a central AGN activity or a large-scale merging process. In particular, the possibility of DM shocks or sharp jumps of mass density and of velocity dispersion in dark matter halo is discussed and such DM shocks might be detectable through gravitational lensing effects. To examine various plausible scenarios for clusters of galaxies, we describe three possible classes of shock flows within our model framework for different types of temperature, density and flow speed profiles. Depending upon sensible model parameters and shock locations, the hot ICM and DM halo may have various combinations of asymptotic behaviours of outflow, breeze, inflow, contraction or static envelopes at large radii at a given time. We refer to asymptotic outflows of hot ICM at large radii as the galaxy cluster wind. As a result of such galaxy cluster winds and simultaneous contractions of DM halo during the course of galaxy cluster evolution, there would be less hot ICM within clusters of galaxies as compared to the average baryon fraction in the Universe. 
Yu-Qing Lou, Yan-Fei Jiang, Chi-Chuan Jin