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Gravitational and distributed heating effects of a cD galaxy on the hydrodynamical structure of its host cluster

We investigate the effects of a cD galaxy's gravity and AGN heating of the host galaxy cluster. We consider a standard prescription for the hydrodynamics, with the structures determined by mass continuity, momentum and energy conservation equations in spherical symmetry. The cluster comprises a dark matter halo (DM) and ionised X-ray emitting intracluster gas (ICM), which jointly determine the gravitational potential. The cD galaxy is an additive gravitational potential component. The DM assumes a polytropic equation of state (determined by its microphysics), which could be non-radiative self-interacting particles or more exotically interacting particles. The AGN provides distributed heating, counteracting radiative cooling. Stationary density and velocity dispersion profiles are obtained by numerically integrating the hydrodynamic equations with appropriate boundary conditions. The minimum gas temperature in the cluster core is higher when a cD galaxy is present than when it is absent. The solutions also yield a point-like mass concentration exceeding a minimum mass: presumably the AGN's supermassive black hole (SMBH). Consistency with observed SMBH masses constrains the possible DM equations of state. The constraints are looser when a cD galaxy is present. Distributed (AGN) heating alters cluster global properties, and also reduces the lower limits for the central point-mass, for the preferred DM models in which the dark particles have greater heat capacity than point particles. Eluding these constraints would require dominant non-spherical or anisotropic effects (e.g. bulk rotation, non-radial streaming, asymmetric lumps, or a strong magnetic field).