arXiv2008
We analyse the radial structure of self-gravitating spheres consisting of multiple interpenetrating fluids, such as the X-ray emitting gas and the dark halo of a galaxy cluster. In these dipolytropic models, adiabatic dark matter sits in equilibrium, while the gas develops a gradual, smooth, quasi-stationary cooling flow. Both affect and respond to the collective gravitational field. We find that all subsonic, radially continuous, steady solutions require a non-zero minimum central point mass. For Mpc-sized halos with 7 to 10 effective degrees of freedom (F2), the minimum central mass is compatible with observations of supermassive black holes. Smaller gas mass influxes enable smaller central masses for wider ranges of F2. The halo comprises a sharp spike around the central mass, embedded within a core of nearly constant density (at 10-10^2.5kpc scales), with outskirts that attenuate and naturally truncate at finite radius (several Mpc). The gas density resembles a broken power law in radius, but the temperature dips and peaks within the dark core. A finite minimum temperature occurs due to gravitational self-warming, without cold mass dropout nor needing regulatory heating. X-ray emission from the intracluster medium mimics a beta-model plus bright compact nucleus. Near-sonic points in the gas flow are bottlenecks to allowed steady solutions; the outermost are at kpc scales. These sites may preferentially develop cold mass dropout during strong perturbations off equilibrium. Within the sonic point, the profile of gas specific entropy is flatter than s r^{1/2}, but this is a shallow ramp and not an isentropic core. When F2 is large, the inner halo spike is only marginally Jeans stable in the central pc, suggesting that a large non-linear disturbance could trigger local dark collapse onto the central object.