Cosmological evolution of gas and supermassive black holes in idealized isolated haloes

We study the evolution of baryonic gas in cosmologically growing dark matter haloes. To accurately model both the inner and outer regions of the haloes, we use a dark matter density profile that transitions smoothly from the Navarro-Frenk-White profile within the virial radius to a more realistic flat profile far beyond the halo. We construct a dark matter gravitational potential consistent with this density profile, and we use a 'cosmological' potential that accounts for gas evolution consistent with Hubble expansion at large radii. Gas is initialized with a density approximate to 0.2 times the dark matter density, consistent with the universal baryon fraction rho(g)/(rho(g) + rho(DM)) approximate to 0.17. We study the formation of the virial shock and evolution of the baryon fraction, including the effects of radiative cooling and active galactic nucleus jet feedback. The feedback is powered by the accretion of cold gas on to a central supermassive black hole (SMBH). The cores of the halo exhibit heating and cooling cycles, whose strength and duration depend on the feedback efficiency and the halo mass. The central SMBH initially grows exponentially with time in the early quasar phase, but the growth slows down at later times. The baryon fraction in the core decreases with increasing feedback efficiency and decreasing halo mass. While the halo outskirts evolve self-similarly, the core density is non-evolving, in agreement with cluster observations. We analyse the correlations between the properties of the gas and the central SMBH, and explore the existence of a Fundamental Plane.