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We study the evolution of baryonic gas in cosmologically growing dark matterhalos. To accurately model both the inner and outer regions of the halos, weuse a dark matter density profile that transitions smoothly from the NFWprofile within the virial radius to a more realistic flat profile far beyondthe halo. We construct a dark matter gravitational potential consistent withthis density profile, and we use a "cosmological" potential that accounts forgas evolution consistent with Hubble expansion at large radii. Gas isinitialized with a density $\approx$ 0.2 times the dark matter density,consistent with the universal baryon fraction $\rho_{\rm g}/(\rho_{\rmg}+\rho_{\rm DM}) \approx 0.17$. We study the formation of the virial shock andevolution of the baryon fraction, including the effects of radiative coolingand AGN jet feedback. The feedback is powered by the accretion of cold gas ontoa central supermassive black hole (SMBH). The cores of the halo exhibit heatingand cooling cycles, whose strength and duration depend on the feedbackefficiency and the halo mass. The central SMBH initially grows exponentiallywith time in the early quasar phase, but the growth slows down at later times.The baryon fraction in the core decreases with increasing feedback efficiencyand decreasing halo mass. While the halo outskirts evolve self-similarly, thecore density is non-evolving, in agreement with cluster observations. Weanalyze the correlations between the properties of the gas and the centralSMBH, and explore the existence of a fundamental plane.

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