The Accretion and Cooling of Preheated Gas in Dark Matter Halos

We use a one-dimensional hydrodynamical code to investigate the effects of preheating on gas accretion and cooling in cold dark matter halos. In the absence of radiative cooling, preheating reduces the amount of gas that can be accreted into a halo, and the accreted gas fraction is determined by the ratio of the initial specific entropy of the gas to the virial entropy of the halo, Sph/Sv. In the presence of radiative cooling, preheating affects the gas fraction that can cool in two different ways. For small halos with masses M < 10 h M⊙, preheating suppresses gas accretion, but most of the accreted gas can cool. For more massive halos, preheating affects the cold gas fraction not only by reducing the amount of accreted gas, but also by reducing the cooling efficiency. For both small and massive halos, gas cooling is delayed by preheating if the halo gas is assumed to be a single-phase medium. However, if the halo gas is assumed to be a multi-phase medium, cooling can occur over a wider range of redshifts. Unlike in a single-phase medium where cooling is inside-out, gas cooling in a preheated multi-phase medium can occur simultaneously over a wide range of radii. As examples, two specific preheating cases are investigated. In the first case, the preheating specific entropy is assumed to be proportional to the virial entropy of the halo, Sph ∝ Sv, as expected from AGN feedback. Such preheating effectively suppresses radiative cooling in halos with M > 10 h M⊙, but has little effect on smaller halos. We suggest that this may be the reason why the stellar mass function of galaxies breaks sharply at the massive end. Such preheating also helps create the hot diffused halos within which the “radio mode” feedback of AGNs can act effectively. In the second case, the intergalactic medium is assumed to be warm. Here the total amount of gas that can cool in a halo scales with halo mass as ∝ M, as would be required to match the observed stellarand HI-mass functions in the current CDM model at the small mass end.