The accretion and cooling of pre-heated gas in dark matter haloes

We use a one-dimensional (1D) hydrodynamical code to investigate the effects of pre-heating on gas accretion and cooling in cold dark matter (CDM) haloes. In the absence of radiative cooling, pre-heating 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, S-ph/S-v. In the presence of radiative cooling, pre-heating affects the gas fraction that can cool in two different ways. For small haloes with masses M < 10(12) h(-1) M-circle dot, pre-heating suppresses gas accretion, but most of the accreted gas can cool. For more massive haloes, pre-heating 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 haloes, gas cooling is delayed by pre-heating if the halo gas is assumed to be a single-phase medium. However, if the halo gas is assumed to be a multiphase 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 pre-heated multiphase medium can occur simultaneously over a wide range of radii. As examples, two specific pre-heating cases are investigated. In the first case, the pre-heating specific entropy is assumed to be proportional to the virial entropy of the halo, S-ph proportional to S-v, as expected from active galactic nucleus (AGN) feedback. Such pre-heating effectively suppresses radiative cooling in haloes with M > 10(13) h(-1) M-circle dot, but has little effect on smaller haloes. We suggest that this may be the reason why the stellar mass function of galaxies breaks sharply at the massive end. Such pre-heating also helps create the hot diffused haloes 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 proportional to M-2, as would be required to match the observed stellar- and H I-mass functions in the current CDM model at the small mass end. Since the accretion in a CDM universe is expected to be lumpy, we discuss the limitation of our model due to the assumption of smooth mass accretion.