Dynamical Treatment of Virialization Heating in Galaxy Formation

In a hierarchical picture of galaxy formation virialization continuallytransforms gravitational potential energy into kinetic energies of the baryonicand dark matter. For the gaseous component the kinetic, turbulent energy istransformed eventually into internal thermal energy through shocks and viscousdissipation. Traditionally this virialization and shock heating has beenassumed to occur instantaneously allowing an estimate of the gas temperature tobe derived from the the virial temperature defined from the embedding darkmatter halo velocity dispersion. As the mass grows the virial temperature of ahalo grows. Mass accretion hence can be translated into a heating term. Wederive this heating rate from the extended Press Schechter formalism anddemonstrate its usefulness in semi-analytical models of galaxy formation. Ourmethod explicitly conserves energy unlike the previous impulsive heatingassumptions. Our formalism can trivially be applied in all currentsemi-analytical models as the heating term can be computed directly from theunderlying merger trees. Our analytic results for the first cooling halos andthe transition from cold to hot accretion are in agreement with numericalsimulations.