Time Dependence of the Mass Accretion Rate in Cluster Cooling Flows

We analyze two time-dependent cluster cooling flow models in sphericalsymmetry. The first assumes that the intracluster gas resides in a staticexternal potential, and includes the effects of optically thin radiativecooling and mass deposition. This corresponds to previous steady-state coolingflow models calculated by White & Sarazin (1987). Detailed agreement is foundbetween steady-state models and time-dependent models at fixed times in thesimulations. The mass accretion rate is found either to increase or remainnearly constant once flows reach a steady state. The time rate of change of theaccretion rate is strongly sensitive to the value of the mass depositionparameter q, but only mildly sensitive to the ratio beta of gravitationalbinding energy to gas temperature. We show that previous scaling argumentspresented by Bertschinger (1988) and White (1988) are valid only for maturecooling flows with weak mass deposition (q ~< 1). The second set of modelsincludes the effects of a secularly deepening cluster potential and secondaryinfall of gas from the Hubble flow. We find that such heating effects do notprevent the flows from reaching a steady state within an initial centralcooling time.Comment: 22 pages (AASTeX) with 16 EPS figures; accepted for publication in The Astrophysical Journa