Simple models of cooling flows

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Abstract
A semi-analytic model of cluster cooling flows is presented. The model assumes that episodic nuclear activity followed by radiative cooling without mass-dropout cycles the cluster gas between a relatively homogeneous, nearly isothermal post-outburst state and a cuspy configuration in which a cooling catastrophe initiates the next nuclear outburst. Fitting the model to Chandra data for the Hydra cluster, a lower limit of 284 Myr until the next outburst of Hydra A is derived. Density, temperature and emission-measure profiles at several times prior to the cooling catastrophe are presented. It proves possible to fit the mass M(sigma) with entropy index P rho^{-gamma} less than sigma to a simple power-law form, which is almost invariant as the cluster cools. To high precision, the central value of sigma decreases linearly in time. The fraction of clusters in a magnitude-limited sample that have gas cooler than T is calculated, and is shown to be small for T=2 keV. Similarly, only 1 percent of clusters in such a sample contain gas with P rho^{-gamma} < 2 keV cm^2. Entropy production in shocks is shown to be small. The entropy that is radiated from the cluster can be replaced if a few percent of the cluster gas passes through bubbles heated during an outburst of the AGN.

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