Stochastic heating of cooling flows

It is generally accepted that the heating of gas in clusters of galaxies by active galactic nuclei (AGN) is a form of feedback. Feedback is required to ensure a long term, sustainable balance between heating and cooling. This work investigates the impact of proportional stochastic feedback on the energy balance in the intracluster medium. Using a generalised analytical model for a cluster atmosphere, it is shown that an energy equilibrium can be reached exponentially quickly. Applying the tools of stochastic calculus it is demonstrated that the result is robust with regard to the model parameters, even though they affect the amount of variability in the system.