Quenching cluster cooling flows with recurrent hot plasma bubbles

The observed cooling rate of hot gas in clusters is much lower than that inferred from the gas density profiles. This suggests that the gas is being heated by some source. We use an adaptive-mesh refinement code (flash) to simulate the effect of multiple, randomly positioned, injections of thermal energy within 50 kpc of the centre of an initially isothermal cluster with mass M200= 3 × 1014 M⊙ and kT= 3.1 keV. We have performed eight simulations with spherical bubbles of energy generated every 108 yr, over a total of 1.5 Gyr. Each bubble is created by injecting thermal energy steadily for 107 yr; the total energy of each bubble lies in the range (0.1–3) ×1060 erg, depending on the simulation. We find that 2 × 1060 erg per bubble (corresponding to an average power of 6.3 × 1044 erg s−1) effectively balances energy loss in the cluster and prevents the accumulation of gas below kT= 1 keV from exceeding the observational limits. This injection rate is comparable to the radiated luminosity of the cluster, and the required energy and periodic time-scale of events are consistent with observations of bubbles produced by central active galactic nuclei in clusters. The effectiveness of this process depends primarily on the total amount of injected energy and the initial location of the bubbles, but is relatively insensitive to the exact duty cycle of events.