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 × 10 14 M ⊙ and kT = 3.1 keV. We have performed eight simulations with spherical bubbles of energy generated every 10 8 years, over a total of 1.5 Gyr. Each bubble is created by injecting thermal energy steadily for 10 7 years; the total energy of each bubble ranges from 0.1–3×10 60 erg, depending on the simulation. We find that 2×10 60 erg per bubble (corresponding to a average power of 6.3 ×10 44 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 timescale of events are consistent with observations of bubbles produced by central AGN 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. Key words: galaxies:clusters:general–cooling flows–X-ray:galaxies:clusters
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