On Heating of Cluster Cooling Flows by Sound Waves

We investigate heating of the cool core of a galaxy cluster through the dissipation of sound waves excited by the activities of the central active galactic nucleus (AGN). Using a weak shock theory, we show that this heating mechanism alone cannot reproduce observed temperature and density profiles of a cluster, because the dissipation length of the waves is much smaller than the size of the core and thus the wave energy is not distributed to the whole core. However, we find that if it is combined with thermal conduction from the hot outer layer of the cluster, the wave heating can reproduce the observational results. Subject headings: cooling flows — galaxies: clusters: general — galaxies: active — galaxies: clusters — waves