On viscosity, conduction and sound waves in the intracluster medium

Recent X-ray and optical observations of the Perseus cluster indicate that a combination of weak shocks at small radii (greater than or similar to 20 kpc) and viscous and conductive dissipation of sound waves at larger radii is responsible for heating the intracluster medium and can balance radiative cooling of cluster cores. We discuss this mechanism more generally and show how the specific heating and cooling rates vary with temperature and radius. It appears that this heating mechanism is most effective above 10(7) K, which allows for radiative cooling to proceed within normal galaxy formation but stifles the growth of very massive galaxies. The scaling of the wavelength of sound waves with cluster temperature and feedback in the system are investigated.