  Galaxy cluster cores are pervaded by hot gas which radiates at far too high a
rate to maintain any semblance of a steady state; this is referred to as the
cooling flow problem. Of the many heating mechanisms that have been proposed to
balance radiative cooling, one of the most attractive is dissipation of
acoustic waves generated by Active Galactic Nuclei (AGN). Fabian (2005) showed
that if the waves are nearly adiabatic, wave damping due to heat conduction and
viscosity must be well below standard Coulomb rates in order to allow the waves
to propagate throughout the core. Because of the importance of this result, we
have revisited wave dissipation under galaxy cluster conditions in a way that
accounts for the self limiting nature of dissipation by electron thermal
conduction, allows the electron and ion temperature perturbations in the waves
to evolve separately, and estimates kinetic effects by comparing to a
semi-collisionless theory. While these effects considerably enlarge the toolkit
for analyzing observations of wavelike structures and developing a quantitative
theory for wave heating, the drastic reduction of transport coefficients
proposed in Fabian (2005) remains the most viable path to acoustic wave heating
of galaxy cluster cores.
