| Recent x-ray observations have led to an important puzzle in the study of galaxy clusters. Although hot intergalactic plasma has a radiative cooling time that is often shorter than a cluster's age, very little intergalactic plasma actually cools to low temperatures. This finding suggests that some heating mechanism largely offsets radiative cooling in the intracluster media (ICNI) of many clusters. This thesis addresses several questions relating to a heating mechanism that has received considerable attention in the literature, namely, turbulent heating. The first part of the thesis develops a semi-empirical model of the ICM in which turbulent dissipation, turbulent diffusion, and thermal conduction balance radiative losses. In the model, the dominant turbulent length scale, l, is left as a free parameter. Using this model, we obtain radial profiles for the turbulent velocity that are consistent with observational estimates. We find that dissipation (diffusion) dominates when l is small (large), that larger velocities are required when the buoyancy of the medium is accounted for, and that the rate of dissipative heating depends sensitively on the rms turbulent velocity, highlighting the need for a self-regulating mechanism. The second part of the thesis explores the possibility that turbulent heating of the ICM arises in a self-regulating way through convection driven by cosmic rays produced by a central active galactic nucleus. We ask how the addition of cosmic-ray pressure alters the convective stability criterion for the ICM. We carry out a local stability analysis including the effects of finite thermal conduction and finite cosmic-ray diffusivity each occurring parallel to the equilibrium magnetic field. We obtain stability criteria for the high-beta and large-perpendicular-wave-number limits and find that an outwardly decreasing cosmic-ray pressure and an outwardly decreasing magnetic pressure are both destabilizing. We explain the stability criteria using simply physical arguments and elucidate the stability criteria further by obtaining approximate analytic solutions to the dispersion relation, which we check by comparing to numerical solutions of the dispersion relation. Our findings support the suggestion that turbulence and convection may play a role in the heating of the ICM. |
