On the Energetics of Advection-Dominated Accretion Flows
  Using mean field MHD, we discuss the energetics of optically thin, two temperature, advection-dominated accretion flows (ADAFs). If the magnetic field is tangled and roughly isotropic, flux freezing is insufficient to maintain the field in equipartition with the gas. In this case, we expect a fraction of the energy generated by shear in the flow to be used to build up the magnetic field strength as the gas flows in; the remaining energy heats the particles. We argue that strictly equipartition magnetic fields are incompatible with a priori reasonable levels of particle heating; instead, the plasma $\beta$ in ADAFs (defined to be the gas pressure divided by magnetic/turbulent pressure) is likely to be $\gsim 5$; correspondingly, the viscosity parameter $\alpha$ is likely to be $\lsim 0.2$ 
Eliot Quataert and Ramesh Narayan (Harvard)