Spectral Models of Convection-Dominated Accretion Flows

At small values of the dimensionless viscosity parameter, $\alpha\lesssim 0.1$, the dynamics of non-radiating accretion flows is dominated by convection; convection strongly suppresses the accretion of matter onto the central object and transports a luminosity $\sim 10^{-3}-10^{-2} \dot M c^2$ from small to large radii in the flow. The fate of this convective luminosity is uncertain; under appropriate conditions it may be radiated at large radii by thermal bremsstrahlung emission. We show that this leads to a correlation between the frequency of maximal bremsstrahlung emission and the luminosity of the source, $\nu_{\rm peak} \propto L^{2/3}$. This is testable with {\it Chandra} and {\it XMM}.