Spectral Models of Convection-Dominated Accretion Flows

For small values of the dimensionless viscosity parameter, namely $\alpha \lesssim 0.1$, 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. A fraction of this convective luminosity is likely to be radiated at large radii via thermal bremsstrahlung emission. We show that this leads to a correlation between the frequency of maximal bremsstrahlung emission and the luminosity of the source, $\nu_{\rm peak} \propto L^{2/3}$\mathrm{.}AccretingblackholeswithX-rayluminosities$10^{-4} L_{Edd}\gtrsim L_X(0.5-10{\rm keV}) \gtrsim 10^{-7}L_{Edd}$ are expected to have hard X-ray spectra, with photon indices $\mathrm{\Gamma }\sim 2$, and sources with $L_X\lesssim {10}^{-9}{L}_{Edd}$ are expected to have soft spectra, with $\mathrm{\Gamma }\sim 3.5$. This is testable with {\it Chandra} and {\it XMM}.