Advection-Dominated Accretion: Underfed Black Holes and Neutron Stars
  We describe new optically thin solutions for rotating accretion flows around black holes and neutron stars. These solutions are advection dominated, so that most of the viscously dissipated energy is advected radially with the flow. We model the accreting gas as a two temperature plasma and include cooling by bremsstrahlung, synchrotron, and Comptonization. We obtain electron temperatures $T_e\sim 10^{8.5}-10^{10}$K. The new solutions are present only for mass accretion rates $\dot M$ less than a critical rate $\dot M_{crit}$ which we calculate as a function of radius $R$ and viscosity parameter $\alpha$. For $\dot M<\dot M_{crit}$ we show that there are three equilibrium branches of solutions. One of the branches corresponds to a cool optically thick flow which is the well-known thin disk solution of Shakura \& Sunyaev (1973). Another branch corresponds to a hot optically thin flow, discovered originally by Shapiro, Lightman \& Eardley (1976, SLE). This solution is thermally unstable. The third branch corresponds to our new advection-dominated solution. This solution is hotter and more optically thin than the SLE solution, but is viscously and thermally stable. It is related to the ion torus model of Rees et al. (1982) and may potentially explain the hard X-ray and $\gamma$-ray emission from X-ray binaries and active galactic nuclei. 
Ramesh Narayan and Insu Yi