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 10^8.5-10¹⁰ K.

The new solutions are present only for mass accretion rates M^ṡ_crit less than a critical rate A crit which we calculate as a function of radius R and viscosity parameter α. For M^ṡ < M^ṡ_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 Another branch corresponds to a hot optically thin flow, discovered originally by Shapiro, Lightman, & Eardley (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. and may potentially explain the hard X-ray and γ-ray emission from X-ray binaries and active galactic nuclei.

For M^ṡ < M^ṡ_crit, our work suggests that an accretion flow can choose between two distinct states, namely, the thin disk solution and the new advection-dominated solution, both of which are apparently stable. We argue that, in certain circumstances, it is only the latter solution that is truly stable, and that a thin disk will spontaneously evaporate and convert itself into an advection-dominated flow. Even for M^ṡ_crit we suggest that a thin disk may evaporate partially so that a fraction of the accretion occurs via an advection-dominated hot corona. If these ideas are correct, then optically thin advection-dominated flows must be very widespread, possibly the most common form of sub-Eddington accretion in black holes.

Our calculations indicate that advection-dominated accretion on black holes differs considerably from similar flows around neutron stars. The crucial physical difference, which has been mentioned previously in the literature, is that in the former the advected energy is lost into the hole, whereas in the latter it is thermalized and re-radiated at the stellar surface, thereby providing soft photons which can Compton-cool the accreting gas. We obtain M^ṡ_crit ∼ α²M^ṡ_Edd for accreting black holes, independent of the black hole mass, whereas it is ∼0.1α²M^ṡ_Edd for neutron stars. Advection-dominated accretion is therefore more likely to occur in accreting black holes, and these systems will be underluminous for their M^ṡ because the bulk of the energy is advected into the hole rather than being radiated. We find that T_e in accreting black hole flows rises up to ∼10⁹ 10¹⁰ K, compared to T_e ∼ 10^8.5-10⁹ K in neutron star systems. Spectra of accreting black holes are therefore expected to be harder than those of accreting neutron stars. Pair effects are also more likely in black hole systems, though only at higher A than those we consider.