ABSTRACT. The mass accretion rate of transonic spherical accretion flow onto compact objects such as black holes is known as the Bondi accretion rate, which is determined only by the density and the temperature of gas at the outer boundary. A rotating accretion flow has angular momentum, which modifies the flow profile from the spherical Bondi flow, and hence its mass accretion rate, but most work on disc accretion has taken the mass flux to be given with the relation between that parameter and external conditions left uncertain. Within the framework of a slim α disk, we have constructed global solutions of the rotating, viscous, hot accretion flow in the Paczyński-Wiita potential and determined its mass accretion rate as a function of density, temperature, and angular momentum of gas at the outer boundary. We find that the low angular momentum flow resembles the spherical Bondi flow and its mass accretion rate approaches the Bondi accretion rate for the same density and temperature at the outer boundary. The high angular momentum flow on the other hand is the conventional hot accretion disk with advection, but its mass accretion rate can be significantly smaller than the Bondi accretion rate with the same boundary conditions. We also find that solutions exist only within a limited range of dimensionless mass accretion rate , where is the mass accretion rate and is the Bondi accretion rate: when the temperature at the outer boundary is equal to the virial temperature, solutions exist only for when α = 0.01. We also find that the dimensionless mass accretion rate is roughly independent of the radius of the outer boundary but inversely proportional to the angular momentum at the outer boundary and proportional to the viscosity parameter, when , where the dimensionless angular momentum measure λ ≡ l _out/l_B is the specific angular momentum of gas at the outer boundary l _out in units of l_B ≡ GM/c _s,out, M is the mass of the central black hole, and c _s,out is the isothermal sound speed at the outer boundary.

Key words: accretion, accretion disks; black hole physics; quasars: general; X-rays: general

Print publication: Issue 1 (2009 November 20)
Received 2008 July 28, accepted for publication 2009 October 9
Published 2009 November 3