The vertical structure and stability of accretion disks surrounding black holes and neutron stars

The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been investigated. Within the framework of the α viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the α parameter, which is less than or equal to unity, is formulated as α₀(h/r)ⁿ, where h is the local scale height and n and α₀ are constants. We neglect advective energy transport associated with radial motions and construct the vertical structure of the disks by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it has been demonstrated that convection is important especially for mass accretion rates, Ṁ, greater than about 0.1 times the Eddington value, Ṁ_Edd. Although the efficiency of convection is not high, convection significantly modifies the vertical structure of the disk (as compared with a purely radiative model) and leads to lower temperatures at a given Ṁ. The results show that the disk can be locally unstable and that for n ≳ 0.75, an S-shaped relation can exist between M and the column density, Σ, at a given radius. While the lower stable branch (dṀ/dΣ < 0) and middle unstable branch (dṀ/dΣ < 0) represent structures for which the gas and radiation pressure dominate respectively, the stable upper branch (dṀ/dΣ > 0) is a consequence of the saturation of α. This saturation of α can occur for large α₀ and at Ṁ ≲ Ṁ_Edd. The instability is found to occur at higher mass accretion rates for neutron stars than for black holes. In particular, the disk is locally unstable for Ṁ ≳ 0.5Ṁ_Edd for neutron stars and for Ṁ ≳ 0.1Ṁ_Edd for black holes for a viscosity prescription characterized by n = 1 and α₀ = 10.