SIMBAD references

The equations governing the vertical structure of a stationary keplerian accretion disc supporting an Eddington atmosphere are presented. The model is based on the α-prescription for turbulent viscosity (two versions are tested), includes the disc vertical self-gravity, convective transport and turbulent pressure. We use an accurate equation of state and wide opacity grids which combine the Rosseland and Planck absorption means through a depth-dependent weighting function. The numerical method is based on single side shooting and incorporates algorithms designed for stiff initial value problems. A few properties of the model are discussed for a circumstellar disc around a sun-like star and a disc feeding a 10⁸M_☉ central black hole. Various accretion rates and α-parameter values are considered. We show the strong sensitivity of the disc structure to the viscous energy deposition towards the vertical axis, specially when entering inside the self-gravitating part of the disc. The local version of the α-prescription leads to a ``singular" behavior which is also predicted by the vertically averaged model: there is an extremely violent density and surface density runaway, a rapid disc collapse and a temperature plateau. With respect, a much softer transition is observed with the ``αP-formalism''. Turbulent pressure is important only for α>0.1. It lowers vertical density gradients, significantly thickens the disc (increases its flaring), tends to wash out density inversions occurring in the upper layers and pushes the self-gravitating region to slightly larger radii. Curves localizing the inner edge of the self-gravitating disc as functions of the viscosity parameter and accretion rate are given. The lower α, the closer to the center the self-gravitating regime, and the sensitivity to the accretion rate is generally weak, except for α > 0.1. This study suggests that models aiming to describe T-Tauri discs beyond about a few to a few tens astronomical units (depending on the viscosity parameter) from the central protostar using the α-theory should consider vertical self-gravity, but additional heating mechanisms are necessary to account for large discs. The Primitive Solar Nebula was probably a bit (if not strongly) self-gravitating at the actual orbit of giant planets. In agreement with vertically averaged computations, α-discs hosted by active galaxies are self-gravitating beyond about a thousand Schwarzchild radii. The inferred surface density remains too high to lower the accretion time scale as requested to fuel steadily active nuclei for a few hundred millions years. More efficient mechanisms driving accretion are required.