## On the transition to self-gravity in low mass AGN and YSO accretion discs
^{1} DAEC et UMR 8631 du CNRS, Observatoire de Paris-Meudon, Place Jules Janssen, 92195 Meudon Cedex, France^{2} Université Paris 7 (Denis Diderot), 2 Place Jussieu, 75251 Paris Cedex 05, France (Jean-Marc.Hure@obspm.fr)
The equations governing the vertical structure of a stationary keplerian accretion disc supporting an Eddington atmosphere are presented. The model is based on the -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 central black hole. Various accretion rates and -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 -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 "-formalism". Turbulent pressure is important only for . 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 , the closer to the center the self-gravitating regime, and the sensitivity to the accretion rate is generally weak, except for . 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 -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, -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.
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. Model for the vertical structure: hypothesis and relevant equations
- 2.1. General considerations. Accounting for self-gravity
- 2.2. The equations for the disc interior
- 2.3. Accounting for turbulent pressure in the framework of the -prescription
- 2.4. On depth-dependent viscosity laws
- 2.5. Equations for the Eddington atmosphere
- 2.6. Boundary conditions and matching conditions at the disc/atmosphere interface
- 3. Ingredients and computational method
- 4. A few applications of the model
- 4.1. The hypothesis of a non irradiated disc
- 4.2. Effect of turbulent pressure on the vertical temperature and density stratification: an example
- 4.3. Effect of the viscosity law: versus
- 4.4. Example of internal structure: 2D-density maps
- 4.5. A criterion to check the importance of vertical self-gravity
- 5. Conclusion
- Acknowledgements
- Appendices
- References
© European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |