Volume 538, February 2012
|Number of page(s)||10|
|Published online||17 February 2012|
Stability of radiation-pressure dominated disks
I. The dispersion relation for a delayed heating α-viscosity prescription
Astronomical Observatory of the Jagiellonian University,
ul. Orla 171, 30-244
2 M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
3 Institute of Micromechanics and Photonics, Warsaw University of Technology, ul. Św. Andrzeja Boboli 8, 02-525 Warszawa, Poland
4 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warszawa, Poland
e-mail: email@example.com; firstname.lastname@example.org
5 Department of Physics, Göteborg University, 412-96 Göteborg, Sweden
6 Institut d’Astrophysique de Paris, UMR 7095 CNRS, UPMC Univ Paris 06, 98bis Boulevard Arago, 75014 Paris, France
7 Kavli Institute for Astrophysics and Space Research, MIT, Cambridge, MA 02139, USA
Accepted: 20 December 2011
We derive and investigate the dispersion relation for accretion disks with retarded or advanced heating. We follow the α-prescription but allow for a time offset τ between heating and pressure perturbations, as well as for a diminished response of heating to pressure variations. We study in detail solutions of the dispersion relation for disks with radiation-pressure fraction, 1 − β, and ξ, the ratio of viscous stress response to pressure perturbations. For τ < 0 (advanced heating) the number and sign of real solutions for the growth rate depend on the values of τ, and ξ: if the magnitude of τ is larger than a critical value (e.g., more than twice the thermal time, −τ > 2 τth, for β = 0 and ξ = 1) two real solutions exist, which are both negative. These results imply that radiation-pressure dominated accretion disks may be stabilized when there is a time delay between stress fluctuations and fluctuations in heating.
Key words: accretion, accretion disks / hydrodynamics / instabilities
© ESO, 2012
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