EDP Sciences
Free access
Issue
A&A
Volume 446, Number 1, January IV 2006
Page(s) 1 - 18
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20053960


A&A 446, 1-18 (2006)
DOI: 10.1051/0004-6361:20053960

Global axisymmetric dynamics of thin viscous accretion disks

O. M. Umurhan1, 2, A. Nemirovsky1, O. Regev1, 3, 4, 5 and G. Shaviv1, 3

1  Department of Physics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
    e-mail: mumurhan@physics.technion.ac.il
2  Department of Astronomy, City College of San Francisco, San Francisco, CA 94112, USA
3  Asher Space Research Institute, Technion-Israel Institute of Technology, 32000 Haifa, Israel
4  Department of Astrophysics, American Museum of Natural History, New York, NY 10024, USA
5  Department of Astronomy, Columbia University, New York, NY 10028, USA

(Received 1 August 2005 / Accepted 22 September 2005)

Abstract
The purpose of this paper is to explore the steady state and dynamical behavior of thin, axisymmetric, viscous accretion disks. To facilitate an analytical treatment we replace the energy equation with a general polytropic assumption. The asymptotic expansion of Kluzniak & Kita (2000, Three-dimensional structure of an alpha accretion disk [arXiv:astro-ph/0006266]), which extended the method of Regev (1983, A&A, 126, 146) to a full steady polytropic disk (with n=3/2), is further developed and implemented for both the steady (for any polytropic index) and time-dependent problems. The spatial form and temporal behavior of selected dynamical disturbances are studied in detail. It is shown that the transient dynamics resulting from initial perturbations on the linearly stable steady state gives rise to substantial growth of perturbations. We identify the initial perturbation space which leads to such transient growth and provide analytical solutions which manifest this behavior three terms (physical causes) responsible for the appearance of transient dynamics are identified. Two depend explicitly on the viscosity while the third one is relevant also for inviscid disks. The main conclusion we draw is that transient dynamics and, in particular, significant perturbation energy amplification occurs in disks on a global scale. We speculate on the possible implications of these findings to accretion disk theory.


Key words: hydrodynamics -- accretion, accretion disks




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