GRAVITATIONAL INSTABILITY OF ROTATING, PRESSURE-CONFINED, POLYTROPIC GAS DISKS WITH VERTICAL STRATIFICATION

Journal Article · Thu Dec 20 04:00:00 EST 2012 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/761/2/131· OSTI ID:22139963

Kim, Jeong-Gyu; Kim, Woong-Tae ^[1]; Seo, Young Min

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1. Center for the Exploration of the Origin of the Universe (CEOU), Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742 (Korea, Republic of)

We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c{sub eff} of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c{sub eff} and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.

• OSTI ID: 22139963
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 761; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
APPROXIMATIONS
ASTRONOMY
ASTROPHYSICS
DISPERSION RELATIONS
EQUILIBRIUM
GRAVITATION
GRAVITATIONAL INSTABILITY
GRAVITY WAVES
HYDRODYNAMICS
SOUND WAVES
STARS
STRATIFICATION
SURFACES