# Local stability criterion for stars and gas in a galactic disc

Jog, Chanda J (1996) Local stability criterion for stars and gas in a galactic disc. In: Monthly Notices of the Royal Astronomical Society, 278 (1). pp. 209-218.

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## Abstract

We obtain the criterion for local stability against axisymmetric perturbations in gravitationally coupled stars and gas in a galactic disc. The stars and gas are treated as two isothermal fluids, with the random velocity dispersion being higher in stars than in gas. The aim is to obtain a quantitative measure of the mutual destabilizing effect of the two components on each other. The problem is phrased in terms of a complete set of three dimensionless parameters: $Q_S$ and $Q_g$, the standard Q parameters for local stability for stars alone and gas alone, respectively, and $\epsilon$, the gas mass fraction in the disc. The results for $Q_{s-g}$, the two-fluid local stability parameter, and $l_{s-g}$, the dimensionless wavelength at which it is hardest to stabilize the two-fluid system, are obtained seminumericaUy as a function of Qs, Qg and $\pounds$ and are presented as contour plots. The $q{s-g}$ values are lower than the one-fluid $Q_S$ or $Q_g$ values, especially for high gas fractions $(\epsilon\geqO.15)$, indicating that the star-gas disc is more unstable than either constituent fluid by itself. $l_{s-g}$ shows a bimodal distribution for low gas fractions $(\epsilon\leq 0.1)$ - that is, for low $Q_s$ values $l_{s-g}$ is in the stellar regime of high wavelengths, and vice versa. In contrast, for high gas fractions $(e\geq0.15)$, the variation is smooth. Some applications of these results for the theoretical studies of stability and evolution of galaxies are discussed.

Item Type: Journal Article http://articles.adsabs.harvard.edu/cgi-b... Copyright of this article belongs to Royal Astronomical Society. Hydrodynamics;instabilities;galaxies;ISM galaxies;Kinematics;dynamics galaxies;Spiral;stellar dynamics Division of Physical & Mathematical Sciences > Physics 20 Sep 2007 19 Sep 2010 04:38 http://eprints.iisc.ernet.in/id/eprint/10971