On the gravitational stability of a galactic disc as a two-fluid system

The gravitational stability of a disc with gaseous and stellar components is studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which both the effective surface density and the velocity dispersion of the gaseous component are scale-dependent as power-law functions of the wavenumber of the perturbations. In addition, the stellar component, which interacts gravitationally with the gas, is considered as a fluid. We calculate growth rates of the perturbations, and find that in most cases the stability of the disc depends strongly on the existence of the stars and on the exponents of the functions for describing the turbulence. Our analysis suggests that the conventional gas and star threshold is not adequate for analysing the stability of two-component discs when turbulence is considered.