An effective Q parameter for two-fluid instabilities in spiral galaxies

The equations for the two-fluid instability developed by Jog & Solomon are reduced to a form in which a single Qeff parameter determines the state of gravitational stability. This parameter has the correct values in the limits of either fluid alone and is a natural extension of the usual one-fluid Q parameter to the two-fluid case. Finite thickness effects are included. Variations in Qeff with radius for typical galaxies are studied. The results suggest that the axisymmetric stability properties of a galactic disc can be estimated from the pure gas stability parameter, Qg, only when Qg≪Qs, the pure-star parameter; otherwise Qeff should be used. Implications for star-formation thresholds and hidden gas at large galactic radii are discussed. If the dark matter required to give the Galactic rotation curve were in the form of in-plane gas with a normal velocity dispersion, then the outer disc would be very unstable.