AN EFFECTIVE Q-PARAMETER FOR 2-FLUID INSTABILITIES IN SPIRAL GALAXIES

The equations for the two-fluid instability developed by Jog and Solomon are reduced to a form in which a single Q(eff) 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 Q(eff) 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, Q(g), only when Q(g) << Q(s), the pure-star parameter; otherwise Q(eff) 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.