Instabilities of galactic discs in the presence of star formation

We discuss the stability of galactic discs in which the energy of interstellar clouds is gained in encounters with expanding supernova (SN) remnants and lost in inelastic collisions. Energy gain and loss processes introduce a phase difference between the pressure and density perturbations, making discs unstable on small scales for several recipes of star formation. This is in contrast to the standard stability analysis in which small-scale perturbations are stabilized by pressure. In the limit of small scales, the dispersion relation for the growth rate reduces to that of thermal instabilities in a fluid without gravity. If instabilities lead to star formation, then our results imply a secondary mode of star formation that operates on small scales and feeds on the existence of a primary mode on intermediate scales. This may be interpreted as positive feedback. Further, the standard stability criterion on intermediate scales is significantly modified.