A Toomre-like stability criterion for the clumpy and turbulent interstellar medium

We explore the gravitational instability of clumpy and turbulent gas discs, taking into account the Larson-type scaling laws observed in giant molecular clouds (GMCs) and HI, as well as more general scaling relations. This degree of freedom is of special interest in view of the coming high-z ISM surveys, and is thus potentially important for understanding the dynamical effects of turbulence at all epochs of galaxy evolution. Our analysis shows that turbulence has a deep impact on the gravitational instability of the disc. It excites a rich variety of stability regimes, several of which have no classical counterpart. Among other diagnostics, we provide two useful tools for observers and simulators: (1) the stability map of turbulence, which illustrates our stability scenario and relates it to the phenomenology of interstellar turbulence: GMC/HI observations, simulations and models; (2) a Toomre-like stability criterion, $Q____geq____bar{Q}$, which applies to a large class of clumpy/turbulent discs. We make specific predictions about GMC and cold-HI turbulence, and point out the implications of our analysis for high-z galaxy surveys