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 H I, as well as more general scaling relations. This degree of freedom is of special interest in view of the coming high-z interstellar medium 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/H I observations, simulations and models; (2) a Toomre-like stability criterion, Graphic, which applies to a large class of clumpy/turbulent discs. We make specific predictions about GMC and cold-H I turbulence and point out the implications of our analysis for high-z galaxy surveys