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Characterizing gravitational instability in turbulent multi-component galactic discs

Gravitational instabilities play an important role in galaxy evolution and in shaping the interstellar medium (ISM). The ISM is observed to be highly turbulent, meaning that observables like the gas surface density and velocity dispersion depend on the size of the region over which they are measured. In this work we investigate, using simulations of Milky Way-like disc galaxies with a resolution of $\sim 9$ pc, the nature of turbulence in the ISM and how this affects the gravitational stability of galaxies. By accounting for the measured average turbulent scalings of the density and velocity fields in the stability analysis, we can more robustly characterize the average level of stability of the galaxies as a function of scale, and in a straightforward manner identify scales prone to fragmentation. Furthermore, we find that the stability of a disc with feedback-driven turbulence can be well described by a "Toomre-like" $Q$ stability criterion on all scales, whereas the classical $Q$ can formally lose its meaning on small scales if violent disc instabilities occur in models lacking pressure support from stellar feedback.