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.
