How Low Can <i>Q</i> Go?

Abstract Gravitational instability plays a substantial role in the evolution of galaxies. Various schemes to include it in galaxy evolution models exist, generally assuming that the Toomre Q parameter is self-regulated to Q crit , the critical Q dividing stable from unstable conditions in a linear stability analysis. This assumption is in tension with observational estimates of Q that find values far below any plausible value of Q crit . While the observations are subject to some uncertainty, this tension can more easily be relieved on the theoretical side by relaxing the common assumption that Q ≥ Q crit . Based on observations of both z ∼ 2 disks and local face-on galaxies, we estimate the effect of gravitational instability necessary to balance out every other physical process that affects Q . In particular, we find that the disk’s response to low Q values can be described by simple functions that depend only on Q . These response functions allow galaxies to maintain Q values below Q crit in equilibrium over a wide range of parameters. Extremely low values of Q are predicted when the gas surface density is ≳10 3 M ⊙ pc −2 , the rotation curve provides minimal shear, the orbital time becomes long, and/or when the gas is much more unstable than the stellar component. We suggest that these response functions should be used in place of the Q ≥ Q crit ansatz.