SDSS-IV MaNGA: Constraints on the Conditions for Star Formation in
  Galaxy Discs
  Regions of disc galaxies with widespread star formation tend to be both
gravitationally unstable and self-shielded against ionizing radiation, whereas
extended outer discs with little or no star formation tend to be stable and
unshielded on average. We explore what drives the transition between these two
regimes, specifically whether discs first meet the conditions for
self-shielding (parameterized by dust optical depth, $\tau$) or gravitational
instability (parameterized by a modified version of Toomre's instability
parameters, $Q_{\rm thermal}$, which quantifies the stability of a gas disc
that is thermally supported at $T=10^4$ K). We first introduce a new metric
formed by the product of these quantities, $Q_{\rm thermal}\tau$, which
indicates whether the conditions for disk instability or self-shielding are
easier to meet in a given region of a galaxy, and we discuss how $Q_{\rm
thermal}\tau$ can be constrained even in the absence of direct gas information.
We then analyse a sample of 13 galaxies with resolved gas measurements and find
that on average galaxies will reach the threshold for disk instabilities
($Q_{\rm thermal}<1$) before reaching the threshold for self-shielding
($\tau>1$). Using integral field spectroscopic observations of a sample of 236
galaxies from the MaNGA survey, we find that the value of $Q_{\rm thermal}\tau$
in star-forming discs is consistent with similar behavior. These results
support a scenario where disc fragmentation and collapse occurs before
self-shielding, suggesting that gravitational instabilities are the primary
condition for widespread star formation in galaxy discs. Our results support
similar conclusions based on recent galaxy simulations.
