The Variability of the Star Formation Rate in Galaxies: I. Star
  Formation Histories Traced by EW(H$\alpha$) and EW(H$\delta_A$)
  To investigate the variability of the star formation rate (SFR) of galaxies,
we define a star formation change parameter, SFR$_{\rm 5Myr}$/SFR$_{\rm
800Myr}$ which is the ratio of the SFR averaged within the last 5 Myr to the
SFR averaged within the last 800 Myr. We show that this parameter can be
determined from a combination of H$\alpha$ emission and H$\delta$ absorption,
plus the 4000 A break, with an uncertainty of $\sim$0.07 dex for star-forming
galaxies. We then apply this estimator to MaNGA galaxies, both globally within
Re and within radial annuli. We find that galaxies with higher global SFR$_{\rm
5Myr}$/SFR$_{\rm 800Myr}$ appear to have higher SFR$_{\rm 5Myr}$/SFR$_{\rm
800Myr}$ at all galactic radii, i.e. that galaxies with a recent temporal
enhancement in overall SFR have enhanced star formation at all galactic radii.
The dispersion of the SFR$_{\rm 5Myr}$/SFR$_{\rm 800Myr}$ at a given relative
galactic radius and a given stellar mass decreases with the (indirectly
inferred) gas depletion time: locations with short gas depletion time appear to
undergo bigger variations in their star-formation rates on Gyr or less
timescales. In Wang et al. (2019) we showed that the dispersion in
star-formation rate surface densities $\Sigma_{\rm SFR}$ in the galaxy
population appears to be inversely correlated with the inferred gas depletion
timescale and interpreted this in terms of the dynamical response of a
gas-regulator system to changes in the gas inflow rate. In this paper, we can
now prove directly with SFR$_{\rm 5Myr}$/SFR$_{\rm 800Myr}$ that these effects
are indeed due to genuine temporal variations in the SFR of individual galaxies
on timescales between $10^7$ and $10^9$ years rather than possibly reflecting
intrinsic, non-temporal, differences between different galaxies.
