The Variability of Star Formation Rate in Galaxies: II. Power Spectrum
  Distribution on the Main Sequence
  We constrain the temporal power spectrum of the sSFR(t) of star-forming
galaxies, using a well-defined sample of Main Sequence galaxies from MaNGA and
our earlier measurements of the ratio of the SFR averaged within the last 5 Myr
to that averaged over the last 800 Myr. We explore the assumptions of
stationarity and ergodicity that are implicit in this approach. We assume a
single power-law form of the PSD but introduce an additional free parameter,
the "intrinsic scatter", to try to account for any non-ergodicity introduced
from various sources. We analyze both an "integrated" sample consisting of
global measurements of all of the galaxies, and also 25 sub-samples obtained by
considering five radial regions and five bins of integrated stellar mass.
Assuming that any intrinsic scatter is not the dominant contribution to the
Main Sequence dispersion of galaxies, we find that the PSDs have slopes between
1.0 and 2.0, indicating that the power (per log interval of frequency) is
mostly contributed by longer timescale variations. We find a correlation
between the returned PSDs and the inferred gas depletion times ($\tau_{\rm
dep,eff}$) obtained from application of the extended Schmidt Law, in that
regions with shorter gas depletion times show larger integrated power and
flatter PSD. Intriguingly, it is found that shifting the PSDs by the inferred
$\tau_{\rm dep,eff}$ causes all of the 25 PSDs to closely overlap, at least in
that region where the PSD is best constrained and least affected by
uncertainties about any intrinsic scatter. A possible explanation of these
results is the dynamical response of the gas regulator system of Lilly et al.
2013 to a uniform time-varying inflow, as previously proposed in Wang et al.
2019.
