Stochastic modelling of star-formation histories II: star-formation
  variability from molecular clouds and gas inflow
  A key uncertainty in galaxy evolution is the physics regulating star
formation, ranging from small-scale processes related to the life-cycle of
molecular clouds within galaxies to large-scale processes such as gas accretion
onto galaxies. We study the imprint of such processes on the time-variability
of star formation with an analytical approach tracking the gas mass of galaxies
("regulator model"). Specifically, we quantify the strength of the fluctuation
in the star-formation rate (SFR) on different timescales, i.e. the power
spectral density (PSD) of the star-formation history, and connect it to gas
inflow and the life-cycle of molecular clouds. We show that in the general case
the PSD of the SFR has three breaks, corresponding to the correlation time of
the inflow rate, the equilibrium timescale of the gas reservoir of the galaxy,
and the average lifetime of individual molecular clouds. On long and
intermediate timescales (relative to the dynamical timescale of the galaxy),
the PSD is typically set by the variability of the inflow rate and the
interplay between outflows and gas depletion. On short timescales, the PSD
shows an additional component related to the life-cycle of molecular clouds,
which can be described by a damped random walk with a power-law slope of
$\beta\approx2$ at high frequencies with a break near the average cloud
lifetime. We discuss star-formation "burstiness" in a wide range of galaxy
regimes, study the evolution of galaxies about the main sequence ridgeline, and
explore the applicability of our method for understanding the star-formation
process on cloud-scale from galaxy-integrated measurements.
