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 on to 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 time-scales, 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 time-scale of the gas reservoir of the galaxy, and the average lifetime of individual molecular clouds. On long and intermediate time-scales (relative to the dynamical time-scale 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 time-scales, 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 approximate to 2 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.