Stochastic modelling of star-formation histories I: the scatter of the star-forming main sequence

Abstract

ABSTRACT We present a framework for modelling the star-formation histories of galaxies as a stochastic process. We define this stochastic process through a power spectrum density with a functional form of a broken power law. Star-formation histories are correlated on short time-scales, the strength of this correlation described by a power-law slope, α, and they decorrelate to resemble white noise over a time-scale that is proportional to the time-scale of the break in the power spectrum density, τbreak. We use this framework to explore the properties of the stochastic process that, we assume, gives rise to the log-normal scatter about the relationship between star-formation rate and stellar mass, the so-called galaxy star-forming main sequence. Specifically, we show how the measurements of the normalization and width (σMS) of the main sequence, measured in several passbands that probe different time-scales, give a constraint on the parameters of the underlying power spectrum density. We first derive these results analytically for a simplified case where we model observations by averaging over the recent star-formation history. We then run numerical simulations to find results for more realistic observational cases. As a proof of concept, we use observational estimates of the main sequence scatter at z ∼ 0 and M⋆ ≈ 1010 M⊙ measured in H α, UV+IR, and the u-band. The result is degenerate in the τbreak-α space, but if we assume α = 2, we measure $\tau _{\rm break}=170^{+169}_{-85}~\mathrm{Myr}$. This implies that star-formation histories of galaxies lose ‘memory’ of their previous activity on a time-scale of ∼200 Myr.