Equilibrium model prediction for the scatter in the star-forming main sequence

The analytic `equilibrium model' for galaxy evolution using a mass balance equation is able to reproduce mean observed galaxy scaling relations between stellar mass, halo mass, star formation rate (SFR), and metallicity across the majority of cosmic time with a small number of parameters related to feedback. Here, we aim to test this data-constrained model to quantify deviations from the mean relation between stellar mass and SFR, I.e. the star-forming galaxy main sequence (MS). We implement fluctuation in halo accretion rates parametrized from merger-based simulations, and quantify the intrinsic scatter introduced into the MS under the assumption that fluctuations in star formation follow baryonic inflow fluctuations. We predict the 1σ MS scatter to be ∼0.2-0.25 dex over the stellar mass range 10⁸-10¹¹ M_⊙ and a redshift range 0.5 ≲ z ≲ 3 for SFRs averaged over 100 Myr. The scatter increases modestly at z ≳ 3, as well as by averaging over shorter time-scales. The contribution from merger-induced star formation is generally small, around 5 per cent today and 10-15 per cent during the peak epoch of cosmic star formation. These results are generally consistent with available observations, suggesting that deviations from the MS primarily reflect stochasticity in the inflow rate owing to halo mergers.