Is main-sequence galaxy star formation controlled by halo mass accretion?

The galaxy stellar-to-halo mass relation (SHMR) is nearly time-independent for z < 4. We therefore construct a time-independent SHMR model for central galaxies, wherein the in situ star formation rate (SFR) is determined by the halo mass accretion rate (MAR), which we call stellar halo accretion rate coevolution (SHARC). We show that the similar to 0.3 dex dispersion of the halo MAR matches the observed dispersion of the SFR on the star formation main sequence (MS). In the context of 'bathtub'-type models of galaxy formation, SHARC leads to mass-dependent constraints on the relation between SFR and MAR. Despite its simplicity and the simplified treatment of mass growth from mergers, the SHARC model is likely to be a good approximation for central galaxies with M-* = 10(9)-10(10.5)M(circle dot) that are on the MS, representing most of the star formation in the Universe. SHARC predictions agree with observed SFRs for galaxies on the MS at low redshifts, agree fairly well at z similar to 4, but exceed observations at z greater than or similar to 4. Assuming that the interstellar gas mass is constant for each galaxy (the 'equilibrium condition' in bathtub models), the SHARC model allows calculation of net mass loading factors for inflowing and outflowing gas. With assumptions about preventive feedback based on simulations, SHARC allows calculation of galaxy metallicity evolution. If galaxy SFRs indeed track halo MARs, especially at low redshifts, that may help explain the success of models linking galaxy properties to haloes (including age-matching) and the similarities between two-halo galaxy conformity and halo mass accretion conformity.