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The galaxy stellar-to-halo mass relation (SHMR) is nearly time-independentfor $z < 4$. We therefore construct a time-independent SHMR model for centralgalaxies, wherein the in-situ star formation rate (SFR) is determined by thehalo mass accretion rate (MAR), which we call Stellar-Halo Accretion RateCoevolution (SHARC). We show that the $\sim0.3$ dex dispersion of the halo MARmatches the observed dispersion of the SFR on the star-formation main sequence(MS). In the context of "bathtub"-type models of galaxy formation, SHARC leadsto mass-dependent constraints on the relation between SFR and MAR. Despite itssimplicity and the simplified treatment of mass growth from mergers, the SHARCmodel is likely to be a good approximation for central galaxies with $M_*=10^9-10^{10.5}M_\odot$ that are on the MS, representing most of the star formationin the Universe. SHARC predictions agree with observed SFRs for galaxies on theMS at low redshifts, agree fairly well at $z\sim4$, but exceed observations at$z>4$. Assuming that the interstellar gas mass is constant for each galaxy (the"equilibrium condition" in bathtub models), the SHARC model allows calculationof net mass loading factors for inflowing and outflowing gas. With assumptionsabout preventive feedback based on simulations, SHARC allows calculation ofgalaxy metallicity evolution. If galaxy SFRs indeed track halo MARs, especiallyat low redshifts, that may help explain the success of models linking galaxyproperties to halos (including age-matching) and the similarities betweentwo-halo galaxy conformity and halo mass accretion conformity.

Is Main Sequence Galaxy Star Formation Controlled by Halo Mass Accretion?