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 $\sim0.3$ 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 $M_*=10^9-
10^{10.5}M_\odot$ 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 $z\sim4$, 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 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 halos (including age-matching) and the similarities between
two-halo galaxy conformity and halo mass accretion conformity.
