  Galaxies strongly self-regulate their growth via energetic feedback from
stars, supernovae, and black holes, but these processes are among the least
understood aspects of galaxy formation theory. We present an analytic galaxy
evolution model that directly constrains such feedback processes from observed
galaxy scaling relations. The equilibrium model, which is broadly valid for
star-forming central galaxies that dominate cosmic star formation, is based on
the ansatz that galaxies live in a slowly-evolving equilibrium between inflows,
outflows, and star formation. Using a Bayesian Monte Carlo Markov chain
approach, we constrain our model to match observed galaxy scaling relations
between stellar mass and halo mass, star formation rate, and metallicity from
0<z<2. A good fit (chi^2~1.6) is achieved with eight free parameters. We
further show that constraining our model to any two of the three data sets also
produces a fit to the third that is within reasonable systematic uncertainties.
The resulting best-fit parameters that describe baryon cycling suggest galactic
outflow scalings intermediate between energy and momentum-driven winds, a weak
dependence of wind recycling time on mass, and a quenching mass scale that
evolves modestly upwards with redshift. This model further predicts a stellar
mass-star formation rate relation that is in good agreement with observations
to z~6. Our results suggest that this simple analytic framework captures the
basic physical processes required to model the mean evolution of stars and
metals in galaxies, despite not incorporating many canonical ingredients of
galaxy formation models such as merging or disk formation.
