We present an analytic formalism that describes the evolution of the stellar, gas, and metal content of galaxies. It is based on the idea, inspired by hydrodynamic simulations, that galaxies live in a slowly-evolving equilibrium between inflow, outfl
ow, and star formation. We argue that this formalism broadly captures the behavior of galaxy properties evolving in simulations. The resulting equilibrium equations for the star formation rate, gas fraction, and metallicity depend on three key free parameters that represent ejective feedback, preventive feedback, and re-accretion of ejected material. We schematically describe how these parameters are constrained by models and observations. Galaxies perturbed off the equilibrium relations owing to inflow stochasticity tend to be driven back towards equilibrium, such that deviations in star formation rate at a given mass are correlated with gas fraction and anti-correlated with metallicity. After an early gas accumulation epoch, quiescently star-forming galaxies are expected to be in equilibrium over most of cosmic time. The equilibrium model provides a simple intuitive framework for understanding the cosmic evolution of galaxy properties, and centrally features the cycle of baryons between galaxies and surrounding gas as the driver of galaxy growth.
We use cosmological hydrodynamic simulations to investigate how inflows, star formation, and outflows govern the the gaseous and metal content of galaxies. In our simulations, galaxy metallicities are established by a balance between inflows and outf
lows as governed by the mass outflow rate, implying that the mass-metallicity relation reflects how the outflow rate varies with stellar mass (M*). Gas content is set by a competition between inflow into and gas consumption within the ISM, the latter being governed by the SF law, while the former is impacted by both wind recycling and preventive feedback. Stochastic variations in the inflow rate move galaxies off the equilibrium M*-Z and Z*-fgas relations in a manner correlated with star formation rate, and the scatter is set by the timescale to re-equilibrate. The evolution of both relations from z=3-0 is slow, as individual galaxies tend to evolve mostly along the relations. Gas fractions at a given M* slowly decrease with time because the cosmic inflow rate diminishes faster than the consumption rate, while metallicities slowly increase as infalling gas becomes more enriched. Observations from z~3-0 are better matched by simulations employing momentum-driven wind scalings rather than constant wind speeds, but all models predict too low gas fractions at low masses and too high metallicities at high M*. All our models reproduce observed second-parameter trends of the mass-metallicity relation with star formation rate and environment, indicating that these are a consequence of equilibrium and not feedback. Overall, the analytical framework of our equilibrium scenario broadly captures the relevant physics establishing the galaxy gas and metal content in simulations, which suggests that the cycle of baryonic inflows and outflows centrally governs the cosmic evolution of these properties in typical star-forming galaxies.
We study the nature of rapidly star-forming galaxies at z=2 in cosmological hydrodynamic simulations, and compare their properties to observations of sub-millimetre galaxies (SMGs). We identify simulated SMGs as the most rapidly star-forming systems
that match the observed number density of SMGs. In our models, SMGs are massive galaxies sitting at the centres of large potential wells, being fed by smooth infall and gas-rich satellites at rates comparable to their star formation rates (SFR). They are not typically undergoing major mergers that significantly boost their quiescent SFR, but they still often show complex gas morphologies and kinematics. Our simulated SMGs have stellar masses of log M*/Mo~11-11.7, SFRs of ~180-500 Mo/yr, a clustering length of 10 Mpc/h, and solar metallicities. The SFRs are lower than those inferred from far-IR data by a factor of 3, which we suggest may owe to one or more systematic effects in the SFR calibrations. SMGs at z=2 live in ~10^13 Mo halos, and by z=0 they mostly end up as brightest group galaxies in ~10^14 Mo halos. We predict that higher-M* SMGs should have on average lower specific SFRs, less disturbed morphologies, and higher clustering. We also predict that deeper far-IR surveys will smoothly join SMGs onto the massive end of the SFR-M* relationship defined by lower-mass z=2 galaxies. Overall, our simulated rapid star-formers provide as good a match to available SMG data as merger-based scenarios, offering an alternative scenario that emerges naturally from cosmological simulations.
