How supernova explosions power galactic winds

Feedback from supernovae is an essential aspect of galaxy formation. In order to improve subgrid models of feedback, we perform a series of numerical experiments to investigate how supernova explosions shape the interstellar medium (ISM) in a disc galaxy and power a galactic wind. We use the FLASH hydrodynamic code to model a simplified ISM, including gravity, hydrodynamics, radiative cooling above 10(4) K and star formation that reproduces the Kennicutt-Schmidt relation. By simulating a small patch of the ISM in a tall box perpendicular to the disc, we obtain subparsec resolution allowing us to resolve individual supernova events. The hot interiors of supernova explosions combine into larger bubbles that sweep-up the initially hydrostatic ISM into a dense, warm cloudy medium, enveloped by a much hotter and tenuous medium, all phases in near pressure equilibrium. The unbound hot phase develops into an outflow with wind speed increasing with distance as it accelerates from the disc. We follow the launch region of the galactic wind, where hot gas entrains and ablates warm ISM clouds leading to significantly increased mass loading of the flow, although we do not follow this material as it interacts with the galactic halo. We run a large grid of simulations in which we vary gas surface density, gas fraction and star formation rate in order to investigate the dependencies of the mass loading, beta = (M) over dot(wind)/(M) over dot(star), In the cases with the most effective outflows, we observe beta = 4; however, in other cases we find beta << 1. We find that outflows are more efficient in discs with lower surface densities or gas fractions. A simple model in which the warm cloudy medium is the barrier that limits the expansion of the blast wave reproduces the scaling of outflow properties with disc parameters at high star formation rates. We extend the scaling relations derived from an ISM patch to infer an effective mass loading for a galaxy with an exponential disc, finding that the mass loading depends on circular velocity as beta proportional to V-d(-alpha) with alpha approximate to 2.5 for a model which fits the Tully-Fisher relation. Such a scaling is often assumed in phenomenological models of galactic winds in order to reproduce the flat faint end slope of the mass function. Our normalization is in approximate agreement with observed estimates of the mass loading for the Milky Way. The scaling we find sets the investigation of galaxy winds on a new footing, providing a physically motivated subgrid description of winds that can be implemented in cosmological hydrodynamic simulations and phenomenological models.