Simulating supernova feedback in galaxy disks

Abstract

In this thesis I examine supernova feedback in hydrodynamical simulations of galaxy disks. Understanding this process entails the numerical evaluation of cooling in radiative shocks, and we present a set of simulations using two widely used numerical schemes: smoothed particle hydro- dynamics and adaptive mesh refinement. We obtain a similarity solution for a shock-tube problem in the presence of radiative cooling, and test how well the solution is reproduced. We interpret our findings in terms of a resolution criterion, and apply it to realistic simulations of cosmological accretion shocks onto galaxy halos, cold accretion and thermal feedback from supernovae or active galactic nuclei. To avoid numerical overcooling of accretion shocks onto halos that should develop a hot corona requires a particle or cell mass resolution of 10^6 M⊙, which is within reach of current state-of-the-art simulations. At this mass resolution, thermal feedback in the interstellar medium of a galaxy requires temperatures of supernova or AGN driven bubbles to be in excess of 10^7 K at densities of n_H = 1.0 cm−3, in order to avoid spurious suppression of the feedback by numerical overcooling.

In order to improve sub-grid models of feedback we perform a series of numerical experiments to investigate how supernova explosions shape the interstellar medium in a disk galaxy and power a galactic wind. We 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 disk, we obtain sub-parsec resolution allowing us to resolve individual supernova events.

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, β ≡ dot M_wind / dot M_star. In the cases with the most effective outflows we observe a β of 4, however in other cases we find β<<1. We find that outflows are more efficient in disks with lower surface densities or gas fractions. A simple model in which the warm clouds are the barriers that limit the expansion of the blast wave reproduces the scaling of outflow properties with disk 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 disk, finding that the mass loading depends on
circular velocity as β ∝ V −α with α ≈ 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 normalisation is in approximate agreement with observed estimates of the mass loading for the Milky Way.

Finally, we extend these simulations to follow the ejecta produced by these SNe, allowing us to track the distribution of metals as they are mixed into the different phases of the ISM and swept out into a galactic wind. Such calculations are important both directly in predicting the enrichment of the intergalactic medium, but also with the sister problem of understanding the enrichment of the host galaxies and the mass-metallicity relation, owing to the unique role that supernovae are believed to play both as the sources of galactic winds and the sources of galactic metals. We study the dependence of the amount of metals released per unit of star formation, β_Z ≡ dot M_z / dot M_star, and the fraction of metals released, β_Z / y. We include thermal and momentum feedback from massive stars and find these make a less significant contribution to the galactic wind than SNe. We build up a model of galactic chemical evolution and we demonstrate that these models are compatible with the metallicity distributions of faint stars and compare to closed box models of chemical evolution. We infer metal retention fractions from the observed data, although this may be complicated by recycling in the galaxy halos. We compare these rates to the fraction of metals ejected in the simulations and demonstrate approximate agreement, although the simulation data has considerable scatter, primarily due to the stochastic nature of the feedback in the limited volumes of the simulations.