A Dynamical Model of Supernova Feedback: Gas Outflows from the Interstellar Medium

Abstract

We present a dynamical model of supernova feedback which follows the evolution of pressurised bubbles driven by supernovae in a multi-phase interstellar medium (ISM). The bubbles are followed until the point of break-out into the halo, starting from an initial adiabatic phase to a radiative phase. We show that a key property which sets the fate of bubbles in the ISM is the gas surface density, through the work done by the expansion of bubbles and its role in setting the gas scaleheight. The multi-phase description of the ISM is essential, and neglecting it leads to order of magnitude differences in the predicted outflow rates. We compare our predicted mass loading and outflow velocities to observations of local and high-redshift galaxies and find good agreement over a wide range of stellar masses and velocities. With the aim of analysing the dependence of the mass loading of the outflow, β (i.e. the ratio between the outflow and star formation rates), on galaxy properties, we embed our model in the galaxy formation simulation, GALFORM, set in the ΛCDM framework. We find that a dependence of β solely on the circular velocity, as is widely assumed in the literature, is actually a poor description of the outflow rate, as large variations with redshift and galaxy properties are obtained. Moreover, we find that below a circular velocity of ≈ 80 km s −1 the mass loading saturates. A more fundamental relation is that between β and the gas scaleheight of the disk, h g , and the gas fraction, f gas , as β ∝ h 1.1 g f 0.4 gas , or the gas surface density, Σ g , and the gas fraction, as β ∝ Σ −0.6 g f 0.8 gas . We find that using the new mass loading model leads to a shallower faint-end slope in the predicted optical and near-IR galaxy luminosity functions.

A Review of Recent Observations of Galactic Winds Driven by Star Formation

“…Relationships between outflow and galaxy properties are key tools for connecting observations to theory. The fitted slope of −0.43 ± 0.07 compares favorably with predictions from numerical simulations at low masses [38,39,41,42]. At higher masses the slope may be steeper, as suggested by some simulations [39,42] and measurements [23].…”

“…While based on a much smaller sample size, this work uses high signal-to-noise spectra, velocity-resolved optical depths and covering factors, and photoionization modeling to estimate the ionization state, density, metallicity, and inner radius of the wind (assuming a model relating velocity and radius). The measured slope (−0.43 ± 0.07) matches predictions from numerical simulations, which are in the range −0.35 to −0.50 at low masses [38,39,41,42].…”

“…The fitted slope of −0.43 ± 0.07 compares favorably with predictions from numerical simulations at low masses [38,39,41,42]. At higher masses the slope may be steeper, as suggested by some simulations [39,42] and measurements [23]. Reproduced with permission from Figure 1 of reference [36].…”

“…The study of integrated spectra [35] finds evidence that η decreases with increasing dynamical mass over the range 10 9.6 − 10 11.2 M , with a log-log slope of −0.43 that is identical to that found in the UV over a much wider mass range ( [36]; Section 2.1; Table 1). (A steeper slope in this relationship at high masses, as previously measured [23], is predicted by some simulations [39,42].) Finally, these authors fit a relationship between η and Σ SFR with a log-log slope of 0.17 [35].…”