Towards simulating star formation in the interstellar medium

As a first step to a more complete understanding of the local physical processes which determine star formation rates (SFRs) in the interstellar medium (ISM), we have performed controlled numerical experiments consisting of hydrodynamical simulations of a kiloparsec-scale, periodic, highly supersonic and `turbulent' three-dimensional flow. Using simple but physically motivated recipes for identifying star-forming regions, we convert gas into stars which we follow self-consistently as they impact their surroundings through supernovae and stellar winds. We investigate how various processes (turbulence, radiative cooling, self-gravity, and supernovae feedback) structure the ISM, determine its energetics, and consequently affect its SFR. We find that the one-point statistical measurement captured by the probability density function (PDF) is sensitive to the simulated physics. The PDF is consistent with a log-normal distribution for the runs which remove gas for star formation and have radiative cooling, but implement neither supernovae feedback nor self-gravity. In this case, the dispersion, sigma(s), ofthe log-normal decays with time and scales with rootln[1 + (M-rms/2)(2)] where M-rms is the root-mean-squared Mach number of the simulation volume, s = ln rho, and rho is the gas density. With the addition of self-gravity, the log-normal consistently underpredicts the high-density end of the PDF which approaches a power law. With supernovae feedback, regardless of whether we consider self-gravity or not, the PDF becomes markedly bimodal with most of the simulation volume occupied by low-density gas. Aside from its effect on the density structure of the medium, including self-gravity and/or supernovae feedback changes the dynamics of the medium by halting the decay of the kinetic energy. Since we find that the SFR depends most strongly on the underlying velocity field, the SFR declines in the runs lacking a means to sustain the kinetic energy, and the subsequent high density contrasts. This strong dependence on the gas velocity dispersion is in agreement with Silk's formula for the SFR which also takes the hot gas porosity, and the average gas density as important parameters. Measuring the porosity of the hot gas for the runs with supernovae feedback, we compare Silk's model for the SFR to our measured SFR and find agreement to better than a factor two.