Supernovae driven turbulence in the interstellar medium

Abstract

I model the multi-phase interstellar medium (ISM) randomly heated and shocked by supernovae (SN), with gravity, differential rotation and other parameters we understand to be typical of the solar neighbourhood. The simulations are in a 3D domain extending horizontally 1 1 kpc2 and vertically 2 kpc, symmetric about the galactic mid-plane. They routinely span gas number densities 10􀀀5–102 cm􀀀3, temperatures 10–108 K, speeds up to 103 km s􀀀1 and Mach number up to 25. Radiative cooling is applied from two widely adopted parameterizations, and compared directly to assess the sensitivity of the results to cooling. There is strong evidence to describe the ISM as comprising well defined cold, warm and hot regions, typified by T 102 ; 104 and 106 K, which are statistically close to thermal and total pressure equilibrium. This result is not sensitive to the choice of parameters considered here. The distribution of the gas density within each can be robustly modelled as lognormal. Appropriate distinction is required between the properties of the gases in the supernova active mid-plane and the more homogeneous phases outside this region. The connection between the fractional volume of a phase and its various proxies is clarified. An exact relation is then derived between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. The origin and structure of the magnetic fields in the ISM is also investigated in nonideal MHD simulations. A seed magnetic field, with volume average of roughly 4 nG, grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992), volume averaging is applied with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0:7 kpc and 0:3 kpc, respectively. Analysis of the dependence of the dynamo on rotation, shear and SN rate is used to clarify its mean and fluctuating contributions. The resulting magnetic field is quadrupolar, symmetric about the mid-plane, with strong positive azimuthal and weak negative radial orientation. Contrary to conventional wisdom, the mean field strength increases away from the mid-plane, peaking outside the SN active region at jzj ' 300 pc. The strength of the field is strongly dependent on density, and in particular the mean field is mainly organised in the warm gas, locally very strong in the cold gas, but almost absent in the hot gas. The field in the hot gas is weak and dominated by fluctuations.