Analysis of turbulent fields in the supernova-driven interstellar medium

Abstract

I model the interstellar medium (ISM) randomly shocked and heated by supernova explosions (SNe), with the inclusion of differential rotation, gravity, radiative cooling and other parameters typical of the Solar neighbourhood. I perform correlation analysis of magnetohydrodynamic simulations detailed in Gent (2012); Gent et al. (2013a,b) in a 1×1×2kpc3 domain, symmetric about the galactic mid-plane, and use Gaussian smoothing to obtain the mean fields. In these simulations, the nG seed magnetic field is amplified by dynamo action to strengths of µG. I have run and analysed a set of hydrodynamic simulations with similar parameters in a smaller domain, varying the supernova rate to investigate its impact on the structure and dynamics of the ISM. The random magnetic field, density, and velocity have different correlation scales. The correlation time of the random velocity is comparable to the eddy turnover time, about 107 yr. The standard deviations of the components of the random magnetic field suggest the field is anisotropic, attributed to the global velocity shear from galactic differential rotation, and locally inhomogeneous outflow to the galactic halo. The correlation length of Faraday depth along the z-axis is greater than for electron density and vertical magnetic field. Uncertainties of the structure functions of synchrotron intensity rapidly increase with the scale, a feature which is hidden in power spectrum analysis. I discuss methods to identify an optimal smoothing scale ` of the Gaussian kernel and the effects of this choice on the results. From spectral analysis of magnetic field, density and velocity, a suitable smoothing length for all three fields, ` = 75pc, is obtained. The properties of third-order statistical moments arising in connection of fluctuations of kinetic energy density in compressible flows and their physical interpretations are discussed. The mean magnetic field significantly alters the distributions of the kinetic energy in space and between scales, reducing the magnitude of the intermediate scale kinetic energy. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows. Increasing the supernova rate results in greater abundances of both hot and cold gas, as a result of increased heating and the formation of more regions of cold, dense gas by increased compression. The increased number of supernovae results in greater turbulent pressures, which thicken the disk. The root-mean-square velocity is increased, attributed to stronger outflows driven by an increased number of buoyant bubbles of hot gas. The depletion of the warm gas and the increased amount of cold gas results in a reduction in the correlation scale of the density fluctuations. The increased driving of motions also reduces the correlation length of the turbulent velocity. The increased supernova rate also results in a smaller correlation time. Further comparison to the eddy turnover time reveals that the eddy turnover time is most appropriate as an estimate of the correlation time in the horizontal directions.