Supernova-regulated ISM: the effects of radiative cooling and thermal conductivity on the multi-phase structure

The hydrodynamic state of the interstellar medium (ISM) heated and randomly stirred by supernovae (SNe) is investigated. We use a three-dimensional non-ideal hydrodynamic ISM model in a domain extending 0.5 x 0.5 kpc horizontally and 2 kpc vertically to explore the relative importance of various physical and numerical effects on the multi-phase, turbulent ISM. We include both Type I and II SNe, the latter occurring only in dense regions. First we investigate the role of the thermal instability in the temperature range 300-6100 K, comparing results obtained for two different cooling functions, one susceptible to the instability, the other stable. The presence of thermal instability in the system is mainly visible as the tendency of the gas to avoid the relevant temperature range, as it quickly evolves towards either colder or warmer phases. Nevertheless, the formation of dense structures for both cooling functions appears to be dominated by expanding and colliding supernova remnants, rather than by the thermal instability. As we need to include a finite thermal conduction coefficient to resolve the thermal instability with our uniform grid, we also explore the effects of changing Prandtl number on the system. The purely divergent SN forcing is found to produce significant amounts of vorticity. The relative vorticity is around 0.6-0.7 for the highest Prandtl numbers explored, Pr=40, and is observed to diminish almost by a factor of two for the lowest Prandtl numbers studied, Pr=1. Rotation laws with angular velocity decreasing or increasing outwards are investigated, enabling us to separate the contributions to kinetic helicity due to rotation and shear. When angular velocity decreases outwards, these two contributions partly cancel each other, resulting in a smaller net helicity.