The density variance–Mach number relation in isothermal and non-isothermal adiabatic turbulence

Abstract

The density variance { Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, eciency, and the initial mass function of stars. Here we use high-resolution hydrodynamical simulations with grid resolutions of up to 1024 3 cells to model compressible turbulence in a regime similar to the observed interstellar medium. We use Fyris Alpha, a shock-capturing code employing a high-order Godunov scheme to track large density variations induced by shocks. We investigate the robustness of the standard relation between the logarithmic density variance ( 2 ) and the sonic Mach number (M) of isothermal interstellar turbulence, in the non-isothermal regime. Specically, we test ideal gases with diatomic molecular ( = 7=5) and monatomic ( = 5=3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fullydeveloped turbulent medium. We nd that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance { Mach number plane, but deviates signicantly from the standard expression for isothermal gases. Our main