## Abstract

The density variance-Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, efficiency, 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 (σ^{2} _{s}) and the sonic Mach number (M) of isothermal interstellar turbulence, in the non-isothermal regime. Specifically, we test ideal gases with diatomic molecular (γ = 7/5) and monatomic (γ = 5/3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fully developed turbulent medium. We find that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance-Mach number plane, but deviates significantly from the standard expression for isothermal gases. Our main result is a new density variance-Mach number relation that takes the adiabatic index into account: σ^{2} _{s} = ln (1 + b^{2}M^{(5γ+1)/3}) and provides good fits for bM≲ 1. A theoretical model based on the Rankine-Hugoniot shock jump conditions is derived, σ^{2} _{s} = ln{1 + (γ + 1)b^{2}M^{2}/[(γ - 1)b^{2}M^{2} + 2]}, and provides good fits also for bM> 1. We conclude that this new relation for adiabatic turbulence may introduce important corrections to the standard relation, if the gas is not isothermal (γ ≠ 1).

Original language | English |
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Pages (from-to) | 1380-1389 |

Number of pages | 10 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 451 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 May 2015 |