The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and initial mass function (IMF) of stars. Turbulence also plays an important role during structure formation in the early Universe. Despite its ubiquity and importance, we have yet to understand the statistics of turbulence. ISM turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and is driven by various stellar feedback and galactic processes. Although some of these parameters were explored, the bulk of previous work assumed that the gas is isothermal. However, cold molecular clouds form out of the warm atomic medium, with the gas passing through various chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal hydrodynamic turbulence with a polytropic equation of state (EOS), P~rho^Gamma. We use grid resolutions of 2048^3 cells and compare polytropic exponents Gamma=0.7 (soft EOS), Gamma=1 (isothermal EOS), and Gamma=5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Gamma<1, while Gamma>1 smoothes out density fluctuations. The probability distribution function (PDF) of the gas density is significantly affected by temperature variations, with a power-law tail developing on the low-density side for Gamma>1. In contrast, for Gamma<1, the PDF becomes closer to a lognormal distribution. We derive and test a new density variance – Mach number relation that takes Gamma into account. This new relation is extremely important for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a star-forming cloud. We derive the SFR as a function of Gamma and find that it decreases by a factor of 5 from Gamma=0.7 to Gamma=5/3, as in real molecular clouds.
C. Federrath and S. Banerjee
Wed, 10 Dec 14
Comments: 18 pages, 10 figures, submitted to MNRAS, comments welcome, simulation movies at this http URL