Fractal Density Distribution of Interstellar Clouds from Numerical Simulations of Compressively Driven Supersonic Turbulence

We present results of a high resolution 3-dimensional numerical simulation of compressively driven supersonic turbulence. A detailed analysis of the fractal mass dimension, which is extracted from data of the density field, yields values of Df ≈ 2.6− 2.7. This is significantly higher than what is usually assumed in the literature (Df ≈ 2.35). However, this value is traditionally obtained by applying the perimeter-area method to maps of nearby molecular cloud complexes, which gives Dper ≈ 1.35 for cloud perimeters, followed by the assumption Df = Dper + 1. Due to projection, noise and opacity effects, Sánchez et al. showed that perimeter-area measures of Dper ≈ 1.35 are better consistent with Df ≈ 2.6− 2.7. We additionally probe the influence of the forcing to excite turbulent motions and the dependence of the fractal density distribution on rms Mach numbers ranging from the subsonic to the highly supersonic regime. At a given Mach number, compressive forcing decreases the fractal mass dimension slightly over solenoidal forcing. Similar holds when increasing the rms Mach number, while keeping the forcing scheme fixed. This is because stronger compressibility of the turbulence forcing and higher rms Mach number flows will both push interstellar gas to a higher degree into sheet-like structures. For high rms turbulent Mach numbers (Mrms ≈ 10) in conjunction with strong compressive forcing, our results suggest that Df can be as small as 2.4. Taking moderate Mrms ≈ 2, typical values are Df ≈ 2.6 for compressive and Df ≈ 2.7 for solenoidal forcing. Subject headings: hydrodynamics — ISM: clouds — ISM: kinematics and dynamics — ISM: structure — methods: numerical — turbulence