The Driving Scale-Density Decorrelation Scale Relation in a Turbulent Medium

Density fluctuations produced by supersonic turbulence are of great importance to astrophysical chemical models. A property of these density fluctuations is that the two-point correlation function decreases with increasing scale separation. The relation between the density decorrelation length scale (Ldec) and the turbulence driving scale (Ldrive) determines how turbulence affects the density and chemical structures in the interstellar medium (ISM), and is a key component for using observations of atomic and molecular tracers to constrain turbulence properties. We run a set of numerical simulations of supersonic magnetohydrodynamic turbulence, with different sonic Mach numbers (. s = 4.5, 7), and driven on varying scales (1/2.5, 1/5, 1/7) the box length. We derive the Ldec-Ldrive relation as a function of Mach number, driving scale, and the orientation of the line-of-sight (LOS) in respect to the magnetic field. We find that the mean ratio Ldec/Ldrive.=.0.19.+/-.0.10, when averaged over snapshots, Mach numbers, driving lengths, and the three LOSs. For LOS parallel to the magnetic field the density structures are statistically smaller and the Ldec-Ldrive relation is tighter, with Ldec/Ldrive.=. 0.112.+/-.0.024. We discuss our results in the context of using observations of chemical tracers to constrain the dominant turbulence driving scale in the ISM.