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 (L_dec) and the turbulence driving scale (L_drive) 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 ( ${{ \mathcal M }}_{s}=4.5,7 ), and driven on varying scales (1/2.5, 1/5, 1/7) the box length. We derive the L_dec-L_drive 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 L_dec/L_drive = 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 L_dec-L_drive relation is tighter, with L_dec/L_drive = 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.