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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 ($L_{\rm dec}$) and the turbulence driving scale ($L_{\rm drive}$) 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 $L_{\rm dec}-L_{\rm drive}$ 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 $L_{\rm dec}/L_{\rm drive} = 0.19 \pm 0.10$, 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 $L_{\rm dec}-L_{\rm drive}$ relation is tighter, with $L_{\rm dec}/L_{\rm drive} = 0.112 \pm 0.024$. We discuss our results in the context of using observations of chemical tracers to constrain the dominant turbulence driving scale in the ISM.