Abstract
Supersonic turbulence results in strong density fluctuations in the interstellar medium (ISM), which have a profound effect on the chemical structure. Particularly useful probes of the diffuse ISM are the ArH+, OH+, H2O+ molecular ions, which are highly sensitive to fluctuations in the density and the H2 abundance. We use isothermal magnetohydrodynamic simulations of various sonic Mach numbers, , and density decorrelation scales, ydec, to model the turbulent density field. We post process the simulations with chemical models and obtain the probability density functions (PDFs) for the H2, ArH+, OH+, and H2O+ abundances. We find that the PDF dispersions increases with increasing and ydec, as the magnitude of the density fluctuations increases, and as they become more coherent. Turbulence also affects the median abundances: when and ydec are high, low-density regions with low H2 abundance become prevalent, resulting in an enhancement of ArH+ compared to OH+ and H2O+. We compare our models with Herschel observations. The large scatter in the observed abundances, as well as the high observed ArH+/OH+ and ArH+/H2O+ ratios are naturally reproduced by our supersonic , large decorrelation scale (ydec = 0.8) model, supporting a scenario of a large-scale turbulence driving. The abundances also depend on the ultraviolet intensity, cosmic-ray ionization rate, and the cloud column density, and the observed scatter may be influenced by fluctuations in these parameters.