Chemical Abundances in a Turbulent Medium-H₂, OH⁺, H₂O⁺, ArH⁺

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, M_s, and density decorrelation scales, y_dec, 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 M_s and y_dec, as the magnitude of the density fluctuations increases, and as they become more coherent. Turbulence also affects the median abundances: when M_s and y_dec 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 (M_s = 4.5), large decorrelation scale (y_dec=0.8) model, supporting a scenario of a largescale 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.