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Supersonic turbulence results in strong density fluctuations in theinterstellar medium (ISM), which have a profound effect on the chemicalstructure. Particularly useful probes of the diffuse ISM are the ArH$^+$,OH$^+$, H$_2$O$^+$ molecular ions, which are highly sensitive to fluctuationsin the density and the H$_2$ abundance. We use isothermal magnetohydrodynamic(MHD) simulations of various sonic Mach numbers, $\mathcal{M}_s$, and densitydecorrelation scales, $y_{\rm dec}$, to model the turbulent density field. Wepost-process the simulations with chemical models and obtain the probabilitydensity functions (PDFs) for the H$_2$, ArH$^+$, OH$^+$ and H$_2$O$^+$abundances. We find that the PDF dispersions increases with increasing$\mathcal{M}_s$ and $y_{\rm dec}$, as the magnitude of the density fluctuationsincreases, and as they become more coherent. Turbulence also affects the medianabundances: when $\mathcal{M}_s$ and $y_{\rm dec}$ are high, low-densityregions with low H$_2$ abundance become prevalent, resulting in an enhancementof ArH$^+$ compared to OH$^+$ and H$_2$O$^+$. We compare our models withHerschel observations. The large scatter in the observed abundances, as well asthe high observed ArH$^+$/OH$^+$ and ArH$^+$/H$_2$O$^+$ ratios are naturallyreproduced by our supersonic $(\mathcal{M}_s=4.5)$, large decorrelation scale$(y_{\rm dec}=0.8)$ model, supporting a scenario of a large-scale turbulencedriving. The abundances also depend on the UV intensity, CR ionization rate,and the cloud column density, and the observed scatter may be influenced byfluctuations in these parameters.

Chemical Abundances in a Turbulent Medium -- H$_2$, OH$^+$, H$_2$O$^+$, ArH$^+$