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 ^ { + } , H _ { 2 } O ^ { + } molecular ions , which are highly sensitive to fluctuations in the density and the H _ { 2 } abundance .
We use isothermal magnetohydrodynamic ( MHD ) simulations of various sonic Mach numbers , \mathcal { 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 H _ { 2 } , ArH ^ { + } , OH ^ { + } and H _ { 2 } O ^ { + } abundances .
We find that the PDF dispersions increases with increasing \mathcal { 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 \mathcal { M } _ { s } and y _ { dec } are high , low density regions with low H _ { 2 } abundance become prevalent , resulting in an enhancement of ArH ^ { + } compared to OH ^ { + } and H _ { 2 } O ^ { + } .
We compare our models with Herschel observations .
The large scatter in the observed abundances , as well as the high observed ArH ^ { + } /OH ^ { + } and ArH ^ { + } /H _ { 2 } O ^ { + } ratios are naturally reproduced by our supersonic ( \mathcal { M } _ { s } = 4.5 ) , large decorrelation scale ( y _ { dec } = 0.8 ) model , supporting a scenario of a large-scale turbulence driving .
The abundances also depend on the UV intensity , CR ionization rate and the cloud column density , and the observed scatter may be influenced by fluctuations in these parameters .