Modelling H ₂ formation in the turbulent interstellar medium: Solenoidal versus compressive turbulent forcing

We present results from high-resolution 3D simulations of the turbulent interstellar medium (ISM) that study the influence of the nature of the turbulence on the formation of molecular hydrogen. We have examined both solenoidal (divergence-free) and compressive (curl-free) turbulent driving, and show that compressive driving leads to faster H ₂ formation, owing to the higher peak densities produced in the gas. The difference in the H ₂ formation rate can be as much as an order of magnitude at early times, but declines at later times as the highest density regions become fully molecular and stop contributing to the total H ₂ formation rate. We have also used our results to test a simple prescription suggested by Gnedin et al. for modelling the influence of unresolved density fluctuations on the H ₂ formation rate in large-scale simulations of the ISM. We find that this approach works well when the H ₂ fraction is small, but breaks down once the highest density gas becomes fully molecular.