The elusive structure of the diffuse molecular gas: shocks or vortices in compressible turbulence?

The cold diffuse interstellar medium must harbor pockets of hot gas to produce the large observed abundances of molecular species, the formation of which require much more energy than available in the bulk of its volume. These hot spots have so far escaped direct detection but observations and modeling severely constrain their phase-space structure i.e. they must have a small volume filling factor (a few %), surface filling factors larger than unity with large fluctuations about average and comparable velocity structure in pencil beams'' and large beams’'. The dissipation of the non-thermal energy of supersonic turbulence occurs in bursts, either in shocks or in the regions of large shear at the boundary of coherent vortices. These two processes are susceptible to generate localized hot regions in the cold medium. Yet, it is of interest to determine which of them, if any, dominates the dissipation of turbulence in the cold interstellar medium. In this paper, we analyze the spatial and kinematic properties of two subsets of hydrodynamical compressible turbulence: the regions of largest negative divergence and those of largest vorticity and confront them with the observational constraints. We find that these two subsets fulfill the constraints equally well. A similar analysis should be conducted in the future on simulations of MHD turbulence.