The sites of extreme turbulent dissipation in the diffuse interstellar medium : structure & properties

Turbulent energy dissipation is a key process in the cold interstellar medium (ISM), not only on the road to star formation but also as a source of suprathermal energy able to open new chemical routes, otherwise inactive at the low gas temperature. Such routes are required, though, to explain the high abundance of species such as $\mathrm{CH}^+$ and $\mathrm{SH}^+$ observed in the ISM. In this context, the space-time intermittency of energy dissipation is particularly relevant because it drives injection of suprathermal energy in the ISM locally far above the average level. The detailed characteristics of the spatial distribution and the geometrical properties of the energy dissipation rate can provide valuable inputs to chemical models. We study them here with the aid of direct numerical simulations with unprecedented dedication to resolve the dissipation processes numerically. As the sonic Mach number in the diffuse interstellar medium can take values in a wide range, we bracket the possible physics by considering two categories of decaying turbulence models. On the incompressible extreme, we perform pseudo-spectral simulations of viscous and resistive magnetohydrodynamics, with a particular emphasis on ambipolar diffusion due the ion-neutral drift. On the compressible extreme we consider grid-based (Godunov) simulations of isothermal resisitive and viscous magnetohydrodynamics where our focus is on numerical dissipation. Our incompressible simulations show that ambipolar diffusion leads to force-free magnetic fields at small scales. As a result, the typical scale of ion-neutral friction heating is displaced to large scales in the inertial range, much greater than dimensional analysis would predict. The structures of high dissipation are spatially coherent sheets, each with a single nature of dissipation (viscous, ohmic or ambipolar). We reveal their statistical scaling laws and compute their intermittency exponents. We show that compressible simulations are subject to a lot of numerical dissipation: in our set up, less than half of the total dissipation is accounted for by the physical terms, the rest is produced by the numerical scheme. We design a method to recover locally the energy lost in the scheme and we use it to examine the sheet-like structure of the dissipation field as in our incompressible simulations. We show that numerical dissipation prevents us to assess the nature of dissipative structures. For instance, although we confirm previous results that physical dissipation in shearing sheets rapidly dominates over shocks, the balance could be reversed if numerical dissipation were shock dominated. Finally, we examine the efficiency of various observational tracers to characterize the structures of high dissipation. In particular, we find that increments of molecular line centroid velocity or of polarization Stokes parameters correlate very well on the plane of the sky with specific structures of high dissipation. We also compute the intermittency exponents measured for these tracers and find they span a broad range of possible values. At last, we mix the Fourier phases to demonstrate the crucial role of coherence in producing the filamentary structure of observable maps of increments such as recently produced by the Planck collaboration.