The structure of the thermally bistable and turbulent atomic gas in the local interstellar medium

This paper is a numerical study of the condensation of the warm neutral medium (WNM) into cold neutral medium (CNM) structures under the effect of turbulence and thermal instability. It addresses the specific question of the CNM formation in the physical condition of the local interstellar medium (ISM). We use the properties of the H I deduced from observations and theoretical work to constrain the physical conditions in the WNM. Using low resolution simulations we explored the impact of the WNM initial density and properties of the turbulence (stirring in Fourier with a varying mix of solenoidal and compressive modes) on the cold gas formation to identify the parameter space that is compatible with the well established observational constraints of the Hi in the local ISM. Two sets of initial conditions that match the observed quantity of CNM in mass were selected to produce high resolution simulations (10243) that allowed the properties of the produced dense structures to be studied in detail. We show that for typical values of the density, pressure and velocity dispersion of the WNM in the solar neighborhood, the turbulent motions of the H I cannot provoke the phase transition from WNM to CNM, regardless of their amplitude and their distribution in solenoidal and compressive modes. On the other hand, a quasi-isothermal increase in WNM density of a factor of 2 to 4 is enough to induce the phase transition, leading to the transition of about 40% of the gas to the cold phase within 1 Myr. This suggests that turbulence only induces the formation of the CNM when the WNM is pressured and put in a thermally unstable state. At the same time turbulence is regulating the formation of the CNM by preventing some of the WNM from moving toward the cold phase; indeed, tests performed on decaying simulations have shown that the fraction of CNM increases slowly in the decaying phase. In general, these results show that turbulence is playing a key role in the structure of the cold medium. The high resolution simulations show that the velocity field shows evidence of subsonic turbulence with a 2D Power spectrum following a Power law (P(k) infinity k(-2.4)) close to Rolmozorov (P(k) infinity k(-2.67)), while the density is highly contrasted with a significantly shallower 2D power spectrum (P(k) x VI 3), reminiscent of what is observed in the cold ISM. The cold structures denser than 5 cm are characterized by power laws, M infinity L-2.25 and sigma(vertical bar nu vertical bar) proportional to L-0.41, that are similar to the ones observed in molecular clouds. The CNM structures are sub- or transonic. and their dynamic is tighly coupled to the WNM velocity field with a lump-to-clump velocity dispersion close to the velocity dispersion of the WNM. From this we conclude that suprathermal linewidth for CNM, inferred from 21 cm observations, might be the result of relative velocity between cold structures along the line of sight.