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

Abstract: 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. 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. Two sets of initial conditions which match the observations were selected to produce high resolution simulations (1024^3) allowing to study in details the properties of the produced dense structures. For typical values of the density, pressure and velocity dispersion of the WNM in the solar neighborhood, the turbulent motions of the HI can not provoque the phase transition from WNM to CNM, whatever their amplitude and their distribution in solenoidal and compressive modes. On the other hand we show that 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 percent of the gas to the cold phase within 1 Myr. Given the observed properties of the HI in the local ISM, the WNM and individual CNM structures in the local ISM are sub or transsonic and their dynamics are tightly interwoven. The velocity field bears the evidence of subsonic turbulence with a 2D power spectrum following the Kolmogorov law as P(k) \sim k^{-8/3} while the density is highly contrasted with a singificantly shallower power spectrum, reminiscent of what is observed in the cold ISM. Supra-thermal line width observed for CNM might be the result of relative velocity between cold structures. Finally, the cold structures denser than 5 cm^{-3} reproduce well the laws M \sim L^{2.25-2.28} and sigma(v) \sim 0.5-0.8L^{1/3} generally observed in molecular clouds.