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## On the structure of the neutral atomic medium

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**On the structure of the neutral atomic medium**Patrick Hennebelle Ecole Normale supérieure-Observatoire de Paris and Edouard Audit Commissariat à l’énergie atomique**Important Physical Scales and Basic Understanding**One static scale Field’s length: size of the thermal fronts connecting cold and warm phases In WNM : 0.1 pc , in CNM: 0.001 pc. =>Smallest structures of size ~0.001 pc =>smallest column densities : 0.001 pc * 100 cm-3 = 3 1017 cm-2 Three dynamical scales Cooling length of WNM: scale at which WNM is linearly unstable (Hennebelle & Pérault 1999, Koyama & Inutsuka 2000) Cs,wnmcool: 10 pc Size of CNM fragments: cooling length divided by phase density contrast (~100) Cs,wnmcool/100: 0.1 pc Size of shocked CNM framents: fragments undergo collision at Mach~10 Isothermal shock =>shock~cnm*102~104 cm-3, Size: 0.1/M2 = 0.001 pc**Numerical experiments**Mandatory resolutions : 104 -105 Can be done in 1D and approached in 2D 2D numerical experiment: 104*104 pixels, 20 pc size box, 0.002 pc of resolution 3D numerical experiment: 1200*1200*1200 pixels, 15 pc size box, 0.01 pc of resolution Initial conditions : compromise between large scale (cooling length of WNM) and small scales (Hennebelle & Pérault 1999, Koyama & Inutsuka 2000, 2002, Audit & Hennebelle 2005): Impose a converging and turbulent flow of WNM from left and right face (pm 1.5 Cs,wnm) The flow can leave the box through the other faces WAIT UNTIL A STATISTICALLY STATIONARY STATE IS REACHED (takes cpu…) Better forcing can be achieved if larger box are used => see Vazquez-Semadeni’s talk (Vazquez-Semadeni et al. 2003, Gazol et al. 2000)**25002**20 pc**104*104 pixels**20 pc**First Zoom**5 pc -the flow is very fragmented, the structures are well defined (Koyama & Inutsuka 2002, Audit & Hennebelle 2005, Heitsch et al 2005) -the structures are in pressure equilibrium with the surrounding gas: 2-phase model -there are large fluctuations in density and pressure**Second Zoom**Density: 104 cm-3 Pressure: 105 K cm-3 Size: 400 AU- TSAS ? 0.2 pc Converging flow**Extracting the individual structures**(achieved by simple clipping algorithm, density > 30 cm-3) Mass powerspectrum of structures (weighted in mass) The mass is equally distributed from the largest structures down to 100-1000 times smaller structures Even with higher resolution : no strict numerical convergence « Kind » of convergence is reached for dx < 0.01 pc**Fluid statistics: density and pressure PDF**Pressure PDF N=5000*5000 Density PDF N=10000*10000 =>significant fraction of the gas at high density (~2%) but depends on numerical resolution (and on thermodynamics)**Energy spectrum (2D)**Fluid statistic: velocity powerspectrum and energy spectrum • Energy spectrum flat (k-1) => energy equally distributed in k-space Velocity powerspectrum (2D)**Energy spectrum (2D simulations)**=>Flat energy spectrum due to flat density spectrum density spectrum (2D simulations)**3D simulations**12003 50,000 cpu hours**Energy spectrum (3D simulations)**density spectrum (3D simulations) =>Behaviour « seems » similar to 2D but … resolution is crude Velocity powerspectrum (3D simulations)**Conclusions**• -small scale structures are produced naturally • -large density and pressure fluctuations (TSAS ?) • Natural consequences of 2-phase fluid (ratio of sound speeds in the 2 phases : 10) • -there is a kind of « duality », coexistence between discrete structures (2-phase models) and classical turbulent behaviour • -energy seems to « pile » up at small scales : cascade a priori different from Kolmogorov. Bulk energy of cnm not easily removed.**Questions**Are the molecular clouds multiphase objects as well ? Indeed molecular clouds: -form by contraction of HI which is a 2-phase medium -are turbulent meaning than there is a mixing with the surrounding HI halo The key question seems to be: Can WNM survive at high pressure ? =>Is there a heating mechanism more efficient than UV ? Hennebelle & Inutsuka (2006, ApJ in press) propose: Heating due to dissipation of MHD waves by ambipolar diffusion (proposed by Falgarone & Puget 86 and Ferrière et al. 87 in different context)**Influence of thermal conduction ?**-« standard » ISM conduction -pas de conduction - pure « WNM » conduction (no variation with T) -conduction 10 times the ISM conduction => Effect of thermal conduction seems to be weak**Questions**-structure of the flow Which description turbulence / static 2-phase description ? -presence of small scale structure ? Density fluctuations ? Mass Distribution ? -Turbulent flow description: Powerspectrum ? -Influence of the numerical resolution. Have we reached convergence ? -Influence of thermal conduction ? -2D versus 3D