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: pc. =>Smallest structures of size ~0.001 pc =>smallest column densities : pc * 100 cm -3 = cm -2 Three dynamical scales Cooling length of WNM: scale at which WNM is linearly unstable (Hennebelle & Pérault 1999, Koyama & Inutsuka 2000) C s,wnm  cool : 10 pc Size of CNM fragments: cooling length divided by phase density contrast (~100) C s,wnm  cool /100: 0.1 pc Size of shocked CNM framents: fragments undergo collision at Mach~10 Isothermal shock =>  shock ~  cnm *10 2 ~10 4 cm -3, Size: 0.1/M 2 = pc

Numerical experiments Mandatory resolutions : Can be done in 1D and approached in 2D 2D numerical experiment: 10 4 *10 4 pixels, 20 pc size box, 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 C s,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)

20 pc

20 pc 10 4 *10 4 pixels

5 pc First Zoom -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

0.2 pc Second Zoom Converging flow Density: 10 4 cm -3 Pressure: 10 5 K cm -3 Size: 400 AU- TSAS ?

The mass is equally distributed from the largest structures down to times smaller structures Even with higher resolution : no strict numerical convergence « Kind » of convergence is reached for dx < 0.01 pc Mass powerspectrum of structures (weighted in mass) Extracting the individual structures (achieved by simple clipping algorithm, density > 30 cm -3 )

Pressure PDF N=5000*5000 N=10000*10000 Density PDF =>significant fraction of the gas at high density (~2%) but depends on numerical resolution (and on thermodynamics) Fluid statistics: density and pressure PDF

Velocity powerspectrum (2D) Fluid statistic: velocity powerspectrum and energy spectrum Energy spectrum (2D)  Energy spectrum flat (k -1 ) => energy equally distributed in k-space

Energy spectrum (2D simulations) density spectrum (2D simulations) =>Flat energy spectrum due to flat density spectrum

3D simulations ,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)

=> Effect of thermal conduction seems to be weak Influence of thermal conduction ? -« standard » ISM conduction -pas de conduction - pure « WNM » conduction (no variation with T) -conduction 10 times the ISM conduction

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