On the structure of the neutral atomic medium

Patrick Hennebelle

Ecole Normale supérieure-Observatoire de Paris

and

Edouard AuditCommissariat 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,wnm cool: 10 pc

Size of CNM fragments: cooling length divided by phase density contrast (~100)

Cs,wnm cool/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)

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20 p

c104*104 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: 104 cm-3

Pressure: 105 K cm-3

Size: 400 AU- TSAS ?

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

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 simulations12003

50,000 cpu hours

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Energy spectrum (3D simulations)

density spectrum (3D simulations)

=>Behaviour « seems » similar to 2D but … resolution is crude

Velocity powerspectrum (3D simulations)

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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