1. Interstellar Turbulence and hierarchical structuring Nicolas Décamp (Univ. della Calabria) Jacques Le Bourlot (Obs. de Paris)

2. Outline The context –Interstellar medium –Turbulence –Interstellar Turbulence The model –Velocity field synthesis –Coupling with the density field –Chemistry

3. The interstellar medium Dust and gas 10% of the stellar mass H:70%, He:28% (in mass) Diverse regions: Ionised, atomic and molecular regions Numerous processes: electromagnetic radiations, gravitation, magnetic field, chemistry, turbulence

4. Chemistry and time scales

5. Turbulence Kolmogorov 41 Scale exponent h=1/3 Structure functions:

6. Intermittency

7. Interstellar Turbulence High Reynolds number Non-thermic lines

8. Interstellar Turbulence High Reynolds number Non-thermic lines Ref: Falgarone E. et al., 1994, Ap. J., 436, 728

9. Interstellar Turbulence High Reynolds number Non-thermic lines Scale laws Cloud structure Effect of turbulent diffusion on chemistry Intermittency (CH+)

10. Evolution through scales of centroids velocity increments IRAM key-project Ref: Falgarone E., Panis J. F., Heithausen A. et al. 1998, A&A, 331, 669

11. Wavelets Local in position t 0 and space  t Wavelet coefficients Reconstruction

12. Analysis and synthesis of the velocity field Wavelet analysis => PDF at various scales From one scale to another: Propagator Log-normal model: 2 parameters Synthesis using this propagator. Ref: Arnéodo A., Muzy J.-F. & Roux S. G. 1997, J. Phys. II (France),7, 363

13. Synthesis of the velocity field Multi-resolution analysis –C j,k =approximation coefficient –D j,k =wavelet coefficient Cascade: M j follow the log-normal model

14. Comparison Model/Observation PDF of the velocity increments at various scales

15. Standard deviation of the velocity field as a function of scale

16. One-dimensional Model 2D velocity field Hypothesis: homogeneous, isotropic and stationary turbulence => 1D velocity field evolving with time Density field from the mass conservation equation

17. Density field

18. Density as a function of scale

19. For a realistic chemistry 35 species Bistability Example: T=10.3K and x= 5.10 -17 s -1 Ref: Le Bourlot J., Pineau des Forets G., Roueff E. 1995, A&A, 297, 251

20. Chemistry K 1 is temperature dependant and the reaction (4) is exothermic Normalisation: Equilibrium, Stability :

22. Different structures for the different species

23. Phase space and time scales

24. Conclusion Analysis and reconstruction of an interstellar turbulent velocity field with a small number of parameters. Test of eventual deviations / log-normal model => much larger maps Possible 2D or 3D generalisation Different distributions for different species without any external mechanism. More realistic chemistry…

25. First results