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

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

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

Chemistry and time scales

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

Intermittency

Interstellar Turbulence High Reynolds number Non-thermic lines

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

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

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

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

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

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

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

Standard deviation of the velocity field as a function of scale

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

Density field

Density as a function of scale

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

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

Different structures for the different species

Phase space and time scales

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…

First results