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-projectRef: Falgarone E., Panis J. F., Heithausen A. et al. 1998, A&A, 331, 669

Wavelets

• Local in position t0 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– Cj,k=approximation coefficient

– Dj,k=wavelet coefficient

• Cascade:

Mj 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= 5.10-17 s-1

Ref: Le Bourlot J., Pineau des Forets G., Roueff E. 1995, A&A, 297, 251

Chemistry

K1 is temperature dependantand 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