Interstellar Turbulence and hierarchical structuring

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Interstellar Turbulence and hierarchical
structuring

• Nicolas Décamp (Univ. della Calabria)
• Jacques Le Bourlot (Obs. de Paris)

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Outline

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

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The interstellar medium

• Dust and gas
• 10 of the stellar mass
• H70, He28 (in mass)
• Diverse regions Ionised, atomic and molecular
  regions
• Numerous processes electromagnetic radiations,
  gravitation, magnetic field, chemistry, turbulence

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Chemistry and time scales
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Turbulence

• Kolmogorov 41
• Scale exponent h1/3
• Structure functions

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Intermittency
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Interstellar Turbulence

• High Reynolds number
• Non-thermic lines

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Interstellar Turbulence

• High Reynolds number
• Non-thermic lines

Ref Falgarone E. et al., 1994, Ap. J., 436, 728
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Interstellar Turbulence

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

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

• Local in position t0 and space Dt
• Wavelet coefficients
• Reconstruction

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Analysis and synthesis of the velocity field

• Wavelet analysis gt 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

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Synthesis of the velocity field

• Multi-resolution analysis
• Cj,kapproximation coefficient
• Dj,kwavelet coefficient
• Cascade
• Mj follow the log-normal model

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Comparison Model/Observation
PDF of the velocity increments at various scales
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Standard deviation of the velocity field as a
function of scale
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One-dimensional Model

• 2D velocity field
• Hypothesis homogeneous, isotropic and stationary
  turbulence
• gt 1D velocity field evolving with time
• Density field from the mass conservation equation

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Density field
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Density as a function of scale

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For a realistic chemistry

• 35 species
• Bistability
• Example T10.3K and x 5.10-17 s-1

Ref Le Bourlot J., Pineau des Forets G., Roueff
E. 1995, AA, 297, 251
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Chemistry
K1 is temperature dependant and the reaction (4)
is exothermic
Normalisation
Equilibrium, Stability
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Different structures for the different species
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Phase space and time scales
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Conclusion

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

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First results