interstellar turbulence and hierarchical structuring
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/1.jpg)
Interstellar Turbulence and hierarchical structuring
Nicolas Décamp (Univ. della Calabria)
Jacques Le Bourlot (Obs. de Paris)
![Page 2: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/2.jpg)
Outline
• The context – Interstellar medium– Turbulence– Interstellar Turbulence
• The model– Velocity field synthesis– Coupling with the density field– Chemistry
![Page 3: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/3.jpg)
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
![Page 4: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/4.jpg)
Chemistry and time scales
![Page 5: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/5.jpg)
Turbulence
• Kolmogorov 41
• Scale exponent h=1/3• Structure functions:
![Page 6: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/6.jpg)
Intermittency
![Page 7: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/7.jpg)
Interstellar Turbulence
• High Reynolds number
• Non-thermic lines
![Page 8: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/8.jpg)
Interstellar Turbulence
• High Reynolds number
• Non-thermic lines
Ref: Falgarone E. et al., 1994, Ap. J., 436, 728
![Page 9: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/9.jpg)
Interstellar Turbulence
• High Reynolds number
• Non-thermic lines
• Scale laws
• Cloud structure
• Effect of turbulent diffusion on chemistry
• Intermittency (CH+)
![Page 10: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/10.jpg)
Evolution through scales of centroids velocity increments
IRAM key-projectRef: Falgarone E., Panis J. F., Heithausen A. et al. 1998, A&A, 331, 669
![Page 11: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/11.jpg)
Wavelets
• Local in position t0 and space t
• Wavelet coefficients
• Reconstruction
![Page 12: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/12.jpg)
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
![Page 13: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/13.jpg)
Synthesis of the velocity field
• Multi-resolution analysis– Cj,k=approximation coefficient
– Dj,k=wavelet coefficient
• Cascade:
Mj follow the log-normal model
![Page 14: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/14.jpg)
Comparison Model/Observation
PDF of the velocity increments at various scales
![Page 15: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/15.jpg)
Standard deviation of the velocity field as a function of scale
![Page 16: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/16.jpg)
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
![Page 17: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/17.jpg)
Density field
![Page 18: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/18.jpg)
Density as a function of scale
![Page 19: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/19.jpg)
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
![Page 20: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/20.jpg)
Chemistry
K1 is temperature dependantand the reaction (4) is exothermic
Normalisation:
Equilibrium,Stability :
![Page 21: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/21.jpg)
![Page 22: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/22.jpg)
Different structures for the different species
![Page 23: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/23.jpg)
Phase space and time scales
![Page 24: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/24.jpg)
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…
![Page 25: Interstellar Turbulence and hierarchical structuring](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814918550346895db650a1/html5/thumbnails/25.jpg)
First results