2002 KAS fall

1
Density Power Spectra of Turbulence in Molecular
Clouds
Korea Astronomy Observatory Jongsoo Kim Chungnam
National University, Korea Dongsu Ryu, Song Chan
Yi
2
Observed Density Power Spectra

• Interstellar scintillation, etc electron
  density
• 21 cm - neutral Hydrogen
• CO line observations - molecular clouds
• Optical polarization of star lights dust
• etc.
• ? Observers said that most of their observational
  results on density PS may be explained by a
  Kolmogorov slope.
• ? However, I would like to remind that they
  observed column-density (not volume-density) PS.

3
Armstrong et al. 1995 ApJ, Nature 1981
11/33.66 the slope of Komogorov 3D PS

• Electron density PS
• Composite PS from observations of ISM velocity,
  RM, DM, ISS fluctuations, etc.
• A dotted line represents the Komogorov PS
• A dash-dotted line does the PS with a -4 slope

4
Crovisier and Dickey 1983

• PS of HI 21cm observations
• Observed with WSRT, Nancay and Arecibo
• l52.5, b0.0
• Easy to find PS from the visibility of
• interferometric observations
• The slopes of PS are -3 for WSRT observations
• and -2 for single dish observations

-2 for Nancay(x) and Arecibo(o)
-3 Westerbork()
5
Stenholm 1984

• B5, a molecular cloud
• Power spectra of peak line temperatures along N-S
  scans
• The mean spectral slope is around -1.67
  (Komogorov type spectra)
• density PS vs column-density PS.

6
Simulated Density Power Spectra Motivation of
this study
Cho and Larzarian, astroph/0411031

• Compressible MHD simulations
• As Mrms increases, the density PS (dotted line in
  each pannel) becomes flat.

7

• Isothermal Hydrodynamic equations

• Two parameters

• Periodic Boundary Condition

• Isothermal TVD Code (Kim, et al. 1998)

8
Velocity power spectra from 1D HD simulations

• Resolution 8196
• Because of 1D, there are only sound waves (no
  eddy motions).
• Slopes of the spectra are nearly equal to -2,
  irrespective of Mrms numbers.

9
Density power spectra from 1D HD simulations

• Resolution 8196
• For subsonic (Mrms0.8) or mildly supersonic
  (Mrms1.7) cases, the slopes of the spectra
• are still nearly -2.
• Slopes of the spectra with higher
• Mach numbers becomes flat especially in the low
  wavenumber region.
• Flat density spectra are not related to B-fields
  and dimensionality.

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Time evolution of velocity and density fields
(I) Mrms0.8

• 1D isothermal HD simulation with 8196 cells
• (Step function-like) Discontinuities in both
  velocity and density fields develop on top of
  sinusoidal perturbations with long-wavelengths
• FT of the step function gives -2 spectral slope.

11
Time evolution of velocity and density fields
(II) Mrms6.0

• 1D isothermal HD simulation with 8196 cells
• Step function-like (spectrum with a slope -2)
  velocity discontinuities are from by shock
  interactions.
• Interactions of strong shocks make density peaks,
  whose functional shape is similar to a delta
  function (flat spectrum).

12
Velocity power spectra from 3D HD simulations

• Resolution 5123
• The slope of a spectrum with Mrms1 is nearly
  equal to the Komogorov slope, -5/3.
• As Mrms increases, the absolute value of the
  spectral slope increases.

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Density power spectra from 3D HD simulations

• Resolution 5123
• As Mrms increases, the slope becomes flat in the
  shorter wavenumber region.

14
Comparison of sliced density images
Mrms10
Mrms1
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Conclusions

• As the Mrms of compressible turbulent flow
  increases, the density power spectrum becomes
  flat. This is due to (delta function-like)
  density peaks formed by shock interactions.
• The spectral slopes of density and velocity
  fields from 1D isothermal simulations are -2,
  irrespectively of Mrms.
• The density spectral slopes of the subsonic and
  mildly supersonic flows may be explained by the
  Kolmogorov slope.
• Because observations tell us only column-density
  PS, it is better to compare observed and
  simulated column-density PS. We are working on
  this project.