P1253814633PyAHM

1
? Statistical Properties (PS, PDF) of Density
Fields in Isothermal Hydrodynamic Turbulent Flows
Jongsoo Kim Korea Astronomy and Space Science
Institute
Collaborators Dongsu Ryu, Enrique
Vazquez-Semadeni
Kim, Ryu 2005, ApJL (PS) Kim, VS, Passot, Ryu
2006, in preparation (PDF)
2
Armstrong et al. 1995 ApJ, Nature 1981
11/3(5/3)3.66(1.66) the 3D (1D) slope of
Komogorov PS

• Electron density PS (M1)
• 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

3
Deshpande et al. 2000

• HI optical depth image
• CAS A
• VLA obs.
• angular resol.
• 7 arcsec
• sampling interval
• 1.6 arcsec
• velocity reol.
• 0.6km/sec

4
Deshpande et al. 2000

• Density PS of cold HI gas
• (M2-3 from Heilies and Troland 03)
• A dash line represents a dirty PS obtained after
  averaging the PW of 11 channels.
• A solid line represents a true PS obtained after
  CLEANing.

-2.4
-2.75
Why is the spectral slope of HI PS shallower than
that of electron PS? ? We would like to answer
this question in terms of Mrms.
5

• Isothermal Hydrodynamic equations

• Driving method (Mac Low 99)

- We adjust the amplitude of the velocity field
in such a way that root-mean-square Mach number,
Mrms, has a certain value.

• Initial Condition uniform density

• Periodic Boundary Condition

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

6
PC cluster in KASI

• 128 Intel Xeon processors (64 nodes)
• Gigabit Ethernet interconnect
• 128GB memory
• 6TB disk space

7
Time evolution of velocity and density fields
(I) Mrms1.0

• Resolution 8196 cells
• 1D isothermal HD simulation driven a flat
  spectrum with a wavenumber range 1ltklt2
• (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.

8
Time evolution of velocity and density fields
(II) Mrms6.0

• Resolution 8196
• 1D isothermal HD simulation driven a flat
  spectrum with a wavenumber range 1ltklt2
• 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
• FT of a delta function gives a flat spectrum.

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Velocity power spectra from 1D HD simulations

• Large scale driving with a wavenumber ranges
  1ltklt2
• 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.

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Density power spectra from 1D HD simulations

• Large scale driving with a wavenumber ranges
  1ltklt2
• 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.

11
Comparison of sliced density images from 3D
simulations

• Large-scale driving with a wavenumber ranges
  1ltklt2
• Resolution 5123
• Filaments and sheets with high density are formed
  in a flow with Mrms12.

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Density power spectra from 3D HD simulations

• Statistical error bars of
• time-averaged density PS
• Large scale driving with a wavenumber ranges
  1ltklt2
• Resolution 5123
• Spectral slopes are obtained with
• least-square fits over the ranges
• 4ltklt14
• As Mrms increases, the slope becomes flat in the
  inertial range.

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Density PDF

• Previous numerical studies (for example, VS94,
  PN97, PN99, Passot and VS 98, E. Ostriker et al.
  01) showed that density PDFs of isothermal
  (gamma1), turbulent flows follow a log-normal
  distribution.

for a mass-conserving system

• However, the density PDFs of large-scale driven
  turbulent flows with high Mrms numbers (for
  example, in molecular clouds) were not explored.

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2D isothermal HD (VS 94)
Mrms0.58
Need to explore flows with higher Mach numbers.
15
3D decaying isothermal MHD (Ostriker et al. 01)
1D Driven isothermal HD (Passot VS 98)
Drive with a flat velocity PS over the wavenumber
range 1ltklt19
initial PS vk 2 k-4
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1D driven experiments with flat velocity spectra
time-averaged density PDF resolution 8196
Driving with a flat spectrum over the wavenumber
range, 1ltklt19
Large-scale driving in the wavenumber range,
1ltklt2
The density PDFs of large-scale driven flows
significantly deviate from the log-normal
distribution.
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2D driven experiments
Mrms 8 1ltklt2 resolution 10242
color-coded density movie
density PDF
When the large-sclae dense filaments and voids
form, the density PDF quite significantly deviate
from the log-nomal distribution.
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2D driven experiments
Mrms 1 15ltklt16 resolution 10242
density PDF
color-coded density image
Density PDFs of the low Mach number flow driven
at small scales almost perfectly follow the
log-nomal distribution.
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2D driven experiments
time-averaged density PDF resolution 10242
1ltklt2
Mrms8
As the Mrms and the driving wavelength increase,
the density PDFs deviate from the log-normal
distribution.
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3D driven experiments
density PDFs with different Mrms resolution 5123
vk2 k-4
1ltklt2
A density PDF of a large-scale driven flow with
Mrms7 quite significantly deviates from the
log-normal distribution.
21
3D decay experiments
time-evolution of density PDF resolution 5123
vk2 k-4
1ltklt2
As the turbulent flows decay, their density PDFs
are converged to the log-normal distribution.
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Conclusions

• As the Mrms of compressible turbulent flow
  increases, the density power spectrum becomes
  flat. This is due to density peaks (filaments
  and sheets) formed by shock interactions.
• The Kolmogorov slope of the electron-density PS
  is explained by the fact that the WIM has a
  transonic Mach number while the shallower slope
  of a patch of cold HI gas is due to the fact that
  it has a Mach number of a few.
• Density PDFs of isothermal HD, turbulent flows
  deviates significantly from the log-normal
  distirbution as the Mrms and the driving scale
  increase.