2002 KAS fall

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Turbulence and Star Formation
Jongsoo Kim Korea Astronomy and Space Science
Institute
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Contents

• Measurements of B-fields in the ISM
• We need to study the compressible MHD turbulence
• MHD TVD code and PC cluster
• Density Power Spectra
• Lifetime of Cores and Star Formation Efficiency

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How do astronomers measure magnetic fields in the
interstellar medium?

• Optical (due to dust absorption of starlight) and
  IR (dust emission) polarizations
• Faraday rotation
• Synchrotron radiation (for external gals.)
• Zeeman splitting

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Dust Polarization
dust emission
dust absorption
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Starlight polarization
Heiles Crutcher 2005

• The magnetic field is generally parallel to the
  plane of the Galaxy.
• Polarization directions point to l80 deg and
  l260 deg, which is the orientation of the local
  spiral arm.
• Bu/Br 0.7 1.0

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IR polarization
Crutcher et al. 2004

• B80mG estimated based a C-F method

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Faraday Rotation
linearly polarized EM wave
left-handed CP wave right-handed CP wave
Electrons gyrate with the Larmor frequency.
e
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Bpara dist. from pulsar RMs
Han et al. 1999

• Local pitch angles 18deg(stars), 13deg(gas),
  8deg (B-field)
• Reversals in the B field directions
  (underestimation of B-field)
• Bpara 1.4 mG - 0.2mG near the Sun
• Bu/Br 0.3

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Synchrotron Radiation

• Synchrotron radiation at 408 MHz (Beuermann et
  al. 1985)
• equipartition between B-field and CR energy
  densities
• From the synchrotron polarization, Bu/Btot 0.7
  and Bu 4mG, Bturb 5mG

6 mG
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Are magnetic fields dynamically important? Yes.

• Sun Most active phenomena are due to a
• B-field in the Sun.
• Stars Magnetically controlled star formation
  compact objects (neutron stars and accretion
  disks ...)
• The ISM Energy density of the B-field is
  comparable to those in other energy forms.
  (large-scale structure, CR generation, etc)
• The Galaxy Dynamo vs. Primordial
• Cosmology Origin of the B-field

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Barnard 68 observed with 8.2m VLT, ESO
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Kim Hong 2002
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Larsons Law (1981)velocity dispersion-size
relation in MCs

• Larson (1981) alpha0.38 for 0.1ltLlt100 pc
• Leung, Kutner, Myers (1983) alpha0.48 for
  0.2ltLlt4 pc
• Myers (1983) alpha0.5 for 0.04 lt L lt 10 pc
• Sanders, Scoville, Solomon(1985) alpha0.62 for
  20ltLlt100 pc
• Dame et al. (1986) alpha0.5 for 10ltLlt150 pc
• Puget Perault (1992) alpha0.4 for 0.01ltLlt100
  pc

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Turbulence and magnetic fields are ubiquitous in
the Universe. ? We need to study the
compressible MHD turbulence.
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(Isothermal) MHD equations

• Slow time variation
• Small drift velocities between electrons and
• ions
• Ohms law
• Non-relativistic transform between the ion and
  the lab. rest frames

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Numerical Codes

• TVD (total variation diminishing second-order
  upwind scheme) Codes for solving
  (adiabatic,isothermal) MHD equations (Ryu et al.
  95a, 95b, Kim et al. 99)

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Kim, Ryu, Jones, Hong 1999
MHD Shock Tube Test
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The MHD code was parallelized using eight basic
MPI routines.
Eight basic
routines MPI_INIT
initialization MPI_FINALIZE termination
MPI_COMM_SIZE define number of
processors MPI_COMM_RANK give a rank on each
processor MPI_SEND send
messages MPI_RECV receive
messages MPI_BCAST send messages
to all processors MPI_REDUCE reduce
values on all the processors to
a single value
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Domain decomposition
communication
PE0
PE1
PE2
PE3
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KASI-ARCSEC CLUSTER

• A dedicate cluster for several numerical
  astrophysicists in Korea.
• 5 SCI papers / year
• We are planning to build the 2nd generation of a
  PC cluster.

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Density Power Spectra
11/3(5/3)3.66(1.66) the 3D (1D) slope of
Kolmogorov PS

• Electron density PS (M1)
• Composite PS from observations of ISM velocity,
  RM, DM, ISS fluctuations, etc.
• A dotted line represents the Kolmogorov PS
• A dash-dotted line does the PS with a -4 slope

Armstrong et al. 1995 ApJ, Nature 1981
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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

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Deshpande et al. 2000

• Density PS of cold HI gas
• (M2-3 from Heiles 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(-0.4)
-2.75(-0.75)
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.
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HI column-image of the SMC
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StanimirovicLazarian 2001
Applying the velocity channel analysis (VCA
Lazarian and Pogosyan 2000) spectral index for 3D
density PS -1.3(-3.3) spectral index for 3D
velocity PS -1.4(-3.4)
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• Isothermal Hydrodynamic equations

• Driving method (Mac Low 99)

is a Gaussian random perturbation field
with a predefined wavenumber ranges.
- 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. 99)

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

• Resolution 8196 cells
• 1D isothermal HD driven simulation with a flat
  spectrum in 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.

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

• Resolution 8196
• 1D isothermal HD driven simulation with a flat
  spectrum in 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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Time-averaged density power spectra from 1D HD
simulations

• Large scale driving in 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.

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Comparison of sliced density images from 3D
simulations

• Large-scale driving in 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 in 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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Observed SFEs

• SFE Ms/(MsMc) is
• - 2-3 for molecular cloud complexes in the
  inner Galaxy (e.g., Myers et al. 1986)
• - 10-30 for cluster-forming regions (e.g.,
  Lada Lada 2003)
• SF theories should explain the low SFEs
  (Zuckerman Evans 1974).

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Myers et al. 1986

• CO 2.6m, 150micron, 250micron,
• 6cm radio continuum,
• H 110alpha recombination
• inner Galaxy, -1 deg lt b lt1 deg,
• 12 deg lt l lt 60deg
• 54 molecular cloud complexes
• mean SFE mean Ms/(MsMc)2

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Two SF Theories
SF regulated by AD
SF regulated by turbulence
magnetically supercritical cloud. (B-field is not
important ingredient.)
magnetically subcritical cloud
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3D, self-gravitating, driven MHD simulations
m (M/F) /(M/F)c0.9, 2.8, 8.8, infinite
n 500 cm-3 cs 0.2 km s-1 L 4pc B 45, 15,
5, 0 mG Mtot 2000 Msun
periodic boundaries
B
uniform density
turbulence is driven at a large scale around
L/2 Mrms 10
L4LJ
resolution 2563 cells
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Magnetically subcritical case, m0.9

• Most density peaks are transient with lifetimes
  at most 1.5Myr.
• The AD timescale is comparable to the lifetimes
  of longest-lived clumps. ? The cores may undergo
  AD-mediated evolution if AD is included even in a
  strongly turbulent, subcritical flow.

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Magnetically supercritical case, m2.8

• A few collapsing cores are formed.
• First collapsing object goes from first
  appearance to a fully collapsed state in less
  than 1 Myr, twice of the local free-fall time.

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Core Formation Efficiency (SFE)
0.12
0.04
M (ngt500n0)
0.05
2.8
8.8
0.025
lifetime of cloud 4Myr (e.g, Hartmann et al.
2001)

• CFE is dependent on the seed for random driving
• velocity fields (Heitsch et al 2001).
• CFEs are lower than 10 in most cases.

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Conclusions

• We need to study the compressible MHD turbulence.
• As the Mrms of compressible turbulent flow
  increases, the density power spectrum gradually
  becomes flat. This is due to density peaks
  (filaments and sheets) formed by shock
  interactions.
• CFEs(SFEs) measured in 3D driven simulations of
  magnetically supercritical MCs are less than 10
  in most cases.