2002 KAS fall

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Numerical Astrophysics
Jongsoo Kim Korea Astronomy and Space Science
Institute

• 
  Contents
• Why are numerical simulations for astrophysical
  flows challenging?
• B-fields in the interstellar medium
• TVD MHD code, PC cluster, and AMR simulation
• SF in the turbulent interstellar medium
• Conclusions

2

• Radiative Transfer and (M)HD

3

• N-body simulations

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Why are numerical simulations for astrophysical
flows challenging?

• Interaction between matter and radiation
• - ultimate goal of numerical experiments is
  to provide information what can be compared with
  observations.
• - 6-D (3D in space, 2D in direction, 1D in
  frequency) problem
• Huge dynamic range
• - for example, need more than 20
  orders-of-magnitude density dynamic range from a
  MC to stars.
• Multi-physics
• - self-gravity, magnetic field, relativistic
  effect, etc

• Indeed, numerical simulations are challenging.
  However, they provide us with a unique laboratory
  for astrophysical experiments.
• ? Due to the rapid development of the computer
  technology and algorithm, numerical simulations
  are now quite successful.

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Topics covered in this workshop

• B-Fields and Star Formation (Jongsoo Kim)
• MHD instabilities (Seung Soo Hong)
• MHD turbulence (Jungyeon Cho)
• Cosmology (Juhan Kim)

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How do astronomers measure magnetic fields in the
interstellar medium?

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

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Dust Polarization
magnetic field line
dust grain
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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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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(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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(Kim et al. 1999)
MHD Shock Tube Test
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The MHD code was parallelized using basic eight
MPI routines.
Eight Basics
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

• The cluster was built by the fund from KASI and
  ARCSEC.
• A dedicate cluster for astronomers in Korea.
• 5 SCI papers / year

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Test problem for a benchmark for the PC cluster
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Speed-up of the IMHD code
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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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Observed SFEs

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

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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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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

• Even though numerical simulations for
  astronomical flows are challenging, some of them
  are quite successful due to rapid development of
  the computer technology and algorithms.
• B-fields are important in almost everywhere in
  the Universe.
• A medium-size cluster based on the Gigabit
  interconnect is fairly good for MHD simulations.
• A SF theory based on turbulence is gaining its
  momentum.