The instability of a self-gravitating gaseous disk

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The instability of aself-gravitating gaseous disk

• by
• Chi Yuan
• Institute of Astronomy Astrophysics
• Academia Sinica, Taipei
• 11-01-2006

Collaborators David C.C. Yen, L.H. Lin, H.H.
Wang, C.C. Yang
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Two kinds of instabilityin astrophysical disks

• Toomres instability starburst rings, star
  formation
• Shear instability of Rayleighs type associated
  with shocks, causing substructure, chaos and
  turbulence

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Governing Equations
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The Antares Code
????

• Second-order 2-D Godunov codes
• Based on exact Riemann solver
• Coupled with the fft Poisson solver (non-periodic
  BC) for disk self-gravity
• True radiation (non-reflecting) boundary
  conditions.
• Cartesian and polar coordinates
• Isothermal and polytropic gas
• All codes parallelized

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Starburst Rings
NGC1512
NGC4313
NGC6782
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Circumnuclear Disk in ngc1068
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Center of M51
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NGC 1068

• Type Sb / AGN

• Distance 14.4 Mpc

( H0 75 km s-1 Mpc-1 )
1 arcsec 74 pc
9.5 arcmin
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Nearly Flat Rotation Curve
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Cases of Double Resonances OLR-OILR
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Toomres Instability
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Onset of Instability
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Disk Instability
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Sub-structure, feathers, chaos
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Sub-structure of M81
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M81
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Shear Instability
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Sub-structure, Patches, Chaos
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Rayleighs Shear Instability (vorticity in the
axisymmetric flow flield has a local extremum)
vorticity divided by surface density orSpecific
vorticity has a local extremum
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Specific Vorticity
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The Mechanism of Rayleighs Criterion for Shear
Instability (C.C. Lin 1944)
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Simple Explanation of Rayleighs shear instability
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Specific Vorticity distribution
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Vorticity Creation by Shock(Cocco, Truesdell,
Lighthill, Hayes, Berndt, Kevlahan)
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Creation of Vorticity along Shocks
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Conclusions

• Disk instability is extremely important in
  astrophysics.
• Toomres instability at work, giving rise
  starburst and star formation activities. It also
  explains the origin of the dense circumnuclear
  molecular disks observed in the center of many
  nearby galaxies.
• Shear instability creates substructures, patches
  and chaos in the middle of the galactic disk
  where shocks are present.
• We believe that the origin of the shear
  instability lies on the vorticity creation on
  shocks.

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Evolution of Streamlines
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Specific Vorticity at different resolution