GLOBAL MODES in GRAVITATING DISKS

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GLOBAL MODES in GRAVITATING DISKS

• Vladimir Korchagin
• (Yale University, Department of Astronomy)

A. Jalali, A. Just, A. Khoperskov, N. Kikuchi,
D. Maitra, S.M. Miyama, N.V. Orlova, Ch.
Theis
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Problem is solved!
I have long suspected on dynamical grounds
that the magnificent spiral structures which have
brought these two galaxies (M51 and M81) into
nearly every introductory textbook (and the
latter also onto the cover of the Hubble Atlas)
are largely transient wavelike relics of those
tidal interactions --- meaning that we would
probably have favored some quite different
examples had mankind come along just 200 million
years earlier or later. (A. Toomre , BAAS 26,
858, 1994)
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Problem is solved!
The success of the present modeling process (M81)
also supports the view that, to a first
approximation, the spiral structure in many
galaxies, essentially isolated at the present
time, is a long-lasting, but in general slowly
evolving, largely intrinsic characteristic of a
galaxy. (Lowe S.A., Roberts W.W., Yang J.,
Bertin G., Lin C.C. ApJ, 427, 184, 1994)
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Practice is criterion of the truth (V. Lenin,
Materialism and Empirio-Criticism)

• Approach
• Hydrodynamcal approximation
• Polytropic equation of state P K.s(r)2
• Galaxies with measured rotation and velocity
  dispersions
• Galactic disks are self-gravitating in vertical
  direction.
• Surface density is related to vertical
  velocity dispersion
• s(r) cz2 /
  pGhz
• Vary unknown disk parameters within observational
  limits
• cz/ cr 0.5 0.8, hz 0.3 0.8 kpc
• Solve linear problem
• Run nonilnear hydrodynamic code and compare
  results with observations

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NGC 1566 rotation and velocity dispersion profile
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NGC 1566
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Velocity dispersion Gerssen et. al. (1997).
Rotation gaseous (Peterson 1980) Stellar
(Gerssen et al.1997)
NGC 488
Rotation curve of NGC 488 based on measurements
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NGC 488
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Time evolution in the model of NGC 488 with
stellar rotation curve
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NGC 628 Velocity dispersion , photometric scale
length of old stellar disk - Van der Kruit and
Freeman (1984)
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NGC 628
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• Velocity dispersion ellipsoid, rotation
• Gerssen et al. (2000)

NGC 2985
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NGC 2985
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• NGC 3938

Rotation curve Jimenez-Vincente et al.,
1999 Velocity dispersion Bottema (1988)
Vertical scale height 0.125 0.25 kpc
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NGC 3938
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NGC 3938
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NGC 3938 Time evolution of perturbations
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• A non-conservation of mass and energy

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• Collisionless disk
• Khoperskov, Just, Korchagin, Jalali, AA, 2007

Equilibrium distributions
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• Time
• evolution

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Fourier decomposition of perturbations
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Conclusions

• Equilibrium properties of the galactic disks
• determine a set of the unstable global modes
• that qualitatively agree with the observed
• spiral patterns
• Artificially imposed absorption of perturbations
• close to a disk center does not prevent spiral
  pattern
• from growing.

• Switch-off disk self-gravity in a vicinity of
  corotation changes the morphology of growing
  spirals
• illustrating that corotation plays a key role in
  spiral generation