Rotating Stellar Core with Massive Disk

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Rotating Stellar Core with Massive Disk

• Shigeyuki Karino
• SISSA, Trieste, Italy

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Summary

• Nearby massive stellar cores are often observed
  with massive disks.
• We computed equilibrium conditions of such
  stardisk systems.
• We found that massive disks tidally regulate
  rotation rates of central stars.
• Consequently, massive young stars may not rotate
  with moderate rotation rates.

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Massive star forming regions

• Massive proto-stars are often observed with
  massive accretion disks
• Disk mass O(M?)O(100M?)
• Disk size O(10AU)O(10,000AU)
• Cf. Shepherd et al. 2001, Sandell et al. 2003,
• Blum et al. 2004, Chini et al. 2004, etc
• Proto-stars evolve in the circumstances with
  massive disk
• (gravitationally) NOT isolated

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• Regulation of stellar rotations?
• YSO rotation is restricted
• Slower than its break-up limit
• Massive young stellar rotations show bimodal
  distributions?
• Littlefair et al. 2005
• Difficult to explain by magnetic interactions
  between disk core
• Gravitational interaction ?

Rapidly rotating group
Slowly rotating group
Rotation period
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Tactics

• Consider systems of star disk
• Compute equilibrium configurations of the systems
  with appropriate treatment
• Stellar rotation and deformation
• Disk mass and self gravity
• Obtain the allowed parameter regions
• Propose
• A new regulation mechanism of the stellar
  rotation due to disk tide
• A new evolution pass of YSO with disk

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• Computational method
• Equilibrium of a system is governed by fluid eqs
• These equations are solved by SCF method
• Rotation and gravity of disk are correctly
  included
• A set of parameters specifies an eq. state of
  system

Hydrostatic equation Equation of state Poisson
equation
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Results
Disk outer radius is fixed to be 1
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• (?) Examples of density contours
• Even when the star rotates slowly, the
  deformation is significant
• The star will be broken up due to strong tidal
  field of the disk (mass shedding),
• When the mass of the disk is large
• When the star-disk separation is small
• When the rotation of the star is rapid
• When the stellar EOS is soft
• The allowed parameter region is limited !!

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Allowed parameter regions
Relative disk size is small Horizontal axis
equatorial stellar radius Vertical axis
stellar rotation rate
Tidal disruption (no equilibrium)

• When
• relative stellar size is large
• relative disk mass is large
• rotating stellar matter will be tidally disrupted

Allowed equilibrium
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Relative disk size is large Horizontal axis
stellar radius Vertical axis stellar rotation
rate (T/I left, axis ratio below)

• Qualitative features are the same
• despite of relatively large disk size
• Spherical configuration cannot exist any longer
• see right figure

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Evolution pass of central stars

• The predicted pass
• Start from arbitrarily equilibrium core (a)
• It arrives at the edge of the allowed region (b)
• Then it evolves toward (1) or (2) along the edge
• Consider ideal accretion / mass-shedding
• ?M0 but ?J?0
• M mass
• J angular momentum
• Now, Jcore(b) gt Jcore(b)
• ?J gt 0 ? evol. pass (1)
• ?J lt 0 ? evol. pass (2)

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• Final outcomes
• If core earns J
• through accretion etc.
• Final outcome
• ? rapidly rotating core with small radius (c)
• If core loses J
• through effective mass-shedding, outflow,
  magnetic interaction etc.
• Final outcome
• ? slowly rotating core with large radius
  (d)
• Bimodality ?
• Moderate rotation rate may be excluded