What

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Whats New With The R-modes?

• Gregory Mendell
• LIGO Hanford Observatory

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Neutron Stars are

• Really compact (2GM/Rc2 .2)
• Spin really fast (Up to 2000 Hz? Fastest known
  642 Hz)
• Have really intense magnetic fields (1012 Gauss)
• Cool from a birth temperature of 1011 K to 109 K
  in 1 year
• Form a solid crust for T lt 1010 K (30 s after
  birth if no heating occurs)

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Neutron Stars
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Gravitational-radiation Driven Instability of
Rotating Stars

• GR tends to drive all rotating stars unstable!

• Internal dissipation in the star can suppress the
  instability

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Ocean Wave Instability
Wind
Current
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Gravitational-radiation Driven Instability of
Rotating Stars

• GR tends to drive all rotating stars unstable!

• Internal dissipation in the star can suppress the
  instability

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The R-modes

• The r-modes corresponds to oscillating flows of
  material (currents) in the star that arise due to
  the Coriolis effect. 
• The current pattern travels in the azimuthal
  direction around the star as exp(i?t im?)
• For the m 2 r-mode
• Phase velocity in the corotating frame -1/3 ?
• Phase velocity in the inertial frame 2/3 ?

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Courtesy Lee Lindblom
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Courtesy Lee Lindblom
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R-mode Instability Calculations

• Gravitation radiation tends to make the r-modes
  grow on a time scale ?GR
• Internal friction (e.g., viscosity) in the star
  tends to damp the r-modes on a time scale ?F
• The shorter time scale wins
• ?GR ? ?F Unstable!
• ?GR ? ?F Stable!

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Key Parameters to Understanding the R-mode
Instability

• Critical angular velocity for the onset of the
  instability
• Saturation amplitude

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Magnetic Effects on Viscous Boundary Layers

• Previously it has been shown that viscous
  boundary layer damping is the most important
  suppression mechanism of the r-modes in neutron
  stars with a solid crust (Bildsten and
  Ushomirsky, ApJ 529, L33 (2000)
• Magnetic effects on the viscous boundary layer
  were expected to be important at high
  temperatures.

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Viscous Boundary Layers
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Add Magnetic Field
B
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Magneto-viscous Boundary Layer With Alfven Waves
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MVBL Critical Angular VelocityMendell
gr-qc/0102042
B 1012
B 1011
B 1010
B 0
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SaturationLindblom, Owen, Ushomirsky, Phys. Rev.
D 62, 084030 (2000)Wu, Matzner, and Arras,
astro-ph/0006123

• Simple definition of the saturation amplitude ?
  maximum value of the perturbed velocity /
  equilibrium velocity at the surface of the star
• Heat generated by in a turbulent VBL melts the
  crust when ? 5.6 X 10-4 (? /?o)-1
• Turbulence in the VBL causes the mode to saturate
  when ? 0.015 (? /?o)5
• Crust melts only if ? /?max gt 0.87 (MVBL heating
  should lower this number.)

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Self-organized Pack Ice in the Presence of the
R-modeLindblom, Owen, Ushomirsky, Phys. Rev. D
62, 084030 (2000)

• If a solid crust forms, heat in the VBL melts the
  crust (for sufficiently large ?)
• If the crust melts, neutrino cooling lowers the
  temperature below the melting temperature
• Thus, chunks of crust will self-organize (by
  adjusting their size) until the heating rate
  equals cooling rates.
• The star continues to spin down until pack ice
  dissipation suppresses the instability. For ?
  1 the star spins down to ? /?o 0.093

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R-mode Movie
See http//www.cacr.caltech.edu/projects/hydrlig
o/rmode.html Lee Lindblom, Joel E. Tohline and
Michele Vallisneri (2001), Phys. Rev. Letters 86,
1152-1155 (2001). Computed using Fortran 90 code
linked wtih the MPI library on CACRs HP Exemplar
V2500.
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Remaining Questions

• Superfluid case (T ? 109 K)?
• Alfven waves are replaced cyclotron vortex waves
  otherwise results could be similar, but it
  depends how vortices pin at crust-core interface
• Nonlinear winding of magnetic field lines
• Mode coupling to g-modes and other saturation
  effects
• Semi-rigid crust

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The R-modes Some New Results

• Greg Mendell, LIGO Hanford Observatory

Log(knowledge)
Learning Curve
Log(time)
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Mar 9 2001 Start planning talk for LHO
Mar 14 2001 Start learning how to write search
code
Enhanced LIGO detects r-modes