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What’s New With The R-modes?

What’s New With The R-modes?. Gregory Mendell LIGO Hanford Observatory. Neutron Stars are…. Really compact (2GM/Rc 2 ~ .2) Spin really fast (Up to 2000 Hz? Fastest known = 642 Hz) Have really intense magnetic fields (10 12 Gauss)

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What’s New With The R-modes?

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  1. What’s New With The R-modes? Gregory Mendell LIGO Hanford Observatory

  2. 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 < 1010 K (30 s after birth if no heating occurs)

  3. Neutron Stars

  4. GR tends to drive all rotating stars unstable! Internal dissipation in the star can suppress the instability Gravitational-radiation Driven Instability of Rotating Stars  

  5. Ocean Wave Instability Wind Current

  11. GR tends to drive all rotating stars unstable! Internal dissipation in the star can suppress the instability Gravitational-radiation Driven Instability of Rotating Stars  

  12. 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 

  13. Courtesy Lee Lindblom

  14. Courtesy Lee Lindblom

  15. 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!

  16. Key Parameters to Understanding the R-mode Instability • Critical angular velocity for the onset of the instability • Saturation amplitude

  17. 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.

  18. Viscous Boundary Layers

  19. Add Magnetic Field… B

  20. Magneto-viscous Boundary Layer With Alfven Waves

  22. MVBL Critical Angular VelocityMendell gr-qc/0102042 B = 1012 B = 1011 B = 1010 B = 0

  23. 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 > 0.87 (MVBL heating should lower this number.)

  24. 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

  25. R-mode Movie See: http://www.cacr.caltech.edu/projects/hydrligo/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 CACR’s HP Exemplar V2500.

  26. 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

  27. The R-modes: Some New Results Greg Mendell, LIGO Hanford Observatory Log(knowledge) Learning Curve Log(time)  Mar 9 2001 Start planning talk for LHO Mar 14 2001 Start learning how to write search code Enhanced LIGO detects r-modes

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