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

3. 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) Cool from a birth temperature of 10 11 K to 10 9 K in 1 year Form a solid crust for T < 10 10 K (30 s after birth if no heating occurs)

4. Neutron Stars

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

6. Ocean Wave Instability Wind Current

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

17. 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 

18. Courtesy Lee Lindblom

20. 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!

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

22. 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.

23. Viscous Boundary Layers

24. Add Magnetic Field… B

25. Magneto-viscous Boundary Layer With Alfven Waves

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31. MVBL Critical Angular Velocity Mendell gr-qc/0102042 B = 10 12 B = 10 11 B = 10 10 B = 0

32. Saturation Lindblom, 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.)

33. Self-organized Pack Ice in the Presence of the R-mode Lindblom, 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

34. R-mode Movie See: http://www.cacr.caltech.edu/projects/hydrligo/rmode.htmlhttp://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.

35. Remaining Questions Superfluid case (T  10 9 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

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