What’s New With The R-modes?

Gregory Mendell

LIGO Hanford Observatory

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)

Neutron Stars

Gravitational-radiation Driven Instability of Rotating Stars

• GR tends to drive all rotating stars unstable!

• Internal dissipation in the star can suppress the instability

Ocean Wave Instability

Wind

Current

Gravitational-radiation Driven Instability of Rotating Stars

• GR tends to drive all rotating stars unstable!

• Internal dissipation in the star can suppress the instability

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(it + im)

• For the m = 2 r-mode: Phase velocity in the corotating frame: -1/3 Phase velocity in the inertial frame: +2/3

Courtesy Lee Lindblom

Courtesy Lee Lindblom

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!

Key Parameters to Understanding the R-mode Instability

• Critical angular velocity for the onset of the instability

• Saturation amplitude

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.

Viscous Boundary Layers

Add Magnetic Field…

B

Magneto-viscous Boundary Layer With Alfven Waves

MVBL Critical Angular VelocityMendell gr-qc/0102042

B = 1012

B = 1011

B = 1010

B = 0

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.)

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

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.

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

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