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Gravitational waves from neutron star instabilities: What do we actually know?. Nils Andersson Department of Mathematics University of Southampton IAP Paris January 2006. binary merger:

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Gravitational waves from neutron star instabilities what do we actually know

Gravitational waves from neutron star instabilities:

What do we actually know?

Nils Andersson

Department of Mathematics

University of Southampton

IAP Paris January 2006

How can ns radiate

binary merger:

the inspiral chirp provides a clean GW signal carrying information about the system, while the merger phase probes strong field gravity

supernova core collapse:

the birth of a NS may lead to a GW burst


crustal asymmetries lead to GWs at twice the spin frequency


free precession is the most general motion of a solid body (cf. Earth’s “Chandler wobble”)


fast spinning NS may suffer both dynamical bar-mode and secular instabilities(r-modes?)

phase transitions (?):

eg. quark deconfinement as NS spins down; may lead to energy being released

How can NS radiate?

In principle, neutron stars are cosmic laboratories of extreme physics. They are expected to be important GW sources, and we hope to be able to probe matter at supranuclear densities.

The bar mode instability
The bar-mode instability

For rapidly (differentially!) rotating stars with

the “bar mode” grows on a dynamical timescale.

  • Wave propagates “backwards” with given pattern speed

  • Spiral arms form: the star sheds material with high specific angular momentum

  • Bar may persist for many (hundreds?) rotation periods; signal relatively easy to estimate:

  • Detection of a bar-mode signal may tell us about the internal rotation law of collapsed stars and merger remnants

  • will the instability set in during “realistic” core collapse?

  • how long lived is the instability?


  • are other modes relevant?

  • how can we explain low b instabilities?

    (differential rotation law)

The cfs instability

An oscillation is unstable if the star thinks it has “negative energy”.

A “neutral” mode of oscillation signals the onset of CFS instability.

The modes that are currently thought to be the most important are the “acoustic” f-modes, and the “Coriolis driven” r-modes.

The CFS instability

Chandrasekhar 1969: Gravitational waves lead to a secular instability

Friedman & Schutz 1978: The instability is generic: for any W modes with sufficiently large m are unstable.

The r modes

? “negative energy”.

The r-modes

The r-modes belong to a large class of “inertial” modes, which are driven unstable by the emission of gravitational waves at all rates of rotation!

The l=m=2 r-mode grows on a timescale of a few tens of seconds, and leads to a stronger instability than the f-modes.

Instability window depends on uncertain core-physics.

Need to account for “exotic” states of matter :

  • hyperon and/or quark bulk viscosity

  • superfluid mutual friction

  • interaction with magnetic field (superconductors?)

Suppressed by superfluidity

Thought to stabilise the f-modes completely!

Evolution scenarios

runaway “negative energy”.


Evolution scenarios

What is the saturates mechanism and what is the maximum amplitude?

  • Nonlinear mode coupling may limit the

    r-modes to small amplitudes, but GWs scenarios are still viable?

  • Limiting spin in LMXBs?

    Will the mode survive saturation?

  • Turbulent cascade leading to regrowth?

    What is the backreaction on the star?

  • Will radiation reaction and/or nonlinear effects lead to differential rotation?

Saturation results need to be confirmed by alternative methods, and stratification, superfluidity, magnetic fields etcetera should be included.

Other instabilities
Other instabilities? “negative energy”.

A number of other instabilities may affect the dynamical evolution of neutron stars. Whether these instabilities are relevant as GW sources is not clear, but they may play a role, eg. by altering the other scenarios…

  • There are hydrodynamics effects that are essentially unknown by our community, eg. the elliptical instability

  • Shearing instabilities in differentially rotating fluids with co- rotation points

  • In multifluid systems (such as a neutron star with superfluid components) a two-stream instability may operate. This could be relevant for pulsar glitches.

  • Magnetic field will have a plethora of instabilities (EM analogue to CFS?)

  • ...