What happened to the rmodes

1
What happened to the r-modes? Nils
Andersson University of Southampton Santa Fe July
2003

• The gravitational-wave driven instability of the
  inertial r-modes may
• govern the spin evolution of nascent neutron
  stars
• halt the accretion induced spin-up of NS in
  LMXBs
• lead to detectable gravitational waves
• but, despite five years of effort, we still do
  not understand the details of this mechanism well
  enough to draw any definite conclusions...

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The r-mode instability
The lm2 r-mode grows on a timescale of a few
tens of seconds, and leads to a strong
instability.
What are the dissipation mechanisms that affect
the instability? - crust-core boundary layers
- hyperon bulk viscosity - superfluid
mutual friction - magnetic field effects What
is the mechanism that saturates the mode, and at
what amplitude does this happen? - nonlinear
mode coupling may limit the r-modes to small
amplitudes Will the mode survive saturation?
What is the backreaction of the mode on the
star - will radiation reaction and/or non-linear
effects lead to differential rotation?
The instability is counteracted by shear and bulk
viscosity, leading to a window of opportunity
around 109 K.
3
Exotic viscosity
Hyperon bulk viscosity may suppress the r-mode
instability significantly.
A conglomerate of s,d,u quarks may be the most
stable form of matter. Strange matter also has a
very strong bulk viscosity In a strange star the
r-mode instability window is located at lower
temperatures.
While accreting NS are likely to undergo a
thermo-gravitational runaway, accreting strange
or hybrid stars may reach quasi-equilibrium and
radiate persistent GWs.
But in order not to be in conflict with cooling
data, the hyperons must be superfluid. Then the
nuclear reactions that lead to the macroscopic
bulk viscosity are suppressed... and the effect
on the instability may not be so great after all.
In order to study the effects of exotic particles
we need to understand the oscillations of fully
relativistic, possibly superfluid, NS!
4
Superfluid hydrodynamics
The simplest model for a superfluid star consists
of two fluids coupled via entrainment. At a basic
level, the system is analogous to two coupled
oscillators. The two dynamical degrees of
freedom lead to independent sets of modes which
tend to be such that the fluids are co- and
counter-moving. Deviation from chemical
equilibrium provides the main restoring agent for
the superfluid modes. The presence of vortices
leads to entrainment and mutual friction
between interpenetrating superfluids. These are
key mechanisms that needs to be understood.
YES!
Two-stream instability
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The saturation amplitude
The r-mode growth phase can be described by
linear theory, but nonlinear effects soon become
important. Phenomenology At some point the
mode saturates and as excess angular momentum
is radiated away the star spins down. Model
using W and a and evolution equations from the
conservation of energy and angular
momentum Note Early estimates used a1 which
is very large, corresponding to
Current evidence r-mode GWs would be detectable
within our galaxy provided signal can be
integrated for two weeks.
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Some challenges

• Our understanding of the r-mode instability is
  still far from satisfactory. We need to face up
  to several difficult challenges.
• Theory
• Must improve our models of exotic physics in NS
  cores Are hyperons and/or deconfined quarks
  present?
• Need better models of superfluid dynamics and
  the associated viscosities.
• Need independent determination of saturation
  amplitude. Numerical evolutions are difficult
  because of the need to resolve short
  lengthscales. What happens in stratified or
  superfluid stars?
• Should study role of magnetic field in detail
  (secular drift leads to wind-up,
  magneto-viscous boundary layer may suppress
  instability).
• Observations
• Does the presence of an instability in the core
  fluid affect the EM signal?
• Are data for young and recycled radio PSRs and
  LMXBs consistent with the presence of a strong
  instability? What about the temperature?
• Need to develop GW detection strategies that
  account for evolution of source, eg. due to
  variation in accretion rate.

Observations may provide a probe of exotic
physics!