3,024 research outputs found
Gravitational radiation from the r-mode instability
The instability in the r-modes of rotating neutron stars can (in principle)
emit substantial amounts of gravitational radiation (GR) which might be
detectable by LIGO and similar detectors. Estimates are given here of the
detectability of this GR based the non-linear simulations of the r-mode
instability by Lindblom, Tohline and Vallisneri. The burst of GR produced by
the instability in the rapidly rotating 1.4 solar mass neutron star in this
simulation is fairly monochromatic with frequency near 960 Hz and duration
about 100 s. A simple analytical expression is derived here for the optimal S/N
for detecting the GR from this type of source. For an object located at a
distance of 20 Mpc we estimate the optimal S/N to be in the range 1.2 to about
12.0 depending on the LIGO II configuration.Comment: 8 pages, 4 figure
Effect of hyperon bulk viscosity on neutron-star r-modes
Neutron stars are expected to contain a significant number of hyperons in
addition to protons and neutrons in the highest density portions of their
cores. Following the work of Jones, we calculate the coefficient of bulk
viscosity due to nonleptonic weak interactions involving hyperons in
neutron-star cores, including new relativistic and superfluid effects. We
evaluate the influence of this new bulk viscosity on the gravitational
radiation driven instability in the r-modes. We find that the instability is
completely suppressed in stars with cores cooler than a few times 10^9 K, but
that stars rotating more rapidly than 10-30% of maximum are unstable for
temperatures around 10^10 K. Since neutron-star cores are expected to cool to a
few times 10^9 K within seconds (much shorter than the r-mode instability
growth time) due to direct Urca processes, we conclude that the gravitational
radiation instability will be suppressed in young neutron stars before it can
significantly change the angular momentum of the star.Comment: final PRD version, minor typos etc correcte
Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode
We study the dynamical evolution of a large amplitude r-mode by numerical
simulations. R-modes in neutron stars are unstable growing modes, driven by
gravitational radiation reaction. In these simulations, r-modes of amplitude
unity or above are destroyed by a catastrophic decay: A large amplitude r-mode
gradually leaks energy into other fluid modes, which in turn act nonlinearly
with the r-mode, leading to the onset of the rapid decay. As a result the
r-mode suddenly breaks down into a differentially rotating configuration. The
catastrophic decay does not appear to be related to shock waves at the star's
surface. The limit it imposes on the r-mode amplitude is significantly smaller
than that suggested by previous fully nonlinear numerical simulations.Comment: Published in Phys. Rev. D Rapid Comm. 66, 041303(R) (2002
Nonlinear Couplings of R-modes: Energy Transfer and Saturation Amplitudes at Realistic Timescales
Non-linear interactions among the inertial modes of a rotating fluid can be
described by a network of coupled oscillators. We use such a description for an
incompressible fluid to study the development of the r-mode instability of
rotating neutron stars. A previous hydrodynamical simulation of the r-mode
reported the catastrophic decay of large amplitude r-modes. We explain the
dynamics and timescale of this decay analytically by means of a single three
mode coupling. We argue that at realistic driving and damping rates such large
amplitudes will never actually be reached. By numerically integrating a network
of nearly 5000 coupled modes, we find that the linear growth of the r-mode
ceases before it reaches an amplitude of around 10^(-4). The lowest parametric
instability thresholds for the r-mode are calculated and it is found that the
r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included.
Using the network of coupled oscillators, integration times of 10^6 rotational
periods are attainable for realistic values of driving and damping rates.
Complicated dynamics of the modal amplitudes are observed. The initial
development is governed by the three mode coupling with the lowest parametric
instability. Subsequently a large number of modes are excited, which greatly
decreases the linear growth rate of the r-mode.Comment: 3 figures 4 pages Submitted to PR
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Second-order rotational effects on the r-modes of neutron stars
Techniques are developed here for evaluating the r-modes of rotating neutron
stars through second order in the angular velocity of the star. Second-order
corrections to the frequencies and eigenfunctions for these modes are evaluated
for neutron star models. The second-order eigenfunctions for these modes are
determined here by solving an unusual inhomogeneous hyperbolic boundary-value
problem. The numerical techniques developed to solve this unusual problem are
somewhat non-standard and may well be of interest beyond the particular
application here. The bulk-viscosity coupling to the r-modes, which appears
first at second order, is evaluated. The bulk-viscosity timescales are found
here to be longer than previous estimates for normal neutron stars, but shorter
than previous estimates for strange stars. These new timescales do not
substantially affect the current picture of the gravitational radiation driven
instability of the r-modes either for neutron stars or for strange stars.Comment: 13 pages, 5 figures, revte
Axial instability of rotating relativistic stars
Perturbations of rotating relativistic stars can be classified by their
behavior under parity. For axial perturbations (r-modes), initial data with
negative canonical energy is found with angular dependence for all
values of and for arbitrarily slow rotation. This implies instability
(or marginal stability) of such perturbations for rotating perfect fluids. This
low -instability is strikingly different from the instability to polar
perturbations, which sets in first for large values of . The timescale for
the axial instability appears, for small angular velocity , to be
proportional to a high power of . As in the case of polar modes,
viscosity will again presumably enforce stability except for hot, rapidly
rotating neutron stars. This work complements Andersson's numerical
investigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of
timescales is corrected and update
R-Modes in Superfluid Neutron Stars
The analogs of r-modes in superfluid neutron stars are studied here. These
modes, which are governed primarily by the Coriolis force, are identical to
their ordinary-fluid counterparts at the lowest order in the small
angular-velocity expansion used here. The equations that determine the next
order terms are derived and solved numerically for fairly realistic superfluid
neutron-star models. The damping of these modes by superfluid ``mutual
friction'' (which vanishes at the lowest order in this expansion) is found to
have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a
``typical'' superfluid neutron-star model. This time-scale is far too long to
allow mutual friction to suppress the recently discovered gravitational
radiation driven instability in the r-modes. However, the strength of the
mutual friction damping depends very sensitively on the details of the
neutron-star core superfluid. A small fraction of the presently acceptable
range of superfluid models have characteristic mutual friction damping times
that are short enough (i.e. shorter than about 5 s) to suppress the
gravitational radiation driven instability completely.Comment: 15 pages, 8 figure
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