159 research outputs found
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
Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness
General relativity predicts that a rotating body produces a frame-dragging
(or Lense-Thirring) effect: the orbital plane of a test particle in a
non-equatorial orbit precesses about the body's symmetry axis. In this paper we
compute the precession frequencies of circular orbits around rapidly rotating
neutron stars for a variety of masses and equations of state. The precession
frequencies computed are expressed as numerical functions of the orbital
frequency observed at infinity. The post-Newtonian expansion of the exact
precession formula is examined to identify the relative magnitudes of the
precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole
effect and relativistic corrections. The first post-Newtonian correction to the
Newtonian quadrupole precession is derived in the limit of slow rotation. We
show that the post-Newtonian precession formula is a good approximation to the
exact precession close to the neutron star in the slow rotation limit (up to
\sim 400 Hz in the present context).
The results are applied to recent RXTE observations of neutron star low-mass
X-ray binaries, which display kHz quasi-periodic oscillations and, within the
framework of beat frequency models, allow the measurement of both the neutron
star spin frequency and the Keplerian frequency of the innermost ring of matter
in the accretion disk around it. For a wide range of realistic equations of
state, we find that the predicted precession frequency of this ring is close to
one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations
seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the
Astrophysical Journa
Quantum Effects in Black Hole Interiors
The Weyl curvature inside a black hole formed in a generic collapse grows,
classically without bound, near to the inner horizon, due to partial absorption
and blueshifting of the radiative tail of the collapse. Using a spherical
model, we examine how this growth is modified by quantum effects of conformally
coupled massless fields.Comment: 13 pages, 1 figure (not included), RevTe
Hydrostatic Expansion and Spin Changes During Type I X-Ray Bursts
We present calculations of the spin-down of a neutron star atmosphere due to
hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and
Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a
factor of two, and (ii) general relativity has a small (5-10%) effect on the
angular momentum conservation law. We rescale our results to different neutron
star masses, rotation rates and equations of state, and present some detailed
rotational profiles. Comparing with recent observations of large frequency
shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if
the atmosphere rotates rigidly is a factor of two to three less than the
observed values. If differential rotation is allowed to persist, we find that
the upper layers of the atmosphere spin down by an amount comparable to the
observed values; however, there is no compelling reason to expect the observed
spin frequency to be that of only the outermost layers. We conclude that
hydrostatic expansion and angular momentum conservation alone cannot account
for the largest frequency shifts observed during Type I bursts.Comment: Submitted to the Astrophysical Journal (13 pages, including 4
figures
Gravitational Radiation Instability in Hot Young Neutron Stars
We show that gravitational radiation drives an instability in hot young
rapidly rotating neutron stars. This instability occurs primarily in the l=2
r-mode and will carry away most of the angular momentum of a rapidly rotating
star by gravitational radiation. On the timescale needed to cool a young
neutron star to about T=10^9 K (about one year) this instability can reduce the
rotation rate of a rapidly rotating star to about 0.076\Omega_K, where \Omega_K
is the Keplerian angular velocity where mass shedding occurs. In older colder
neutron stars this instability is suppressed by viscous effects, allowing older
stars to be spun up by accretion to larger angular velocities.Comment: 4 Pages, 2 Figure
Measuring the neutron star equation of state using X-ray timing
One of the primary science goals of the next generation of hard X-ray timing
instruments is to determine the equation of state of the matter at supranuclear
densities inside neutron stars, by measuring the radius of neutron stars with
different masses to accuracies of a few percent. Three main techniques can be
used to achieve this goal. The first involves waveform modelling. The flux we
observe from a hotspot on the neutron star surface offset from the rotational
pole will be modulated by the star's rotation, giving rise to a pulsation.
Information about mass and radius is encoded into the pulse profile via
relativistic effects, and tight constraints on mass and radius can be obtained.
The second technique involves characterising the spin distribution of accreting
neutron stars. The most rapidly rotating stars provide a very clean constraint,
since the mass-shedding limit is a function of mass and radius. However the
overall spin distribution also provides a guide to the torque mechanisms in
operation and the moment of inertia, both of which can depend sensitively on
dense matter physics. The third technique is to search for quasi-periodic
oscillations in X-ray flux associated with global seismic vibrations of
magnetars (the most highly magnetized neutron stars), triggered by magnetic
explosions. The vibrational frequencies depend on stellar parameters including
the dense matter equation of state. We illustrate how these complementary X-ray
timing techniques can be used to constrain the dense matter equation of state,
and discuss the results that might be expected from a 10m instrument. We
also discuss how the results from such a facility would compare to other
astronomical investigations of neutron star properties. [Modified for arXiv]Comment: To appear in Reviews of Modern Physics as a Colloquium, 23 pages, 9
figure
Fermions Tunnelling from Black Holes
We investigate the tunnelling of spin 1/2 particles through event horizons.
We first apply the tunnelling method to Rindler spacetime and obtain the Unruh
temperature. We then apply fermion tunnelling to a general non-rotating black
hole metric and show that the Hawking temperature is recovered.Comment: 22 pages, v2: added references, v3: fixed minor typos, v4: added a
new section applying fermion tunnelling method to Kruskal-Szekers
coordinates, fixed minor typo, and added references, v5: modified
introduction and conclusion, fixed typo
Atmospheric Effects on Neutron Star Parameter Constraints with NICER
We present an analysis of the effects of uncertainties in the atmosphere
models on the radius, mass, and other neutron star parameter constraints for
the NICER observations of rotation-powered millisecond pulsars. To date, NICER
has applied the X-ray pulse profile modeling technique to two
millisecond-period pulsars: PSR J0030+0451 and the high-mass pulsar PSR
J0740+6620. These studies have commonly assumed a deep-heated fully-ionized
hydrogen atmosphere model, although they have explored the effects of
partial-ionization and helium composition in some cases. Here we extend that
exploration and also include new models with partially ionized carbon
composition, externally heated hydrogen, and an empirical atmospheric beaming
parametrization to explore deviations in the expected anisotropy of the emitted
radiation. None of the studied atmosphere cases have any significant influence
on the inferred radius of PSR J0740+6620, possibly due to its X-ray faintness,
tighter external constraints, and/or viewing geometry. In the case of PSR
J0030+0451 both the composition and ionization state could significantly alter
the inferred radius. However, based on the evidence (prior predictive
probability of the data), partially ionized hydrogen and carbon atmospheres are
disfavored. The difference in the evidence for ionized hydrogen and helium
atmospheres is too small to be decisive for most cases, but the inferred radius
for helium models trends to larger sizes around or above 14-15 km. External
heating or deviations in the beaming that are less than at emission
angles smaller than 60 degrees, on the other hand, have no significant effect
on the inferred radius.Comment: 26 pages, 12 figures (2 of which are figure sets), 3 tables. Accepted
for publication in Ap
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