57 research outputs found
Quasi-normal modes of rotating relativistic stars - neutral modes for realistic equations of state
We compute zero-frequency (neutral) quasi-normal f-modes of fully
relativistic and rapidly rotating neutron stars, using several realistic
equations of state (EOSs) for neutron star matter. The zero-frequency modes
signal the onset of the gravitational radiation-driven instability. We find
that the l=m=2 (bar) f-mode is unstable for stars with gravitational mass as
low as 1.0 - 1.2 M_\odot, depending on the EOS. For 1.4 M_\odot neutron stars,
the bar mode becomes unstable at 83 % - 93 % of the maximum allowed rotation
rate. For a wide range of EOSs, the bar mode becomes unstable at a ratio of
rotational to gravitational energies T/W \sim 0.07-0.09 for 1.4 M_\odot stars
and T/W \sim 0.06 for maximum mass stars. This is to be contrasted with the
Newtonian value of T/W \sim 0.14. We construct the following empirical formula
for the critical value of T/W for the bar mode,
(T/W)_2 = 0.115 - 0.048 M / M_{max}^{sph}, which is insensitive to the EOS to
within 4 - 6 %. This formula yields an estimate for the neutral mode sequence
of the bar mode as a function only of the star's mass, M, given the maximum
allowed mass, M_{max}^{sph}, of a nonrotating neutron star. The recent
discovery of the fast millisecond pulsar in the supernova remnant N157B,
supports the suggestion that a fraction of proto-neutron stars are born in a
supernova collapse with very large initial angular momentum. Thus, in a
fraction of newly born neutron stars the instability is a promising source of
continuous gravitational waves. It could also play a major role in the
rotational evolution (through the emission of angular momentum) of merged
binary neutron stars, if their post-merger angular momentum exceeds the maximum
allowed to form a Kerr black hole.Comment: 12 pages, 5 figures, submitted to Ap
The Oblate Schwarzschild Approximation for Light Curves of Rapidly Rotating Neutron Stars
We present a simple method for including the oblateness of a rapidly rotating
neutron star when fitting X-ray light curves. In previous work we showed that
the oblateness induced by rotation at frequencies above 300 Hz produces a
geometric effect which needs to be accounted for when modelling light curves to
extract constraints on the neutron star's mass and radius. In our model X-rays
are emitted from the surface of an oblate neutron star and propagate to the
observer along geodesics of the Schwarzschild metric for a spherical neutron
star. Doppler effects due to rotation are added in the same manner as in the
case of a spherical neutron star. We show that this model captures the most
important effects due to the neutron star's rotation. We also explain how the
geometric oblateness effect can rival the Doppler effect for some emission
geometries.Comment: 8 pages, 4 figures. v2: minor changes. Accepted by the Astrophysical
Journa
Measuring Neutron Star Radii via Pulse Profile Modeling with NICER
The Neutron-star Interior Composition Explorer (NICER) is an X-ray
astrophysics payload that will be placed on the International Space Station.
Its primary science goal is to measure with high accuracy the pulse profiles
that arise from the non-uniform thermal surface emission of rotation-powered
pulsars. Modeling general relativistic effects on the profiles will lead to
measuring the radii of these neutron stars and to constraining their equation
of state. Achieving this goal will depend, among other things, on accurate
knowledge of the source, sky, and instrument backgrounds. We use here simple
analytic estimates to quantify the level at which these backgrounds need to be
known in order for the upcoming measurements to provide significant constraints
on the properties of neutron stars. We show that, even in the
minimal-information scenario, knowledge of the background at a few percent
level for a background-to-source countrate ratio of 0.2 allows for a
measurement of the neutron star compactness to better than 10% uncertainty for
most of the parameter space. These constraints improve further when more
realistic assumptions are made about the neutron star emission and spin, and
when additional information about the source itself, such as its mass or
distance, are incorporated.Comment: Submitted to Ap
Light Curves for Rapidly-Rotating Neutron Stars
We present raytracing computations for light emitted from the surface of a
rapidly-rotating neutron star in order to construct light curves for X-ray
pulsars and bursters. These calculations are for realistic models of
rapidly-rotating neutron stars which take into account both the correct
exterior metric and the oblate shape of the star. We find that the most
important effect arising from rotation comes from the oblate shape of the
rotating star. We find that approximating a rotating neutron star as a sphere
introduces serious errors in fitted values of the star's radius and mass if the
rotation rate is very large. However, in most cases acceptable fits to the
ratio M/R can be obtained with the spherical approximation.Comment: Accepted by the Astrophysical Journal. 13 pages & 7 figure
Correlations in the QPO Frequencies of Low Mass X-Ray Binaries and the Relativistic Precession Model
A remarkable correlation between the centroid frequencies of quasi periodic
oscillations, QPOs, (or peaked noise components) from low mass X-ray binaries,
has been recently discovered by Psaltis, Belloni and van der Klis (1999). This
correlation extends over nearly 3 decades in frequency and encompasses both
neutron star and black hole candidate systems. We discuss this result in the
light of the relativistic precession model, which has been proposed to
interpret the kHz QPOs as well as some of the lower frequency QPOs of neutron
star low mass X-ray binaries of the Atoll and Z classes. Unlike other models
the relativistic precession model does not require the compact object to be a
neutron star and can be applied to black hole candidates as well. We show that
the predictions of the relativistic precession model match both the value and
dependence of the correlation to a very good accuracy without resorting to
additional assumptions.Comment: To appear in ApJ Letters. AASTEX Latex v. 5.0, 1 figure not include
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
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