606 research outputs found
Numerical approach for high precision 3-D relativistic star models
A multi-domain spectral method for computing very high precision 3-D stellar
models is presented. The boundary of each domain is chosen in order to coincide
with a physical discontinuity (e.g. the star's surface). In addition, a
regularization procedure is introduced to deal with the infinite derivatives on
the boundary that may appear in the density field when stiff equations of state
are used. Consequently all the physical fields are smooth functions on each
domain and the spectral method is absolutely free of any Gibbs phenomenon,
which yields to a very high precision. The power of this method is demonstrated
by direct comparison with analytical solutions such as MacLaurin spheroids and
Roche ellipsoids. The relative numerical error reveals to be of the order of
. This approach has been developed for the study of relativistic
inspiralling binaries. It may be applied to a wider class of astrophysical
problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres
Inertial modes in slowly rotating stars : an evolutionary description
We present a new hydro code based on spectral methods using spherical
coordinates. The first version of this code aims at studying time evolution of
inertial modes in slowly rotating neutron stars. In this article, we introduce
the anelastic approximation, developed in atmospheric physics, using the mass
conservation equation to discard acoustic waves. We describe our algorithms and
some tests of the linear version of the code, and also some preliminary linear
results. We show, in the Newtonian framework with differentially rotating
background, as in the relativistic case with the strong Cowling approximation,
that the main part of the velocity quickly concentrates near the equator of the
star. Thus, our time evolution approach gives results analogous to those
obtained by Karino {\it et al.} \cite{karino01} within a calculation of
eigenvectors. Furthermore, in agreement with the work of Lockitch {\it et al.}
\cite{lockandf01}, we found that the velocity seems to always get a
non-vanishing polar part.Comment: 36 pages, 27 figures, accepted for publication in Phys. Rev. D
(discussion added in the introduction
Directionality effects in the transfer of X-rays from a magnetized atmosphere: Beam pulse shape
A formalism is presented for radiation transfer in two normal polarization modes in finite and semiinfinite plane parallel uniform atmospheres with a magnetic field perpendicular to the surface and arbitrary propagation angles. This method is based on the coupled integral equations of transfer, including emission, absorption, and scattering. Calculations are performed for atmosphere parameters typical of X-ray pulsars. The directionality of the escaping radiation is investigated for several cases, varying the input distributions. Theoretical pencil beam profiles and X-ray pulse shapes are obtained assuming the radiation is emitted from the polar caps of spinning neutron stars. Implications for realistic models of accreting magnetized X-ray sources are briefly discussed
An improved, "phase-relaxed" F-statistic for gravitational-wave data analysis
Rapidly rotating, slightly non-axisymmetric neutron stars emit nearly
periodic gravitational waves (GWs), quite possibly at levels detectable by
ground-based GW interferometers. We refer to these sources as "GW pulsars". For
any given sky position and frequency evolution, the F-statistic is the optimal
(frequentist) statistic for the detection of GW pulsars. However, in "all-sky"
searches for previously unknown GW pulsars, it would be computationally
intractable to calculate the (fully coherent) F-statistic at every point of a
(suitably fine) grid covering the parameter space: the number of gridpoints is
many orders of magnitude too large for that. Here we introduce a
"phase-relaxed" F-statistic, which we denote F_pr, for incoherently combining
the results of fully coherent searches over short time intervals. We estimate
(very roughly) that for realistic searches, our F_pr is ~10-15% more sensitive
than the "semi-coherent" F-statistic that is currently used. Moreover, as a
byproduct of computing F_pr, one obtains a rough determination of the
time-evolving phase offset between one's template and the true signal imbedded
in the detector noise. Almost all the ingredients that go into calculating F_pr
are already implemented in LAL, so we expect that relatively little additional
effort would be required to develop a search code that uses F_pr.Comment: 8 pages, 4 figures, submitted to PR
MHD of rotating compact stars with spectral methods: description of the algorithm and tests
A flexible spectral code for the study of general relativistic
magnetohydrodynamics is presented. Aiming at investigating the physics of
slowly rotating magnetized compact stars, this new code makes use of various
physically motivated approximations. Among them, the relativistic anelastic
approximation is a key ingredient of the current version of the code. In this
article, we mainly outline the method, putting emphasis on algorithmic
techniques that enable to benefit as much as possible of the non-dissipative
character of spectral methods, showing also a potential astrophysical
application and providing a few illustrative tests.Comment: 15 pages, 4 figures (new figure added, misprints corrected) Article
accepted for publication in a special issue of Classical and Quantum Gravity
"New Frontiers in Numerical Relativity
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