379 research outputs found
Numerical models of irrotational binary neutron stars in general relativity
We report on general relativistic calculations of quasiequilibrium
configurations of binary neutron stars in circular orbits with zero vorticity.
These configurations are expected to represent realistic situations as opposed
to corotating configurations. The Einstein equations are solved under the
assumption of a conformally flat spatial 3-metric (Wilson-Mathews
approximation). The velocity field inside the stars is computed by solving an
elliptical equation for the velocity scalar potential. Results are presented
for sequences of constant baryon number (evolutionary sequences). Although the
central density decreases much less with the binary separation than in the
corotating case, it still decreases. Thus, no tendency is found for the stars
to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett.
in pres
Binary black holes in circular orbits. II. Numerical methods and first results
We present the first results from a new method for computing spacetimes
representing corotating binary black holes in circular orbits. The method is
based on the assumption of exact equilibrium. It uses the standard 3+1
decomposition of Einstein equations and conformal flatness approximation for
the 3-metric. Contrary to previous numerical approaches to this problem, we do
not solve only the constraint equations but rather a set of five equations for
the lapse function, the conformal factor and the shift vector. The orbital
velocity is unambiguously determined by imposing that, at infinity, the metric
behaves like the Schwarzschild one, a requirement which is equivalent to the
virial theorem. The numerical scheme has been implemented using multi-domain
spectral methods and passed numerous tests. A sequence of corotating black
holes of equal mass is calculated. Defining the sequence by requiring that the
ADM mass decrease is equal to the angular momentum decrease multiplied by the
orbital angular velocity, it is found that the area of the apparent horizons is
constant along the sequence. We also find a turning point in the ADM mass and
angular momentum curves, which may be interpreted as an innermost stable
circular orbit (ISCO). The values of the global quantities at the ISCO,
especially the orbital velocity, are in much better agreement with those from
third post-Newtonian calculations than with those resulting from previous
numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the
regularization procedure for the shift vector, new section devoted to the
check of the momentum constraint, references added + minor corrections,
accepted for publication in Phys. Rev.
Relativistic stars with purely toroidal magnetic fields
We investigate the effects of the purely toroidal magnetic field on the
equilibrium structures of the relativistic stars. The master equations for
obtaining equilibrium solutions of relativistic rotating stars containing
purely toroidal magnetic fields are derived for the first time. To solve these
master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for
calculating relativistic rotating stars containing no magnetic field to
incorporate the effects of the purely toroidal magnetic fields. By using the
numerical scheme, we then calculate a large number of the equilibrium
configurations for a particular distribution of the magnetic field in order to
explore the equilibrium properties. We also construct the equilibrium sequences
of the constant baryon mass and/or the constant magnetic flux, which model the
evolution of an isolated neutron star as it loses angular momentum via the
gravitational waves. Important properties of the equilibrium configurations of
the magnetized stars obtained in this study are summarized as follows ; (1) For
the non-rotating stars, the matter distribution of the stars is prolately
distorted due to the toroidal magnetic fields. (2) For the rapidly rotating
stars, the shape of the stellar surface becomes oblate because of the
centrifugal force. But, the matter distribution deep inside the star is
sufficiently prolate for the mean matter distribution of the star to be
prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of
the stars at the lower angular velocity. (4) For some equilibrium sequences of
the constant baryon mass and magnetic flux, the stars can spin up as they lose
angular momentum.Comment: 13 figures, 7 tables, submitted to PR
Equilibrium sequences of irrotational binary polytropic stars : The case of double polytropic stars
Solutions to equilibrium sequences of irrotational binary polytropic stars in
Newtonian gravity are expanded in a power of , where R and
are the orbital separation of the binary system and the radius of each
star for . For each order of , we should solve ordinary
differential equations for arbitrary polytropic indices n. We show solutions
for polytropic indices n= 0.5, 1, 1.5 and 2 up to orders. Our
semi-analytic solutions can be used to check the validity of numerical
solutions.Comment: 59 pages including 15 tables and 13 figures, revtex, accepted to
Phys. Rev.
Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
We present a numerical method to compute quasiequilibrium configurations of
close binary neutron stars in the pre-coalescing stage. A hydrodynamical
treatment is performed under the assumption that the flow is either rigidly
rotating or irrotational. The latter state is technically more complicated to
treat than the former one (synchronized binary), but is expected to represent
fairly well the late evolutionary stages of a binary neutron star system. As
regards the gravitational field, an approximation of general relativity is
used, which amounts to solving five of the ten Einstein equations (conformally
flat spatial metric). The obtained system of partial differential equations is
solved by means of a multi-domain spectral method. Two spherical coordinate
systems are introduced, one centered on each star; this results in a precise
description of the stellar interiors. Thanks to the multi-domain approach, this
high precision is extended to the strong field regions. The computational
domain covers the whole space so that exact boundary conditions are set to
infinity. Extensive tests of the numerical code are performed, including
comparisons with recent analytical solutions. Finally a constant baryon number
sequence (evolutionary sequence) is presented in details for a polytropic
equation of state with gamma=2.Comment: Minor corrections, references updated, 42 pages, 25 PostScript
figures, accepted for publication in Phys. Rev.
Equilibrium Configurations of Strongly Magnetized Neutron Stars with Realistic Equations of State
We investigate equilibrium sequences of magnetized rotating stars with four
kinds of realistic equations of state (EOSs) of SLy (Douchin et al.), FPS
(Pandharipande et al.), Shen (Shen et al.), and LS (Lattimer & Swesty).
Employing the Tomimura-Eriguchi scheme to construct the equilibrium
configurations. we study the basic physical properties of the sequences in the
framework of Newton gravity. In addition we newly take into account a general
relativistic effect to the magnetized rotating configurations. With these
computations, we find that the properties of the Newtonian magnetized stars,
e.g., structure of magnetic field, highly depends on the EOSs.
The toroidal magnetic fields concentrate rather near the surface for Shen and
LS EOSs than those for SLy and FPS EOSs. The poloidal fields are also affected
by the toroidal configurations. Paying attention to the stiffness of the EOSs,
we analyze this tendency in detail. In the general relativistic stars, we find
that the difference due to the EOSs becomes small because all the employed EOSs
become sufficiently stiff for the large maximum density, typically greater than
. The maximum baryon mass of the magnetized stars
with axis ratio increases about up to twenty percents for that of
spherical stars. We furthermore compute equilibrium sequences at finite
temperature, which should serve as an initial condition for the hydrodynamic
study of newly-born magnetars. Our results suggest that we may obtain
information about the EOSs from the observation of the masses of magnetars.Comment: submitted to MNRA
Analytical theory for the initial mass function: CO clumps and prestellar cores
We derive an analytical theory of the prestellar core initial mass function
based on an extension of the Press-Schechter statistical formalism. With the
same formalism, we also obtain the mass spectrum for the non self-gravitating
clumps produced in supersonic flows. The mass spectrum of the self-gravitating
cores reproduces very well the observed initial mass function and identifies
the different mechanisms responsible for its behaviour. The theory predicts
that the shape of the IMF results from two competing contributions, namely a
power-law at large scales and an exponential cut-off (lognormal form) centered
around the characteristic mass for gravitational collapse. The cut-off exists
already in the case of pure thermal collapse, provided that the underlying
density field has a lognormal distribution. Whereas pure thermal collapse
produces a power-law tail steeper than the Salpeter value, dN/dlog M\propto
M^{-x}, with x=1.35, this latter is recovered exactly for the (3D) value of the
spectral index of the velocity power spectrum, n\simeq 3.8, found in
observations and in numerical simulations of isothermal supersonic turbulence.
Indeed, the theory predicts that x=(n+1)/(2n-4) for self-gravitating structures
and x=2-n'/3 for non self-gravitating structures, where n' is the power
spectrum index of log(rho). We show that, whereas supersonic turbulence
promotes the formation of both massive stars and brown dwarfs, it has an
overall negative impact on star formation, decreasing the star formation
efficiency. This theory provides a novel theoretical foundation to understand
the origin of the IMF and to infer its behaviour in different environments. It
also provides a complementary approach and useful guidance to numerical
simulations exploring star formation, while making testable predictions.Comment: To appear in Ap
Effects of Strong Magnetic Fields on Neutron Star Structure
We study static neutron stars with poloidal magnetic fields and a simple
class of electric current distributions consistent with the requirement of
stationarity. For this class of electric current distributions, we find that
magnetic fields are too large for static configurations to exist when the
magnetic force pushes a sufficient amount of mass off-center that the
gravitational force points outward near the origin in the equatorial plane. (In
our coordinates an outward gravitational force corresponds to , where and are respectively time and radial
coordinates and is coefficient of in the line element.) For the
equations of state (EOSs) employed in previous work, we obtain configurations
of higher mass than had been reported; we also present results with more recent
EOSs. For all EOSs studied, we find that the maximum mass among these static
configurations with magnetic fields is noticeably larger than the maximum mass
attainable by uniform rotation, and that for fixed values of baryon number the
maximum mass configurations are all characterized by an off-center density
maximum.Comment: Submitted to the Astrophysical Journal. 37 pages, 8 figures, uses
aastex macro
Gravitational waves from inspiralling compact binaries with magnetic dipole moments
We investigate the effects of the magnetic dipole-dipole coupling and the
electromagnetic radiation on the frequency evolution of gravitational waves
from inspiralling binary neutron stars with magnetic dipole moments. This study
is motivated by the discovery of the superstrongly magnetized neutron stars,
i.e., magnetar. We derive the contributions of the magnetic fields to the
accumulated cycles in gravitational waves as , where denotes the strength of the polar magnetic
fields of each neutron star in the binary system. It is found that the effects
of the magnetic fields will be negligible for the detection and the parameter
estimation of gravitational waves, if the upper limit for magnetic fields of
neutron stars are less than G, which is the maximum magnetic
field observed in the soft gamma repeaters and the anomalous X-ray pulsars up
to date. We also discuss the implications of electromagnetic radiation from the
inspiralling binary neutron stars for the precursory X-ray emission prior to
the gamma ray burst observed by the Ginga satellite.Comment: 15 pages, no figures, accepted for publication in Ap
Structure, Deformations and Gravitational Wave Emission of Magnetars
Neutron stars can have, in some phases of their life, extremely strong
magnetic fields, up to 10^15-10^16 G. These objects, named magnetars, could be
powerful sources of gravitational waves, since their magnetic field could
determine large deformations. We discuss the structure of the magnetic field of
magnetars, and the deformation induced by this field. Finally, we discuss the
perspective of detection of the gravitational waves emitted by these stars.Comment: 11 pages, 2 figures, prepared for 19th International Conference on
General Relativity and Gravitation (GR19), Mexico City, Mexico, July 5-9,
201
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