520 research outputs found
Truncated post-Newtonian neutron star model
As a preliminary step towards simulating binary neutron star coalescing
problem, we test a post-Newtonian approach by constructing a single neutron
star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic
equilibrium by the power of , where is the speed of light, and
truncate at the various order. We solve the system using the polytropic
equation of state with index and 3, and show how this
approximation converges together with mass-radius relations. Next, we solve the
Hamiltonian constraint equation with these density profiles as trial functions,
and examine the differences in the final metric. We conclude the second
`post-Newtonian' approximation is close enough to describe general relativistic
single star. The result of this report will be useful for further binary
studies.
(Note to readers) This paper was accepted for publication in Physical Review
D. [access code dsj637]. However, since I was strongly suggested that the
contents of this paper should be included as a section in our group's future
paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in
PRD (Brief Report), but will not appea
Excitation of the odd-parity quasi-normal modes of compact objects
The gravitational radiation generated by a particle in a close unbounded
orbit around a neutron star is computed as a means to study the importance of
the modes of the neutron star. For simplicity, attention is restricted to
odd parity (``axial'') modes which do not couple to the neutron star's fluid
modes. We find that for realistic neutron star models, particles in unbounded
orbits only weakly excite the modes; we conjecture that this is also the
case for astrophysically interesting sources of neutron star perturbations. We
also find that for cases in which there is significant excitation of quadrupole
modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.
Simulation of merging binary neutron stars in full general relativity: case
We have performed 3D numerical simulations for merger of equal mass binary
neutron stars in full general relativity. We adopt a -law equation of
state in the form where P, , \varep and
are the pressure, rest mass density, specific internal energy, and the
adiabatic constant with . As initial conditions, we adopt models of
corotational and irrotational binary neutron stars in a quasi-equilibrium state
which are obtained using the conformal flatness approximation for the three
geometry as well as an assumption that a helicoidal Killing vector exists. In
this paper, we pay particular attention to the final product of the
coalescence. We find that the final product depends sensitively on the initial
compactness parameter of the neutron stars : In a merger between sufficiently
compact neutron stars, a black hole is formed in a dynamical timescale. As the
compactness is decreased, the formation timescale becomes longer and longer. It
is also found that a differentially rotating massive neutron star is formed
instead of a black hole for less compact binary cases, in which the rest mass
of each star is less than 70-80% of the maximum allowed mass of a spherical
star. In the case of black hole formation, we roughly evaluate the mass of the
disk around the black hole. For the merger of corotational binaries, a disk of
mass may be formed, where M_* is the total rest mass of the
system. On the other hand, for the merger of irrotational binaries, the disk
mass appears to be very small : < 0.01M_*.Comment: 27 pages, to appear in Phys. Rev.
Gravitational waves from a test particle scattered by a neutron star: Axial mode case
Using a metric perturbation method, we study gravitational waves from a test
particle scattered by a spherically symmetric relativistic star. We calculate
the energy spectrum and the waveform of gravitational waves for axial modes.
Since metric perturbations in axial modes do not couple to the matter fluid of
the star, emitted waves for a normal neutron star show only one peak in the
spectrum, which corresponds to the orbital frequency at the turning point,
where the gravitational field is strongest. However, for an ultracompact star
(the radius ), another type of resonant periodic peak appears in
the spectrum. This is just because of an excitation by a scattered particle of
axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This
excitation comes from the existence of the potential minimum inside of a star.
We also find for an ultracompact star many small periodic peaks at the
frequency region beyond the maximum of the potential, which would be due to a
resonance of two waves reflected by two potential barriers (Regge-Wheeler type
and one at the center of the star). Such resonant peaks appear neither for a
normal neutron star nor for a Schwarzschild black hole. Consequently, even if
we analyze the energy spectrum of gravitational waves only for axial modes, it
would be possible to distinguish between an ultracompact star and a normal
neutron star (or a Schwarzschild black hole).Comment: 21 pages, revtex, 11 figures are attached with eps files Accepted to
Phys. Rev.
The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity
We study the dynamical stability against bar-mode deformation of rapidly
spinning neutron stars with differential rotation. We perform fully
relativistic 3D simulations of compact stars with , where is
the total gravitational mass and the equatorial circumferential radius. We
adopt an adiabatic equation of state with adiabatic index . As in
Newtonian theory, we find that stars above a critical value of (where is the rotational kinetic energy and the gravitational
binding energy) are dynamically unstable to bar formation. For our adopted
choices of stellar compaction and rotation profile, the critical value of
is , only slightly smaller than the
well-known Newtonian value for incompressible Maclaurin spheroids.
The critical value depends only very weakly on the degree of differential
rotation for the moderate range we surveyed. All unstable stars form bars on a
dynamical timescale. Models with sufficiently large subsequently form
spiral arms and eject mass, driving the remnant to a dynamically stable state.
Models with moderately large do not develop spiral
arms or eject mass but adjust to form dynamically stable ellipsoidal-like
configurations. If the bar-mode instability is triggered in supernovae collapse
or binary neutron star mergers, it could be a strong and observable source of
gravitational waves. We determine characteristic wave amplitudes and
frequencies.Comment: 17 pages, accepted for publication in AP
Matter flows around black holes and gravitational radiation
We develop and calibrate a new method for estimating the gravitational
radiation emitted by complex motions of matter sources in the vicinity of black
holes. We compute numerically the linearized curvature perturbations induced by
matter fields evolving in fixed black hole backgrounds, whose evolution we
obtain using the equations of relativistic hydrodynamics. The current
implementation of the proposal concerns non-rotating holes and axisymmetric
hydrodynamical motions. As first applications we study i) dust shells falling
onto the black hole isotropically from finite distance, ii) initially spherical
layers of material falling onto a moving black hole, and iii) anisotropic
collapse of shells. We focus on the dependence of the total gravitational wave
energy emission on the flow parameters, in particular shell thickness, velocity
and degree of anisotropy. The gradual excitation of the black hole quasi-normal
mode frequency by sufficiently compact shells is demonstrated and discussed. A
new prescription for generating physically reasonable initial data is
discussed, along with a range of technical issues relevant to numerical
relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to
Phys. Rev.
Scattering of particles by neutron stars: Time-evolutions for axial perturbations
The excitation of the axial quasi-normal modes of a relativistic star by
scattered particles is studied by evolving the time dependent perturbation
equations. This work is the first step towards the understanding of more
complicated perturbative processes, like the capture or the scattering of
particles by rotating stars. In addition, it may serve as a test for the
results of the full nonlinear evolution of binary systems.Comment: 7 pages, 5 figures, Phys. Rev. D in pres
- âŠ