308 research outputs found
Inferring the neutron star equation of state from binary inspiral waveforms
The properties of neutron star matter above nuclear density are not precisely
known. Gravitational waves emitted from binary neutron stars during their late
stages of inspiral and merger contain imprints of the neutron-star equation of
state. Measuring departures from the point-particle limit of the late inspiral
waveform allows one to measure properties of the equation of state via
gravitational wave observations. This and a companion talk by J. S. Read
reports a comparison of numerical waveforms from simulations of inspiraling
neutron-star binaries, computed for equations of state with varying stiffness.
We calculate the signal strength of the difference between waveforms for
various commissioned and proposed interferometric gravitational wave detectors
and show that observations at frequencies around 1 kHz will be able to measure
a compactness parameter and constrain the possible neutron-star equations of
state.Comment: Talk given at the 12th Marcel Grossman Meeting, Paris, France, 12-18
Jul 200
Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation
A quasi-equilibrium (QE) computational scheme was recently developed in
general relativity to calculate the complete gravitational wavetrain emitted
during the inspiral phase of compact binaries. The QE method exploits the fact
that the the gravitational radiation inspiral timescale is much longer than the
orbital period everywhere outside the ISCO. Here we demonstrate the validity
and advantages of the QE scheme by solving a model problem in relativistic
scalar gravitation theory. By adopting scalar gravitation, we are able to
numerically track without approximation the damping of a simple, quasi-periodic
radiating system (an oscillating spherical matter shell) to final equilibrium,
and then use the exact numerical results to calibrate the QE approximation
method. In particular, we calculate the emitted gravitational wavetrain three
different ways: by integrating the exact coupled dynamical field and matter
equations, by using the scalar-wave monopole approximation formula
(corresponding to the quadrupole formula in general relativity), and by
adopting the QE scheme. We find that the monopole formula works well for weak
field cases, but fails when the fields become even moderately strong. By
contrast, the QE scheme remains quite reliable for moderately strong fields,
and begins to breakdown only for ultra-strong fields. The QE scheme thus
provides a promising technique to construct the complete wavetrain from binary
inspiral outside the ISCO, where the gravitational fields are strong, but where
the computational resources required to follow the system for more than a few
orbits by direct numerical integration of the exact equations are prohibitive.Comment: 15 pages, 14 figure
Regular networks of Luttinger liquids
We consider arrays of Luttinger liquids, where each node is described by a
unitary scattering matrix. In the limit of small electron-electron interaction,
we study the evolution of these scattering matrices as the high-energy single
particle states are gradually integrated out. Interestingly, we obtain the same
renormalization group equations as those derived by Lal, Rao, and Sen, for a
system composed of a single node coupled to several semi-infinite 1D wires. The
main difference between the single node geometry and a regular lattice is that
in the latter case, the single particle spectrum is organized into periodic
energy bands, so that the renormalization procedure has to stop when the last
totally occupied band has been eliminated. We therefore predict a strongly
renormalized Luttinger liquid behavior for generic filling factors, which
should exhibit power-law suppression of the conductivity at low temperatures
E_{F}/(k_{F}a) >
1. Some fully insulating ground-states are expected only for a discrete set of
integer filling factors for the electronic system. A detailed discussion of the
scattering matrix flow and its implication for the low energy band structure is
given on the example of a square lattice.Comment: 16 pages, 7 figure
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
A relativistic formalism for computation of irrotational binary stars in quasi equilibrium states
We present relativistic hydrostatic equations for obtaining irrotational
binary neutron stars in quasi equilibrium states in 3+1 formalism. Equations
derived here are different from those previously given by Bonazzola,
Gourgoulhon, and Marck, and have a simpler and more tractable form for
computation in numerical relativity. We also present hydrostatic equations for
computation of equilibrium irrotational binary stars in first post-Newtonian
order.Comment: 5 pages, corrected eqs.(2.10), (2.11) and (3.1
Models of helically symmetric binary systems
Results from helically symmetric scalar field models and first results from a
convergent helically symmetric binary neutron star code are reported here;
these are models stationary in the rotating frame of a source with constant
angular velocity omega. In the scalar field models and the neutron star code,
helical symmetry leads to a system of mixed elliptic-hyperbolic character. The
scalar field models involve nonlinear terms that mimic nonlinear terms of the
Einstein equation. Convergence is strikingly different for different signs of
each nonlinear term; it is typically insensitive to the iterative method used;
and it improves with an outer boundary in the near zone. In the neutron star
code, one has no control on the sign of the source, and convergence has been
achieved only for an outer boundary less than approximately 1 wavelength from
the source or for a code that imposes helical symmetry only inside a near zone
of that size. The inaccuracy of helically symmetric solutions with appropriate
boundary conditions should be comparable to the inaccuracy of a waveless
formalism that neglects gravitational waves; and the (near zone) solutions we
obtain for waveless and helically symmetric BNS codes with the same boundary
conditions nearly coincide.Comment: 19 pages, 7 figures. Expanded version of article to be published in
Class. Quantum Grav. special issue on Numerical Relativit
Various features of quasiequilibrium sequences of binary neutron stars in general relativity
Quasiequilibrium sequences of binary neutron stars are numerically calculated
in the framework of the Isenberg-Wilson-Mathews (IWM) approximation of general
relativity. The results are presented for both rotation states of synchronized
spins and irrotational motion, the latter being considered as the realistic one
for binary neutron stars just prior to the merger. We assume a polytropic
equation of state and compute several evolutionary sequences of binary systems
composed of different-mass stars as well as identical-mass stars with adiabatic
indices gamma=2.5, 2.25, 2, and 1.8. From our results, we propose as a
conjecture that if the turning point of binding energy (and total angular
momentum) locating the innermost stable circular orbit (ISCO) is found in
Newtonian gravity for some value of the adiabatic index gamma_0, that of the
ADM mass (and total angular momentum) should exist in the IWM approximation of
general relativity for the same value of the adiabatic index.Comment: Text improved, some figures changed or deleted, new table, 38 pages,
31 figures, accepted for publication in Phys. Rev.
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
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.
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