摘要：We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such hypermassive models in full general relativity and show that there do exist configurations that are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.

摘要：Rapidly spinning neutron stars, with angular Velocity higher than a given threshold, may become secularly unstable to an I = m = 2 mode and deform into a bar configuration. This instability sets in only in the presence of a suitable dissipative mechanism, such as viscosity or gravitational wave emission, and in Newtonian theory its point of onset does not depend on the nature of dissipation. The first numerical investigations, however, seem to suggest that, in general relativity, the instability is weakened when driven by viscous dissipation and strengthened when driven by gravitational radiation. After a review of the physical problem and of previous investigations, we schematically present an analytic treatment carried out in the framework of post-Newtonian (PN) gravitation. In this analysis, we model rotating stars by homogeneous, rigidly rotating, triaxial ellipsoids employing an energy Variational principle to construct relativistic equilibrium sequences and locate the point of onset of the bar mode instability along each sequence. The spacetime metric is obtained by solving Einstein's equations of general relativity in 3+1 ADM form, and we focus on the viscosity-driven instability. We find that the value of the eccentricity, as well as related ratios like Ohm (2)/(pi rho0) and T/\W\ (= rotational kinetic energy/gravitational potential energy), all increase at the onset of instability as the star becomes more relativistic. Since higher degrees of rotation are required to trigger a viscosity-driven bar mode instability as the star becomes more compact, the effect of general relativity is to weaken the instability even to PN order.

摘要：Hydrodynamic simulations of the merger of stellar mass black hole-neutron star binaries are compared with mergers of binary neutron stars. The simulations are Newtonian but take into account the emission and back-reaction of gravitational waves. The use of a physical nuclear equation of state allows us to include the effects of neutrino emission. For low neutron star-to-black hale mass ratios, the neutron star transfers mass to the black hole during a few cycles of orbital decay and subsequent widening before finally being disrupted, whereas for ratios near unity the neutron star is destroyed during its first approach. A gas mass between similar to 0.3 and similar to 0.7 M. is left in an accretion torus around the black hole and radiates neutrinos at a luminosity of several times 10(53) ergs s(-1) during an estimated accretion timescale of about 0.1 a. The emitted neutrinos and antineutrinos annihilate into e(+/-) pairs with efficiencies of 1%-3% and rates of up to similar to 2 x 10(52) ergs s(-1), thus depositing an energy E-nu<(nu)over bar> less than or similar to 10(51) ergs above the poles of the black hole in a region that contains less than 10(-5) M. of baryonic matter. This could allow for relativistic expansion with Lorentz factors around 100 and is sufficient to explain apparent burst luminosities L-gamma similar to E-nu<(nu)over bar>(f(Omega)t(gamma)) up to several times 10(53) ergs s(-1) for burst durations t(gamma) approximate to 0.1-1 s, if the gamma emission is collimated in two moderately focused jets in a fraction f(Omega) = 2 delta Omega/(4 pi) approximate to (1/100)-(1/10) of the sky.

摘要：We include matter sources in Einstein's held equations and show that our recently proposed 3 + 1 evolution scheme can stably evolve strong-field solutions. We insert in our code known matter solutions, namely the Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder solution for homogeneous dust sphere collapse to a black hole, and evolve the gravitational field equations. We fmd that we ran evolve stably static, strong-field stars for arbitrarily long times and can follow dust sphere collapse accurately well past black hale formation. These tests are useful diagnostics for fully self-consistent, stable hydrodynamical simulations in 3 + 1 general relativity. Moreover, they suggest a successive approximation scheme for determining gravitational waveforms from strong-field sources dominated by longitudinal fields, such as binary neutron stars: approximate quasi-equilibrium models can serve as sources for the transverse field equations, which can be evolved without having to re-solve the hydrodynamical equations (hydro without hydro). [S0556-2821(99)03118-5].

摘要：In a coalescing neutron star-neutron star or neutron star-black hole binary, oscillation modes of the neutron star can be resonantly excited by the companion during the final minutes of the binary inspiral, when the orbital frequency sweeps up from a few Hz to a few thousand Hz. The resulting resonant energy transfer between the orbit and the neutron star speeds up or slows down the inspiral, depending on whether the resonant mode has positive or negative energy, and induces a phase change in the emitted gravitational waves from the binary. While only g-modes can be excited for a non-rotating neutron star, f-modes and r-modes can also be excited when the neutron star is spinning. A tidal resonance, designated by the index (jk, m) ({jk} specifies the angular order of the mode, as in the spherical harmonic Y-jk), occurs when the mode frequency equals m times the orbital frequency. For the f-mode resonance to occur before coalescence, the neutron star must have rapid rotation, with spin frequency v(s) greater than or similar to 710Hz for the (22,2)-resonance and v(s) greater than or similar to 570Hz for the (33,3)-resonance (assuming canonical neutron star mass, M = 1.4M., and radius, R = 10km; however, for R = 15 km, these critical spin frequencies become 330 and 260 Hz, respectively). Although current observations suggest that such high rotation rates may be unlikely for coalescing binary neutron stars, these rates are physically allowed. Because of their strong tidal coupling, the f-mode resonances induce a large change in the number of orbital cycles of coalescence, Delta N-orb with the maximum hN(orb) similar to 10-1000 for the (22,2)-resonance and Delta N-orb b similar to 1 for the (33,3)-resonance. Such f-mode resonant effects, if present, must be included in constructing the templates of waveforms used in searching for gravitational wave signals. Higher order f-mode resonances can occur at slower rotation rates, but the induced orbital change is much smaller (Delta N-orb less than or similar to 0.1) For the dominant g-mode (22,2)-resonance, even modest rotation (v(s) less than or similar to 100 Hz) can enhance the resonant effect on the orbit by shifting the resonance to a smaller orbital frequency. However, because of the weak coupling between the g-mode and the tidal potential, Delta N-orb lies in the range 10(-3)-10(-2) (depending strongly on the neutron star equation of state) and is probably negligible for the purpose of detecting gravitational waves. Resonant excitations of r-modes require misaligned spin-orbit inclinations, and the dominant resonances correspond to octopolar excitations of the j = k = 2 mode, with (jk, m)=(22, 3) and (22,1). Since the tidal coupling of the r-mode depends strongly on rotation rate, Delta N-orb less than or similar to 10(-2)(R/10km)(10)(M/1.4M.)(-20/3) is negligible for canonical neutron star parameters, but can be appreciable if the neutron star radius is larger.

摘要：Using optimal matched filtering, we search 25 hours of data from the LIGO 40-m prototype laser interferometric gravitational-wave detector for gravitational-wave chirps emitted by coalescing binary systems within our Galaxy. This is the first test of this filtering technique on real interferometric data. An upper limit on the rate R of neutron star binary inspirals in our Galaxy is obtained: with 90% confidence, R < 0.5 h(-1). Similar experiments with LIGO interferometers will provide constraints on the population of tight binary neutron star systems in the Universe.

摘要：Coalescing compact binaries with neutron star or black hole components provide the most promising sources of gravitational radiation for detection by the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact has motivated several different theoretical studies of the inspiral and hydrodynamic merging of compact binaries. Analytic analyses of the inspiral waveforms have been performed in the post-Newtonian approximation. Analytic and numerical treatments of the coalescence waveforms from binary neutron stars have been performed using Newtonian hydrodynamics and the quadrupole radiation approximation. Numerical simulations of coalescing black hole and neutron star binaries are also underway in full general relativity. Recent results from each of these approaches will be described and their virtues and Limitations summarized.

摘要：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 I = m = 2 (bar) f-mode is unstable for stars with gravitational mass as low as 1.0-1.2 M-., depending on the EOS. For 1.4 M-. 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 similar to 0.07-0.09 for 1.4 M-. stars, and T/W similar to 0.06 for maximum mass stars. This is to be contrasted with the Newtonian value of TIW similar to 0.14. We construct the following empirical formula for the critical value of T/W for the bar mode, (T/W)(2) =0.115 - 0.048M/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. If some neutron stars are born in an accretion-induced collapse of a white dwarf, then they will also have very large angular momentum at birth. 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 postmerger angular momentum exceeds the maximum allowed to form a Kerr black hole.

摘要：Hydrodynamic simulations were performed of the dynamical phase of the merging of binary neutron stars (NS-NS) and of neutron star black hole binaries (NS-BH), using a physical nuclear equation of state (Lattimer & Swesty, 1991) and taking into account the emission of gravitational waves and neutrinos.

摘要：Hydrodynamic simulations were performed of the dynamical phase of the merging of binary neutron stars (NS+NS) and of neutron star black hole binaries (NS+BH), using a physical nuclear equation of state (Lattimer & Swesty 1991) and taking into account the emission of gravitational waves and neutrinos.