Binary Neutron Stars in General Relativity: Quasiequilibrium Models (original) (raw)
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General relativistic models of binary neutron stars in quasiequilibrium
Physical Review D, 1998
We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit (ISCO) and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft >= 1.5. A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.
Binary Neutron Stars in Quasi-Equilibrium Circular Orbit: A Fully Relativistic Treatment
1997
We present a numerical scheme that solves the initial value problem in full general relativity for a binary neutron star in quasi-equilibrium. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can adopt a quasi-equilibrium approximation. In this approximation, we integrate a subset of the Einstein equations coupled to the equations of relativistic hydrodynamics to solve the initial value problem for binaries of arbitrary separation, down to the innermost stable orbit.
Numerical Models of Irrotational Binary Neutron Stars in General Relativity
Physical Review Letters, 1999
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.
Post-Newtonian models of binary neutron stars
Physical Review D, 1997
Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc 2. We find that, for a given GM/Rc 2 , the innermost stable circular orbit along an irrotational
Physical Review D, 2001
We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity. The solving method is a multi-domain spectral method which we have recently developed. An improvement is introduced here for accurate computations of binary systems with stiff equation of state (γ > 2). The computations are performed for both cases of synchronized and irrotational binary systems with adiabatic indices γ = 3, 2.5, 2.25, 2 and 1.8. It is found that the turning points of total energy along a constant-mass sequence appear only for γ ≥ 1.8 for synchronized binary systems and γ ≥ 2.3 for irrotational ones. In the synchronized case, the equilibrium sequences terminate by the contact between the two stars. On the other hand, for irrotational binaries, it is found that the sequences terminate at a mass shedding limit which corresponds to a detached configuration.
Stability of relativistic neutron stars in binary orbit
Physical Review D, 1998
We analyze the stability of relativistic, quasi-equilibrium binary neutron stars in synchronous circular orbit. We explore stability against radial collapse to black holes prior to merger, and against orbital plunge. We apply theorems based on turning points along uniformly rotating sequences of constant angular momentum and rest mass to locate the onset of secular instabilities. We find that inspiraling binary neutron stars are stable against radial collapse to black holes all the way down to the innermost stable circular orbit.
Physical Review D, 1996
We study how the neutron-star equation of state affects the onset of the dynamical instability in the equations of motion for inspiraling neutron-star binaries near coalescence. A combination of relativistic effects and Newtonian tidal effects cause the stars to begin their final, rapid, and dynamicallyunstable plunge to merger when the stars are still well separated and the orbital frequency is ≈ 500 cycles/sec (i.e. the gravitational wave frequency is approximately 1000 Hz). The orbital frequency at which the dynamical instability occurs (i.e. the orbital frequency at the innermost stable circular orbit) shows modest sensitivity to the neutron-star equation of state (particularly the mass-radius ratio, M/Ro, of the stars). This suggests that information about the equation of state of nuclear matter is encoded in the gravitational waves emitted just prior to the merger.
Impact of the nuclear equation of state on the last orbits of binary neutron stars
Astronomy & Astrophysics, 2005
We present calculations of quasi-equilibrium sequences of irrotational binary neutron stars based on realistic equations of state (EOS) for the whole neutron star interior. Three realistic nuclear EOSs of various softness and based on different microscopic models have been joined with a recent realistic EOS of the crust, giving in this way three different EOSs of a neutron-star interior. Computations of quasi-equilibrium sequences are performed within the Isenberg-Wilson-Mathews approximation to general relativity. For all evolutionary sequences, the innermost stable circular orbit (ISCO) is found to be given by mass-shedding limit (Roche lobe overflow). The EOS dependence on the last orbits is found to be quite important: for two 1.35 M neutron stars, the gravitational wave frequency at the ISCO (which marks the end of the inspiral phase) ranges from 800 Hz to 1200 Hz, depending upon the EOS. Detailed comparisons with 3rd order post-Newtonian results for point-mass binaries reveals a very good agreement until hydrodynamical effects (dominated by high-order functions of frequency) become important, which occurs at a frequency ranging from 500 Hz to 1050 Hz, depending upon the EOS.
Nuclear Physics A, 2012
We formulate the equations of equilibrium of neutron stars taking into account strong, weak, electromagnetic, and gravitational interactions within the framework of general relativity. The nuclear interactions are described by the exchange of the σ, ω, and ρ virtual mesons. The equilibrium conditions are given by our recently developed theoretical framework based on the Einstein-Maxwell-Thomas-Fermi equations along with the constancy of the general relativistic Fermi energies of particles, the "Klein potentials", throughout the configuration. The equations are solved numerically in the case of zero temperatures and for selected parameterizations of the nuclear models. The solutions lead to a new structure of the star: a positively charged core at supranuclear densities surrounded by an electronic distribution of thickness ∼h/(mec) ∼ 10 2h /(mπc) of opposite charge, as well as a neutral crust at lower densities. Inside the core there is a Coulomb potential well of depth ∼ mπc 2 /e. The constancy of the Klein potentials in the transition from the core to the crust, impose the presence of an overcritical electric field ∼ (mπ/me) 2 Ec, the critical field being Ec = m 2 e c 3 /(eh). The electron chemical potential and the density decrease, in the boundary interface, until values µ crust e < µ core e and ρcrust < ρcore. For each central density, an entire family of core-crust interface boundaries and, correspondingly, an entire family of crusts with different mass and thickness, exist. The configuration with ρcrust = ρ drip ∼ 4.3 × 10 11 g/cm 3 separates neutron stars with and without inner crust. We present here the novel neutron star mass-radius for the especial case ρcrust = ρ drip and compare and contrast it with the one obtained from the traditional Tolman-Oppenheimer-Volkoff treatment.
Multiple-Orbit Simulations of Binary Neutron Stars
arXiv: General Relativity and Quantum Cosmology, 2016
We study the general relativistic hydrodynamic evolution of neutron stars in binary orbits and analyze the equation of state dependence of the orbits as the stars approach the inner most last stable circular orbit. We show that by employing a conformally flat condition on the metric, one can stably numerically evolve ~100 quasi-circular orbits and could straightforwardly extend the calculation to the ~10,000 orbits needed to follow stars through the LIGO frequency band. We apply this code to orbiting neutron stars in the quasi-circular orbit approximation to both demonstrate the stability of this approach and explore the equation of state dependence of the orbital properties. We employ variety of available realistic neutron star equations of state as well as a Gamma=2 polytrope. We confirm that both the orbital and emergent gravity wave frequency evolve more slowly for a softer equation of state as the stars approach the innermost stable circular orbit.