Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation

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 gravitatio...

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the 4-metric and an extrinsic curvature whose time derivative vanishes in a comoving frame. Two independent numerical codes are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are succ...

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 equation...

We introduce a computational framework which avoids solving explicitly hydrodynamic equations and is suitable to study the pre-merger evolution of black hole-neutron star binary systems. The essence of the method consists of constructing a neutron star model with a black hole companion and freezing the internal degrees of freedom of the neutron star during the course of the evolution of the space-time geometry. We present the main ingredients of the framework, from the formul...

We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's equations together with the relativistic equation of hydrostatic equilibrium to solve the initial value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasi-equilibrium maximum allowed mass of a neutron s...

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant'' initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein fi...

We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to construct high-accuracy solutions at a relatively low computational cost. We provide convergence tests of the method for both isolated neutron stars and irrotational binaries. In the second case, we show that we can resolve the small inconsi...

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 i...

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 ...

We investigate close binary neutron stars in quasiequilibrium states in a general relativistic framework. We assume conformal flatness for the spatial metric and irrotational velocity field for the neutron stars. We adopt the polytropic equation of state. The computation is performed for the polytropic index n(=0.5, 0.66667, 0.8, 1, 1.25), and compactness of neutron stars M/R(=0.03 - 0.3). Results of this paper are as follows. (i) The sequences of the irrotational binary are ...