Quasiequilibrium sequences of black-hole–neutron-star binaries in general relativity

Abstract

We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index n = 1, mass ratio M Coalescing black hole-neutron star (hereafter BHNS) binaries are among the most promising sources of gravitational waves for laser interferometers [1,2,3,4]. BHNS mergers may reveal a wealth of astrophysical information (see e.g. [5]), and, along with mergers of binary neutron stars, are also considered primary candidates for central engines of short-duration gamma-ray bursts (SGRBs) [6,7,8]. Recent observations of several SGRBs localized by the Swift and HETE-2 satellites in regions with low star formation strongly suggest that a compact binary merger scenario for SGRBs is favored over models involving the collapse of massive stars (see, e.g., [9] and references cited therein).Significant effort has gone into the study of binary neutron stars and binary black holes, which are also promising sources of gravitational radiation. Fully relativistic simulations of BHNS binaries have received far less attention. Most BHNS calculations to date, including quasiequilibrium (QE) calculations [10,11,12,13,14,15,16,17,18] and dynamical treatments [19,20,21,22,23,24,25], employ Newtonian gravitation in either some or all aspects of their formulation. We have recently launched a new effort to study BHNS binaries in a fully relativistic framework (see also [26,27]), first by constructing QE models [28,29] and then by employing them as initial data in dynamical simulations [7,30]. So far we have focused on binaries for which the black hole mass is much greater than the neutron star mass. For binaries with such extreme mass ratios the rotation axis can be taken to pass through the center of the black hole, and the tidal effects of the neutron star on the black * Also at: Department of Physics, University of Illinois at UrbanaChampaign, Urbana, Illinois 61801, USA † Also at: Department of Astronomy and NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA hole may be ignored. These approximations simplify the problem considerably (see [28]). However, they break down for binaries containing comparable mass companions. Such systems are more suitable as SGRB candidates, because the tidal disruption of the neutron star by the black hole will occur near or outside the innermost stable circular orbit. This disruption may be necessary to create a gaseous accretion disk around the black hole capable of generating a SGRB [7]. Gravitational wav...

Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method

“…Earlier results showed that initial configurations built using a Kerr-Schild conformal metric were significantly inferior to their conformally flat counterparts [19,20]. Here, adapting a method developed by Lovelace for BBH [28], we show that a modified Kerr-Schild metric can lead to high-precision initial data.…”

“…Indeed, we only use the EOS to reconstruct the matter quantitiesẼ,J,S, and ρ 0 needed in Eqs. (19), (20), (21) and (29) from the enthalpy h. We use a Γ = 2 polytrope as a reasonable first approximation to the nuclear equation of state, which will allow direct comparison with previous numerical results in Sec. IV C.…”

“…The choice ofγ ij and K is, however, less obvious. Taniguchi et al [19,20] showed that a conformally flat metric (γ ij = δ ij ) with maximal slicing (K = 0) gives good results -better than using a Kerr-Schild background at least. For the tests in this paper, we will make the same choice.…”

“…(19) and (20) are the momentum and Hamiltonian constraints, while Eq. (21) can be derived from the evolution equation for K ij .…”

“…Previous results on initial data for BH-NS evolutions include the early work of Taniguchi et al [17] and Sopuerta et al [18], as well as more recent initial configurations generated by Taniguchi et al [19,20,21] and Grandclement [22]. Both Taniguchi and Grandclement use codes based on the lorene package [23], and their most recent publications are similar in accuracy, computational cost, and numerical results.…”