Computation of gravitational waves from inspiraling binary neutron stars in quasiequilibrium circular orbits : Formulation and calibration

TL;DR

This paper introduces an approximate method to compute gravitational waves from inspiraling binary neutron stars in quasiequilibrium circular orbits, using conformal flatness and linear perturbation equations, and compares results with post-Newtonian models.

Contribution

It proposes a new two-step method combining conformal flatness approximation and linear perturbation equations to accurately compute gravitational waves from binary neutron stars.

Findings

Method produces waveforms consistent with post-Newtonian results

Tidal and relativistic effects significantly alter waveforms for close binaries

Systematic errors due to conformal flatness approximation are notable for compact systems

Abstract

Gravitational waves from binary neutron stars in quasiequilibrium circular orbits are computed using an approximate method which we propose in this paper. In the first step of this method, we prepare general relativistic irrotational binary neutron stars in a quasiequilibrium circular orbit, neglecting gravitational waves. We adopt the so-called conformal flatness approximation for a three-metric to obtain the quasiequilibrium states in this paper. In the second step, we compute gravitational waves, solving linear perturbation equations in the background spacetime of the quasiequilibrium states. Comparing numerical results with post Newtonian waveforms and luminosity of gravitational waves from two point masses in circular orbits, we demonstrate that this method can produce accurate waveforms and luminosity of gravitational waves. It is shown that the effects of tidal deformation of neutron stars and strong general relativistic gravity modify the post Newtonian results for compact binary neutron stars in close orbits. We indicate that the magnitude of a systematic error in quasiequilibrium states associated with the conformal flatness approximation is fairly large for close and compact binary neutron stars. Several formulations for improving the accuracy of quasiequilibrium states are proposed.