General Relativistic Models of Binary Neutron Stars in Quasiequilibrium

TL;DR

This paper develops fully relativistic models of binary neutron stars in quasiequilibrium, identifying the innermost stable orbit and constructing the first contact binaries in full general relativity.

Contribution

It introduces a method to model binary neutron stars in quasiequilibrium using Einstein equations and hydrostatic equilibrium, including the first full GR contact binaries.

Findings

Located the innermost stable circular orbit (ISCO).

Constructed the first contact binary systems in full general relativity.

Found no collapse tendency to black holes before merger.

Abstract

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.