Review of Conformally Flat Approximation for Binary Neutron Star Initial Conditions

TL;DR

This paper reviews the conformally flat approximation method for setting initial conditions in binary neutron star simulations, highlighting its stability, dependence on the equation of state, and impact on gravitational wave predictions.

Contribution

It provides a comprehensive review of the conformally flat approximation for neutron star initial conditions and demonstrates its stability and effects on gravitational wave signals.

Findings

Stable evolution of ~100 quasi-circular orbits using CFA.

Dependence of initial conditions on the neutron star equation of state.

Influence of initial conditions on gravitational wave frequency near the innermost stable orbit.

Abstract

The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here we review the status of the original formulation of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasi-circular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasi-circular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect the emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.