On the Circular Orbit Approximation for Binary Compact Objects In General Relativity

TL;DR

This paper evaluates the validity of the circular orbit approximation in binary black hole systems within general relativity, quantifying how initial conditions affect gravitational wave detection accuracy.

Contribution

It provides a quantitative analysis of the circular orbit approximation using high-order post-Newtonian calculations, linking initial separation to detection loss rates.

Findings

Minimum initial separation of 6 orbits reduces detection loss to <5%.

Detection loss exceeds 95% for initial separations near the innermost circular orbit.

Approximation validity depends critically on initial conditions in gravitational wave modeling.

Abstract

One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued that the timescale of this dissipation is much longer than the orbital timescale so that the approximation of circular orbits is valid. Here, we quantitatively analyze this approximation using a post-Newtonian approach that includes terms up to order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the evolution of equal mass black hole / black hole binary systems starting with circular orbit configurations and comparing them to the more astrophysically relevant quasicircular solutions, we show that a minimum initial separation corresponding to at least 6 (3.5) orbits before plunge is required in order to bound the detection event loss rate in gravitational wave detectors to < 5% (20%). In addition, we show that the detection event loss rate is > 95% for a range of initial separations that include all modern calculations of the innermost circular orbit (ICO).