Circular orbit approximation for binary compact objects in general relativity

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 time scale of this dissipation is much longer than the orbital time scale 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 $\left[{Gm/(rc}^2\right){]}^{9/2}$ for nonspinning 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 merger is required in order to bound the detection event loss rate in gravitational wave detectors to below 5% (20%). In addition, we show that the detection event loss rate is greater than 95% for a range of initial separations that includes all modern calculations of the innermost stable circular orbit.