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

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).

10 pages, 12 figures, revtex4

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• Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers
• Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
• Eccentric binary neutron star mergers
• Dynamical evolution of quasi-circular binary black hole data
• Non-conformally flat initial data for binary compact objects
• Binary neutron stars: Equilibrium models beyond spatial conformal flatness
• Accuracy requirements for the calculation of gravitational waveforms from coalescing compact binaries in numerical relativity
• Initial data for neutron star binaries with arbitrary spins
• Eccentricity content of binary black hole initial data