Intermediate Mass-Ratio Black Hole Binaries: Applicability of Small Mass-Ratio Perturbation Theory

The inspiral phasing of binary black holes at intermediate mass ratios (m₂/m₁∼10^-3) is important for gravitational wave observations, but not accessible to standard modeling techniques: The accuracy of the small mass-ratio (SMR) expansion is unknown at intermediate mass ratios, whereas numerical relativity simulations cannot reach this regime. This article assesses the accuracy of the SMR expansion by extracting the first three terms of the SMR expansion from numerical relativity data for nonspinning, quasicircular binaries. We recover the leading term predicted by SMR theory and obtain a robust prediction of the next-to-leading term. The influence of higher-order terms is bounded to be small, indicating that the SMR series truncated at next-to-leading order is quite accurate at intermediate mass ratios and even at nearly comparable mass binaries. We estimate the range of applicability for SMR and post-Newtonian series for nonspinning, quasicircular inspirals.