Abstract
The inspiral phasing of binary black holes at intermediate mass ratios (m_{2}/m_{1}∼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.
Highlights
Inspiraling and merging black hole (BH) binaries are the most numerous source of gravitational waves (GWs) observed by the Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo detectors [1,2] and are one of the key science targets for third-generation ground-based GW detectors [3], as well as the space-based Laser Interferometer Space Antenna (LISA) observatory [4]
The LIGO and Virgo observations [5,6,7] mostly report q close to unity, with GW190412 [8] and GW190814 [9] the first systems with clearly unequal masses (q ∼ 0.28 and q ∼ 0.11)
Third-generation ground-based detectors with improved low frequency sensitivity will be able to detect the capture of stellar mass BHs by intermediate mass BHs with mass ratios down to q ∼ 10−3 [11]
Summary
Inspiraling and merging black hole (BH) binaries are the most numerous source of gravitational waves (GWs) observed by the Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo detectors [1,2] and are one of the key science targets for third-generation ground-based GW detectors [3], as well as the space-based Laser Interferometer Space Antenna (LISA) observatory [4]. Given the expectation of binaries at all mass ratios, the question arises how to model intermediate mass-ratio binaries at small separation: post-Newtonian theory is not accurate close to merger, owing to the high velocities; numerical relativity simulations are limited to large mass ratios, q ≳ 0.1; and the SMR approximation is presently only available at leading order in q, and may be inaccurate at intermediate mass ratios.
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