Efficient gravitational-wave model for fully-precessing and moderately-eccentric, compact binary inspirals

Abstract

Future gravitational-wave detectors, especially the Laser Interferometer Space Antenna (LISA), will be sensitive to black hole binaries formed in astrophysical environments that promote large eccentricities and spin-induced orbital precession. Approximate models of gravitational waves that include both effects have only recently begun to be developed. The Efficient Fully Precessing Eccentric (EFPE) family is one such model, covering the inspiral stage with small-eccentricity-expanded gravitational-wave amplitudes accurate for initial time eccentricities $e < 0.3$ at 4 years before reaching an orbital frequency of 1 Hz. In this work, we extend this model to cover a larger range of initial eccentricities. The new EFPE for moderate eccentricities (EFPE_ME) model is able to accurately represent the leading-order gravitational-wave amplitudes to $e \leq 0.8$. Comparing the EFPE and the EFPE_ME models in the LISA band, however, reveals that there is no significant difference when the eccentricity at 4 years before merger, $e_0$, is less than or equal to 0.5, as radiation reaction circularizes supermassive black hole binaries too quickly. This suggests that the EFPE model may have a larger regime of validity in eccentricity space than previously thought, making it suitable for some inspiral parameter estimation with LISA data. On the other hand, for systems with $e_0 > 0.5$, the deviations between the models are significant, particularly for binaries with total masses below $10^5\, \mathrm{M}_{\odot}$. This suggests that the EFPE_ME model will be crucial to avoid systematic bias in parameter estimation with LISA in the future, once this model has been hybridized to include the merger and ringdown and the computation of the amplitudes is optimized.