Handle orbital eccentricity in PN–NR hybridization despite supertranslation degeneracy

Develop a robust hybridization procedure that incorporates orbital eccentricity into post-Newtonian–numerical relativity (PN–NR) waveform hybrids while correctly fixing the Bondi-Metzner-Sachs (BMS) frame, overcoming the degeneracy between eccentricity-induced amplitude oscillations and supertranslation effects in the strain and Bondi news. The method should enable reliable estimation of eccentricity and consistent mapping to the PN BMS frame so that eccentric PN waveforms can be attached to slightly eccentric Cauchy-characteristic evolution NR waveforms without bias.

Background

In the analysis of spin-aligned systems, the authors show that the dominant hybridization error at early inspiral originates from small but nonzero orbital eccentricity in NR waveforms, while PN models assume strictly quasicircular motion. They demonstrate that the normalized L2 error scales approximately as the square of the eccentricity and matches the expected eccentricity damping behavior.

However, they also find that supertranslations in the BMS frame cause oscillations in mode amplitudes and angular velocity that are degenerate with eccentricity signatures. Measurements of eccentricity from strain are strongly frame-dependent, and even measurements using Bondi news show significant time-dependent oscillations, complicating the inclusion of eccentricity in the hybridization process. As a result, they leave the integration of eccentricity into their PN–NR hybridization method for future work.