Usefulness of the coprecessing frame with orbital eccentricity

Determine whether the minimally rotating coprecessing frame transformation—defined as a time-dependent SO(3) rotation aligning the z-axis with the principal gravitational-wave emission direction—continues to provide a physically meaningful and accurate separation of precession-induced kinematics from the intrinsic signal for gravitational waveforms from binary black holes with non-negligible orbital eccentricity.

Background

The coprecessing frame is central to contemporary modeling of spin-precessing binary black hole signals. It separates the waveform into an approximately non-precessing component in a rotating frame and a time-dependent rotation encoding precession, and is used across Effective-One-Body and Phenomenological families as well as NR surrogate models.

Orbital eccentricity complicates waveform morphology and couples to spin-precession dynamics. While the coprecessing frame is well-established for quasicircular binaries, its applicability when eccentricity is present is not guaranteed. Prior work has shown the frame can be defined and suggested similarities between coprecessing-frame modes of eccentric precessing systems and those of eccentric aligned-spin systems, but a comprehensive assessment of its validity and effectiveness remained unresolved. This paper investigates that question using numerical relativity simulations and comparisons to eccentric aligned-spin models.