Post-adiabatic waveform-generation framework for asymmetric precessing binaries

TL;DR

This work develops a complete first post-adiabatic (1PA) waveform-generation framework for generic asymmetric binaries with a spinning secondary around a Kerr primary, combining a multiscale SF expansion with a Fermi-Walker spin parametrization. It shows that at 1PA order the secondary spin enters linearly, affecting the waveform through spin-corrected second-order amplitudes, spin-affected orbital frequencies, and dissipative 1PA forcing, while allowing gauge freedom to move contributions between these channels. The analysis leverages a detailed spin decomposition via Marck and Fermi-Walker frames, and uses recent flux-balance results to compute spin effects from asymptotic Teukolsky amplitudes, avoiding local self-force evaluations. The framework demonstrates waveform invariance under gauge choices and maps spin contributions onto accessible Teukolsky-based inputs, enabling practical, scalable generation of 1PA waveforms for generic precessing, eccentric binaries. This lays the groundwork for fully generic 1PA models and their calibration, with implications for LISA EMRIs and ground-based asymmetric binaries as detector sensitivities improve.

Abstract

Recent years have seen rapid progress in calculations of gravitational waveforms from asymmetric compact binaries containing spinning secondaries. Here we outline a complete waveform-generation scheme, through first post-adiabatic order (1PA) in gravitational self-force theory, for generic secondary spin and generic (eccentric, precessing) orbital configurations around a generic Kerr primary. We emphasize the utility of a Fermi-Walker frame in parametrizing the secondary spin, and we analyse precession and nutation effects in the spin-orbit dynamics. We also explain convenient gauge choices within the waveform-generation scheme, and the gauge invariance of the resulting waveform. Finally, we highlight that, thanks to recent results due to Grant and Witzany et al., all relevant spin effects at 1PA order can now be computed without evaluating local self-forces or torques.