Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary

TL;DR

This paper advances gravitational self-force waveform modelling by incorporating a slowly spinning primary and a generically precessing spinning secondary in quasi-circular binaries, within a two-timescale, multiscale framework. It derives the 1PA evolution using flux-balance arguments and the first law of binary black hole mechanics, and develops five waveform variants—including a re-summed model 1PAT1R—validated against NR simulations for modest mass ratios and spins. The results show strong NR agreement and reveal the advantages of the re-summed approach for equal-mass, higher-spin systems, with public availability in WaSABI. The work lays groundwork for extending self-force waveforms toward broader parameter spaces and future merger modelling, with practical impact for LISA-era data analysis of precessing binaries.

Abstract

Recent progress in gravitational self-force theory has led to the development of a first post-adiabatic (1PA) waveform model for nonspinning, quasicircular compact binaries [Phys. Rev. Lett. 130, 241402 (2023)]. In this paper, we extend that model to allow for a slowly spinning primary black hole and a generic, precessing spin on the secondary object, restricting to the case of small misalignment between the primary spin and the orbital angular momentum. We demonstrate excellent agreement between our waveforms and fully nonlinear numerical relativity simulations for mass ratios $q\gtrsim 5$ and primary spins $|χ_1|\lesssim 0.1$ and arbitrary secondary spin $χ_2 \lesssim 1$. In particular we present the re-summed 1PAT1R waveform model, which significantly improves the accuracy of the original 1PAT1 waveforms for comparable masses and increasing primary spin. Our models are publicly available in the WaSABI package.

Figures (9)

• Figure 1: (Top) Comparison of the flux computed from the $\delta\chi_1$ perturbation and the linear-in-$\chi_1$ Teukolsky flux. We also plot the leading PN behaviour given in Eq. \ref{['eq:spin_flux_PN']}. (Bottom) The relative difference between the $\delta\chi_1$ and the linearized-in-$\chi_1$ Teukolsky flux. For orbital radii in the range $6 < r_0/m^{(0)}_1 \le 30$, the relative error is always less than $1.5\times10^{-5}$.
• Figure 2: The amplitude terms in Eq. \ref{['eq:ampexpand']} as functions of the separation, $r_0$. Top: the various contributions to the $(\ell, m)=(2,2)$ mode (real and imaginary part respectively). Bottom: the same but with $(\ell, m)=(2,1)$. Notice that the precessing modes ($k\neq0$) are represented by the dashed lines and are generally at least an order of magnitude smaller than the leading amplitude even before being suppressed by the additional factor of $\epsilon$.
• Figure 3: Top: Waveform comparison for the same nonspinning binary configuration considered in Figure 1 of Ref. Wardell:2021fyy. The NR simulation sxs_collaboration_2019_3302023 is in black. In blue is the 1PAT1e-$a$ waveform. In green is the original 1PAT1 waveform, which is not visible in the plot due to excellent overlap with the 1PAT1e-$a$ waveform. In orange is the difference between the 1PAT1e-$a$ waveform and the 1PAT1 waveform scaled by a factor of 100. Bottom left (right): The evolution of the primary's mass (spin) correction. Their values remain small over the entire inspiral, hence the very small difference between the 1PAT1 and 1PATe-$a$ waveforms.
• Figure 5: Waveform comparisons for a binary configuration with a rapid anti-aligned spin on the secondary. Top: Comparison of the NR simulation sxs_collaboration_2019_3272906 (in black) with the 1PAT1e-$a$ model (in blue) and the 1PAT1e-$\chi$ model (in orange). The binary has anti-aligned spins with a very small spin on the primary. Bottom: The same comparison but against the 1PAT1R model (in red).
• Figure 7: Waveform comparisons for a binary with aligned spins and a small spin on the primary. Top: Comparison of an NR simulation jonathan_blackman_2019_2644087 (in black) with the 1PAT1e-$a$ model (in blue) and the 1PAT1e-$\chi$ model (in orange). Bottom: The same comparison but against the 1PAT1R model (in red).