Hybrid waveform model for asymmetric spinning binaries: Self-force meets post-Newtonian theory

TL;DR

This work develops a fully first-principles SF+PN hybrid waveform model (WaSABI-C) for quasicircular inspirals with a spinning primary and nonspinning secondary, extending SF accuracy into the PN regime without NR calibration and excluding merger/ringdown. By formulating the dynamics via flux-balance laws and hybridizing energy fluxes, horizon fluxes, binding energy, and mode amplitudes, the model achieves rapid, multiscale waveform generation with offline precomputation and online evaluation. Validation against 50 SXS NR waveforms shows large improvements over pure PN or 0PA SF waveforms, with median mismatches improved by factors of about 40 and 2000 in respective comparisons, and dephasings typically below ~1 rad in the inspiral window. The results demonstrate that a carefully constructed SF-forward hybrid, which preserves exact 0PA SF information and incorporates high-order PN data, provides a highly accurate, efficient tool for modeling IMRIs and EMRIs in current and future GW observations, including potential integration into FEW and LISA data-analysis pipelines. The approach is modular and ready for extensions to eccentricity, inclination, and merger regimes, and is released as WaSABI-C v0.9 with plans for v1.0 that include broader SF/PN data and secondary-spin effects.

Abstract

We develop and implement a new hybrid waveform model for quasicircular inspirals with a spinning primary and nonspinning secondary, excluding the merger and ringdown. This model, which is a core component of the more extensive WaSABI-C model, consistently assembles all available first-order self-force and post-Newtonian results through a hybridization procedure without any tuning to numerical relativity, making it particularly suited for intermediate to extreme mass ratios. For almost all masses and primary spins, the resulting hybrid model significantly improves the faithfulness of both post-Newtonian and adiabatic self-force waveforms considered separately. We provide detailed comparisons with 50 simulations from the SXS catalog with mass ratios ranging from 1 to 15 and primary spins ranging from -0.8 to 0.8. The hybrid model improves the median mismatch against numerical relativity waveforms by a factor of 2000 with respect to adiabatic waveforms and 40 with respect to post-Newtonian waveforms. The mismatches are comparable to those obtained from the SEOBNRv5EHM model in the quasicircular limit over most of the parameter space covered by NR simulations.

Figures (14)

• Figure 1: Self-force/post-Newtonian hybrid waveform (in red) and NR waveform SXS:BBH:2105 (in black) Boyle:2019kee for a quasicircular binary with primary spin ${\mathring\chi}=0.9$ and mass ratio $\mathring q=1$. The inset zooms in on the shaded gray region close to the merger. The hybrid model is described in the core of this article. We also display $0$PA and 4PN waveforms for comparison (in orange and blue, respectively), aligned with the NR waveform at the same (early) reference time as the hybrid waveform.
• Figure 2: $(\ell,m)=(2,2)$ mode of the gravitational waveform from three comparable-mass binary configurations with differing primary spins. Numerical relativity (in black), hybrid (red), $0$PA (orange), PN (blue), and 1PAT1 (purple) waveforms are displayed. The references of the SXS simulations are listed in Table \ref{['tab:mismatchdephasing']}.
• Figure 3: $(\ell,m)=(2,2)$ mode of the gravitational waveform from three $\mathring q=15$ binary configurations with differing primary spins. Numerical relativity (in black), hybrid (red), $0$PA (orange), PN (blue), and 1PAT1 (purple) waveforms are displayed. The references of the SXS simulations are listed in Table \ref{['tab:mismatchdephasing']}.
• Figure 4: Accumulated phase error, as defined through Eq. \ref{['eq:dephasing']}, of the hybrid (red), PN (blue), and 0PA (orange) waveform models against NR simulations for a set of prograde quasicircular orbits with primary spin $\mathring \chi=+0.5$. The mass ratio ranges from $\mathring q=1$ (top panel) to $\mathring q=15$ (bottom panel). The grey horizontal lines indicate the value of the phase error accumulated when the hybrid model reaches the primary ISCO frequency: $\Delta\psi_{22}^H(t_\star)$ where $\omega(t_\star) = \Omega_\star(\mathring \chi)$. The SXS simulations used in this figure are those with $\mathring \chi=0.5$ in Table \ref{['tab:mismatchdephasing']}.
• Figure 5: Accumulated phase error of the hybrid (red), PN (blue), and 0PA (orange) waveform models against NR simulations for a set of retrograde quasicircular orbits with primary spin $\mathring \chi=-0.5$, and with other details as in Fig. \ref{['fig:dephasingprograde']}. The SXS simulations used in this figure are those with $\mathring \chi=-0.5$ in Table \ref{['tab:mismatchdephasing']}.