Hybrid waveforms for precessing quasi-circular binary systems

TL;DR

This work tackles the challenge of constructing long, accurate gravitational-wave hybrids for precessing quasi-circular binaries by developing a framework that uses coprecessing and quadrupole-aligned frames to suppress mode-mixing and gauge ambiguities. It systematically aligns inspiral and merger descriptions in a frame where precession is minimized, anchored by a gauge-independent reference point based on the orbit-averaged frequency $\langle f_{22}^{QA} \rangle$, and then blends the two regimes within a coprecessing frame before rotating back to the inertial frame. The approach reduces frame-induced discrepancies, enables multi-mode alignment, and provides robust parameter-estimation prospects for future detectors by relying on minimal information about the merger waveform. Overall, the method broadens the applicability of hybrid waveform construction to precessing systems, with demonstrated resilience against common alignment pitfalls and clear paths for future enhancements, including eccentricity, higher-order modes, and BMS-frame consistency.

Abstract

The demand for long and accurate gravitational waveforms is increasing as we prepare for the next generation of detectors and seek to improve current waveform models. However, numerical relativity waveforms, while highly accurate, are often too short for these applications due to their high computational cost. Hybrid waveforms, which stitch together gravitational wave signals from different modeling approaches, provide a way to generate complete inspiral-merger-ringdown signals. While hybridization is well-established for aligned-spin systems, precession introduces additional complexities due to gauge ambiguities, frame dependence, or spin dynamics. Here we study the challenges associated with alignment of precessing waveforms and present a systematic approach for constructing hybrid waveforms of precessing quasi-circular systems. Our approach relies on minimal assumptions about the merger waveforms and employs the quadrupole-aligned frame to mitigate mode-mixing. Our method is designed to be robust and broadly applicable, imposing minimal constraints on the input waveforms. This framework expands the applicability of hybridization techniques, facilitating flexible hybrid construction for parameter estimation, model calibration, and gravitational-wave data analysis.

Figures (10)

• Figure 1: Illustration of a binary system with its key vector quantities: $\bm{\chi_1}$, $\bm{\chi_2}$, ${\bm{L}}$, and ${\bm{J}}$. Different frame choices offer advantages in various contexts. In frames where ${\hat{\bm{z}}}\ \parallel {\bm{L}}$, the x-y plane moves to match the orbital plane.
• Figure 2: Comparison of the (2,2)-mode frequency in an inertial frame (blue), in the coprecessing frame (orange), and the orbit-averaged value in a coprecessing frame (red) for the NR waveform SXS:BBH:0165. Top panel shows frequency and bottom panel shows its first derivative, where the non-monotonicity of $f_{22}$ and $f^\mathrm{QA}_{22}$ appears evident.
• Figure 3: Illustration of the frame-fixing: orientation of the ${\hat{\bm{z}}}$-axis of the QA frame for two descriptions (A and B) of the same system, with respect to an inertial frame. In the left panel, we visualize the trajectory of ${\hat{\bm{L}}}(t)$ on the unit sphere for two descriptions (in two different inertial frames) of the same system. One can acknowledge the similar shape of the two trajectories. The center panel shows an unsatisfactory choice of the freedom, where two degrees of freedom have been used to match the trajectories at a single point, like the first step in the procedure in Schmidt:2012rh. The right panel shows the right choice of fixing the freedom, which uses three degrees of freedom and for the whole trajectory is aligned.
• Figure 4: Comparison of ${\hat{\bm{L}}}$, ${\hat{\bm{L}}}_N$ and ${\hat{\bm{Q}}}$ for the 4 waveforms described in Tab. \ref{['tab:discussion_parameters']} generated with the SEOBNRv5PHM approximant. Colors correspond to Systems B (orange), C (green), and D (red), comparing ${\hat{\bm{Q}}}$ with ${\hat{\bm{L}}}$ (solid lines) and ${\hat{\bm{L}}}_N$ (dashed lines). The line corresponding to System A (non-precessing waveform) is exactly $0$ since, by construction, ${\hat{\bm{L}}}={\hat{\bm{L}}}_N={\hat{\bm{Q}}}={\hat{\bm{z}}}$. As expected, precessing effects become more important later in the evolution, and with them, the difference between ${\hat{\bm{Q}}}$ and ${\hat{\bm{L}}}$ increases. The lower panel shows a more detailed view of the last part of the evolution.
• Figure 5: Comparison of ${\hat{\bm{L}}}$ and ${\hat{\bm{Q}}}$ for a set of 50 waveforms generated with SEOBNRv5PHM approximant. Each waveform is represented by a line and its color corresponds to its effective precessing spin $\chi_p$ (top panel) or mass ratio $q$ (bottom panel). Systems with higher $\chi_p$ exhibit larger differences between ${\hat{\bm{Q}}}$ and ${\hat{\bm{L}}}$, with all values remaining below $1^\circ$ until the last few orbits.