Spin-aligned inspiral waveforms from self-force and post-Newtonian theory

Abstract

We present the state-of-the-art waveform model WaSABI-C for quasicircular inspirals of spinning black hole binaries with aligned or anti-aligned spins. Our model synthesizes the most up-to-date first- and second-order gravitational self-force results with high-order post-Newtonian expansions through a systematic hybridization procedure. This approach captures both strong-field and weak-field dynamics with high fidelity, enabling accurate modeling of spin-(anti)aligned inspirals across a wide parameter space. The resulting waveforms mark a significant advance in the precision of self-force-based templates, providing critical input for the detection and interpretation of gravitational waves from compact binaries with future observatories such as LISA and ET. We accompany this work with the release of WaSABI (Waveform Simulations of Asymmetric Binary Inspirals), a public package implementing our model for community use and further development.

Figures (4)

• Figure 1: $(2,2)$ mode of the gravitational waveform, with the NR simulation SXS:BBH:2209 in black and the WaSABI-C model in blue. The inset zooms on the gray shaded region, with an adiabatic 0PA model in purple for reference. The waveforms have been aligned at the reference time of the NR simulation using the same alignment procedure as described in Ref. PaperIII.
• Figure 2: Mismatch as a function of mass ratio on a fixed waveform frequency range $[0.044/M,0.12/M]$ for inspirals with initial spins $\chi_{1,0}=0.4$, $\chi_{2,0}=0.8$, using a flat power spectral density. The frequency range corresponds to an orbital separation going from $12.7M$ to $6.3M$. Upper panel: mismatches of the four models WaSABI-C, 0PA, SEOBNRv5HM and TEOBResumS-GIOTTO against 5 NR simulations from the SXS catalog. The mismatch between the two highest NR resolutions is indicated for reference. Lower panel: mismatches between WaSABI-C and either SEOBNRv5HM or TEOBResumS-GIOTTO, which extend to lower mass ratios than covered by NR. The dotted line is a reference power law $\nu^{-2}$.
• Figure 3: Upper panel: histogram of mismatches between NR simulations and either WaSABI-C, SEOBNRv5HM or TEOBResumS-GIOTTO. For each simulation, the frequency window ranges from the reference frequency of the simulation to the breakdown frequency of WaSABI-C. We used the Virgo O5 design curve LVK_PSD and set the initial total mass of the system at $M_0=20 M_\odot$. Bottom panel: Population of NR simulations used for this study. The secondary spin axis dimension has been suppressed for clarity. For each point on parameter space, we report the mismatch between WaSABI-C and the corresponding SXS simulation. All simulation IDs can be found in the supplementary material.
• Figure 4: Content of the hybrid functions $Q=\{\mathcal{F}_\infty , \mathcal{F}_{\mathcal{H}_i} , \mathcal{G}_{\mathcal{H}_i},E, A_{\ell m}\}$ built as part of the WaSABI-C model. The information is stored as follows. Each entry $(\overline{k},\overline{n})$ for each pair $(\chi_1,\chi_2)$ in a given table denotes the maximal orders $(\overline k,\overline n)$ being summed over in the hybridization of the corresponding function \ref{['QSFPN']}. For quantities other than ${\cal F}_{{\cal H}_i}$ and ${\cal G}_{{\cal H}_i}$, $(\overline{k},\overline{n})$ denotes $\overline{k}$PA and $\frac{\overline{n}}{2}$PN information. As the spin content $\chi_i$, $i=1,2$, is limited to cubic order in the current PN approximation, we denote as $\infty$ all powers of spin larger than $3$ up to $\infty$. The emptyset symbol $\emptyset$ means that no data is being used. Shaded gray entries indicate sectors where 2SF information is being used.