A parametrized model for gravitational waves from eccentric, precessing binary black holes: theory-agnostic tests of General Relativity with pTEOBResumS

TL;DR

pTEOBResumS introduces a parametrized, eccentric, precessing effective-one-body waveform model to enable null tests of General Relativity in the inspiral, merger, and ringdown. It extends TEOBResumS-Dalí by allowing deviations in high-order PN coefficients ($a_6^c$, $c_{ m{N}^3 m{LO}}$), per-mode peak amplitudes and frequencies, QNM frequencies and damping times ($oldsymbol{\omega_{\ell m 0}}$, $ au_{oldsymbol{\ell m 0}}$), and remnant mass/spin, as well as amplitude and frequency at peak. The authors validate with NR waveforms and NR-bh-boson-star simulations; apply to nine BBH events from GWTC-3 to constrain deviations, finding no significant evidence for GR violations, though some eccentric and data-quality issues arise (e.g., GW200129). They discuss potential systematics and emphasize that eccentricity neglect can bias beyond-GR inferences, especially for high-SNR events. They outline future work to expand NR-informed calibration and extend parameter space, improving tests with next-generation detectors.

Abstract

Gravitational waves from binary black hole (BBH) mergers allow us to test general relativity in the strong-field, high-curvature regime. However, existing gravitational wave-based tests have so far assumed non-eccentric signal sources, limiting their applicability to more general astrophysical scenarios. In this work, we present pTEOBResumS, a new parametrized inspiral-merger-ringdown model for null tests of GR that incorporates both orbital eccentricity and spin precession. Building on the effective-one-body model TEOBResumS-Dalí, we introduce parametrized deviations from GR both in the inspiral and the merger-ringdown regimes. We validate the model via parameter estimation of synthetic signals, including from numerical relativity simulations of BBHs and a boson star binary. These allow us to establish the model's consistency, demonstrate its capability to identify beyond-GR effects, and gauge the impact of eccentricity in tests of GR. We then analyze a set of BBH events from the first three LIGO-Virgo-KAGRA observing runs, testing whether they are best explained by a GR or non-GR waveform, under either the eccentric, spin-aligned or precessing, quasi-circular hypotheses. We find no significant statistical evidence in favor of deviations from GR. Consistent with previous works, we infer a mild preference for longer remnant quasi-normal mode damping times than expected in GR, though the limited sample and potential systematics reduce its significance. In addition, when weighting by signal strength, joint posteriors combining the individual events are still compatible with GR. We find no strong evidence for imprints of orbital eccentricity in the analyzed events, with the exception of GW200129. For this, our analysis finds a strong preference for an eccentric, GR-consistent description, although as previous works have noted this result could be influenced by data quality issues.

Figures (19)

• Figure 1: Effect of the variation of $a_6^{\rm c}$ on the real part (top) and frequency (bottom) of $h_{22}$ for a binary with $q = 1, \chi_1 = \chi_2 = 0.6$, and initial eccentricity $e_0 = 0.5$ at a reference frequency of $20$ Hz for a total mass of $40 M_\odot$. Waveforms here are aligned to begin at $t = 0$ to highlight the cumulative effect of the deformed dynamics. $\delta a_6^c$ causes a delayed ($\delta a_6^c > 0$) or accelerated ($\delta a_6^c < 0$) late inspiral and plunge. The model is sensitive to the increase of $a_6^c$, delivering unphysical results for deviations $\gtrsim 8$ in this case.
• Figure 2: Changing $\delta c_{\rm{N}^3\rm{LO}}$ for a moderately eccentric ($e_0 = 0.5$ at an orbit-averaged frequency of 20 Hz with total mass $M = 40 M_\odot$) binary with $q = 1$ and $\chi_1 = \chi_2 = 0.95$. Left: real part and instantaneous frequency of the $(2,2)$ mode; right: dynamics (orbital separation $r$ and frequency $\Omega$). Waveforms are aligned to start at $t=0$. The high spins enhance the effect of the deviation in $c_{\rm{N}^3\rm{LO}}$. A negative value of $\delta c_{\rm{N}^3\rm{LO}}$ delays the merger for positive spins; the opposite would happen if they were anti-aligned with the orbital angular momentum. Within the displayed range the effective potential warped by the changing $c_{\rm{N}^3\rm{LO}}$ can induce an additional, smaller orbit after what would have been the onset of the plunge.
• Figure 3: Effective potential $V_{\rm eff} = H_{\rm EOB} (r, p_\varphi, p_{r_*} = 0)/M$ throughout the inspiral of an equal-mass bbh system with $\chi_1 = \chi_2 = 0.6$; these are the same parameters used in Fig. \ref{['fig:a6_ecc']}, save for the eccentricity, set here to 0 for easier visualization. The black line is the evolving energy of the system, $E = H_{\rm EOB}(t)/M$, the dots corresponding to the times of the potential plots. Left: default TEOBResumS-Dalí model; Right:pTEOBResumS with a large, positive deviation to the fitted $a_6^c$.
• Figure 4: Effect of the variation of $\tau_{220}$ on the $(2,2)$ mode amplitude and frequency for a binary with $q = 1, \chi_1 = \chi_2 = 0.6$ and initial eccentricity $e_0 = 0.5$ at a reference frequency of $20$ Hz for a total mass of $40 M_\odot$. $t = 0$ corresponds to the peak of $|h_{22}|$ for the zero-deviation waveform. A decrease in the damping time leads to a faster decaying ringdown, and vice-versa; this also affects the frequency evolution due to the structure of the ringdown model.
• Figure 5: Effect of the variation of $\omega_{220}$ on the $(2,2)$ mode frequency for an eccentric, precessing binary system with $q = 3, \bm{\chi_1} = (0.3, -0.2, 0.45), \bm{\chi_2} = (-0.5, -0.1, 0.2)$, and initial eccentricity $e_0 = 0.2$, measured at a reference frequency of $20$ Hz for a total mass of $40 M_\odot$. $t = 0$ corresponds to the peak of $|h_{22}|$ for the zero-deviation waveform. The changing qnm frequency can also be appreciated in the oscillations of $\omega_{22}$ during the ringdown, which are due to the mixing of the co-precessing $\ell = 2$ modes in the inertial frame.