No Love for black holes: tightest constraints on tidal Love numbers of black holes from GW250114 (2512.01918v1)

Abstract: Tidal Love numbers of black holes, zero in classical general relativity for Kerr black holes in vacuum, become non-vanishing in the presence of exotic matter or in alternative theories of gravity, making them a powerful probe of fundamental physics. The gravitational-wave event GW250114, observed with an unprecedented signal-to-noise ratio, provides a unique opportunity to test this prediction. By analyzing this event, we conclude that the data is consistent with the binary black hole hypothesis, and we place a 90\% upper limit on the effective tidal deformability of $\tildeΛ < 34.8$. These bounds imply that any environment surrounding the black holes must contribute less than $\sim 7\times 10^{-3}$ of their mass, and they rule out some models of boson stars. Our findings provide the strongest observational constraints yet on black hole tidal deformability and show that the data remain fully consistent with the Kerr black hole prediction of vanishing tidal Love numbers.

• The paper constrains tidal Love numbers by analyzing GW250114, yielding 90% upper limits (e.g., 𝚯̃ < 34.8) that support the vacuum-Kerr hypothesis.
• It employs tidal phase corrections in the IMRPhenomPv2 waveform and Bayesian inference to overcome previous limitations in sensitivity.
• The study rules out minimally coupled boson stars and limits environmental effects to below 0.7% of black hole mass, narrowing models beyond GR.

Constraints on Black Hole Tidal Love Numbers from GW250114

Background and Motivations

Gravitational-wave (GW) detections have enabled precision probes of compact object properties, testing general relativity (GR) in the strong-field regime. Among such probes, the tidal Love numbers (TLNs) play a central role; they quantify the multipolar tidal response of a body in a binary system. Classical GR predicts identically vanishing TLNs for Kerr black holes (BHs) in vacuum, meaning that their event horizons are unable to support static tidal deformation. Any measurement of non-zero TLNs in a BH binary therefore unambiguously signals deviations from standard GR or the presence of matter/environmental effects, such as accretion disks, boson clouds, or dark matter halos.

The gravitational-wave event GW250114, characterized by an unprecedented signal-to-noise ratio (SNR ≈ 80) due to improved detector sensitivity, provides an ideal opportunity to empirically constrain black hole TLNs with maximal rigor. Previous constraints from LVK data were limited by lower SNR and the fact that tidal phase corrections only enter at high post-Newtonian (PN) order, resulting in weak bounds. The analysis of GW250114 presented in this work thus offers the most sensitive test to date.

Methodology

Waveform Modeling and Bayesian Inference

The study implements tidal phase corrections ($\Lambda_1$, $\Lambda_2$) in the IMRPhenomPv2 waveform model, affecting the inspiral regime where tidal effects are most prominent. Only leading electric quadrupolar TLNs are considered, neglecting higher-order or magnetic contributions due to their sub-dominant nature in current data. Bayesian inference is performed using the Bilby library and dynesty nested sampling. The analysis marginalizes over calibration uncertainties and employs log-uniform priors on tidal deformabilities to ensure conservativeness and avoid artificial prior-volume bias.

Posterior distributions and Bayes factors are computed for both the null hypothesis (vanishing TLNs) and the alternative hypothesis (non-zero TLNs).

Empirical Results

Upper Limits on Tidal Deformability

The data indicate no evidence for non-zero tidal deformability in GW250114. The peak of posterior distributions for tidal parameters is concentrated near zero, as shown below.

Figure 1: Marginalized posteriors for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ (left), and effective tidal deformability $\tilde{\Lambda}$ (right), for GW250114; vertical lines denote 90% credible upper limits.

The stringent 90% upper limits obtained are:

• $\tilde{\Lambda} < 34.8$
• $\Lambda_1 < 28.2$
• $\Lambda_2 < 45.7$
• $k_{2,1} < 42.4$, $k_{2,2} < 69.5$

These constraints improve upon prior results (Chia et al., 2023) by more than an order of magnitude.

Null Preference for TLNs

The log-Bayes factor between tidal and non-tidal models is $$\ln \mathcal{B}^{\Lambda_i \neq 0}_{\Lambda_i = 0} = -0.063 \pm 0.182$$, indicating no statistical preference for the inclusion of TLNs.

Source Parameter Consistency and Prior Impact

The inclusion of TLNs does not bias other relevant parameters (chirp mass, mass ratio, spins), as illustrated below.

Figure 2: Posterior comparison for chirp mass, mass ratio, and spins with (red) and without (black) tidal effects, showing negligible changes.

Spin orientation and magnitude posteriors are also robust against the tidal hypothesis:

Figure 3: Posterior distributions for primary (top) and secondary (bottom) spin components; both tidal and non-tidal models yield highly concordant results.

Use of log-uniform priors is critical for avoiding misleading prior-driven biases in the recovered parameters.

Theoretical and Astrophysical Implications

Constraints on Environmental Effects

The null result constrains the mass of any environment surrounding the black holes to $$m_{\mathrm{env}}/m_{\mathrm{BH}} < 7 \times 10^{-3}$$ for a typical environmental scale $\tilde{L} \gtrsim 6$. Tighter bounds apply for larger environments due to the steep scaling of $k_2 \propto (L/m_{\mathrm{BH}})^5$. The analysis remains agnostic to environment composition, and systematic biases due to possible tidal disruption are estimated at the $\mathcal{O}(10\%)$ level.

Constraints on Exotic Compact Objects

Empirical TLN upper bounds place strong restrictions on alternative compact object models, especially boson stars (BS):

Figure 4: TLN $k_2$ as a function of $m\mu$ for several boson star models; the shaded region is excluded by the present analysis.

• Minimally coupled BS: Ruled out at $>90\%$ credibility (all viable $k_2$ exceed empirical bound).
• Massive BS $(\alpha=100)$, Solitonic BS $(\sigma_0=0.05)$: Primary component excluded, thereby ruling out binary mergers of these types.
• Massive BS $(\alpha=10^3)$, $(\alpha=10^4)$: Only high-compactness configurations remain viable, with correspondingly tight constraints on boson mass: $\mu \in [7.3 \times 10^{-12}, 8.1 \times 10^{-12}]$ eV ($\alpha=10^3$); $\mu \in [1.8 \times 10^{-11}, 2.2 \times 10^{-11}]$ eV ($\alpha=10^4$).

ECOs with negative TLNs (e.g., wormholes, gravastars) are inaccessible to the positive-TLN analysis presented.

Waveform Faithfulness and TLN Detectability

Systematic examination of waveform phase shifts for varying TLN values reveals that, for GW250114, models with TLNs in the empirical upper bound range yield faithfulness values exceeding 0.97, signifying indistinguishability from the GR BBH scenario.

Figure 5: Phase comparison for binary waveform with $\Lambda_{1,2} = 0$ (black), $50$ (red), $150$ (gray).

Figure 6: Faithfulness in equal-mass binaries, showing detectability threshold as a function of tidal deformability.

Prospects for Fundamental Physics and Future Observations

The constraints presented demonstrate the capability of current GW observatories for ruling out substantial sectors of exotic compact object phenomenology and environmental scenarios. Future GW detectors (e.g., Einstein Telescope, Cosmic Explorer) with enhanced low-frequency sensitivity and SNR are poised to probe larger environmental scales and smaller TLNs, further tightening bounds on physics beyond GR. Incorporating subdominant modes in analysis pipelines will refine these limits further.

Conclusion

The analysis of GW250114 places the most stringent empirical bounds yet on black hole tidal Love numbers, demonstrating full consistency with the vacuum-Kerr black hole hypothesis as predicted by GR. The observed upper limits decisively exclude minimally coupled boson stars and the majority of massive and solitonic BS scenarios as viable interpretations. Constraints on environmental effects are strong, limiting any surrounding matter to less than $0.7\%$ of each BH’s mass. These results restrict the parameter space for alternative compact objects and environmental models and validate the use of high-SNR GW events for probing strong-field gravity and fundamental physics. Continued progress in detector sensitivity and waveform modeling will allow for even more robust constraints and open further avenues in gravitational-wave astronomy and fundamental tests of gravity.