No Love for black holes: tightest constraints on tidal Love numbers of black holes from GW250114

Author(s)

Andrés-Carcasona, M., Caneva Santoro, G.

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.

Figures

\textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$. The vertical line shows the 90\% credible upper bound.
Caption \textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$. The vertical line shows the 90\% credible upper bound.
\textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$. The vertical line shows the 90\% credible upper bound.
Caption \textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$. The vertical line shows the 90\% credible upper bound.
Corner plot comparing the posterior distributions for the chirp mass, mass ratio and spins with (red) and without (black) TLNs.
Caption Corner plot comparing the posterior distributions for the chirp mass, mass ratio and spins with (red) and without (black) TLNs.
Comparison of posterior distributions for the orientation and magnitude of the primary (top) and secondary (bottom) spin components, for models with $\Lambda_i = 0$ (black) and $\Lambda_i \neq 0$ (red). A spin angle of zero corresponds to perfect alignment with the orbital angular momentum.
Caption Comparison of posterior distributions for the orientation and magnitude of the primary (top) and secondary (bottom) spin components, for models with $\Lambda_i = 0$ (black) and $\Lambda_i \neq 0$ (red). A spin angle of zero corresponds to perfect alignment with the orbital angular momentum.
Comparison of posterior distributions for the orientation and magnitude of the primary (top) and secondary (bottom) spin components, for models with $\Lambda_i = 0$ (black) and $\Lambda_i \neq 0$ (red). A spin angle of zero corresponds to perfect alignment with the orbital angular momentum.
Caption Comparison of posterior distributions for the orientation and magnitude of the primary (top) and secondary (bottom) spin components, for models with $\Lambda_i = 0$ (black) and $\Lambda_i \neq 0$ (red). A spin angle of zero corresponds to perfect alignment with the orbital angular momentum.
Value of the TLN as a function of the product $m\mu$ for various models reported in Ref.~\cite{Cardoso:2017cfl}. Shaded regions indicate excluded regions by the results of our analysis.
Caption Value of the TLN as a function of the product $m\mu$ for various models reported in Ref.~\cite{Cardoso:2017cfl}. Shaded regions indicate excluded regions by the results of our analysis.
Comparison of the phase of the waveform for a non-spinning binary BH system with $m_1= 33.6~\msun$ and $m_2=32.2~\msun$ for the vacuum GR case and for the one augmented with TLNs for $\Lambda_1=\Lambda_2=50$ (red) and $\Lambda_1=\Lambda_2=150$ (gray).
Caption Comparison of the phase of the waveform for a non-spinning binary BH system with $m_1= 33.6~\msun$ and $m_2=32.2~\msun$ for the vacuum GR case and for the one augmented with TLNs for $\Lambda_1=\Lambda_2=50$ (red) and $\Lambda_1=\Lambda_2=150$ (gray).
Faithfulness for equal-mass binaries for different tidal deformabilities.
Caption Faithfulness for equal-mass binaries for different tidal deformabilities.
Comparison of the maximum log-likelihoodwaveform without TLNs ($\Lambda_i=0$) and the one containing the TLN deviations ($\Lambda_i\neq0$), compared to the real data for the two LIGO detectors.
Caption Comparison of the maximum log-likelihoodwaveform without TLNs ($\Lambda_i=0$) and the one containing the TLN deviations ($\Lambda_i\neq0$), compared to the real data for the two LIGO detectors.
\textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114 using Uniform priors. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$ using Uniform priors. The vertical line shows the 90\% credible upper bound.
Caption \textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114 using Uniform priors. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$ using Uniform priors. The vertical line shows the 90\% credible upper bound.
\textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114 using Uniform priors. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$ using Uniform priors. The vertical line shows the 90\% credible upper bound.
Caption \textit{(Left}) Marginalized posterior distributions for individual tidal deformabilities $\Lambda_i$ and tidal Love numbers $k_2$ for GW250114 using Uniform priors. Vertical lines indicate 90\% credible upper limits. (\textit{Right}) Marginalized posterior distribution for the effective tidal deformability $\tilde{\Lambda}$ using Uniform priors. The vertical line shows the 90\% credible upper bound.
Joint 90\% credible-level constraints on component tidal deformabilities compared with O3 results from Ref.~\cite{Chia:2023tle}. The lower-left corner corresponds to the vanishing-TLN scenario expected for BHs.
Caption Joint 90\% credible-level constraints on component tidal deformabilities compared with O3 results from Ref.~\cite{Chia:2023tle}. The lower-left corner corresponds to the vanishing-TLN scenario expected for BHs.
Violin plots comparing the posterior distributions of key parameters ($\mathcal{M}_c$, $q$, $\chi{\rm eff}$, $\Lambda_i$) for injections with $\Lambda_1=\Lambda_2 \in \{ 0, 200, 1000\}$. The horizontal lines indicate the injected values.
Caption Violin plots comparing the posterior distributions of key parameters ($\mathcal{M}_c$, $q$, $\chi{\rm eff}$, $\Lambda_i$) for injections with $\Lambda_1=\Lambda_2 \in \{ 0, 200, 1000\}$. The horizontal lines indicate the injected values.
Violin plot comparing the result of an injection with vanishing TLNs with a LogUniform[$10^{-3},5000$] prior and with a Uniform$[0,5000]$ prior.
Caption Violin plot comparing the result of an injection with vanishing TLNs with a LogUniform[$10^{-3},5000$] prior and with a Uniform$[0,5000]$ prior.
References
  • [1] B. P. Abbott et al. (LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc].
  • [2] B. P. Abbott et al. (LIGO Scientific, Virgo), GWTC1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X 9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE].
  • [3] R. Abbott et al. (LIGO Scientific, Virgo), GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X 11, 021053 (2021), arXiv:2010.14527 [grqc].
  • [4] R. Abbott et al. (LIGO Scientific, Virgo, KAGRA), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X 13, 041039 (2023), arXiv:2111.03606 [gr-qc].
  • [5] A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run, (2025), arXiv:2508.18082 [gr-qc].
  • [6] A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog, (2025), arXiv:2508.18080 [gr-qc].
  • [7] A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: Methods for Identifying and Characterizing Gravitational-wave Transients, (2025), arXiv:2508.18081 [gr-qc].
  • [8] B. P. Abbott et al. (LIGO Scientific, Virgo), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016), [Erratum: Phys.Rev.Lett. 121, 129902 (2018)], arXiv:1602.03841 [gr-qc].
  • [8] B. P. Abbott et al. (LIGO Scientific, Virgo), Tests of general relativity with GW150914, Phys. Rev. Lett. 116, 221101 (2016), [Erratum: Phys.Rev.Lett. 121, 129902 (2018)], arXiv:1602.03841 [gr-qc].
  • [9] A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation, (2025), arXiv:2509.04348 [astro-ph.CO].
  • [10] A. G. Abac et al. (LIGO Scientific, VIRGO, Kagra), GW230814: investigation of a loud gravitationalwave signal observed with a single detector, (2025), arXiv:2509.07348 [gr-qc].
  • [11] R. Abbott et al. (LIGO Scientific, VIRGO, KAGRA), Tests of General Relativity with GWTC-3, (2021), arXiv:2112.06861 [gr-qc].
  • [12] E. E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77, 021502 (2008), arXiv:0709.1915 [astro-ph].
  • [13] J. Vines, E. E. Flanagan, and T. Hinderer, Post-1Newtonian tidal effects in the gravitational waveform from binary inspirals, Phys. Rev. D 83, 084051 (2011), arXiv:1101.1673 [gr-qc].
  • [14] L. Blanchet, Post-Newtonian Theory for Gravitational Waves, Living Rev. Rel. 17, 2 (2014), arXiv:1310.1528 [gr-qc].
  • [15] T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80, 084018 (2009), arXiv:0906.1366 [gr-qc].
  • [16] M. M. Ivanov and Z. Zhou, Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes, Phys. Rev. Lett. 130, 091403 (2023), arXiv:2209.14324 [hep-th].
  • [17] V. Cardoso, E. Franzin, A. Maselli, P. Pani, and G. Raposo, Testing strong-field gravity with tidal Love numbers, Phys. Rev. D 95, 084014 (2017), [Addendum: Phys.Rev.D 95, 089901 (2017)], arXiv:1701.01116 [gr-qc].
  • [17] V. Cardoso, E. Franzin, A. Maselli, P. Pani, and G. Raposo, Testing strong-field gravity with tidal Love numbers, Phys. Rev. D 95, 084014 (2017), [Addendum: Phys.Rev.D 95, 089901 (2017)], arXiv:1701.01116 [gr-qc].
  • [18] E. Berti et al., Testing General Relativity with Present and Future Astrophysical Observations, Class. Quant. Grav. 32, 243001 (2015), arXiv:1501.07274 [gr-qc].
  • [19] H. S. Chia, Tidal deformation and dissipation of rotating black holes, Phys. Rev. D 104, 024013 (2021), arXiv:2010.07300 [gr-qc].
  • [20] P. Charalambous, S. Dubovsky, and M. M. Ivanov, On the Vanishing of Love Numbers for Kerr Black Holes, JHEP 05, 038, arXiv:2102.08917 [hep-th].
  • [21] A. Le Tiec, M. Casals, and E. Franzin, Tidal Love Numbers of Kerr Black Holes, Phys. Rev. D 103, 084021 (2021), arXiv:2010.15795 [gr-qc].
  • [22] V. De Luca, J. Khoury, and S. S. C. Wong, Nonlinearities in the tidal Love numbers of black holes, Phys. Rev. D 108, 024048 (2023), arXiv:2305.14444 [gr-qc].
  • [23] V. De Luca and P. Pani, Tidal deformability of dressed black holes and tests of ultralight bosons in extended mass ranges, JCAP 08, 032, arXiv:2106.14428 [gr-qc].
  • [24] V. Cardoso, M. Kimura, A. Maselli, and L. Senatore, Black Holes in an Effective Field Theory Extension of General Relativity, Phys. Rev. Lett. 121, 251105 (2018), [Erratum: Phys.Rev.Lett. 131, 109903 (2023)], arXiv:1808.08962 [gr-qc].
  • [24] V. Cardoso, M. Kimura, A. Maselli, and L. Senatore, Black Holes in an Effective Field Theory Extension of General Relativity, Phys. Rev. Lett. 121, 251105 (2018), [Erratum: Phys.Rev.Lett. 131, 109903 (2023)], arXiv:1808.08962 [gr-qc].
  • [25] P. Pani, I-Love-Q relations for gravastars and the approach to the black-hole limit, Phys. Rev. D 92, 124030 (2015), [Erratum: Phys.Rev.D 95, 049902 (2017)], arXiv:1506.06050 [gr-qc].
  • [25] P. Pani, I-Love-Q relations for gravastars and the approach to the black-hole limit, Phys. Rev. D 92, 124030 (2015), [Erratum: Phys.Rev.D 95, 049902 (2017)], arXiv:1506.06050 [gr-qc].
  • [26] D. R. Mayerson, Fuzzballs and Observations, Gen. Rel. Grav. 52, 115 (2020), arXiv:2010.09736 [hep-th].
  • [27] V. Cardoso, L. Gualtieri, and C. J. Moore, Gravitational waves and higher dimensions: Love numbers and KaluzaKlein excitations, Phys. Rev. D 100, 124037 (2019), arXiv:1910.09557 [gr-qc].
  • [28] D. Consoli, F. Fucito, J. F. Morales, and R. Poghossian, CFT description of BH’s and ECO’s: QNMs, superradiance, echoes and tidal responses, JHEP 12, 115, arXiv:2206.09437 [hep-th].
  • [29] M. V. S. Saketh, Z. Zhou, and M. M. Ivanov, Dynamical tidal response of Kerr black holes from scattering amplitudes, Phys. Rev. D 109, 064058 (2024), arXiv:2307.10391 [hep-th].
  • [30] V. Cardoso and F. Duque, Environmental effects in gravitational-wave physics: Tidal deformability of black holes immersed in matter, Phys. Rev. D 101, 064028 (2020), arXiv:1912.07616 [gr-qc].
  • [31] V. De Luca, J. Khoury, and S. S. C. Wong, Implications of the weak gravity conjecture for tidal Love numbers of black holes, Phys. Rev. D 108, 044066 (2023), arXiv:2211.14325 [hep-th].
  • [32] D. Baumann, H. S. Chia, and R. A. Porto, Probing Ultralight Bosons with Binary Black Holes, Phys. Rev. D 99, 044001 (2019), arXiv:1804.03208 [gr-qc].
  • [33] R. Brito and S. Shah, Extreme mass-ratio inspirals into black holes surrounded by scalar clouds, Phys. Rev. D 108, 084019 (2023), [Erratum: Phys.Rev.D 110, 109902 (2024)], arXiv:2307.16093 [gr-qc].
  • [33] R. Brito and S. Shah, Extreme mass-ratio inspirals into black holes surrounded by scalar clouds, Phys. Rev. D 108, 084019 (2023), [Erratum: Phys.Rev.D 110, 109902 (2024)], arXiv:2307.16093 [gr-qc].
  • [34] L. Capuano, L. Santoni, and E. Barausse, Perturbations of the Vaidya metric in the frequency domain: Quasinormal modes and tidal response, Phys. Rev. D 110, 084081 (2024), arXiv:2407.06009 [gr-qc].
  • [35] V. Cardoso, K. Destounis, F. Duque, R. P. Macedo, and A. Maselli, Black holes in galaxies: Environmental impact on gravitational-wave generation and propagation, Phys. Rev. D 105, L061501 (2022), arXiv:2109.00005 [grqc].
  • [36] T. Katagiri, H. Nakano, and K. Omukai, Stability of relativistic tidal response against small potential modification, Phys. Rev. D 108, 084049 (2023), arXiv:2304.04551 [gr-qc].
  • [37] V. De Luca, G. Franciolini, and A. Riotto, Flea on the elephant: Tidal Love numbers in subsolar primordial black hole searches, Phys. Rev. D 110, 104041 (2024), arXiv:2408.14207 [gr-qc].
  • [38] S. Roy, R. Vicente, J. C. Aurrekoetxea, K. Clough, and P. G. Ferreira, Scalar fields around black hole binaries in LIGO-Virgo-KAGRA, (2025), arXiv:2510.17967 [gr-qc].
  • [39] E. Barausse, V. Cardoso, and P. Pani, Environmental Effects for Gravitational-wave Astrophysics, J. Phys. Conf. Ser. 610, 012044 (2015), arXiv:1404.7140 [astro-ph.CO].
  • [40] E. Barausse, V. Cardoso, and P. Pani, Can environmental effects spoil precision gravitational-wave astrophysics?, Phys. Rev. D 89, 104059 (2014), arXiv:1404.7149 [gr-qc].
  • [41] Q. Alnasheet, V. Cardoso, F. Duque, and R. Panosso Macedo, Gravitational-wave tails and memory effect for mergers in astrophysical environments, Phys. Rev. D 112, 044066 (2025), arXiv:2508.20238 [gr-qc].
  • [42] G. Caneva Santoro, S. Roy, R. Vicente, M. Haney, O. J. Piccinni, W. Del Pozzo, and M. Martinez, First Constraints on Compact Binary Environments from LIGO-Virgo Data, Phys. Rev. Lett. 132, 251401 (2024), arXiv:2309.05061 [gr-qc].
  • [43] C. Lan, Y.-L. Tian, H. Yang, Z.-X. Zhang, and Y.-G. Miao, Quasinormal modes of regular black holes surrounded by skewed dark matter distributions, (2025), arXiv:2507.21414 [gr-qc].
  • [44] L. Pezzella, K. Destounis, A. Maselli, and V. Cardoso, Quasinormal modes of black holes embedded in halos of matter, Phys. Rev. D 111, 064026 (2025), arXiv:2412.18651 [gr-qc].
  • [45] E. Berti et al., Black hole spectroscopy: from theory to experiment, (2025), arXiv:2505.23895 [gr-qc].
  • [46] S. H. W. Leong, J. Calderón Bustillo, M. Gracia-Linares, and P. Laguna, Detectability of dense-environment effects on black-hole mergers: The scalar field case, higherorder ringdown modes, and parameter biases, Phys. Rev. D 108, 124079 (2023), arXiv:2308.03250 [gr-qc].
  • [47] V. De Luca, L. Del Grosso, F. Iacovelli, A. Maselli, and E. Berti, Systematic biases from ignoring environmental tidal effects in gravitational wave observations, Phys. Rev. D 111, 124046 (2025), arXiv:2503.10746 [gr-qc].
  • [48] T. Narikawa, N. Uchikata, and T. Tanaka, Gravitationalwave constraints on the GWTC-2 events by measuring the tidal deformability and the spin-induced quadrupole moment, Phys. Rev. D 104, 084056 (2021), [Erratum: Phys.Rev.D 111, 089903 (2025)], arXiv:2106.09193 [grqc].
  • [48] T. Narikawa, N. Uchikata, and T. Tanaka, Gravitationalwave constraints on the GWTC-2 events by measuring the tidal deformability and the spin-induced quadrupole moment, Phys. Rev. D 104, 084056 (2021), [Erratum: Phys.Rev.D 111, 089903 (2025)], arXiv:2106.09193 [grqc].
  • [49] H. S. Chia, T. D. P. Edwards, D. Wadekar, A. Zimmerman, S. Olsen, J. Roulet, T. Venumadhav, B. Zackay, and M. Zaldarriaga, In pursuit of Love numbers: First templated search for compact objects with large tidal deformabilities in the LIGO-Virgo data, Phys. Rev. D 110, 063007 (2024), arXiv:2306.00050 [gr-qc].
  • [50] A. G. Abac et al. (KAGRA, Virgo, LIGO Scientific), GW250114: Testing Hawking’s Area Law and the Kerr Nature of Black Holes, Phys. Rev. Lett. 135, 111403 (2025), arXiv:2509.08054 [gr-qc].
  • [51] A. G. Abac et al. (LIGO Scientific, VIRGO, KAGRA), Black Hole Spectroscopy and Tests of General Relativity with GW250114, (2025), arXiv:2509.08099 [gr-qc].
  • [52] E. Capote et al., Advanced LIGO detector performance in the fourth observing run, Phys. Rev. D 111, 062002 (2025), arXiv:2411.14607 [gr-qc].
  • [53] S. Soni et al. (LIGO), LIGO Detector Characterization in the first half of the fourth Observing run, Class. Quant. Grav. 42, 085016 (2025), arXiv:2409.02831 [astro-ph.IM].
  • [54] T. Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677, 1216 (2008), [Erratum: Astrophys.J. 697, 964 (2009)], arXiv:0711.2420 [astro-ph].
  • [54] T. Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677, 1216 (2008), [Erratum: Astrophys.J. 697, 964 (2009)], arXiv:0711.2420 [astro-ph].
  • [55] T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral, Phys. Rev. D 81, 123016 (2010), arXiv:0911.3535 [astro-ph.HE].
  • [56] T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80, 084035 (2009), arXiv:0906.0096 [gr-qc].
  • [57] K. Yagi and N. Yunes, I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics, Phys. Rev. D 88, 023009 (2013), arXiv:1303.1528 [gr-qc].
  • [58] M. A. Amin, M. Jain, R. Karur, and P. Mocz, Smallscale structure in vector dark matter, JCAP 08 (08), 014, arXiv:2203.11935 [astro-ph.CO].
  • [59] T. E. Riley et al., A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation, Astrophys. J. Lett. 887, L21 (2019), arXiv:1912.05702 [astro-ph.HE].
  • [60] M. Ryan and D. Radice, Exotic compact objects: The dark white dwarf, Phys. Rev. D 105, 115034 (2022), arXiv:2201.05626 [astro-ph.HE].
  • [61] R. Brito, V. Cardoso, C. A. R. Herdeiro, and E. Radu, Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles, Phys. Lett. B 752, 291 (2016), arXiv:1508.05395 [gr-qc].
  • [62] C. A. R. Herdeiro, G. Panotopoulos, and E. Radu, Tidal Love numbers of Proca stars, JCAP 08, 029, arXiv:2006.11083 [gr-qc].
  • [63] R. F. Diedrichs, N. Becker, C. Jockel, J.-E. Christian, L. Sagunski, and J. Schaffner-Bielich, Tidal deformability of fermion-boson stars: Neutron stars admixed with ultralight dark matter, Phys. Rev. D 108, 064009 (2023), arXiv:2303.04089 [gr-qc].
  • [64] M. Jain and M. A. Amin, Polarized solitons in higherspin wave dark matter, Phys. Rev. D 105, 056019 (2022), arXiv:2109.04892 [hep-th].
  • [65] T. Abdelsalhin, L. Gualtieri, and P. Pani, PostNewtonian spin-tidal couplings for compact binaries, Phys. Rev. D 98, 104046 (2018), arXiv:1805.01487 [grqc].
  • [66] S. Husa, S. Khan, M. Hannam, M. Pürrer, F. Ohme, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal, Phys. Rev. D 93, 044006 (2016), arXiv:1508.07250 [gr-qc].
  • [67] S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. Jiménez Forteza, and A. Bohé, Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era, Phys. Rev. D 93, 044007 (2016), arXiv:1508.07253 [gr-qc].
  • [68] M. Hannam, P. Schmidt, A. Bohé, L. Haegel, S. Husa, F. Ohme, G. Pratten, and M. Pürrer, Simple Model of Complete Precessing Black-Hole-Binary Gravitational Waveforms, Phys. Rev. Lett. 113, 151101 (2014), arXiv:1308.3271 [gr-qc].
  • [69] M. Agathos, W. Del Pozzo, T. G. F. Li, C. Van Den Broeck, J. Veitch, and S. Vitale, TIGER: A data analysis pipeline for testing the strong-field dynamics of general relativity with gravitational wave signals from coalescing compact binaries, Phys. Rev. D 89, 082001 (2014), arXiv:1311.0420 [gr-qc].
  • [70] S. Roy, M. Haney, G. Pratten, P. T. H. Pang, and C. Van Den Broeck, An improved parametrized test of general relativity using the IMRPhenomX waveform family: Including higher harmonics and precession, (2025), arXiv:2504.21147 [gr-qc].
  • [71] T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M. Agathos, J. Veitch, K. Grover, T. Sidery, R. Sturani, and A. Vecchio, Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence, Phys. Rev. D 85, 082003 (2012), arXiv:1110.0530 [gr-qc].
  • [72] J. Meidam et al., Parametrized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method, Phys. Rev. D 97, 044033 (2018), arXiv:1712.08772 [gr-qc].
  • [73] M. De Laurentis, O. Porth, L. Bovard, B. Ahmedov, and A. Abdujabbarov, Constraining alternative theories of gravity using GW150914 and GW151226, Phys. Rev. D 94, 124038 (2016), arXiv:1611.05766 [gr-qc].
  • [74] B. P. Abbott et al. (LIGO Scientific, Virgo), Tests of General Relativity with GW170817, Phys. Rev. Lett. 123, 011102 (2019), arXiv:1811.00364 [gr-qc].
  • [75] B. P. Abbott et al. (LIGO Scientific, Virgo), Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1, Phys. Rev. D 100, 104036 (2019), arXiv:1903.04467 [gr-qc].
  • [76] R. Abbott et al. (LIGO Scientific, Virgo), Tests of general relativity with binary black holes from the second LIGOVirgo gravitational-wave transient catalog, Phys. Rev. D 103, 122002 (2021), arXiv:2010.14529 [gr-qc].
  • [77] K. Wette, SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis libraries, SoftwareX 12, 100634 (2020), arXiv:2012.09552 [astroph.IM].
  • [78] LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, LVK Algorithm Library - LALSuite, Free software (GPL) (2018).
  • [79] G. Ashton et al., BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. 241, 27 (2019), arXiv:1811.02042 [astro-ph.IM].
  • [80] I. M. Romero-Shaw et al., Bayesian inference for compact binary coalescences with bilby: validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. Roy. Astron. Soc. 499, 3295 (2020), arXiv:2006.00714 [astro-ph.IM].
  • [81] J. S. Speagle, dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. Roy. Astron. Soc. 493, 3132 (2020), arXiv:1904.02180 [astro-ph.IM].
  • [82] W. M. Farr, B. Farr, and T. Littenberg, Modelling calibration errors in cbc waveforms, Tech. Rep. T1400682 (LIGO, 2014).
  • [83] M. Andrés-Carcasona and G. Caneva Santoro, Data release for ”No Love for black holes: tightest constraints on tidal Love numbers of black holes from GW250114”, https://doi.org/10.5281/zenodo. 17772027 (2025), Zenodo.
  • [84] Data release for Testing strong-field gravity with tidal Love numbers, https://centra.tecnico.ulisboa.pt/ network/grit/files/tidal-love-numbers/, accessed: 2025-11-02.
  • [85] L. Wade, J. D. E. Creighton, E. Ochsner, B. D. Lackey, B. F. Farr, T. B. Littenberg, and V. Raymond, Systematic and statistical errors in a bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors, Phys. Rev. D 89, 103012 (2014), arXiv:1402.5156 [gr-qc].
  • [86] M. van der Sluys, V. Raymond, I. Mandel, C. Rover, N. Christensen, V. Kalogera, R. Meyer, and A. Vecchio, Parameter estimation of spinning binary inspirals using Markov-chain Monte Carlo, Class. Quant. Grav. 25, 184011 (2008), arXiv:0805.1689 [gr-qc].
  • [87] M. V. van der Sluys, C. Röver, A. Stroeer, V. Raymond, I. Mandel, N. Christensen, V. Kalogera, R. Meyer, and A. Vecchio, Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries, Astrophys. J. Lett. 688, L61 (2008), arXiv:0710.1897 [astro-ph].
  • [88] J. Veitch and A. Vecchio, A Bayesian approach to the follow-up of candidate gravitational wave signals, Phys. Rev. D 78, 022001 (2008), arXiv:0801.4313 [gr-qc].
  • [89] V. De Luca, A. Maselli, and P. Pani, Modeling frequency-dependent tidal deformability for environmental black hole mergers, Phys. Rev. D 107, 044058 (2023), arXiv:2212.03343 [gr-qc].
  • [90] A. Abac et al. (ET), The Science of the Einstein Telescope, (2025), arXiv:2503.12263 [gr-qc].
  • [91] D. J. Kaup, Klein-Gordon Geon, Phys. Rev. 172, 1331 (1968).
  • [92] M. Colpi, S. L. Shapiro, and I. Wasserman, Boson Stars: Gravitational Equilibria of Selfinteracting Scalar Fields, Phys. Rev. Lett. 57, 2485 (1986).
  • [93] R. Friedberg, T. D. Lee, and Y. Pang, Scalar Soliton Stars and Black Holes, Phys. Rev. D 35, 3658 (1987). Details of the analysis The PN-phase deviations during the inspiral are implemented in the IMRPhenomPv2 waveform of the LALSuite [78] package by exploiting its reliance on the TaylorF2 approximation in the inspiral regime. During this regime, the strain is approximated, in the frequency domain, as h̃(f) = Af−7/6 exp [iψ(f)] , (7) where A is the amplitude and ψ(f) the phase. Since the tidal corrections add linearly to the point-particle phase of the TaylorF2, the phase simply becomes [85] ψ(f) = ψpp(f) + δψtidal(f) . (8) In the IMRPhenomPv2, the total phase is built piecewise from inspiral, intermediate and merger-ringdown sectors using smooth window functions to ensure C1 continuity at the transition frequencies.Since our tidal modification is applied at the phase level only during the inspiral, we subtract the constant and linear contributions of the tidal phase at a reference frequency to avoid shifting the coalescence time and phase, which are re-fit as free parameters. This is the same stitching strategy used in LAL