Measurability of Quadrupole Deviations from Kerr in Binary black hole Mergers

Abstract: We investigate the measurability of black hole quadrupole deviations from Kerr using five binary black hole mergers observed by the LIGO-Virgo-KAGRA Collaboration with the beyond-general-relativity full-waveform model $Ψ<em>{\mathrm{FD}}$. While earlier lower-SNR events mildly favored nonzero quadrupole deviations, the newly included high-SNR GWTC-4 events GW231226, GW230814, and GW250114 yield results increasingly consistent with the Kerr prediction. In particular, GW230814 and GW250114, the two highest-SNR events in our sample, yield deviations consistent with zero. We further perform separate inspiral and post-inspiral analyses and find both the posterior distributions centered close to $ΔQ/Q=0$ for GW230814 and GW250114. Overall, the full-waveform, inspiral, and post-inspiral results for GW230814 and GW250114 reveal no observable departure from the no-hair theorem within the sensitivity of the current data and the $Ψ</em>{\mathrm{FD}}$ framework. Although the limited number of events prevents a definitive conclusion, future detections of additional high-SNR binary black hole mergers will enable increasingly stringent and robust tests of the Kerr nature of black holes.