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According to the "no-hair" conjecture, a Kerr black hole (BH) is completelydescribed by its mass and spin. In particular, the spin-induced quadrupolemoment of a Kerr BH with mass $m$ and dimensionless spin $\chi$ can be writtenas $Q=-\kappa\,m^3\chi^2$, where $\kappa_{\rm BH}=1$. Thus by measuring thespin-induced quadrupole parameter $\kappa$, we can test the binary black holenature of compact binaries and distinguish them from binaries comprised ofother exotic compact objects, as proposed in [N. V. Krishnendu et al., PRL 119,091101 (2017)]. Here, we present a Bayesian framework to carry out this testwhere we measure the symmetric combination of individual spin-inducedquadrupole moment parameters fixing the anti-symmetric combination to be zero.The analysis is restricted to the inspiral part of the signal as thespin-induced deformations are not modeled in the post-inspiral regime. Weperform detailed simulations to investigate the applicability of this methodfor compact binaries of different masses and spins and also explore variousdegeneracies in the parameter space which can affect this test. We then applythis method to the gravitational wave events, GW151226 and GW170608 detectedduring the first and second observing runs of Advanced LIGO and Advanced Virgodetectors. We find the two events to be consistent with binary black holemergers in general relativity. By combining information from several more ofsuch events in future, this method can be used to set constraints on the blackhole nature of the population of compact binaries that are detected by theAdvanced LIGO and Advanced Virgo detectors.

Constraints on the binary black hole nature of GW151226 and GW170608 from the measurement of spin-induced quadrupole moments