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Gravitational-wave (GW) measurements of physical effects such as spin-inducedquadrupole moments can distinguish binaries consisting of black holes fromnon-black hole binaries. While these effects may be poorly constrained forsingle-event inferences with the second-generation detectors, combininginformation from multiple detections can help uncover features of non-blackhole binaries. The spin-induced quadrupole moment has specific predictions fordifferent types of compact objects, and a generalized formalism must consider apopulation where different types of compact objects co-exist. In this study, weintroduce a hierarchical mixture-likelihood formalism to estimate the {\itfraction of non-binary black holes in the population}. We demonstrate theapplicability of this method using simulated GW signals injected into Gaussiannoise following the design sensitivities of the Advanced LIGO Advanced Virgodetectors. We compare the performance of this method with atraditionally-followed hierarchical inference approach. Both the methods areequally effective to hint at inhomogeneous populations, however, we find themixture-likelihood approach to be more natural for mixture populationscomprising compact objects of diverse classes. We also discuss the possiblesystematics in the mixture-likelihood approach, caused by several reasons,including the limited sensitivity of the second-generation detectors, specificfeatures of the astrophysical population distributions, and the limitationsposed by the waveform models employed. Finally, we apply this method to theLIGO-Virgo detections published in the second GW transient catalog (GWTC-2) andfind them consistent with a binary black hole population within the statisticalprecision.

Population inference of spin-induced quadrupole moments as a probe for non-black hole compact binaries