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The physical degrees of freedom of a gravitational wave (GW) are imprints ofthe nature of gravity. We can test a gravity theory by searching forpolarization modes beyond general relativity. The LIGO-Virgo collaborationanalyzed several GW events in the O1 and O2 observing runs in the purepolarization framework, where they perform the Bayesian model selection betweengeneral relativity and the theory allowing only scalar or vector polarizationmodes. In this paper, we reanalyze the polarizations of GW170814 (binary blackhole merger) and GW170817 (binary neutron star merger) in the improvedframework of pure polarizations including the angular patterns of nontensorialradiation. We find logarithms of the Bayes factors of 2.775 and 3.636 forGW170814 in favor of the pure tensor polarization against pure vector andscalar polarizations, respectively. These Bayes factors are consistent with theprevious results by the LIGO-Virgo collaboration, though the estimatedparameters of the binaries are significantly biased. For GW170817 with thepriors on the location of the binary from NGC4993, we find logarithms of theBayes factors of 21.078 and 44.544 in favor of the pure tensor polarizationagainst pure vector and scalar polarizations, respectively. These more stronglysupport GR, epecially compared to the scalar polarization, than the previousresults by the LIGO-Virgo collaboration due to the location prior. In addition,by utilizing the orientation information of the binary from a gamma-ray burstjet, we find logarithms of the Bayes factor of 51.043 and 60.271 in favor ofthe pure tensor polarization against pure vector and pure scalar polarization,much improved from those without the jet prior.

Pure polarization test of GW170814 and GW170817 using waveforms consistent with modified theories of gravity