http://arxiv.org/abs/2201.10258
Detection of the gravitational-wave events revealed that there are numerous population of the black hole binaries which can merge within the age of the Universe. Although several formation channels of such binaries are known, considerable theoretical uncertainties associated in each channel defeats the robust prediction of how much each channel contributes to the total merger rate density. Given that the time evolution of the merger rate density in some channels is (exactly or nearly) independent of the BH masses, clarifying this feature from the observational data will shed some light on the nature of the black hole binaries. Based on this motivation, we formulate the methodology to perform the statistical test of whether the mass distribution of the black hole mergers evolves in time or not by means of the hypothesis testing. Our statistical test requires neither a priori specification of the mass distribution which is largely uncertain nor that of the time dependence of the merger rate. We then apply it to the mock data for some concrete shapes of the merger rate density and show that the proposed method rejects/(does not reject) the null hypothesis correctly for the large sample size. We also investigate if the catalog of the gravitational-wave events obtained during the LIGO-Virgo’s third observing run has a large sample size enough to apply our hypothesis testing. We find that the number of the events is too small to draw any statistical conclusion regarding our test and the meaningful result of our hypothesis testing can be obtained only by the future detectors having much better sensitivity. These results demonstrate the effectiveness of our hypothesis testing to determine from the (future) observational data whether the merger rate density evolves in time independently of the BH masses or not.
S. Okano and T. Suyama
Wed, 26 Jan 22
5/53
Comments: 19 pages, 6 figures