Bounds on the spatial anisotropy of foreground binary black hole merger detections in the third LIGO-Virgo-KAGRA catalog

The detection of about one hundred binary black hole mergers in the first three LIGO-Virgo-KAGRA observing runs has turned GW astrophysics into a precision observational science. In large-scale astrophysics and observational cosmology, the two-point auto-correlation function (or its homolog in the frequency space, the power spectrum) is commonly used to describe the spatial distribution of galaxies or the density fluctuations in the cosmic microwave background. We measure the level of anisotropy in the observed spatial distribution of gravitational-wave binary black hole mergers by computing the power spectrum and the two-dimensional correlation function of detections from the third LIGO-Virgo-KAGRA catalog, GWTC-3. The degree of clustering in the spatial and angular distribution of BBH mergers at different angular scales is measured by comparing the observed power spectrum with the power spectrum of uniformly distributed synthetic data sets produced according to the latest GWTC-3 rate and population functions. This method complements traditional stochastic gravitational-wave background searches as it probes anisotropy through resolved foreground sources. Even though the two methods essentially target the same signal in the limit of a large number of detections, the foreground analysis is expected to have higher resolution at smaller angular scales. With the expected rapid growth in the number of binary black hole coalescence detections and the improvement in their sky localizations, this method could be used in the future to produce direct upper limits on the degree of correlation between gravitational-wave sources and other populations of extragalactic objects.