Detecting Black-Hole Binary Clustering via the Second-Generation Gravitational-Wave Detectors

The first discovery of the gravitational wave (GW) event, GW150914, suggests a higher merger rate of black-hole (BH) binaries. If this is true, a number of BH binaries will be observed via the second-generation GW detectors, and the statistical properties of the observed BH binaries can be scrutinized. A naive but important question to ask is whether the spatial distribution of BH binaries faithfully traces the matter inhomogeneities in the Universe or not. Although the BH binaries are thought to be formed inside the galaxies in most of the scenarios, there is no observational evidence to confirm such a hypothesis. Here, we estimate how well the second-generation GW detectors can statistically confirm the BH binaries to be a tracer of the large-scale structure by looking at the auto- and cross-correlation of BH binaries with photometric galaxies and weak lensing measurements, finding that, with a 3 year observation, the $>3\sigma$ detection of non-zero signal is possible if the BH merger rate today is $\dot{n}_0\gtrsim100$ Gpc$^{-3}$yr$^{-1}$ and the clustering bias of BH binaries is $b_{\rm BH,0}\gtrsim1.5$.