Searching for cross-correlation between stochastic gravitational-wave background and galaxy number counts

Advanced LIGO and Advanced Virgo have recently published the upper limit measurement of persistent directional stochastic gravitational wave background (SGWB) based on data from their first and second observing runs (O1 and O2). In this paper we investigate whether a correlation exists between this maximal likelihood SGWB map and the electromagnetic tracers of matter structure in the universe, such as galaxy number counts. The method we develop will improve the sensitivity of future searches for anisotropy in the SGWB and expand the use of SGWB anisotropy to probe the formation of structure in the universe. In order to compute the cross-correlation, we used the spherical harmonic decomposition of SGWB in multiple frequency bands and converted them into pixel-based sky maps in HEALPix basis. For the electromagnetic (EM) part, we use the Sloan Digital Sky Survey (SDSS) galaxy catalog and form HEALPix sky maps of galaxy number counts at the same angular resolution as the SGWB maps. We compute the pixel-based coherence between these SGWB and galaxy count maps. After evaluating our results in different SGWB frequency bands and in different galaxy redshift bins, we conclude that the coherence between the SGWB and galaxy number count maps is dominated by the null measurement noise in the SGWB maps, and therefore not statistically significant. We expect the results of this analysis to be significantly improved by using the more sensitive upcoming SGWB measurements based on the third observing run (O3) of Advanced LIGO and Advanced Virgo.