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.
