Measurement of the cross-correlation angular power spectrum between the stochastic gravitational wave background and galaxy overdensity

We study the cross-correlation between the stochastic gravitational-wave background (SGWB) generated by binary black hole mergers across the Universe and the distribution of galaxies across the sky. We use the anisotropic SGWB measurement obtained using data from the third observing run (O3) of Advanced LIGO detectors and galaxy overdensity obtained from the Sloan Digital Sky Survey spectroscopic catalog. We compute, for the first time, the angular power spectrum of their cross-correlation. Instead of integrating the SGWB across frequencies, we analyze the cross-correlation in 10-Hz-wide SGWB frequency bands to study the frequency dependence of the cross-correlation angular power spectrum. Finally, we compare the observed cross-correlation to the spectra predicted by astrophysical models. We apply a Bayesian formalism to explore the parameter space of the theoretical models, and we set constraints on a set of (effective) astrophysical parameters describing the galactic process of gravitational-wave (GW) emission. Parametrizing with a Gaussian function the astrophysical kernel describing the local process of GW emission at galactic scales, we find the 95% upper limit on kernel amplitude to be $2.88\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}32}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{cm}}^{\ensuremath{-}3}\text{ }{\mathrm{s}}^{\ensuremath{-}1/3}$ when ignoring the shot noise in the GW emission process and $2.52\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}32}\text{ }\text{ }\mathrm{erg}\text{ }{\mathrm{cm}}^{\ensuremath{-}3}\text{ }{\mathrm{s}}^{\ensuremath{-}1/3}$ when the shot noise is included in the analysis. As the sensitivity of the LIGO-Virgo-KAGRA network improves, we expect to be able to set more stringent bounds on this kernel function and constrain its parameters.