The Route to Unveil the Cosmic Genealogy of Supermassive Black Hole Binaries Using Nanohertz Gravitational Waves and Galaxy Surveys

The nanohertz stochastic gravitational wave background (SGWB), generated by unresolved supermassive black hole binaries (SMBHBs), provides a unique probe of their population and its cosmic evolution. In this work, we explore the potential of uncovering the SMBHB population and its redshift dependence by combining the SGWB signal and its anisotropies with galaxy distribution through cross-correlation analyses. Using a Fisher analysis technique, we show that the SGWB power spectrum alone can not provide any information on the evolutionary history of SMBHBs, whereas the inclusion of the angular power spectrum of the SGWB and its cross-correlation with the galaxy distribution substantially improves constraints on the redshift evolution parameters. Assuming pulsar timing array configurations achievable in the Square Kilometre Array era, we find that the combined use of isotropic and anisotropic SGWB signals, together with galaxy surveys, can provide valuable measurements of the redshift evolution of the SMBH–galaxy connection and the frequency distribution of SMBHBs. These results highlight the potential of joint gravitational wave–galaxy studies to address the long-standing open question of SMBH growth and evolution across cosmic time.