The nanohertz gravitational wave background (GWB) is believed to be dominated by GW emission from supermassive black hole binaries (SMBHBs). Observations of several dual active galactic nuclei (AGN) strongly suggest a link between AGN and SMBHBs, given that these dual AGN systems will eventually form bound binary pairs. Here we develop an exploratory SMBHB population model based on empirically constrained quasar populations, allowing us to decompose the GWB amplitude into an underlying distribution of SMBH masses, SMBHB number density, and volume enclosing the GWB. Our approach also allows us to self-consistently predict the GWB amplitude and the number of local SMBHB systems. Interestingly, we find the local number density of SMBHBs implied by the common-process signal in the NANOGrav 12.5-yr dataset to be roughly five times larger than previously predicted by other models. We also find that at most $sim 25 %$ of SMBHBs can be associated with quasars. Furthermore, our quasar-based approach predicts $gtrsim 95%$ of the GWB signal comes from $z lesssim 2.5$, and that SMBHBs contributing to the GWB have masses $gtrsim 10^8 M_odot$. We also explore how different empirical galaxy-black hole scaling relations affect the local number density of GW sources, and find that relations predicting more massive black holes decrease the local number density of SMBHBs. Overall, our results point to the important role that a measurement of the GWB will play in directly constraining the cosmic population of SMBHBs, as well as their connections to quasars and galaxy mergers.
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