Coherence of Supermassive Black Hole Binary Demographics with the nHz Stochastic Gravitational Wave Background

We present a refined estimation of the stochastic gravitational wave background (SGWB) based on observed dual active galactic nuclei (AGNs) together with AGN X-ray luminosity functions, in light of recent Pulsar Timing Array detections of an nHz SGWB. We identify a characteristic luminosity dependence in dual AGN fractions by compiling recent observational datasets, providing crucial constraints on supermassive black hole binary (SMBHB) populations. Our AGN-based model reproduces the current SGWB measurements within PTA observational uncertainties of $2 - 4 \sigma$ uncertainties, demonstrating consistency between electromagnetic and gravitational wave observations. These findings establish SMBHBs as the dominant source of the nHz gravitational wave signal, providing crucial insights into their demographics and evolution.