Forecasting Supermassive Black Hole Binary Gravitational Wave Probes: Prospects for Future Pulsar Timing Array and Space-Borne Detectors

We present a comprehensive framework for predicting the detection prospects of supermassive black hole binaries (SMBHBs) by future gravitational wave (GW) observatories, examining both space-borne detectors (LISA, Taiji, TianQin) and next-generation pulsar timing array (PTA) combined with the Square Kilometre Array (SKA-PTA). Leveraging dual active galactic nucleus (AGN) fractions and AGN X-ray luminosity functions, we systematically evaluate the detectable SMBHB populations with a detection threshold of signal-to-noise ratio $\geq 5$ for each GW observatory. Our analysis reveals that space-borne detectors are expected to identify approximately $\sim 1 \text{--} 2$ to $\sim 20$ events per year, depending on the SMBHB orbital evolution prescriptions. On the other hand, SKA-PTA demonstrates the potential to reach the first GW detection from individual SMBHBs within a few years of observation and achieve detectable GW source counts of $10^2 \text{--} 10^3$ after about 10 years, depending on PTA configurations. These facilities will significantly improve SMBHB detectability and enable characterization of their properties across different frequency bands.