Pulsar timing array detections of supermassive binary black holes: implications from the detected common process signal and beyond

Pulsar timing arrays (PTAs) are anticipated to detect the stochastic gravitational wave background (GWB) from supermassive binary black holes (BBHs) as well as the gravitational waves from individual BBHs. Recently, a common process signal was reported by several PTAs. In this paper, we investigate the constraints on the BBH population model(s) by current PTA observations and further study the detections of both the GWB and individual BBHs by current/future PTAs. We find that the MBH--host galaxy scaling relation, an important ingredient of the BBH population model, is required to either evolve significantly with redshift or have a normalization $\sim0.86-1.1$ dex higher than the empirical ones, if the GWB is the same as the common process signal. For both cases, the estimated detection probability for individual BBHs is too small for a positive detection by current PTAs. By involving either the constrained scaling relations or those empirical ones into the BBH population models, we estimate that the GWB may be detected with a signal-to-noise ratio $\gtrsim3$ by the PTAs based on the Five hundred meter Aperture Spherical radio Telescope (CPTA) and the Square Kilometer Array (SKAPTA) after $\sim2-3$ (or $\sim6-11$) years' observation, if it is the same as (or an order of magnitude lower than) the common process signal. The detection time of individual BBHs by CPTA and SKAPTA is close to that of the GWB detection. We show that the BBH population model can be strongly constrained by the number and property distributions of BBHs to be detected by future PTAs.