Implications for the supermassive black hole binaries from the NANOGrav 15-year data set

Several pulsar timing array (PTA) collaborations, including NANOGrav, EPTA, PPTA, and CPTA, have announced the evidence for a stochastic signal consistent with a stochastic gravitational wave background (SGWB). Supermassive black hole binaries (SMBHBs) are supposed to be the most promising gravitational-wave (GW) sources for this signal. In this paper, we use the NANOGrav 15-year data set to constrain the parameter space in an astro-informed formation model for SMBHBs. Our results prefer a large turn-over eccentricity of the SMBHB orbit when GWs begin to dominate the SMBHB evolution. Furthermore, the SGWB spectrum is extrapolated to the space-borne GW detector frequency band by including inspiral-merge-cutoff phases of SMBHBs, indicating that the SGWB from SMBHBs should be detected by LISA, Taiji and TianQin in the near future.