Description
In 2023, NANOGrav and other pulsar timing arrays (PTAs), reported evidence for a stochastic gravitational-wave background (GWB) in the nanohertz (nHz) frequency band. One of the most promising candidates for the origin of this signal is the merger of supermassive black hole binaries (SMBHBs). Supermassive black holes (SMBHs), with masses exceeding $10^6 M_\odot$, are believed to reside at the centers of nearly all massive galaxies. However, the formation and growth mechanisms of these black holes remain poorly understood. Previous simulation studies have suggested that the amplitude of the stochastic GWB generated by SMBHB mergers is smaller than the value reported by the NANOGrav 15-year data (NG15). In this study, we propose that the nHz-band GWB recently reported by the NANOGrav 15-year dataset can be explained by mergers of SMBHBs with masses of $10^9 M_\odot$ that are formed through the growth of primordial black holes (PBHs). If PBHs accrete matter at a high rate, they emit a large number of high-energy photons, which heat the surrounding plasma and induce cosmological 21 cm radiation at high redshifts. Since such radiation has not been observed, stringent upper limits are imposed on the accretion rate. We show that, for a PBH abundance in the range $10^{-14} \lesssim f_{\rm PBH} \lesssim 10^{-12}$ and PBH masses of $1 M_\odot \lesssim m_{\rm PBH} \lesssim 10^3 M_\odot$, it is possible to explain the nHz-band GWB observed by the NANOGrav 15-year data while avoiding constraints from 21 cm radiation. We propose that future gravitational-wave observations and cosmological 21 cm measurements will provide critical tests of this scenario.
