In this paper, we explain the recently reported a nHz-band gravitational-wave background from NANOGrav 15-year through the merger of binary super-massive black holes with masses of ${10}^9{M}_{\odot }$ formed by the growth of primordial black holes. When a primordial black hole accretes at a high accretion rate, it emits a large number of high-energy photons. These heat the plasma, causing high-redshift cosmological 21 cm line emission. Since this has not been detected, there is a strict upper bound on the accretion rate. We have found that with the primordial black hole abundance ${10}^{-14}\lesssim f_{\mathrm{PBH}}\lesssim {10}^{-12}$ and the mass $1M_{\odot }\lesssim m_{\mathrm{PBH}}\lesssim {10}^3{M}_{\odot }$, we successfully fit the nHz band gravitational wave background from NANOGrav 15-year while avoiding the 21 cm line emission. In addition, we also discuss the implication for the origins of the little red dots. We propose that future observations of the gravitational wave background and the cosmological 21 cm line can test this scenario.

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• Cosmology
• Gravitational waves