Primordial black hole contribution to the stochastic background of gravitational waves
The amplitude of the detected stochastic gravitational-wave background (SGWB) measured by pulsar timing arrays (PTAs) and the discovery of early and over-massive central black holes at high redshift by the James Webb Space Telescope (JWST) challenge current models of supermassive black hole (SMBH) formation. We aim to study if halos containing a significant population of primordial black holes (PBHs) would increase the amplitude of the PTA signal. PBHs add an iso-curvature component to the matter power spectrum, accelerating the formation and merger of dark-matter halos at all redshifts. We propose that black holes in the halo sink to the center via dynamical friction. The central black hole grows through hierarchical merging in addition to the gas-accretion channel. We computed the resulting GW amplitude and performed a Bayesian inference analysis using the NANOGrav 15-year dataset. We show that the predicted amplitude of the gravitational-wave background agrees with the observations. Our model only requires $0.09\%-0.12\%$ of the total mass of the halo to fall to the center; this is compatible with a fraction of $f_{\rm pbh}\sim 0.1$ PBHs being dark matter if the in-falling PBHs in the stellar mass range represent about $1\%$ of the total population, as was found in our previous estimation of the formation of SMBHs at $z\sim 6-10$. The PBH model that explains the JWST new found populations of SMBHs also explain the amplitude of the stochastic background of gravitational waves.