Primordial black holes as supermassive black holes seeds

The presence of supermassive black holes (SMBHs, $M_{\bullet}\sim 10^{6-10}~M_{\odot}$) in the first cosmic Gyr ($z\gtrsim 6$) challenges current models of BH formation and evolution. We propose a novel mechanism for the formation of early SMBH seeds based on primordial black holes (PBHs). We assume a non-Gaussian primordial power spectrum as expected in inflationary models; these scenarios predict that PBHs are initially clustered and preferentially formed in the high-$\sigma$ fluctuations of the large-scale density field, out of which dark matter (DM) halos are originated. Our model accounts for (i) PBH accretion and feedback, (ii) DM halo growth, and (iii) gas dynamical friction. PBHs lose angular momentum due to gas dynamical friction, sink into a dense core, where BH binaries form and undergo a runaway merger, eventually leading to the formation of a single, massive seed. This mechanism starts at $z\sim 20-40$ in rare halos ($M_h\sim 10^7\ M_\odot$ corresponding to $\sim 5-7\sigma$ fluctuations), and provides massive ($\sim 10^{4-5}~ M_{\odot}$) seeds by $z\sim 10-30$. We derive a physically-motivated seeding prescription that provides the mass of the seed, $M_{\rm seed}(z)=3.1\times 10^{5}\ { M_{\odot}}[(1+z)/10]^{-1.2}$, and seeded halo, $M_{h}(z)=2\times 10^{9}\ {M_{\odot}}[(1+z)/10]^{-2}e^{-0.05z}$ as a function of redshift. This seeding mechanism requires that only a small fraction of DM is constituted by PBHs, namely $f_{\rm PBH}\sim 3 \times 10^{-6}$. We find that $z\sim 6-7$ quasars can be explained with $6\times 10^4 M_{\rm \odot}$ seeds planted at $z\sim 32$, and growing at sub-Eddington rates, $\langle\lambda_{\rm E}\rangle\sim 0.55$. The same scenario reproduces the BH mass of GNz11 at $z=10.6$, while UHZ1 ($z=10.1$) and GHZ9 ($z=10$) data favour instead slightly later ($z\sim 20-25$), more massive ($10^5~M_{\rm \odot}$) seeds. [Abridged]