Primordial black holes as supermassive black hole seeds

Abstract The presence of supermassive black holes (SMBHs, M • ∼ 10 6-10 M ⊙ ) in the first cosmic Gyr ( z ≳ 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- σ 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 ∼ 20-40 in rare halos ( M h ∼ 10 7 M ⊙ corresponding to ∼ 5-7 σ fluctuations), and provides massive (∼ 10 4-5 M ⊙ ) seeds by z ∼ 10-30. We derive a physically-motivated seeding prescription that provides the mass of the seed, M seed ( z ) = 3.1 × 10 5 M ⊙ [(1 + z )/10] -1.2 , and seeded halo, M h ( z ) = 2 × 10 9 M ⊙ [(1 + z )/10] -2 e -0.05 z as a function of redshift. This seeding mechanism requires that only a small fraction of DM is constituted by PBHs, namely f PBH ∼ 3 × 10 -6 . We find that z ∼ 6 - 7 quasars can be explained with 6 × 10 4 M ⊙ seeds planted at z ∼ 32, and growing at sub-Eddington rates, 〈λ E 〉 ∼ 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 ∼ 20-25), more massive (10 5 M ⊙ ), and efficiently accreting (〈λ E 〉 ≃ 0.9) seeds. During the runaway phase of the proposed seed formation process, PBH-PBH mergers are expected to copiously emit gravitational waves. These predictions can be tested through future Einstein Telescope observations and used to constrain inflationary models.