Constraining supermassive primordial black hole clustering with the angular auto-correlation of $z\simeq 6$ quasars

Abstract

High-redshift quasars provide a direct probe of the origin and environment of the earliest supermassive black holes. We use their angular auto-correlation function at $z\simeq 6$ to test scenarios in which supermassive primordial black holes (SMPBHs) are associated with the observed quasar population. The evolved PBH correlation functions, for both Poisson fluctuations and initial PBH clustering, are projected over the quasar redshift window and compared with the measured angular correlation function using Markov chain Monte Carlo inference. It is observed that for the Poisson model, the posterior favors a small abundance, $f_{\rm PBH}\sim 10^{-3}$, and a supermassive effective mass scale, $m_{\rm PBH}\sim 10^{12}M_\odot$, interpreted here as a scale controlling quasar host-halo formation and clustering, and for the initially clustered model, the data prefer an effective clustering amplitude $ξ_{\rm eff}\simeq 2.1$ and a top-hat boundary scale $r_{\rm cl}\simeq 76\,{\rm Mpc}$, corresponding to weak relative contraction of PBH pairs in comoving coordinates.