Black hole merger rates in the first billion years in light of JWST data

Recent James Webb Space Telescope (JWST) discoveries have unveiled an abundance of faint and massive active galactic nuclei (AGNs) at high redshifts (z=4-9) that surpass the extrapolated bolometric and ultraviolet luminosity functions from previous AGN campaigns by ten to one hundred times. The two main models that have been put forward to explain these observations correspond to light seeds (≈ 150 M_⊙) accreting in episodes of super Eddington, and heavy seeds (≈ 10^3 - 10^5 M_⊙) growing at the Eddington limit. Future gravitational observatories such as the Laser Interferometer Satellite Antenna (LISA) will help disentangle these models by reporting the black hole merger events from mid to high redshifts. With this work, we aim to report the predicted merger rates in the heavy seed scenario in light of recent JWST data. In our models we explores (i) instantaneous merging between BHs, and (ii) delayed merging after a dynamical timescale, as well as extreme spin configurations (a=0.99, a=-0.99) to bracket BH mass growth. We used Delphi, a semi-analytical model that tracks baryonic physics over a hierarchical evolution of dark matter halos through cosmic time within the first billion years of the Universe. We calibrated this model for it to simultaneously reproduce galaxy and JWST-AGN observables. We show reasonable agreement with the bolometric luminosity function at z=6, where BHs must accrete ten to one hundred times more gas than in previous works calibrated to pre-JWST data. However, we underpredict (overpredict) the bright end 10^45.5erg s -1 $ (all luminosity range) at z=7 (z=5) by 1-3.2 dex (0.22-1.6 dex). Regarding BH-BH merger events, the instantaneous (delayed) models predict a total of 28.06 (19.61) yr^-1 for BHs at z$≥5, which is within the range of merger rates reported in previous literature.