The Emerging Black Hole Mass Function in the High-Redshift Universe

Observations with the James Webb Space Telescope (JWST) have identified an abundant population of supermassive black holes (SMBHs) already in place during the first few hundred million years of cosmic history. Most of them appear overmassive relative to the stellar mass in their host systems, challenging models of early black hole seeding and growth. Multiple pathways exist to explain their formation, including heavy seeds formed from direct collapse/supermassive stars or sustained super-Eddington accretion onto light stellar remnant seeds. We use the semi-analytical code A-SLOTH to predict the emerging SMBH mass function under physically motivated models for both light and heavy seed formation, to be compared with upcoming ultra-deep JWST surveys. We find that both pathways can reproduce observations at $z\sim5-6$, but have distinct features at higher redshifts of $z\sim10$. Specifically, JWST observations have the potential to constrain the fraction of efficiently accreting (super-Eddington) SMBHs, as well as the existence and prevalence of heavy seeds, in particular through ultra-deep observations of blank fields and/or gravitational lensing surveys. Such observations will provide key insights to understand the process of SMBH formation and evolution during the emergence of the first galaxies. We further emphasize the great promise of possible SMBH detections at $z\gtrsim 15$ with future JWST observations to break the degeneracy between light- and heavy-seed models.