Too many or too massive? Investigating the high-$z$ demography of active SMBHs from JWST
Recent JWST observations have unveiled a numerous population of low-luminosity active galactic nuclei (AGN) at $4< z<10$, with space densities roughly an order of magnitude above pre-JWST estimates, and many of these AGN have masses orders of magnitude above the local black hole mass-stellar mass ($M_{\rm BH}-M_{*}$) scaling relations. We investigate the consistency of these observations within a data-driven framework that links the galaxy stellar mass function to the supermassive black hole (SMBH) mass function and AGN luminosity functions using different $M_{\rm BH}-M_{*}$ relations and the observed Eddington-ratio distribution. By comparing our predictions against observed AGN luminosity functions at $z\sim 5.5$ we find that observations can be reproduced either by highly-elevated $M_{\rm BH}-M_{*}$ relations paired with low duty cycles, or moderate relations with higher duty cycles. Through the Soltan argument, we find that $M_{\rm BH}-M_{*}$ relations that are modestly above the local relation for AGN produce consistency between multiple tracers of the SMBH demography at $z\sim 5.5$, while more extreme normalisations would require a weakly-evolving luminosity function at $z> 5.5$. Continuity-equation modelling shows that initially high $M_{\rm BH}-M_{*}$ relations predict a strong two-phase evolutionary scenario and very steep low-mass SMBH mass functions in tension with several current estimates, while more moderate relations generate local SMBH mass functions in better agreement with present determinations and near-constant scaling relations. Our results favour a scenario where SMBHs at $z \sim 5$ on average lie modestly above local AGN scaling relations, with elevated but physically plausible duty cycles. Future wide-field clustering and demographic studies will help break the remaining degeneracies between SMBH scaling relations and AGN duty cycles at early cosmic times.