JADES reveals a large population of low mass black holes at high redshift
JWST has revealed a large population of active galactic nuclei (AGN) in the distant universe, which are challenging our understanding of early massive black hole seeding and growth. We expand the exploration of this population to lower luminosities by stacking $\sim 600$ NIRSpec grating spectra from the JWST Advanced Deep Extragalactic Survey (JADES) at $3<z<7$, in bins of redshift, [OIII]5007 luminosity and equivalent width, UV luminosity and stellar mass. In various stacks, we detect a broad component of H$α$ without a counterpart in [OIII], implying that it is not due to outflows but is tracing the Broad Line Region (BLR) of a large population of low-luminosity AGN not detected in individual spectra. We also consider the possible contribution from Supernovae (SNe) and Very Massive Stars and conclude that while this is very unlikely, we cannot exclude some potential contribution by SNe to some of the stacks. The detection, in some stacks, of high [OIII]4363/H$γ$, typical of AGN, further confirms that such stacks reveal a large population of AGN. We infer that the stacks probe black holes with masses of a few times $10^6~M_\odot$ accreting at rates $L/L_{Edd}\sim 0.02-0.1$, i.e. a low mass and dormant parameter space poorly explored by previous studies on individual targets. We identify populations of black holes that fall within the scatter of the local $M_{BH}-M_{*}$ scaling relation, indicating that there is a population of high-z BHs that are not overmassive relative to their host galaxies and which have been mostly missed in previous JWST observations. Yet, on average, the stacks are still overmassive relative the local relation, with some of them 1-2 dex above it. We infer that the BH mass function (BHMF) at $3<z<5$ rises steeply at low masses. The BHMF is consistent with models in which BHs evolve through short bursts of super-Eddington accretion.