Establishing accretion flares from massive black holes as a major source of high-energy neutrinos.

High-energy neutrinos have thus far been observed in coincidence with time-variable emission from three different accreting black holes: a gamma-ray flare from a blazar (TXS 0506+056), an optical transient following a stellar tidal disruption (AT2019dsg), and an optical outburst from an active galactic nucleus (AT2019fdr). Here we present a unified explanation for the latter two of these sources: accretion flares that reach the Eddington limit. A signature of these events is a luminous infrared reverberation signal from circumnuclear dust that is heated by the flare. Using this property we construct a sample of similar sources, revealing a third event coincident with a PeV-scale neutrino. This sample of three accretion flares is correlated with high-energy neutrinos at a significance of 3.7 sigma. Super-Eddington accretion could explain the high particle acceleration efficiency of this new population.