In the distant Cigar Galaxy, there is an unusual beacon. It doesn't shine in the usual sense: its rays are born in a scorching cloud around a black hole that is devouring matter from a companion star. Such objects are called ultraluminous X-ray sources. Their X-ray brilliance is so intense that it outshines entire galaxies.

This cloud, the corona, is like a boiling cauldron. Plasma particles race at tremendous speeds, colliding and accelerating. But to produce neutrinos (ghost particles that pass straight through planets), a special condition is required: the plasma must be sparse, like a desert where grains of sand rarely meet. Otherwise, protons waste energy on frequent collisions and never reach the required speeds.

The authors of the new study found that this regime only kicks in if the black hole consumes no more than five "portions" of matter per unit time (a portion being the mass the hole can swallow at a certain limit). Then protons accelerate to energies of tens of TeV, as if each one gets struck by lightning. Colliding with light quanta or other particles, they produce neutrinos. Moreover, the denser the corona becomes, the greater the contribution of direct proton-proton collisions, and the neutrino spectrum broadens.

The calculations revealed a curious relationship: the brightness of neutrino emission grows faster than the X-ray brightness — roughly as the square and a half. This means that the brightest X-ray sources could be even more prominent in neutrino light. Future observatories might catch this signal and unveil a new class of cosmic accelerators. Thus, a beacon we've only seen in X-rays will speak the language of ghost particles.