🧭 First, what are we talking about?

Imagine a giant drain in space. Gas and dust spiral into it, heating up and glowing as they fall. That’s an accretion disk around a supermassive black hole in the center of an active galaxy (an AGN). These systems can also launch thin, fast jets of particles that shoot out above and below the disk.

Now add one more ingredient: neutrinos. These are almost invisible, ghost-like particles that fly through matter as if it were mostly empty. They carry information straight from the most extreme places in the universe, because they rarely get stopped or bent. The big question is: how do AGN make neutrinos, and how many should we expect to see?

🔧 The core idea: a cosmic particle pinball machine

Think of the jet above the disk as a particle accelerator. It revs up protons to enormous energies. Some of these fast protons wander back down into the disk, which is packed with gas. When they crash into that gas (protons hitting protons), they set off a chain reaction called a hadronic cascade—like a multi-level pinball machine where each bounce creates new balls.

Here’s the simple chain:

  • Fast protons slam into protons in the disk and make short-lived particles called pions.
  • Neutral pions quickly turn into high-energy light (gamma rays).
  • Charged pions decay into muons and then into neutrinos and electrons.

Result: the crash makes two types of stuff we can notice far away—electromagnetic radiation (X-rays and gamma rays) and neutrinos. In this model, nearly half of the energy ends up in neutrinos, and the rest in light.

đŸ—ïž Why the disk is a great factory for neutrinos

The inner disk around the black hole is dense enough to keep the proton–proton crash going. It acts like a thick target: once a fast particle dives in, it’s very likely to interact and feed the cascade. The physics here is actually simpler than in Earth’s atmosphere because, in the disk, most of the short-lived particles decay before they can collide again. That makes the outcome more predictable: lots of pions, lots of neutrinos.

There are two routes for feeding the disk with energetic particles:

  • A source very close to the disk sprays particles in all directions. About half naturally hit the disk.
  • A source farther up the jet sends a biased stream downward (for example, by turning some protons into neutrons that shoot straight into the disk and then convert back). This can make the highest-energy neutrinos more beamed.

For the main estimate, the study uses the simple, close-in source picture.

📈 A neat trick: using X-rays to guess the neutrino rain

Electromagnetic light from the cascade doesn’t escape unchanged. Inside the disk, it gets reprocessed by many interactions, which pushes a lot of the energy into the X-ray band we can observe with telescopes. That means the total X-ray and gamma-ray glow from many AGN acts like a “receipt” for how much particle crashing is happening overall.

So the researchers asked: if a chunk of the diffuse X-ray background across the sky comes from these AGN cascades, what neutrino background should go with it? Using that X-ray budget, they predict a diffuse neutrino flux with a simple shape called a power law—roughly an E⁻ÂČ spectrum. Translation: as energy goes up, the number of neutrinos drops smoothly and predictably.

The key point: the predicted levels sit just below the sensitivity limits of early neutrino experiments at the time of the study, which made this a testable idea. Today’s big detectors in ice and water are well placed to probe this range.

🎯 What the model specifically predicts

  • The neutrino spectrum follows a clean E⁻ÂČ trend from the GeV range up to very high energies, set by how energetic the original protons can get in the jet.
  • About two-thirds of the neutrinos are of the muon type (the kind many detectors are best at spotting).
  • Nearly half of the energy from the proton crashes ends up in neutrinos; the rest appears as light, mainly X-rays and gamma rays after reprocessing in the disk.
  • Because this mechanism relies on proton–proton collisions (not just proton–photon collisions), it produces neutrinos even if the proton energies are “only” modest by cosmic standards.

đŸ§© What could change the picture?

There are knobs you can turn in this cosmic machine:

  • If the proton energies cut off at lower values, the highest-energy neutrinos disappear first.
  • If the proton spectrum gets steeper (fewer high-energy protons), the overall neutrino signal drops.
  • If the proton spectrum is flatter than E⁻ÂČ, proton–photon crashes become more important at the top end, boosting ultra‑high‑energy neutrinos while reducing the lower‑energy ones—changing the ‘shape’ of the expected signal.

Even with these twists, the link between the X-ray glow and the neutrino output remains a powerful way to connect what we see with telescopes to what neutrino detectors might catch.

🚀 Why this matters now

This is a wonderfully simple, testable idea: use the sky’s X-ray background as a ruler to estimate the universe’s neutrino background from active galaxies. It gives a clear prediction—an E⁻ÂČ spectrum over a wide energy range—and explains why AGN are such promising neutrino factories. As modern neutrino observatories continue to improve, this model provides a clean benchmark to compare against. If the neutrino sky matches this pattern, it’s a strong hint that the bustling disks around monster black holes are hard at work, forging ghostly messengers that cross the cosmos to reach us.

Source Paper’s Authors: L. Nellen, K. Mannheim, P. L. Biermann

PDF: http://arxiv.org/pdf/hep-ph/9211257v1