If you stand outside on a sunny afternoon, a thousand or so neutrinos pass through every square centimeter of your skin every second. Most come from the Sun. A much smaller fraction — perhaps one or two per second per square centimeter at energies above a few hundred MeV — come from something else entirely: cosmic rays striking the upper atmosphere, producing showers of charged particles whose decays trickle down into a steady, low-level rain of neutrinos.
This is the atmospheric neutrino flux. It is the most important calibration source for every underground neutrino detector. It was the signal in which neutrino oscillation was first discovered. It is the dominant high-energy background for almost every rare-event search the field undertakes. Understanding it in detail is essential infrastructure for nearly all of modern neutrino physics.
How they are made
The production chain is straightforward but worth following step by step.
Step one: cosmic rays arrive. A high-energy proton or helium nucleus, accelerated to TeV or higher energies by some distant astrophysical source (perhaps a supernova remnant within our galaxy, perhaps an extragalactic active galactic nucleus), enters Earth’s upper atmosphere. By the time it has penetrated a few tens of kilometers into the atmosphere, it has collided with an atomic nucleus — usually nitrogen or oxygen — at high enough energy to produce a spray of secondary particles.
Step two: pions and kaons. The most abundant secondary particles are charged and neutral pions, along with smaller numbers of charged and neutral kaons. The neutral pions decay almost immediately into two gamma rays and do not contribute to the neutrino flux. The charged pions and kaons, however, are unstable but live long enough at high energies that they can travel measurable distances before decaying.
Step three: pion and kaon decay. A charged pion at rest has a lifetime of about 26 nanoseconds and decays almost always into a muon plus a muon neutrino:
π⁺ → μ⁺ + ν_μ
π⁻ → μ⁻ + ν̄_μ
Charged kaons live for about 12 nanoseconds at rest and decay through several channels, including muon-plus-neutrino at about 64% branching ratio. At higher cosmic-ray energies, the boosted lifetime allows the pions and kaons to travel further before decaying — sometimes far enough to reach the ground first.
Step four: muon decay. The muons produced in pion and kaon decay are themselves unstable. At rest, a muon lives for about 2.2 microseconds before decaying:
μ⁺ → e⁺ + ν_e + ν̄_μ
μ⁻ → e⁻ + ν̄_e + ν_μ
For muons produced low in the atmosphere or at very high energies, the relativistic lifetime dilation can be enough that the muon reaches the ground before decaying. In that case, the second muon neutrino in the chain is “missing” — it was never produced. The result is an energy-dependent shift in the muon-to-electron neutrino ratio.
Step five: the survivor reaches the detector. The final neutrinos travel essentially in straight lines from their production point. Some come straight down through the atmosphere into an underground detector. Others were produced on the opposite side of the planet and travel through the entire Earth to arrive coming up from below. At GeV energies, the Earth is effectively transparent to neutrinos, so both directions produce comparable rates.
The Honda flux and its calculation
Modeling the atmospheric neutrino flux precisely is a substantial computational task. The leading calculation, called the Honda flux after the Japanese theorist Morihiro Honda who has led the work for two decades, uses Monte Carlo simulation of cosmic-ray showers in the atmosphere, with detailed treatment of every relevant interaction.
The required inputs include:
The primary cosmic-ray spectrum. The composition and energy spectrum of cosmic rays entering the top of the atmosphere, measured by balloon-borne and satellite experiments.
Hadronic interaction models. How a proton or nucleus interacts with an atmospheric nucleus, including pion and kaon production cross-sections at relevant energies. Different hadronic interaction models (SIBYLL, QGSJET, EPOS) sometimes disagree by 10–20%, and this disagreement is one of the larger sources of uncertainty in the flux calculation.
Atmospheric density profile. The density and composition of the atmosphere at every altitude, which affects how quickly pions and muons reach the air densities at which their decays are dominated by collisions rather than free flight.
Geomagnetic cutoffs. The Earth’s magnetic field deflects low-energy charged cosmic rays away from low geomagnetic latitudes. The flux at the equator is therefore smaller than at high latitudes for low-energy cosmic rays. This is sometimes called the “east-west asymmetry.”
Solar modulation. The Sun’s activity cycle affects the low-energy cosmic-ray flux that reaches Earth. Calculations are typically done for specific epochs of the solar cycle.
The combined result is a prediction of the atmospheric neutrino flux as a function of energy, direction (zenith and azimuth angle), neutrino flavor, and matter-antimatter status. The Honda flux has been refined over many years and is now accurate to roughly 10–15% in the energy range from about 100 MeV to about 10 TeV.
What atmospheric neutrinos look like in a detector
In a water Cherenkov detector like Super-Kamiokande, an atmospheric neutrino interaction looks the same as any other charged-current neutrino interaction. A neutrino exchanges a W boson with a nucleon, producing the corresponding charged lepton plus a spray of hadrons. The charged lepton produces a Cherenkov ring. The hadrons produce additional rings or showers.
Super-Kamiokande sees roughly 15 atmospheric neutrino events per day. About half are muon-flavor (producing muon Cherenkov rings) and about half are electron-flavor (producing electron rings). Some are downward-going; some are upward-going.
The key signature of atmospheric neutrino oscillation is the zenith-angle dependence of the muon-neutrino rate. Downward-going muon neutrinos, having traveled only a few tens of kilometers through the atmosphere, oscillate by very little. Upward-going muon neutrinos, having traveled through the entire diameter of the Earth (about 13,000 kilometers), have had plenty of time to oscillate into other flavors. The ratio of upward-to-downward muon-neutrino rates is therefore less than 1 — and the deficit measures the oscillation parameters.
At higher energies, IceCube sees atmospheric neutrinos at much higher rates than Super-K but with less detailed event reconstruction. IceCube’s atmospheric neutrino sample is dominated by very-high-energy events — many GeV up to TeV — where the muon flavor dominates and the oscillation pattern is shifted to longer effective baselines. IceCube can therefore measure oscillation parameters in a different energy regime than Super-K, providing complementary constraints.
Atmospheric neutrinos as background
For experiments that are not designed to study atmospheric neutrinos, the flux is often a dominant irreducible background.
Solar neutrino experiments. At solar neutrino energies (below about 15 MeV), the atmospheric flux is small but non-zero. Experiments like Borexino and SNO had to carefully model atmospheric neutrino backgrounds in their solar-flux measurements.
Neutrinoless double-beta decay experiments. 0νββ experiments operate at energies of 1–3 MeV. Atmospheric neutrinos at these energies are rare but not negligible, and they contribute to the long-term background budget for the most sensitive searches.
Diffuse supernova neutrino background. The DSNB search is centered at 10–30 MeV, an energy range where atmospheric neutrinos are a significant background. The DSNB signal-to-background ratio depends in part on how well the atmospheric flux is understood at low energies.
Dark matter direct detection. At higher recoil energies (above 10 keV nuclear recoil), atmospheric neutrinos via CEvNS contribute to the neutrino fog for dark matter searches. This becomes important for the heaviest WIMP masses.
Supernova-neutrino monitoring. The galactic supernova alert system has to distinguish a real supernova burst from background fluctuations driven primarily by atmospheric neutrinos. The required signal-to-background separation is enormous because supernova bursts produce many thousands of events in seconds, while atmospheric events are spread out over years.
Atmospheric neutrinos as a discovery signal
While atmospheric neutrinos are a background for many experiments, they are themselves a powerful signal in their own right. Beyond Super-Kamiokande’s 1998 oscillation discovery, they have produced:
Three-flavor mixing constraints. Detailed analysis of atmospheric data with full three-flavor treatment, including matter effects through the Earth, constrains θ₁₃, the mass-squared differences, and the mass ordering.
Mass-ordering hints. Atmospheric neutrinos passing through the Earth experience the MSW effect at energies of a few GeV in resonance with the Earth’s matter density. The sign of the effect depends on the mass ordering. Atmospheric data alone has weak sensitivity to the ordering, but in combination with long-baseline data it provides useful constraints.
Search for unitarity violation. If there are additional neutrino species, the three-flavor PMNS matrix would not be exactly unitary. Atmospheric oscillation data is one of the strongest tests of three-flavor unitarity.
Search for new physics. Atmospheric data are sensitive to non-standard neutrino interactions, neutrino decay, and a variety of other proposed extensions of the Standard Model.
A constant rain
The atmospheric neutrino flux is, in some sense, the simplest natural neutrino source. It does not require a supernova event or an active galaxy or a nuclear reactor. It just requires cosmic rays from anywhere, hitting any atmosphere with any composition, and the same chain of pion and muon decays produces the same flux of neutrinos everywhere on Earth.
This consistency is what makes it so useful as a calibration source and a discovery signal. It is also what makes it so persistent as a background. Every detector buried under any mountain in any country, regardless of what it was built to measure, sees the same atmospheric neutrino rain dripping through it constantly.
The fact that we can model it well enough to discover neutrino oscillation, to extract precision oscillation parameters, and to predict next-generation experiment backgrounds is one of the underappreciated achievements of modern particle physics.
For the discovery that came from atmospheric neutrinos, see Super-Kamiokande 1998. For why the matter effect inside Earth affects atmospheric oscillation, see The MSW effect. For the high-energy regime atmospheric neutrinos open up, see Inside IceCube. For how atmospheric flux becomes a problem for rare-event searches, see The neutrino fog.
Frequently asked
What are atmospheric neutrinos?
Atmospheric neutrinos are produced when high-energy cosmic rays — mostly protons and helium nuclei from space — collide with atoms in Earth's upper atmosphere. The collisions create showers of pions and kaons, which decay into muons and muon neutrinos. The muons themselves then often decay into electrons plus additional neutrinos. The combined result is a steady flux of atmospheric neutrinos with a well-understood energy spectrum that washes over the entire planet.
What is the typical flux of atmospheric neutrinos?
At Earth's surface, the atmospheric neutrino flux above 100 MeV is roughly 1 per square centimeter per second integrated over all directions. Higher energies are less abundant — the flux falls roughly as energy to the −3.7 power. Most current neutrino detectors see atmospheric neutrino events at rates of a few thousand events per year per kiloton of target mass.
What is the muon-to-electron neutrino ratio?
Above about 1 GeV, where pion decay is the dominant source, the predicted ratio at production is roughly 2:1 muon-flavor to electron-flavor neutrinos. This is because each pion decay produces a muon plus muon neutrino, and the subsequent muon decay produces an electron plus an electron neutrino plus another muon neutrino — so the count comes out to two muon-flavor for every one electron-flavor neutrino. Above ~10 GeV, the ratio increases as muons increasingly reach the ground before decaying.
Why do atmospheric neutrinos matter as a signal?
They were the signal in which neutrino oscillation was first discovered: Super-Kamiokande's 1998 result identified a flavor-dependent zenith-angle asymmetry in atmospheric muon neutrinos. They remain a major source of constraint on oscillation parameters today, particularly at high energies relevant to IceCube. They also serve as a calibration sample for almost all underground neutrino detectors.
Why do atmospheric neutrinos matter as a background?
For experiments that aren't designed to study atmospheric neutrinos — solar neutrino searches, 0νββ experiments, supernova-neutrino monitors, dark matter detectors — the atmospheric flux is often the dominant irreducible background at the relevant energies. Underground placement reduces the rate, but eventually contributes to the 'neutrino floor' that limits all rare-event searches.
Cite this article 5 formats
APA
Neutrino Times Editorial Team. (2025, November 17). The atmospheric neutrino flux: how cosmic rays bathe the planet in invisible particles. Neutrino Times. https://neutrino-times.com/articles/atmospheric-neutrino-flux-cosmic-rays/
Chicago
Neutrino Times Editorial Team. "The atmospheric neutrino flux: how cosmic rays bathe the planet in invisible particles." Neutrino Times, November 17, 2025. https://neutrino-times.com/articles/atmospheric-neutrino-flux-cosmic-rays/.
MLA
Neutrino Times Editorial Team. "The atmospheric neutrino flux: how cosmic rays bathe the planet in invisible particles." Neutrino Times, 17 Nov. 2025, https://neutrino-times.com/articles/atmospheric-neutrino-flux-cosmic-rays/.
BibTeX
@misc{neutrino-times-atmospheric-neutrino-flux-cosmic-rays,
author = {Neutrino Times Editorial Team},
title = {The atmospheric neutrino flux: how cosmic rays bathe the planet in invisible particles},
howpublished = {Neutrino Times},
year = {2025},
month = {nov},
url = {https://neutrino-times.com/articles/atmospheric-neutrino-flux-cosmic-rays/},
note = {Accessed: 2025-11-17}
} RIS
TY - GEN TI - The atmospheric neutrino flux: how cosmic rays bathe the planet in invisible particles AU - Neutrino Times Editorial Team PY - 2025 DA - 2025-11-17 PB - Neutrino Times UR - https://neutrino-times.com/articles/atmospheric-neutrino-flux-cosmic-rays/ ER -