The cosmic-ray spectrum reaching Earth — measured for over a century by various detectors on the ground and in space — covers more than ten orders of magnitude in energy. From a few hundred MeV per particle to beyond 10²⁰ eV, the flux falls steeply but smoothly with energy. Up close, however, the spectrum has several distinct features. Around 3 × 10¹⁵ eV (3 PeV), the spectrum steepens noticeably. Around 10¹⁸ eV, it flattens again. Around 10²⁰ eV, it cuts off sharply.
The first feature — the steepening at 3 PeV — has been called the cosmic-ray knee since the 1950s. The terminology compares the log-log spectrum to a human leg: the higher-energy “shin” at a steeper slope, the lower-energy “thigh” at a shallower one, with the knee bending between them.
For most of the twentieth century, the physical origin of the knee was unclear. It is now broadly believed to mark the maximum energy reachable by the dominant galactic cosmic-ray accelerators — most likely the shock waves of supernova remnants. The knee, in other words, tells us about the limits of what our own galaxy can produce.
For neutrino astronomy, this matters. Cosmic rays produce neutrinos when they interact with ambient matter, and the resulting neutrino spectrum inherits features from the parent cosmic-ray spectrum. The knee should therefore translate into a corresponding upper-energy cutoff in the galactic neutrino flux at around 100 TeV — and that prediction is now being tested by IceCube’s 2023 galactic plane detection.
What “the knee” actually is
A cosmic-ray spectrum is normally plotted as the differential flux dN/dE versus energy E, on a log-log scale. To make features visible, the spectrum is often multiplied by some power of E — typically E² or E².⁷ — which makes a featureless power law appear as a horizontal line.
In such a plot, the cosmic-ray spectrum below about 3 PeV follows a roughly straight line with slope corresponding to a differential power law of approximately E⁻²·⁷. Above 3 PeV, the line bends downward to a slope of approximately E⁻³·¹. The transition is not razor-sharp — it spans about half a decade in energy — but it is unmistakable.
The bend can be seen in multiple independent datasets: KASCADE in Germany, IceTop and IceCube in Antarctica, Tibet AS-gamma, the Pierre Auger Observatory, and many others. The detailed shape of the knee depends on the composition of cosmic rays — protons knee at one energy, helium at slightly higher, and heavier nuclei at higher still — but the overall feature is robust.
A second feature appears around 10¹⁷ eV, sometimes called the “second knee” or “iron knee,” interpreted as the cutoff for the heaviest galactic nuclei. Together, the knee structure spans from 3 × 10¹⁵ to about 10¹⁷ eV.
Why supernova remnants are the leading suspects
The dominant theoretical picture is that supernova remnants — the expanding shock waves left behind by massive-star explosions — accelerate the galactic cosmic-ray population via a process called diffusive shock acceleration (also called first-order Fermi acceleration). Particles trapped on either side of the shock front by magnetic turbulence repeatedly cross the shock, gaining a small amount of energy each crossing, until they escape or until the shock dies.
The mechanism produces a power-law cosmic-ray spectrum with a slope of about E⁻²·¹, broadly consistent with what is observed after accounting for energy-dependent propagation through the galaxy. The maximum energy a given supernova remnant can reach depends on its size, magnetic-field strength, age, and the surrounding density. For a typical supernova remnant, the maximum is calculated to be in the few-PeV range, with the upper-energy cutoff occurring roughly at the observed knee position.
This is not a proof — the theoretical calculation has uncertainties, and not every supernova remnant is created equal. But the broad agreement between predicted and observed maximum energies is one of the strongest pieces of evidence that supernova remnants are responsible for most galactic cosmic rays.
What the knee means for galactic neutrinos
When a cosmic-ray proton accelerated in a galactic source eventually interacts with a hydrogen nucleus in the interstellar medium, the resulting hadronic interaction produces pions. Charged pions decay to muons and neutrinos. Neutral pions decay to gamma rays. The neutrino energy is typically about 5% of the parent proton’s energy.
This relationship means that a cosmic-ray spectrum that cuts off at 3 PeV produces neutrinos that cut off at roughly 150 TeV. The galactic neutrino flux, if its origin is cosmic-ray-driven hadronic processes, should follow the cosmic-ray spectrum down to this cutoff.
The 2023 IceCube detection of neutrinos from the galactic plane measured a flux that extends to about 100 TeV — squarely consistent with this prediction. The observed neutrino energy spectrum is also consistent with what you would predict from the locally-measured cosmic-ray spectrum plus a model of how cosmic rays propagate through the galactic disk.
Above the knee energy — say, at 1 PeV neutrino energy — the galactic flux should be much smaller. This is exactly the regime where extragalactic sources begin to dominate the IceCube astrophysical sample. The 2017 TXS 0506+056 neutrino, at about 300 TeV, sits in the transition region where galactic and extragalactic contributions are comparable.
Why the knee is not perfectly sharp
The transition at the cosmic-ray knee is gradual rather than sharp for several reasons.
Different elements knee at different energies. Heavier cosmic-ray nuclei carry more charge, and the maximum energy from diffusive shock acceleration scales with charge. So protons knee around 3 PeV, helium around 6 PeV, oxygen around 25 PeV, and iron around 80 PeV. The composite all-particle spectrum is a sum of these individual cutoffs, which spreads the apparent knee over a wider energy range.
Source population variation. Not all supernova remnants are identical. Some are younger, some are older, some are in denser environments, some are more energetic. The maximum reachable energy varies from source to source. The integrated cosmic-ray spectrum from many sources is a sum over this distribution.
Propagation effects. Cosmic rays travel through the galactic magnetic field for millions of years before escaping. The propagation modifies the spectrum slightly, particularly at energies where the gyroradius becomes comparable to the galactic disk scale.
Possibly additional source populations. Some authors have proposed that a second class of accelerator — perhaps the supermassive black hole at the galactic center, or specific pulsar wind nebulae — contributes to the cosmic-ray flux around the knee. The contributions, if present, would smooth out the transition.
What IceCube can teach about galactic accelerators
The combination of cosmic-ray observations and galactic neutrino observations provides a kind of two-channel test of acceleration theories. Both channels constrain the parent proton spectrum, but they probe different things.
Cosmic-ray observations measure the local proton flux at Earth — the result of all galactic accelerators plus all the propagation that has happened over the cosmic rays’ travel times. The local spectrum cannot easily be back-traced to specific sources, because charged cosmic rays are bent by magnetic fields.
Neutrino observations measure the spatially-integrated cosmic-ray flux throughout the galaxy. Neutrinos point back to their production locations. With enough events, the neutrino sky map should reveal where cosmic rays are abundant — and therefore where the accelerators are.
IceCube-Gen2 is expected to improve the angular resolution and the event rate of the galactic neutrino sample by factors of several. Within a decade, it should resolve specific supernova remnants and other galactic accelerators as individual sources, rather than seeing only the diffuse galactic glow we observe now.
Beyond the knee
For neutrino energies above about 100 TeV, the galactic contribution becomes small, and extragalactic sources dominate. The transition from galactic to extragalactic is a window into what kinds of objects produce the highest-energy cosmic rays.
The leading extragalactic candidates include blazars, Seyfert galaxies like NGC 1068, starburst galaxies, gamma-ray bursts, and various exotic objects. Identifying which of these dominates the extragalactic flux — and at what energies — is the central program of high-energy neutrino astronomy in the 2020s and 2030s.
The cosmic-ray knee is, in some sense, the dividing line between two physics regimes. Below it, the cosmic-ray and neutrino signals are dominated by familiar galactic objects whose physics is reasonably well-understood. Above it, the signals carry information from the most violent and least-understood objects in the universe. The next decade of neutrino observations will map both sides of this transition in detail.
A bend in a graph
The cosmic-ray knee is, geometrically, just a bend in a graph. Below 3 PeV, the spectrum slopes one way. Above, it slopes more steeply. The bend has been measured since the 1950s with steadily improving precision.
But the bend encodes one of the deeper facts about our galaxy. It tells us how far ordinary stellar processes — supernova explosions and the resulting shocks — can push particles. It tells us where the galactic regime ends and the extragalactic regime begins. And it tells neutrino astronomers what to expect when they look at the galactic neutrino sky: a flux that extends to perhaps 100 TeV and then falls steeply, just as the cosmic-ray spectrum does at 3 PeV.
A simple bend in a graph, in the end, is one of the more useful diagnostic tools we have for understanding the energetic life of our own galaxy.
For the galactic neutrino flux this bend predicts, see The Milky Way’s neutrino glow. For the extragalactic sources that dominate at higher energies, see TXS 0506+056 and NGC 1068. For the high-energy detection capability, see Inside IceCube and IceCube-Gen2. For the broader cosmic neutrino story, see Bert and Ernie.
Frequently asked
What is the cosmic-ray knee?
The cosmic-ray knee is a steepening of the cosmic-ray energy spectrum at about 3 × 10¹⁵ eV (3 PeV). Below the knee, the spectrum falls roughly as energy to the -2.7 power. Above the knee, it falls more steeply, as energy to about -3.1. The break is interpreted as the maximum energy to which the dominant galactic cosmic-ray accelerators — most likely supernova remnants — can push particles.
Why is this relevant to neutrinos?
Because cosmic rays accelerated in galactic sources produce neutrinos through their interactions with interstellar gas. The neutrino energy spectrum is shaped by the parent cosmic-ray spectrum. If galactic accelerators have an upper limit at the knee, the galactic neutrino flux should also have a corresponding upper-energy cutoff around 100 TeV (since neutrinos carry roughly 1/20 of the parent cosmic-ray energy).
What is above the knee?
Above the knee, cosmic rays are increasingly extragalactic in origin — coming from distant active galaxies, gamma-ray bursts, or other accelerators outside our galaxy. The transition is gradual rather than sharp. The 'ankle' feature at about 10¹⁸ eV is generally taken as the regime where extragalactic cosmic rays dominate the observed flux.
How does this connect to the IceCube galactic neutrino signal?
The 2023 IceCube detection of neutrinos from our galaxy's plane is consistent with cosmic-ray protons accelerated below the knee, then interacting with interstellar hydrogen to produce neutrinos. The observed galactic neutrino energy spectrum extends to perhaps 100 TeV, exactly as expected if the parent cosmic rays follow the spectrum we see locally, including the knee feature.
Does the knee mean we know where galactic cosmic rays come from?
The knee tells us about the maximum energy galactic accelerators can reach, but not which specific accelerators are responsible. The leading candidates are supernova remnants — explosions of massive stars whose expanding shocks can accelerate cosmic rays via the diffusive shock acceleration mechanism. Direct evidence for supernova remnant cosmic-ray acceleration has been collected over the past two decades, but identifying specific sources of specific cosmic-ray energies remains an active research area.
Cite this article 5 formats
APA
Neutrino Times Editorial Team. (2025, October 6). The cosmic-ray knee: where galactic neutrino production probably ends. Neutrino Times. https://neutrino-times.com/articles/cosmic-ray-knee-galactic-neutrino-production-limit/
Chicago
Neutrino Times Editorial Team. "The cosmic-ray knee: where galactic neutrino production probably ends." Neutrino Times, October 6, 2025. https://neutrino-times.com/articles/cosmic-ray-knee-galactic-neutrino-production-limit/.
MLA
Neutrino Times Editorial Team. "The cosmic-ray knee: where galactic neutrino production probably ends." Neutrino Times, 6 Oct. 2025, https://neutrino-times.com/articles/cosmic-ray-knee-galactic-neutrino-production-limit/.
BibTeX
@misc{neutrino-times-cosmic-ray-knee-galactic-neutrino-production-limit,
author = {Neutrino Times Editorial Team},
title = {The cosmic-ray knee: where galactic neutrino production probably ends},
howpublished = {Neutrino Times},
year = {2025},
month = {oct},
url = {https://neutrino-times.com/articles/cosmic-ray-knee-galactic-neutrino-production-limit/},
note = {Accessed: 2025-10-06}
} RIS
TY - GEN TI - The cosmic-ray knee: where galactic neutrino production probably ends AU - Neutrino Times Editorial Team PY - 2025 DA - 2025-10-06 PB - Neutrino Times UR - https://neutrino-times.com/articles/cosmic-ray-knee-galactic-neutrino-production-limit/ ER -