How much is known about the composition of ultra high energy cosmic rays (say $E>10^{20}\text{ eV}$)? I get the impression that the particles are often assumed to be protons or other heavier nuclei, but what empirical basis do we have for this? Is there experimental evidence that excludes photons or leptons as candidates? Do we know if the UHE's are matter or antimatter?

I understand that there is quite a bit of literature examining the possible mechanisms of production of UHE's as nuclei of various masses. For example, it could be easier for Iron nuclei to get up to high energies in a magnetic field since they would have to be accelerated for less time than protons.

However, I don't want to put the cart before the horse; the fact is that we don't know where they come from, and so we should not base our knowledge of what they are made of on these theories.


4 Answers 4


We can make a reasonable guess by taking a look at the Hillas criterion. The gist of this criterion is that the maximum energy of the particle, $E$, is limited by the size of the accelerator, $R$ ($\sim R_L$ the Larmor radius), and the strength of the magnetic field, $B$. The relation gives $$ E_{max}=10^{18}\,Z\beta B_{\mu G}R_{kpc}\,{\rm eV} $$ where $B_{\mu G}$ is the magnetic field measured in micro-Gauss, $R$ measured in kiloparsecs, $\beta=v/c$ the velocity of the accelerator site (i.e., the shock wave), and $Z$ its atomic number. This relation is best understood by looking at it:

enter image description here (image source)

The blue lines represent the maximum energy of a proton in different accelerator sites ($\beta=1/300$ is representative of a non-relativistic shock (e.g. supernova remnant shock) whereas $\beta=1$ is representative of the relativistic shocks (e.g. AGN jets)), the red for iron nuclei. The gray blobs in the plot are characteristic of the astronomical objects magnetic field sizes and radii. Any class of objects above the diagonal line will be able to accelerate the proton/iron nuclei to the marked energies.

Clearly, from the chart, it requires a huge magnetic field ($10^{15}$ Gauss) to accelerate iron to $10^{20}$ eV, hence the magnetar being the only candidate. As for protons, active galactic nuclei (AGN) and their jets are able to accelerate a proton to $10^{20}$ eV with seeming ease, same with galaxy clusters.

So from a heuristic stand-point, the idea that our UHECR's being heavy nuclei appears to be ruled out (note that this criterion has not completely eliminated it or is proof that it's not heavy nuclei, just that it's not likely; and as dmckee says, we get so few at that energy it's just not worth the money to put the equipment to discern it).

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    $\begingroup$ For the uninitiated, the criterion is set by the fact that once the particle gets too energetic, its Larmor radius is bigger than the region with the magnetic field, and so it will escape with no chance for further acceleration. Thus you need either a very strong a very extended field (or both! but this tends not to exist) to accelerate UHE's. $\endgroup$
    – user10851
    Feb 5, 2014 at 3:31
  • $\begingroup$ This is very interesting. But I would still have to file this under "putting the cart before the horse" as phrased in my original question. I understand that we have candidate mechanisms for producing UHE's out of protons. Perhaps it's Iron and we just haven't been clever enough to think of how they're accelerated yet. I am looking for an answer as to whether we have observational evidence for the composition of the UHE's that we have already seen. Do we know for sure that they're not say, photons? Never mind whether we have an idea as to how to produce 10^20 eV photons. $\endgroup$
    – chase
    Feb 6, 2014 at 5:36
  • $\begingroup$ @chase: Two points: (1) by definition of "cosmic ray" it cannot be photons and (2) we know how the big accelerators work, we use the same principal with linacs. Note that dmckee has answered your question: we have no observational evidence because they are so infrequent that it's just not worth spending money investigating it (and partly because it's reasonable to assume it's protons, given my heuristic argument). $\endgroup$
    – Kyle Kanos
    Feb 6, 2014 at 13:40
  • $\begingroup$ @KyleKanos, re: (2) I'm not saying it's bad science, in fact I think this is the most reasonable approach to learn about the CRs. I was just wondering if we can actually look at the events and tell what they are. For example, if we looked at them and knew they were photons, we probably wouldn't have cranked out a generation of theorists searching for ways to accelerate nuclei to explain the UHE spectrum. Instead, they'd be inventing theories for energetic photons. $\endgroup$
    – chase
    Feb 6, 2014 at 19:45
  • $\begingroup$ @KyleKanos, re: (1) so the nomenclature would be "gamma ray" if it were photons. Then rephrase the question: how do we know the air showers associated with UHE CR's are not caused by hard gamma rays? We know that some primary cosmic rays are composed of positrons, and in collider detectors photons and electrons look awfully similar. $\endgroup$
    – chase
    Feb 6, 2014 at 19:47

To address the actual question of how we know the composition of UHECR without relying on source information (of which we have none), we have to look at their extensive air showers (EAS). After an UHECR hits the top of the atmosphere an EAS is created in the air, but p and Fe will create EAS with different shapes. Properties of hadronic interactions are measured at the LHC and these are then extrapolated to the higher energies (50 TeV and above) of UHECR. Then, shower simulations are done in the atmosphere (with varying atmospheric density, the earth's magnetic field, and everything) to predict the shape of the shower. As these showers propagate through the atmosphere, they fluoresce. Telescopes at the Pierre Auger Observatory (largest CR observatory in the world, is in Argentina) and High-Res (in Utah, provides northern hemisphere information, although is much smaller) measure this fluorescence and plot something they call $X_{max}$ - the depth of the shower from the initial interaction point (in units of $X$: g/cm$^2$ - such that when it is divided by a density it gives a length) at which the maximum radiation is observed. The average and RMS values are then calculated over a series of events and then compared to the simulations.

Auger and High-Res continue to disagree on this point. You can see the Auger data here (arxiv abs) on page 11 by the author or page 16 of the pdf. The red lines are for the predictions for protons across various hadronic interaction models and the blue lines for iron. Auger seems to clearly favor a heavy (or at least heavier) composition at the highest energies.

High-Res data favors proton composition up to the highest energies. Of course, they have significantly less data, but they still claim a significant result. Their data is presented here (arxiv abs) along with pretty plots of representative shower events.

One known problem in the hadronic simulation is that low energy muons aren't being taken into account correctly. It is a problem that CR and LHC physicists are working together to correct, but it will probably be at least a year or two before it is incorporated into the necessary models. Also, there is a working group comprised of members of both Auger and High-Res that is working on sorting out of number of ongoing discrepancies between the two experiments. While the largest has to do with the energy spectrum, I am sure that this is on their list as well.

A rather comprehensive overview from Auger can be found here (arxiv abs).

Conclusion: this is very much an open problem. Future telescopes such as JEM-EUSO on the ISS may be able to improve the data here and solve this problem. In addition, improved data from the LHC may bring the experiments into agreement, or improving the experiments' systematics may resolve the problem. Finally, JEM-EUSO may provide enough data that could be confined with galactic and extra-galactic magnetic field information (that would have to be dramatically improved) to put some limits on charge once one or more source(s) is(are) identified.

  • $\begingroup$ Thank you for addressing my question head on! I have two sub-questions if you can elaborate: (1) Can these events be photons? Or the EAS just would look completely wrong? (2) Can you elaborate a bit more (or link me to a source) on how LHC physics is coming into play? This is interesting to me as I'm an ATLAS student myself. $\endgroup$
    – chase
    Feb 21, 2014 at 15:38
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    $\begingroup$ 1. No. Photons don't go to these high of energies. The top performer there is HAWC (arxiv overview abs page) which is being built in Mexico now (should be online soon). The reason has ore to do with propagation than anything. The abstract here (arxiv abs) should provide some reasons why (basically, they pair produce or double pair produce). 2. The LHC helps with pdf measurements which are used in hadronic shower simulations. This (arxiv abs) paper provides an okay overview. $\endgroup$
    – jazzwhiz
    Feb 21, 2014 at 17:42

I'm a bit outside of my expertise here, and perhaps someone who knows in detail will be along, but here goes...

  • The composition of UHE cosmic rays is not directly measured because they are too rare to justify putting a spectrometer sufficient to test them in space.
  • The composition of normal cosmic rays has been tested and they are mostly protons with a few heavier stable particles. The testing is done by putting a small superconducting magnet spectrometer on a satellite. These missions have limited lifespan but have been highly successful. The cosmic rays have to be stable, because time dilation or not they have been a long time in transit: all the unstable initial composition has decayed.
  • UHE events come from so far away that they also have to be stable, despite the ferocious $\gamma$.
  • UHE cosmic rays are generated in incredibly energetic events.

Given all the above it becomes reasonable to assume protons.

  • $\begingroup$ In point 3, I presume you're referring to the GZK limit? But GZK assumes CR is protons; a non-nuclear candidate would be potentially be subject to weaker interactions with CMB photons. $\endgroup$
    – chase
    Feb 4, 2014 at 22:44
  • $\begingroup$ Yes. I may have had a overly rosy understanding of the real situation. I've been search for arXiv papers to support what I thought I knew and they don't seem to be there. $\endgroup$ Feb 4, 2014 at 22:46
  • $\begingroup$ Re: point 1&2; I knew that we had measured the lower spectrum to be comprised of mostly protons, but extrapolation can be dangerous! It is the high energy spectrum that is potentially problematic, so we have to be careful using what we know about low energy CRs. And indeed we have so few observations of UHE's that it would be hard to make comparisons between different compositions, which is why I am worrying about it ;) $\endgroup$
    – chase
    Feb 4, 2014 at 22:49
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    $\begingroup$ I'm sorry, but I don't see how any of this rules out e.g. alpha particles, or other stable particles. $\endgroup$ Feb 5, 2014 at 15:06
  • $\begingroup$ @EmilioPisanty It doesn't. I'd have deleted this after Kyle's answer came in, only he alludes to this answer. $\endgroup$ Feb 5, 2014 at 15:23

Folks are remarkably coy about stating explicit compositions. I suggest contacting the Pierre Auger Collaboration for datasets or explicit references,


arXiv:1106.3048, The Pierre Auger Collaboration
Z = 6 (219 events), 13 (797 events), 26 (2887 events) for angular window of 18◦ around Cen A. Another example is given.

arXiv:1201.6265 "Studying the nuclear mass composition of Ultra-High Energy Cosmic Rays with the Pierre Auger Observatory." I don't see any nuclear masses listed, though there are some suggestive graphs.

arXiv:1312.7459 "Galactic CRs should extend to energies of the order of a few 10^17 eV and that at such energies the chemical composition should be dominated by iron nuclei." "Should" is not bolstered by listed numbers

4.2 Chemical composition of UHECR I don't see any chemical compositions.

  • $\begingroup$ Thanks for the references. In arXiv:1106.3048, they state that the chemical composition is inferred by comparing the structure of the observed air showers with Monte Carlo simulations. However, for the UHE's we've only got maybe 100's of data points; it seems it would be very hard to use this technique to infer composition above the GZK cutoff. $\endgroup$
    – chase
    Feb 4, 2014 at 23:06
  • $\begingroup$ Decent detection statistics require a near-planetary detection area. Would the Earth's magnetic field selectively channel them for relativistic reasons, the magnetic field transforming as an electric charge? $\endgroup$
    – Uncle Al
    Feb 5, 2014 at 0:22
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    $\begingroup$ Bending radius in a magnetic field is $\propto p/B$, so no. The Earth's magnetic field is not an analyzer worth speaking of. $\endgroup$ Feb 5, 2014 at 1:37
  • $\begingroup$ Don't forget that the other main UHECR experiment, TA, consistently disagrees with Auger on the issue of composition. If the issue is due to a systematic in their reconstruction process, then their results may be incorrect. $\endgroup$
    – jazzwhiz
    Nov 2, 2016 at 15:21

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