The GZK cutoff

The earth is hit by cosmic rays all the time. Those with the highest energies collide with atoms already in the upper atmosphere, and produce a cascade of secondary particles, a so-called cosmic ray shower. These secondary cosmic rays include pions (which quickly decay to produce muons, neutrinos and gamma rays), as well as electrons and positrons produced by muon decay and gamma ray interactions with atmospheric atoms.

Nowadays, the showers can be simulated with appropriate software. The picture below, from Hajo Drescher, illustrates such a cosmic ray shower

Here, the primary particle was a proton with an energy of 10¹⁹ eV, the colors indicate blue: electrons/positrons, cyan: photons, red: neutrons, orange: protons, gray: mesons, green: muons. (Unfortunately, one can't see the colors very clearly, you can decompose the shower into colors on the website. The incoming proton is the line from the upper left, the other upgoing line is cyan and a photon). If you have Quicktime installed, you can also look at this very illustrative movie, which shows the particles cascading down on earth. The above figure has be created using the software SENECA (down-loadable here), the competitor is AIRES, which has a somewhat more impressive advertisement movie (the exact differences between both codes elude me).

The number of particles reaching the earth's surface is related to the energy of the cosmic ray that struck the upper atmosphere. Cosmic rays with energies beyond 10¹⁴ eV are studied with large "air shower" arrays of detectors distributed over many square kilometers that sample the particles produced, e.g. at HiRes in Utah, AGASA in Japan and Pierre Auger in Agentinia, the latter has a very nice homepage, summarizing the mysteries that still need to be solved.

Energies over 10¹⁴ eV sounds extremely large. In comparison, the collision energy that the LHC will reach is 10¹³ eV. However, one has to keep in mind that in cosmic ray events the energy is typically that of the incoming particle in the earth rest frame and not actually the collision energy in the center of mass frame (LHC collides two beams head on, thus the lab frame is identical to the center of mass frame).

To give you an example, the energy in the center of mass frame of an incoming proton with an already extremely high (and rare) energy of 10¹⁷ eV hitting a proton in rest is roughly the square-root of 10¹⁷ eV times the proton rest-mass, 10⁹ eV, which is approx 10¹³ eV and comparable to LHC energies. However, one has to keep in mind that cosmic ray events, despite their potentially large energy, are far less in control and attached with higher uncertainties than collider experiments. Most of the air showers are believed to be created by protons. Since the incoming directions are evenly distributed (and inside our galaxy no mechanism is known to accelerate them to these high energies) the proton's origin is most likely not in our galaxy. That means the protons must have travelled at least roughly 50 Mpc [1] before they reach earth.

Now, if the incoming proton's energy increases further, then eventually it will not only react with our atmosphere, but also with the photons in the cosmic microwave background (CMB). That is, for photons with sufficiently high energies, the universe will stop being transparent. The protons will start to scatter on the photons in the microwave background, loose energy and can't reach earth any more. The first reaction that can take place with increasing energy is photo-pion production which happens at a center of mass energy of roughly 200 MeV. This pion production is extremely well measured in earth's laboratories, where photons are scattered on nuclei in rest. If one sets the energy of the photon to be that of the CMB temperature (3 K is approximately 2.5 10^-4 eV), one finds that the proton needs an energy of roughly 10²¹ eV to cross the threshold for pion production. (It is roughly (200 MeV)² divided by the photon's energy).

The figure to the left (credits go to Stefan) shows the cross-section for photon-proton scattering in the laboratory (proton in rest), the blue dots are data from the particle data booklet. The red line indicates the initial threshold for the process to take place, the orange lines are the delta resonances where the cross-section has peaks.

However, what one actually wants to know is when the mean free path of the protons drops below typically 50 Mpc. To get a better result than the above estimate one has to take into account that the CMB has a small percentage of photons with larger energy than the temperature, the distribution given by the Planck spectrum. Such, the mean free path of the protons drops significantly already at a somewhat smaller energy than the above 10²¹ eV because the proton has a chance to hit the higher energetic photons.

My husband, as usual, has made a lot of effort to answer my yesterday's question and produced the figure to the right, which very nicely illustrates that indeed roughly 10% of the photons have energies five times larger than the background temperature.

The exact calculation for the cut-off has been done by Stecker (Effect of Photomeson Production by the Universal Radiation Field on High-Energy Cosmic Rays), and one finds the drop to happen at roughly 6 x 10¹⁹ eV. At this energy, one thus expects a cut-off in the cosmic ray spectrum because the sources for the showers can no longer reach earth. First pointed out by Greisen[2], Zatsepin and Kuzmin this is referred to as the GZK-cutoff. To summarize, this prediction relies on

a) The initial particle of the shower being a proton from outside our galaxy
b) The total cross-section of protons with photons, and
c) The assumption that the cross-section (a Lorentz scalar itself) can be boosted from the earth laboratory (proton in rest) into the rest-frame of the CMB (photon in rest).

Now AGASA claimed to have observed cosmic ray events with energies above this cut-off (see e.g. Has the GZK suppression been discovered, by Bahcall and Waxman). This has lead to a significant amount of speculation how this could be explained. One of the explanations for example is that a violation or deformation of Lorentz invariance might be the cause for a shift in this threshold, which has been argued to be a signature for quantum gravity (see e.g. Alfaro and Palma, Loop quantum gravity corrections and cosmic ray decays, hep-th/0208193).

I have explained previously that I find these explanations implausible - as mentioned above, the energy in the center of mass frame is somewhere around a GeV, now could please somebody explain me why on earth (pun intended) you'd expect quantum gravitational effects in that energy range?

One should also keep in mind, that HiRes on the other hand has observed the cutoff where it is supposed to be. Their new data analysis again confirms the cutoff. The recent paper is here, and last month there was a brief article in Physics Today "Fluorescence Telescopes Observe the Predicted Ultrahigh-Energy Cutoff of the Cosmic-Ray Spectrum" by Betram Schwarzschild.

It is expected that Pierre Auger will present first results at the 30iest International Cosmic Ray Conference, which will take place in Merida, Yucatan, Mexico from July 3 - 11, 2007. Hopefully, the situation will be clarified then.

So stay tuned...

I too am on my way to Mexico, to another conference, the Loops 2007.

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[1]: Mpc means Mega parsec. Mega is 10⁶, one parsec is approx 3 lightyears.
[2]: Kenneth I. Greisen, Cornell professor emeritus of physics and a pioneer in the study of cosmic rays, died March 17 2007 at age 89.

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TAGS: PHYSICS, COSMIC RAYS, GZK CUTOFF