The name of this blog is “Mass”, but I really haven’t made many posts on the subject of physics. The reason is that I do not yet understand mass, and don’t have a great desire to explain pieces of things that I think I know but that are not well motivated to the reader. But a recent post on Backreaction on the subject of the GZK cutoff has motivated me to write on some of the anomalies seen in ultra high energy cosmic rays.
Cosmic rays are events in the atmosphere that are caused when a very high energy “primary particle” leaves the vastness of empty space and collides with the crowded environment of our planet’s atmosphere. A series of collisions turn the primary particle into a shower of debris. Primary particles with very high energies are extremely rare and so only experiments that examine very large regions of the atmosphere can hope to be lucky enough to see them.
Such an experiment must cover hundreds of square kilometers, it is not possible for the experiment to see the primary particle. The primary particle disintegrates at high altitude, it is only the shower of debris that the experiments can measure. For this reason, there is some question as to the nature of the primary particles.
Even in the emptiness of interstellar space there are things to run into, things that would slow a light weight particle down. For this reason, physicists believe that the primary particles cannot be light particles such as electrons or muons. A tau lepton could be heavy enough, but it decays too quickly. Heavier nuclei, such as an alpha particle are too delicate and would break up too easily in the minor collisions that would happen in interstellar space. This pretty much leaves only protons, so physicists frequenly assume that the primary particles in very high energy cosmic rays are protons.
Protons are stable particles, but if they have extremely high energy they will interact with the photons of the cosmic microwave background radiation. This would decrease their energy below 6 x 10^19 eV. The people who made this calculation had initials of G, Z, and K, and so this is called the GZK cutoff.
There is some question as to whether or not the GZK cutoff is observed in high energy cosmic rays. In sort, Akeno / AGASA and Yakutsk see cosmic rays above the GZK cutoff, High Resolution Fly’sEye (HiRes), SUGAR and Auger do not. A recent review article. shows the differences in flux measurements between these experiments. I reproduce the left part of figure 11 here. The AGASA and Yakutsk figures are the circles, triangles, and plus signs that are higher than the other data at the right (higher energy) side:
In the above figure, the horizontal axis gives the measured energy. The vertical axis gives the flux, or the number of observed particles, but it has been scaled according to the cube of energy. If this scaling were left off, the curves would drop sharply on the right. So the scaling is there only to make the curves seem more flat, and therefore easier to compare.
If you choose a vertical scaling that gives the absolute number of events detected, it becomes clear that the data differences can be easily explained by a small difference in the energy measurements of the experiments. That is, you can fix the data by adjusting the measured energies of AGASA and Yakutsk down slightly. This has been widely suggested as the explanation for the spread in measurements, and the review article linked above shows that this explains most of the discrepancy in the data.
Almost all theoreticians who have examined this data have concluded that AGASA and Yakutsk simply mismeasured their energies, and that is all there is to say. The discrepancy has been known for many years, and while it has not bothered the experimentalists, it has attracted a great deal of attention from the experimentalists. Of course they would like to beat their experiments into compliance with one another. We now examine how the experimentalists have been working to explain these differences.
The first thing to note is that AGASA and Yakutsk use similar techniques for energy measurement and this technique is different from that used by the other experiments. If this energy measurement technique gives wrong results, then the fact that AGASA and Yakutsk both have high energy measurements is explained. A recent article by the Yakutsk experimenters gives a clue:
“At Yakutsk array and at AGASA a nearly similar logarithmic RC–converters of the signal from photomultiplier tube (PMT) to digital code with t ~ 10 mcsec are used.”
A PMT converts an input light (from the cosmic ray shower) into an electrical pulse. The amount of light is proportional to the area under the curve. In AGASA and Yakutsk, the amount of light is measured not by digitizing the current, but instead by letting the pulse relax through an RC time constant. Instead of measuring the pulse itself, they measure how long the pulse lasts. The RC time constant turns the pulse, whose area is proportional to the energy, into a time period, which is proportional to the logarithm of the energy. Here’s the circuit (my drawing):
In the above, the PMT output is in current mode. That is, a given size event at the PMT dumps a given amount of charge into the capacitor. This charge on the capacitor is bled off through the resistor to ground. The time that the capacitor voltage stays above the comparator voltage is proportional to the logarithm of the charge injected into the capacitor. This logarithm is measured by digitzing the comparator output. That is, by counting the number of clocks that the comparator output is high. The clock rate to the flip flop defines how accurate the digitization is, but because of the RC time constant, this accuracy will be the same relative accuracy at all energy levels. For example, if the period of the XTL clock is a tenth of the RC time constant, then the inherent accuracy of the digitizer will be about 10.5% because exp(1/10) = 1.105.
By using a logarthimic circuit, AGASA and Yakutsk end up with a logarithmic measurement of the energy of a pulse. This has the advantage of giving them approximately equal accuracy for small pulses as for large. Since the energy deposited in a PMT depends very greatly on how far from the shower core the PMT is located, this logarithmic energy measurement is very efficient.
If all the energy of the cosmic ray always arrived in just a single instantaneous pulse, there would be no problems with this sort of energy measurement. But suppose that the energy is split into two pulses, and the second pulse arrives just as the first pulse decays away. The length of time measured by the digitizer will be twice that of a single pulse, and because of the logarithm, this will square the energy measured.
Cosmic ray showers tend to arrive on the ground as very short pulses because all the particles are going in approximately the same direction, and they are going approximately the same speed (that of light). One can get into problems when cosmic rays happen to arrive at the same time, and also when the duration of cosmic ray showers are longer than expected.
Hans-Joachim Drescher and Glennys R. Farrar wrote a paper Late Arriving Particles in Cosmic Ray Air Showers and AGASA’s Determination of UHECR Energies. This discusses how late arriving particles can spoof AGASA’s energy measurements. The same argument applies to Yakutsk. But after careful calculation, they could find no reason why late arriving particles would be a problem. Instead, they independently confirmed AGASA’s calculations:
“We confirm AGASA’s estimation of the error in their energy determination associated with late-arriving particles, assuming primary protons.”
If you’ve found my description of the logarithmic RC time constant energy measurement circuits confusing, their article will explain the details at great length.
In addition to measuring the energy of cosmic rays, the UHECR experiments also have attempted to measure the direction from which the cosmic rays arrived. Low energy cosmic rays are expected to be bent by various magnetic fields, but the higher energy rays are expected to be either absorbed (by GZK if they travel very far from this galaxy), or be relatively unbent (if they come from near this galaxy). A natural place to suppose that UHECRs are made is in the local black holes, what the astronomers call the BL-Lac objects. So, naturally, astrophysicists have compared the directions in which UHECR’s are detected and checked to see if these directions correlate with directions in which astronomers see BL-Lac objects.
In fact, some correlations have been seen between cosmic ray arrival directions and BL-Lac objects. More surprising to the reader may be the fact that these correlations were seen first at Yakutsk and AGASA rather than the experiments that have higher statistics such as HiRes. A typical paper announcing clustering at AGASA is Chad B. Finley and Stefan Westerhoff, one denying clustering from HiRes is astro-ph/040137 or astro-ph/0507120.
As time has gone on, the AGASA and Yakutsk correlations have survived, and appear to be tighter than the random nature of magnetic fields in our galaxy would allow. This has caused theorists to speculate that neutral particles cause some UHECRs. If so, they are expected to lie outside the standard model:
“The recently observed correlation between HiRes stereo cosmic ray events with energies E ~ 10 EeV and BL Lacs occurs at an angle which strongly suggests that the primary particles are neutral. We analyze whether this correlation, if not a statistical fluctuation, can be explained within the Standard Model, i.e., assuming only known particles and interactions. We have not found a plausible process which can account for these correlations. The mechanism which comes closest — the conversion of protons into neutrons in the IR background of our Galaxy — still under-produces the required flux of neutral particles by about 2 orders of magnitude. The situation is different at E ~ 100 EeV where the flux of cosmic rays at Earth may contain up to a few percent of neutrons pointing back to the extragalactic sources.”
The presence of neutral particles in the UHECR spectrum suggests that the explanation for the energy discrepancies seen in AGASA and Yakutsk could be due to an exotic particle. This is the explanation I put forth two years ago in this paper, which mostly has to do with the Centauro and Chiron anomalies that are also seen in cosmic rays.
But I do not think that my alternative explanations for anomalous cosmic ray behavior will make any progress until I have a complete model of where mass comes from. I’m writing this up not because I think that anyone will find the evidence convincing. It would only be convincing to someone who has seen and understood the rest of the things that intertwine with this, and to explain this takes too much time. And since the rest of those calculations and coincidences are not complete, I must leave this topic here.