Martin Lemoine

This French expert on Cosmic Rays, writes in "The optical depth of the Universe for ultra-high energy cosmic ray scattering in the magnetized large scale structure"; the following:

"For instance, if most sources lie beyond the last scattering surface, one could mistake the scattering centers on the last scattering surface (such as starbursts, old radio-galaxies or giant shock waves) with the source of ultra-high energy cosmic rays."

Given the real possibility now of finding the sources for the highest energy cosmic rays, one should understand well the interaction of these particles with the magnetic field between galaxies.

He then goes on to argue:

"Since scattering centers are highly magnetized regions, and as such are probably associated with active objects such as radio-galaxies, one may be deceived by their presence on the line of sight, and interpret them as the source of ultra-high energy cosmic rays. The smoking gun of such counterfeiting is the distance scale to these objects: in this optically thick regime, most counterparts would be located at a distance scale d (which can be measured) significantly smaller than the expected distance scale l_max (which is known)."

Almost at the end they write:

"In particular, in the semi-transparent or opaque regime, the closest object lying in the cosmic ray arrival direction should be a scattering center. Since these scattering centers are sites of intense magnetic activity (radio-galaxies, starburst galaxies, shock waves, ...), they might be mistaken with the source. This peculiar feature does not arise in models in which magnetic deflection is a continuous process in an all-pervading magnetic field.
One could thus conceive an “ironic” scenario, in which cosmic rays are accelerated in gamma-ray bursts, but scatter against radio-galaxies magnetized lobes, so that one interpret these latter as the source of cosmic rays because they are the only active objects seen on the line of sight. If such counterfeiting is taking place, one should observe that the apparent distance scale to the source (actually the distance to the last scattering surface) is smaller than the expected distance scale to the source (determined by the energy losses). This offers a simple way to test for the above effect.
In the semi-transparent regime, the source is displaced from the arrival direction by a non-zero (yet smaller than unity) deflection angle. Increasing the threshold energy above which one searches for counterparts certainly provides the way to evade this magnetic effect and identify the source. Indeed, as shown in Section II, the optical depth falls rapidly with increasing energy, in combination of the decreasing distance scale to the sources (which is limited by energy losses) and the decreasing deflection angle per scattering. Furthermore, a fraction exp( −τ ) of all events should have suffered negligible deflection in the intergalactic magnetic field. Hence it appears important to consider searches for counterparts on an event by event basis, focusing on events with extreme energies > 10²⁰ eV, rather than a statistical correlation with astrophysical catalogs. This, however, requires large aperture experiments such as Auger North [74] in view of the strongly decreasing flux at the highest energies."

Even more important, they point out:

"As mentioned previously, this scenario can be tested by comparing the expected source distance scale with the counterpart distance scale. Interestingly, both do not match, as the source distance scale for particles with observed energy 6 × 10¹⁹ eV is of the order of 200 Mpc, significantly larger than the maximum distance of 75 Mpc for the observed counterparts. This fact has been noted in Ref. [2]; it remained mostly unexplained, although it was suggested in this work that both distance scales would agree if the energy scale were raised by 30%.
More quantitatively, one can calculate the probability that a given event with a given observed energy originates from a certain distance, using the fraction of the flux contributed by sources within a certain distance at a certain energy. This probability law can be calculated using the techniques developed in Ref. [70], then tabulated. It is then possible to calculate the probability of seeing 20 out 27 events from a source located within 75 Mpc using the events energies reported in Ref. [2]. This probability is small, about 3%; the mean lies at 15 events out of 27 coming from within 75 Mpc. If one restricts the set of events to those that lie outside the Galactic plane ( |b| >12 ◦ ), with 19 out of 21 seen to correlate, the probability becomes marginal, of order 0.1% (the mean lies at 12 out 21 within 75 Mpc). Finally, if one restricts oneself to the second set of events collected after May 27 2006, and on those which lie outside of the Galactic plane, with 9 out of 11 seen to correlate, the probability becomes of order 10%, with a mean at 7 out 11 within 75 Mpc. In this latter case, the signal is less significant, but the statistics is also smaller. Since the above estimates do not take into account the uncertainty on the energy, and since they assume continuous instead of stochastic energy losses, these numbers should be taken with caution."

They conclude:

"In this framework, it becomes imperative to probe the arrival directions on an event by event basis, focussing on the most energetic events. In the catalog reported in Ref. [2], there is only one event above 10²⁰ eV, whose arrival direction has a relatively small super-Galactic latitude, b_SG ≃ −6.5 ◦ . In the above scenario, one should expect to find a scattering center on the line of sight, hence it should prove useful to perform a deep search in this direction in the radio domain, looking for traces of synchrotron emission that would attest of the presence of a locally enhanced intergalactic magnetic field. More events at higher energies, as expected from future detectors, will certainly help in this regard."