The small scale clustering properties of ultra-high energy cosmic rays as a constraint on the particle charge and intervening magnetic fields

The observations of anisotropy above 57 EeV and of a suppression of flux above 40 EeV are supportive of two long held hypotheses: (1) the ultra-high energy cosmic ray (UHECR) sources are extragalactic, and (2) the Greisen-Zatsepin-Kuz’min effect is operational. If these hypotheses are true, we should expect that the flux of UHECR from the few brightest sources comprises a large fraction of the total flux. In fact, it is likely that groups of two or more events that are associated with a single source have already been observed. Such groups of events will cluster at an angular scale s̄, the apparent angular size of the brightest UHECR sources. This implies that the value of s̄ is embedded within the autocorrelation spectrum of event directions. An indication of s̄ in a certain energy range can be used to infer limits on the particle charge and intervening magnetic fields, both of which are not well constrained. This is possible since s̄ is similar in scale to the average magnetic deflection. In this work, we describe a method for obtaining an indication of s̄ in the energy range E > 57 EeV. A metric m, which indicates whether structure in the arrival directions extends to small angular scales, is defined. Then, Monte Carlo simulations are used to estimate the expected range of m for two different scenarios, s̄ = 2.5 and s̄ = 10. The results of the simulations are not strongly dependent on input parameters that are poorly constrained, such as the spatial distribution of sources. We show that m differentiates between the two scenarios for a data set that contains 92 events above energy E > 57 EeV. Such a data set will be available from the Pierre Auger Observatory in late 2010 or early 2011. We discuss the implications of different values of m being observed in the near future and the corresponding limits on the value of s̄, the particle charge, and intervening magnetic fields.