On the evidence for clustering in the arrival directions of AGASA's ultrahigh energy cosmic rays

Constraints on the local sources of ultra high-energy cosmic rays

“…The sources have not been robustly identified, and the models of particle acceleration are challenged by the fact that the energy spectrum extends to > 10 20 eV. Several observational clues suggest that the UHECR flux is dominated by extra-Galactic light nuclei: the spectrum flattens at ∼ 10 19 eV (Nagano & Watson 2000), there is evidence for a composition change from heavy to light nuclei at ∼ 10 19 eV (Bird et al 1993;Abbasi et al 2005), and the UHECR arrival direction distribution is nearly isotropic (Finley & Westerhoff 2004;Abbasi et al 2004). The recent detection of a weak anisotropy in the arrival distribution of > 6 × 10 19 eV cosmic-rays (Auger Collaboration et al 2008), is consistent with that predicted by assuming that the spatial distribution of UHECR sources correlates with the large-scale distribution of galaxies (Waxman, Fisher & Piran 1997;Kashti & Waxman 2008).…”

Search for clustering of ultra high energy cosmic rays from the Pierre Auger Observatory

“…Tinyakov and Tkachev [4] computed the penalisation arising from making a scan in the energy threshold and obtained a probability of 3 × 10 −4 . Finley and Westerhoff [5] took also into account the penalisation for a scan in the angular scale and obtained a probability of 3.5 × 10 −3 . The HiRes observatory has found no significant clustering signal at any angular scale up to 5 • for any energy threshold above 10 EeV [6].…”

“…The significance of an autocorrelation signal at a given angle and energy, when these values have not been fixed a priori, is a delicate issue that has made, for example, the significance of the AGASA small scale clustering claim very controversial. We adopt here the method proposed by Finley and Westerhoff [5], in which a scan over the energy threshold and the angular separation is performed. For each value of E and α, we compute the fraction f of simulations having an equal or larger number of pairs than the data by generating 10 6 simulated isotropic data sets modulated by the exposure.…”

A search for arrival direction clustering in the HiRes-I monocular data above 1019.5 eV

“…In 1999 [1] and again in 2001 [2], the AGASA collaboration reported observing what eventually became seven clusters (six "doublets" and one "triplet") with estimated energies above ∼ 3.8 × 10 19 eV. Several attempts that have been made to ascertain the significance of these clusters returned chance probabilities of 4 × 10 −6 [3] to 0.08 [4].…”