A method to constrain the characteristic angular size of the brightest cosmic-ray sources observed above 57 × 1018 eV

We introduce a method to constrain the characteristic angular size of the brightest cosmic-ray sources observed above 57 × 1018 eV. By angular size of a source, we mean the effective angular extent over which cosmic-rays from that source arrive at earth. The method is based on the small-scale (<10°) self-clustering of cosmic-ray arrival directions. The method is applicable to sparse data sets in which strong localizations of CR* directions are not yet observed. We show that useful constraints on the source size can be made in the near future and that these constraints are not strongly dependent on the assumed spatial distribution and luminosity function of the cosmic-ray sources. We suggest that an indication of the source size is quite telling. For example, an indication of the source size can be used to infer limits on the particle charge and intervening magnetic fields (not independently), both of which are not well constrained so far. This is possible because the source size is similar in scale to the magnetic deflection.