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We introduce a method to constrain the characteristic angular size of thebrightest cosmic-ray sources observed above 57 \times 1018 eV. By angular sizeof a source, we mean the effective angular extent over which cosmic-rays fromthat source arrive at earth. The method is based on the small-scale (< 10\circ)self-clustering of cosmic-ray arrival directions. The method is applicable tosparse data sets in which strong localizations of CR* directions are not yetobserved. We show that useful constraints on the source size can be made in thenear future and that these constraints are not strongly dependent on theassumed 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 particlecharge and intervening magnetic fields (not independently), both of which arenot well constrained so far. This is possible because the source size issimilar in scale to the magnetic deflection.

A method to constrain the characteristic angular size of the brightest cosmic-ray sources observed above 57 $\times$ 10^{18} eV