Constraining the cosmic ray source spectrum from observations in the GZK regime

We present a method to constrain the injection spectrum of ultrahigh energy cosmic rays (CRs) from supposedly identified extragalactic sources, which can be applied even when only one or two events per source are observed, and is more efficient than a simple fit of the CR energy spectrum including only the contribution of all identified sources. The method is based on the analysis of the probability for a given source to populate different energy bins, depending on the actual CR injection spectral index. In particular, we show that for a typical source density of 4 × 10 Mpc, a data set of 100 events above 6× 10 eV allows one in 97% of the cases to distinguish a source spectrum dN/dE ∝ E from one with E at 95% confidence level. Constraining the cosmic ray source spectrum from observations in the GZK regime 2