We calculate numerically the spectrum of ultra-high energy cosmic rays on Earth assuming that their sources are distributed in space like the observed galaxies. We use the CfA2 and the PSCz galaxy redshift surveys to model the local galaxy distribution, properly taking into account the galaxy selection functions for each survey. When the survey selection effects are included, we find that the local overdensity is only a factor of 2, an order of magnitude less than used in some earlier studies. An overdensity of 2 is not enough to bridge the gap between the predicted number of events above 10(20) eV and the measured flux at these highest energies. This conclusion is particularly strong for soft injection spectra (proportional to E-3) where the observed number of events is 6 sigma higher than the expected one. However, if the injection spectrum is hard (proportional to E-2), the small local overdensity helps bring the present data within 2 sigma of the low number of events predicted above 1020 eV. In this case, the Greisen-Zatzepin-Kurmin cutoff is not a cutoff but rather a feature in the cosmic ray spectrum. (C) 2001 Elsevier Science B.V. All rights reserved.
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