We explore the possibility of a local origin for ultra high energy cosmic rays (UHECRs). Using the catalogue of Karachentsev et al. including nearby galaxies with distances less than 10Mpc (Local Volume), we search for a correlation with the sample of UHECR events released so far by the Pierre Auger collaboration. The counterpart sample selection is performed with variable distance and luminosity cuts which extract the most likely sources in the catalogue. The probability of chance correlation after penalizing for scans is 0.96%, which corresponds to a correlation signal of 2.6sigma. We find that the parameters that maximize the signal are psi=3.0deg, D_{max}=4Mpc and M_B=-15 for the maximum angular separation between cosmic rays and galaxy sources, maximum distance to the source, and sources brighter than B-band absolute magnitude respectively. This implies a preference for the UHECRs arrival directions to be correlated with the nearest and most luminous galaxies in the Local Volume. We note that nearby galaxies with D<10Mpc show a similar correlation with UHECRs as compared to that found by The Pierre Auger Collaboration using active galactic nuclei (AGNs) within 70-100Mpc instead of local galaxies, although less than 20% of cosmic ray events are correlated to a source in our study. However, the observational evidence for mixed composition in the high-energy end of the cosmic ray spectrum supports the possibility of a local origin for UHECRs, as CNO nuclei can travel only few Mpc without strong attenuation by the GZK effect, whereas the observed suppression in the energy spectrum would require more distant sources in the case of pure proton composition interacting with the CMB.
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