Modelling cross-correlations of ultra-high-energy cosmic rays and galaxies

The astrophysical engines that power ultra-high-energy cosmic rays (UHECRs) remain to date unknown. Since the propagation horizon of UHECRs is limited to the local, anisotropic Universe, the distribution of UHECR arrival directions should be anisotropic. In this paper we expand the analysis of the potential for the angular, harmonic cross-correlation between UHECRs and galaxies to detect such anisotropies. We do so by studying simulations performed assuming proton, oxygen and silicon injection models, each simulation containing a number of events comparable to a conservative estimate of currently available datasets, as well as by extending the analytic treatment of the magnetic deflections. Quantitatively, we find that, while the correlations for each given multipole are generally weak, (1) the total harmonic power summed over multipoles is detectable with signal-to-noise ratios well above~5 for both the auto-correlation and the cross-correlation (once optimal weights are applied) in most cases studied here, with peaks of signal-to-noise ratio around between~8 and~10 at the highest energies; (2) if we combine the UHECR auto-correlation and the cross-correlation we are able to reach detection levels of (3\sigma) and above for individual multipoles at the largest scales, especially for heavy composition. In particular, we predict that the combined-analysis quadrupole could be detected already with existing data.