The Signature of a Correlation between Cosmic‐Ray Sources above 1019eV and Large‐Scale Structure

We analyze the anisotropy signature expected if the high energy (above$10^{19}$eV) cosmic ray (CR) sources are extra-Galactic and trace thedistribution of luminous matter on large scales. We investigate the dependenceof the anisotropy on both the relative bias between the CR sources and thegalaxy distribution and on the (unknown) intrinsic CR source density. We findthat the expected anisotropy associated with the large scale structure (LSS)should be detected once the number of CR events observed above $10^{19}{\rmeV}$ is increased by a factor of $\sim10$. This would require $\sim30$observation-years with existing experiments, but less then $1$ year with theproposed $\sim5000\ {\rm km}^2$ Auger detectors. We find that the recentlyreported concentration of the Haverah Park CR events towards the super-galacticplane is not consistent with the known LSS. If real, the Haverah Park resultsuggests that the CR sources are much more concentrated towards thesuper-galactic plane than the known LSS. Our results are not sensitive to thenumber density of CR sources. We show that once the number of detected eventsis increased by a factor of $\sim10$, the number density would be stronglyconstrained by considering the probability for having repeating sources.Comment: Submitted to the ApJ; 19 pages (LaTeX file, 7 PostScript figures, aaspp4.sty style file, tar'ed, gzip'ed and uuencoded