Systematic Survey of the Correlation between Northern HECR Events and SDSS Galaxies

We investigated the spatial correlation between the arrival directions of the highest energy cosmic rays (HECRs) detected by the Akeno Giant Air Shower Array (AGASA) with energies above $4 \times 10^{19}$ eV and the positions of galaxies observed by the Sloan Digital Sky Survey (SDSS) within $z = 0.024$. We systematically tested the dependence of the correlation on the redshift ranges and properties of the galaxies, i.e., absolute luminosity, color, and morphology, to understand where HECR sources are and what objects are HECR sources. In the systematic survey, we found potential signals of the positive correlation at small angular scale ($<10^{\circ}$) with the (non-penalized) chance probability less than 5% in intermediate redshift ranges. Then, we estimated penalized probabilities to compensate the trial effects of angular scan, and found that the strongest correlation is produced by early-type galaxies in $0.012 \leq z < 0.018$ at 90% C.L. The possible origin of HECRs which correlating galaxies imply is also discussed.