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We investigated the spatial correlation between the arrival directions of thehighest 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 galaxiesobserved by the Sloan Digital Sky Survey (SDSS) within $z = 0.024$. Wesystematically tested the dependence of the correlation on the redshift rangesand properties of the galaxies, i.e., absolute luminosity, color, andmorphology, to understand where HECR sources are and what objects are HECRsources. In the systematic survey, we found potential signals of the positivecorrelation at small angular scale ($<10^{\circ}$) with the (non-penalized)chance probability less than 5% in intermediate redshift ranges. Then, weestimated penalized probabilities to compensate the trial effects of angularscan, and found that the strongest correlation is produced by early-typegalaxies in $0.012 \leq z < 0.018$ at 90% C.L. The possible origin of HECRswhich correlating galaxies imply is also discussed.

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