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.
