Revision of the Selection Function of the Optical Redshift Survey Using the Sloan Digital Sky Survey Early Data Release: Toward an Accurate Estimate of the Source Number Density of Ultra-High Energy Cosmic Rays

If Ultra-High Energy Cosmic Rays (UHECRs) are originated from nearbygalaxies, modeling of the distribution of nearby galaxies is important to anaccurate estimate the source number density of UHECRs. We investigateuncertainty of the selection function of the Optical Redshift Survey (ORS),which we used to construct a source model of UHECRs. The investigation is basedon a comparison of numbe counts of ORS galaxies with those of the spectroscopicsample of the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). Wecarefully count galaxies in the same absolute magnitude bin from the twosamples. We find a slight systematic overestimate of the ORS counts outside5000 km s$^{-1}$ by about a factor of 2. We revise the selection function ofthe ORS assuming that the SDSS counts are correct. Our revision is based on theabsorption given in the ORS catalog as well as that computed from Schlegel etal. (1998), which is systematically larger than the former by $A_B \sim 0.1$mag in the region of low absorption. It is found that introduction of Schlegelet al.'s absorption changes one of the parameters of the ORS selection functionby more than 10%. The revision should be taken into account in the futureanalysis of the source number density of UHECRs based on the ORS. Using therevised selection function, we determine the global structure of the LocalSupercluster (LSC) with a source model of UHECRs, that is, a number-densitymodel consisting of a uniform spherical halo and an exponential disk. We findthat the revision is insignificant in terms of the structure of the LSC.However, the revised selection function will be useful to other studies such aspeculiar velocity and correlation function.Comment: 22 pages, 13 figures. accepted for publication in PAS