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) originate from nearby galaxies, modeling of the distribution of nearby galaxies is important for an accurate estimate of the source number density of UHECRs. We investigate the uncertainty of the selection function of the Optical Redshift Survey (ORS), which we use to construct a source model of UHECRs. The investigation is based on a comparison of the number counts of ORS galaxies with those of the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). We carefully count galaxies of the same absolute magnitude bin from two samples. We find a slight systematic overestimate of the ORS counts outside $5000 \,\mathrm{km} \,\mathrm{s}^{-1}$ by about a factor of 2, and revise the selection function of the ORS. The revision should be taken into account in any future analysis of the source number density of UHECRs based on the ORS. Using the revised selection function, we determined the global structure of the Local Supercluster (LSC) with a source model of UHECRs consisting of a uniform spherical halo and an exponential disk. We find that the revision is insignificant in terms of the structure of the LSC. However, the revised selection function will be useful for other studies, such as those involving a peculiar velocity and the correlation function.