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

Abstract

If Ultra-High Energy Cosmic Rays (UHECRs) are originated from nearby galaxies, modeling of the distribution of nearby galaxies is important to an accurate estimate the source number density of UHECRs. We investigate uncertainty of the selection function of the Optical Redshift Survey (ORS), which we used to construct a source model of UHECRs. The investigation is based on a comparison of numbe counts of ORS galaxies with those of the spectroscopic sample of the Sloan Digital Sky Survey (SDSS) Early Data Release (EDR). We carefully count galaxies in the same absolute magnitude bin from the two samples. We find a slight systematic overestimate of the ORS counts outside 5000 km s$^{-1}$ by about a factor of 2. We revise the selection function of the ORS assuming that the SDSS counts are correct. Our revision is based on the absorption given in the ORS catalog as well as that computed from Schlegel et al. (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 Schlegel et al.'s absorption changes one of the parameters of the ORS selection function by more than 10%. The revision should be taken into account in the future analysis of the source number density of UHECRs based on the ORS. Using the revised selection function, we determine the global structure of the Local Supercluster (LSC) with a source model of UHECRs, that is, a number-density model 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 to other studies such as peculiar velocity and correlation function.