The stages of galaxy interactions and mergers play a very important role on galaxy evolution and structure formation. A high merger rate in the past can change the morphology, luminosity, stellar population, and number density of galaxies dramatically. Therefore, the evolution of the merger rate is directly connected to the structure formation of the universe. For this study, we focus on close pairs of galaxies because they are good candidates of early-stage mergers, and the pair fractions can be converted to the merger rates easily. We study the evolution of the number of companions per galaxy (Nc) by choosing a volume-limited subset of the photometric redshift catalog from the Red-Sequence Cluster Survey (RCS). The RCS provides a large and deep photometric catalog of galaxies in the z ′ and R c bands for 90 square degrees of sky, and supplemental V and B data have been obtained for 33.6 deg 2. We compile a photometric redshift catalog from these 4-band data by utilizing the empirical quadratic polynomial photometric redshift fitting technique in combination with CNOC2 and GOODS/HDF-N redshift data. The training set includes 4924 spectral redshifts. The resulting catalog contains more than one million galaxies with photometric redshifts < 1.5 and Rc < 24, giving an rms scatter σ(Δz) < 0.06 within the redshift range 0.2 < z < 0.5 and σ(Δz) < 0.11 for galaxies at 0.0 < z < 1.5. We describe the empirical quadratic polynomial photometric redshift fitting technique which we use to determine the relation between redshift and photometry. A kd-tree algorithm is used to divide up our sample to improve the accuracy of our catalog. We also present a method for estimating the photometric redshift error for individual galaxies. We show that the redshift distribution of our sample is in excellent agreement with smaller and much deeper photometric and spectroscopic redshift surveys. We choose a subsample of the RCS photometric redshift catalog, which contains over 60,000 objects with a moderate redshift range at 0.25 ≦ z ≦ 0.8 and with MR c ≦ -20. After applying incompleteness and background corrections, Nc shows a clear evolution with redshift. The Nc value for the whole sample grows with redshift as (1+z) m with m = 3.52±0.06 for z < 0.5, but drops with m = -1.01±0.04 for z > 0.5. However, if the galaxies are separated into several different absolute magnitude bins, the m values for z > 0.5 increase with luminosity; while they are similar for different magnitude bins for z < 0.5. The m values determined in many previous observational results are very diverse (0 < m < 4) which is probably just simply due to that they look at different mass (luminosity) ranges and do not have adequate object numbers to reduce the error to detect the decrease of Nc for z > 0.5. We interpret our result by using the “down-sizing” structure formation scenario claiming bigger galaxies are formed earlier and they stop being formed at a certain epoch at z > 0.8, while smaller galaxies are formed later and have a formation peak at z ? 0.5 which is consistent with the study of star formation rate for galaxies with different masses at different epoch from Heavens et al. (2004).
