Evolution of the Galaxy Luminosity Function for Redshift and Density Environment at 0.03 < z < 0.5

Using the galaxy sample observed by the Beijing-Arizona-Taiwan-Connecticut (BATC) large-field multicolor sky survey and the galaxy data of the Sloan Digital Sky Survey (SDSS) in overlapping fields, we study the dependence of the rest-frame r-band galaxy luminosity function on redshift and on the large-scale environment. The large-scale environment is defined by isodensity contours with density contrast dr/r. The data set is a composite sample of 69,671 galaxies with redshifts 0.03 < z < 0.5 and r < 21.5 mag. The redshift data are composed of three parts: (1) spectroscopic redshifts in SDSS for local and the most luminous galaxies, (2) 20-color photometric redshifts derived from BATC and SDSS, and (3) five-color photometric redshifts in SDSS. We find that the faint-end slope a steepens slightly from - 1.21 at z 6 0.06 to -1.35 at z 6 0.4, which is the natural consequence of the hierarchical formation of galaxies. The luminosity function also differs with different environments. The value of a changes from -1.21 in underdense regions to -1.37 in overdense regions, and the corresponding M* brightens from - 22.26 to -22.64. This suggests that the fraction of faint galaxies is larger in high-density regions than in low-density regions.