Internal and Collective Properties of Galaxies in the Sloan Digital Sky Survey

We examine volume-limited samples of galaxies drawn from the Sloan Digital Sky Survey to look for relations among internal and collective physical parameters of galaxies as faint as Mr = −17.5. The internal physical properties of interest include morphology, luminosity, color, color gradient, concentration, size, velocity dispersion, equivalent width of Hα line, and axis ratio. Collective properties that we measure include the luminosity and velocity dispersion functions. We morphologically classify galaxies using the three dimensional parameter space of u−r color, g−i color gradient, and concentration index. All relations are inspected separately for early and late type galaxies. At fixed morphology and luminosity, we find that bright (Mr < −20) early type galaxies show very small dispersions in color, color gradient, concentration, size, and velocity dispersion. These dispersions increase at fainter magnitudes, where the fraction of blue star-forming early types increases. Late types show wider dispersions in all physical parameters compared to early types at the same luminosity. Concentration indices of early types are well correlated with velocity dispersion, but are insensitive to luminosity and color for bright galaxies, in particular. The slope of the Faber-Jackson relation (L ∝ σ) continuously changes from γ = 4.6± 0.4 to 2.7± 0.2 when luminosity changes from Mr = −22 to −20. The size of early types is well-correlated with stellar velocity dispersion, σ, when σ > 100 km s. We find that passive spiral galaxies are well separated from star-forming late type galaxies at Hα equivalent width of about 4. An interesting finding is that many physical parameters of galaxies manifest different behaviors across the absolute magnitude of about M∗ ± 1. The morphology fraction as a function of luminosity depends less sensitively on large-scale structure than the luminosity function (LF) does, and thus seems to be more universal. The effects of internal extinction in late type galaxies on the completeness of volume-limited samples and on the LF and morphology fraction are found to be very important. An important improvement of our analyses over most previous works is that the extinction effects are effectively reduced by excluding the inclined late type galaxies with axis ratios of b/a < 0.6. Subject headings: galaxies:general – galaxies:luminosity function, mass function – galaxies:formation – galaxies:fundamental parameters – galaxies:statistics