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 M _ { r } = -17.5 .
The internal physical properties of interest include morphology , luminosity , color , color gradient , concentration , size , velocity dispersion , equivalent width of H { \alpha } 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 ( M _ { r } < -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 \propto { \sigma } ^ { \gamma } ) continuously changes from \gamma = 4.6 \pm 0.4 to 2.7 \pm 0.2 when luminosity changes from M _ { r } = -22 to -20 .
The size of early types is well-correlated with stellar velocity dispersion , \sigma , when \sigma > 100 km s ^ { -1 } .
We find that passive spiral galaxies are well separated from star-forming late type galaxies at H { \alpha } 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 _ { \ast } \pm 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 .