We analyse the bivariate distribution , in color versus absolute magnitude ( u - r vs . M _ { r } ) , of a low redshift sample of galaxies from the Sloan Digital Sky Survey ( SDSS ; 2400 deg ^ { 2 } , 0.004 < z < 0.08 , -23.5 < M _ { r } < -15.5 ) .
We trace the bimodality of the distribution from luminous to faint galaxies by fitting double-Gaussians to the color functions separated in absolute magnitude bins .
Color-magnitude ( CM ) relations are obtained for red and blue distributions ( early- and late-type , predominantly field , galaxies ) without using any cut in morphology .
Instead , the analysis is based on the assumption of normal Gaussian distributions in color .
We find that the CM relations are well fit by a straight line plus a tanh function .
Both relations can be described by a shallow CM trend ( slopes of about -0.04 , -0.05 ) plus a steeper transition in the average galaxy properties over about two magnitudes .
The midpoints of the transitions ( M _ { r } = -19.8 and -20.8 for the red and blue distributions , respectively ) occur around 2 \times 10 ^ { 10 } { \cal M } _ { \odot } after converting luminosities to stellar mass .
Separate luminosity functions are obtained for the two distributions .
The red distribution has a more luminous characteristic magnitude and a shallower faint-end slope ( M ^ { * } = -21.5 , \alpha = -0.8 ) compared to the blue distribution ( \alpha \approx - 1.3 depending on the parameterization ) .
These are approximately converted to galaxy stellar mass functions .
The red distribution galaxies have a higher number density per magnitude for masses greater than about 3 \times 10 ^ { 10 } { \cal M } _ { \odot } .
Using a simple merger model , we show that the differences between the two functions are consistent with the red distribution being formed from major galaxy mergers .