We analyze the absolute magnitude ( M _ { r } ) and color ( u - r ) of low redshift ( z < 0.06 ) galaxies in the Sloan Digital Sky Survey Data Release 6 .
Galaxies with nearly exponential profiles ( Sloan parameter { fracDeV } < 0.1 ) all fall on the blue sequence of the color – magnitude diagram ; if , in addition , these exponential galaxies have M _ { r } < -19 , they show a dependence of u - r color on apparent axis ratio q expected for a dusty disk galaxy .
By fitting luminosity functions for exponential galaxies with different values of q , we find that the dimming is well described by the relation \Delta M _ { r } = 1.27 ( \log q ) ^ { 2 } , rather than the \Delta M \propto \log q law that is frequently assumed .
When the absolute magnitudes of bright exponential galaxies are corrected to their “ face-on ” value , M _ { r } ^ { f } = M _ { r } - \Delta M _ { r } , the average u - r color is linearly dependent on M _ { r } ^ { f } for a given value of q .
Nearly face-on exponential galaxies ( q > 0.9 ) have a shallow dependence of mean u - r color on M _ { r } ^ { f } ( 0.096 magnitudes redder for every magnitude brighter ) ; by comparison , nearly edge-on exponential galaxies ( q < 0.3 ) are 0.265 magnitudes redder for every magnitude brighter .
When the dimming law \Delta M _ { r } \propto ( \log q ) ^ { 2 } is used to create an inclination-corrected sample of bright exponential galaxies , their apparent shapes are confirmed to be consistent with a distribution of mildly non-circular disks , with median short-to-long axis ratio \gamma \approx 0.22 and median disk ellipticity \epsilon \approx 0.08 .