For a sample of 96,951 galaxies from the Sloan Digital Sky Survey Data Release 3 , we study the distribution of apparent axis ratios as a function of r -band absolute magnitude and surface brightness profile type .
We use the parameter fracDeV to quantify the profile type ( \texttt { fracDeV } = 1 for a pure de Vaucouleurs profile ; \texttt { fracDeV } = 0 for a pure exponential profile ) .
When the apparent axis ratio q _ { am } is estimated from the moments of the light distribution , the roundest galaxies are very bright ( M _ { r } \sim - 23 ) de Vaucouleurs galaxies and the flattest are modestly bright ( M _ { r } \sim - 18 ) exponential galaxies .
When the axis ratio q _ { 25 } is estimated from the axis ratio of the 25 mag/arcsec ^ { 2 } isophote , we find that de Vaucouleurs galaxies , at this low surface brightness , are flatter than exponential galaxies of the same absolute magnitude .
For a given surface brightness profile type , very bright galaxies are rounder , on average , than fainter galaxies .
We deconvolve the distributions of apparent axis ratios to find the distribution of the intrinsic short-to-long axis ratio \gamma , making the assumption of constant triaxiality T .
For all profile types and luminosities , the distribution of axis ratios is inconsistent with a population of oblate spheroids , but is usually consistent with a population of prolate spheroids .
Bright galaxies with a de Vaucouleurs profile ( M _ { r } \leq - 21.84 , \texttt { fracDeV } > 0.9 ) have a distribution of q _ { am } that is consistent with triaxiality in the range 0.4 \lesssim T \lesssim 0.8 , with mean axis ratio 0.66 \lesssim \langle \gamma \rangle \lesssim 0.69 .
The fainter de Vaucouleurs galaxies are best fit with prolate spheroids ( T = 1 ) with mean axis ratio \langle \gamma \rangle \approx 0.51 .