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For a sample of 96,951 galaxies from the Sloan Digital Sky Survey DataRelease 3, we study the distribution of apparent axis ratios as a function ofr-band absolute magnitude and surface brightness profile type. We use theparameter fracDeV to quantify the profile type (fracDeV = 1 for a deVaucouleurs profile; fracDeV = 0 for an exponential profile). When the apparentaxis ratio q_{am} is estimated from the moments of the light distribution, theroundest galaxies are very bright (M_r \sim -23) de Vaucouleurs galaxies andthe flattest are modestly bright (M_r \sim -18) exponential galaxies. When theapparent axis ratio q_{25} is estimated from the axis ratio of the 25mag/arcsec^2 isophote, we find that de Vaucouleurs galaxies are flatter thanexponential galaxies of the same absolute magnitude. For a given surfacebrightness profile type, very bright galaxies are rounder, on average, thanfainter galaxies. We deconvolve the distributions of apparent axis ratios tofind the distribution of the intrinsic short-to-long axis ratio gamma, assumingconstant triaxiality T. For all profile types and luminosities, thedistribution of apparent axis ratios is inconsistent with a population ofoblate spheroids, but is usually consistent with a population of prolatespheroids. Bright galaxies with a de Vaucouleurs profile (M_r < -21.84, fracDeV> 0.9) have a distribution of q_{am} that is consistent with triaxiality in therange 0.4 < T < 0.8, with mean intrinsic axis ratio 0.66 < gamma < 0.69. Thefainter de Vaucouleurs galaxies are best fit with prolate spheroids (T = 1)with mean axis ratio gamma = 0.51.Comment: 32 pages, 12 figures, to appear in Ap

The Dependence of Galaxy Shape on Luminosity and Surface Brightness Profile