The shapes of galaxies in the Sloan Digital Sky Survey

We determine the underlying shapes of spiral and elliptical galaxies in the Sloan Digital Sky Survey Data Release 6 (SDSS DR6) from the observed distribution of projected galaxy shapes, taking into account the effects of dust extinction and reddening. We assume that the underlying shapes of spirals and ellipticals are well approximated by triaxial ellipsoids. The elliptical galaxy data are consistent with oblate spheroids, with a correlation between luminosity and ellipticity: the mean values of minor to middle axis ratios are 0.41 +/- 0.03 for M-r approximate to -18 ellipticals and 0.76 +/- 0.04 for M-r approximate to -22.5 ellipticals. Ellipticals show almost no dependence of axial ratio on galaxy Colour, implying a negligible dust optical depth. There is a strong variation of spiral galaxy shapes with colour indicating the presence of dust. The intrinsic shapes of spiral galaxies in the SDSS DR6 are consistent with flat discs with a mean and dispersion of thickness to diameter ratio of (21 +/- 2) per cent, and a face-on ellipticity, e, of ln(e) = -2.33 +/- 0.79. Not including the effects of dust in the model leads to discs that are systematically rounder by Lip to 60 per cent. More luminous spiral galaxies tend to have thicker and rounder discs than lower luminosity spirals. Both elliptical and spiral galaxies tend to be rounder for larger galaxies. The marginalized value of the edge-on r-band dust extinction E-0 in spiral galaxies is E-0 similar or equal to 0.45 mag for galaxies of median colours, increasing to E-0 = 1 mag for g - r > 0.9 and E-0 = 1.9 for the luminous and most compact galaxies, with half-light radii < 2 h(-1) kpc.