We present a study of large-scale bars in the local Universe, based on a large sample of ~3692 galaxies, with -18.5 <= M_g < -22.0 mag and redshift 0.01 <= z < 0.03, drawn from the SDSS. Our sample includes many galaxies that are disk-dominated and of late Hubble types. Both color cuts and Sersic cuts yield a similar sample of ~2000 disk galaxies. We characterize bars and disks by ellipse-fitting r-band images and applying quantitative criteria. After excluding highly inclined (>60 degrees) systems, we find the following results. (1) The optical r-band fraction (f_opt-r) of barred galaxies is ~48%-52%. (2) When galaxies are separated according to normalized half light radius (r_e/R_24), a remarkable result is seen: f_opt-r rises sharply, from ~40% in galaxies that have small r_e/R_24 and visually appear to host prominent bulges, to ~70% for galaxies that have large r_e/R_24 and appear disk-dominated. (3) f_opt-r rises for galaxies with bluer colors and higher central surface brightness. A weaker rise is seen toward lower masses. (4) We find that ~20% of our sample of disk galaxies appear to be ``quasi-bulgeless. (5) If we restrict our sample to bright galaxies and only consider bars that are strong (ellipticity >=0.4) and large enough (semi-major axis >=1.5 kpc) to be reliably characterized via ellipse-fitting out to z~0.8, we get an optical r-band fraction for strong bars f_opt-s of ~34%. This value is higher only by a modest factor of 1.4, compared to the value of ~24%+-4% reported at z~0.7-1.0. If one assumes that the increasing obscuration by dust and star formation over z~0 to 1.0 causes a further artificial loss of bars, the data even allow for a constant or rising fraction of strong bars with redshift.
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