Quantitative characterization of galaxy morphology is vital in enabling comparison of observations to predictions from galaxy formation theory. However, without significant overlap between the observational footprints of deep and shallow galaxy surveys, the extent to which structural measurements for large galaxy samples are robust to image quality (e.g., depth, spatial resolution) cannot be established. Deep images from the Sloan Digital Sky Survey (SDSS) Stripe 82 co-adds provide a unique solution to this problem - offering $1.6-1.8$ magnitudes improvement in depth with respect to SDSS Legacy images. Having similar spatial resolution to Legacy, the co-adds make it possible to examine the sensitivity of parametric morphologies to depth alone. Using the Gim2D surface-brightness decomposition software, we provide public morphology catalogs for 16,908 galaxies in the Stripe 82 $ugriz$ co-adds. Our methods and selection are completely consistent with the Simard et al. (2011) and Mendel et al. (2014) photometric decompositions. We rigorously compare measurements in the deep and shallow images. We find no systematics in total magnitudes and sizes except for faint galaxies in the $u$-band and the brightest galaxies in each band. However, characterization of bulge-to-total fractions is significantly improved in the deep images. Furthermore, statistics used to determine whether single-Sersic or two-component (e.g., bulge+disc) models are required become more bimodal in the deep images. Lastly, we show that asymmetries are enhanced in the deep images and that the enhancement is positively correlated with the asymmetries measured in Legacy images.
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