Systematically Measuring Ultra-diffuse Galaxies (SMUDGes). II. Expanded Survey Description and the Stripe 82 Catalog

We present 226 large ultra-diffuse galaxy (UDG) candidates (r ( e ) > 5.'' 3, mu (0,g ) > 24 mag arcsec(-2)) in the SDSS Stripe 82 region recovered using our improved procedure developed in anticipation of processing the entire Legacy Surveys footprint. The advancements include less constrained structural parameter fitting, expanded wavelet filtering criteria, consideration of Galactic dust, estimates of parameter uncertainties and completeness based on simulated sources, and refinements of our automated candidate classification. We have a sensitivity similar to 1 mag fainter in mu (0,g ) than the largest published catalog of this region. Using our completeness-corrected sample, we find that (1) there is no significant decline in the number of UDG candidates as a function of mu (0,g ) to the limit of our survey (similar to 26.5 mag arcsec(-2)); (2) bluer candidates have smaller Sersic n; (3) most blue (g-r < 0.45 mag) candidates have mu (0,g ) less than or similar to 25 mag arcsec(-2) and will fade to populate the UDG red sequence we observe to similar to 26.5 mag arcsec(-2); (4) any red UDGs that exist significantly below our mu (0,g ) sensitivity limit are not descendent from blue UDGs in our sample; and (5) candidates with lower mu (0,g ) tend to smaller n. We anticipate that the final SMUDGes sample will contain similar to 30 x as many candidates.