?????We present the first results of an ongoing project to investigate the present-day chemical abundances of the extreme outer parts of galactic disks, as probed by the emission-line spectra of a new sample of H II regions. The galaxies studied here, NGC 628, NGC 1058, and NGC 6946, are all late-type spiral galaxies, characterized by larger than average H I?to?optical sizes. Our deep H? images have revealed the existence of recent massive star formation, traced by H II regions, out to and beyond two optical radii in these galaxies (defined by the B-band 25th magnitude isophote). Optical spectra of these newly discovered H II regions are used to investigate their densities, ionization parameters, extinctions, and, in particular, their oxygen and nitrogen abundances. Our measurements reveal gas-phase abundances of O/H ~ 10%?15% of the solar value and N/O ~ 20%?25% of the solar value at radii of (1.5?2)R25. Clear evidence also exists for diminished dust extinction (AV ~ 0?0.2 mag) at large radii. The combination of our measurements of outer disk H II region abundances with those for inner disk H II regions published in the literature is a powerful probe of the shape of abundance gradients over unprecedented radial baselines. The predictions of models of chemical evolution often diverge most strongly in the outer parts of galaxies. Both the oxygen and the nitrogen-to-oxygen abundances generally decrease with increasing radius. Within the limits of the current data set, the radial abundance variations are consistent with single log-linear relationships, although the derived slopes can often differ considerably from those found if only inner disk H II regions are used to define the fit. The small number of H II regions in our present sample, together with uncertainties in the calibrations of the empirical methods used here to determine abundances, limit the ability to constrain both subtle changes in the radial gradient and intrinsic scatter at a fixed radius. Nitrogen-to-oxygen ratios appear to be consistent with a combination of primary and secondary production of nitrogen. Interestingly, both the mean level of enrichment and the N/O ratio measured in extreme outer galactic disks are similar to those values measured in some high-redshift damped Ly? absorbers, suggesting that outer disks at the present epoch are relatively unevolved.
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