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We use high signal-to-noise ratio spectra of 20 H II regions in the giant spiral galaxy M101 to derive electron temperatures for the H II regions and robust metal abundances over radii R = 0.19-1.25 R 0 (6-41 kpc). We compare the consistency of electron temperatures measured from the [O III] λ4363, [N II] λ5755, [S III] λ6312, and [O II] λ7325 auroral lines. Temperatures from [O III], [S III], and [N II] are correlated with relative offsets that are consistent with expectations from nebular photoionization models. However, the temperatures derived from the [O II] λ7325 line show a large scatter and are nearly uncorrelated with temperatures derived from other ions. We tentatively attribute this result to observational and physical effects, which may introduce large random and systematic errors into abundances derived solely from [O II] temperatures. Our derived oxygen abundances are well fitted by an exponential distribution over six disk scale lengths, from approximately 1.3 (O/H) ☉ in the center to 1/15 (O/H) ☉ in the outermost region studied [for solar 12 + log(O/H) = 8.7]. We measure significant radial gradients in N/O and He/H abundance ratios, but relatively constant S/O and Ar/O. Our results are in approximate agreement with previously published abundances studies of M101 based on temperature measurements of a few H II regions. However, our abundances are systematically lower by 0.2-0.5 dex than those derived from the most widely used strong-line "empirical" abundance indicators, again consistent with previous studies based on smaller H II region samples. Independent measurements of the Galactic interstellar oxygen abundance from ultraviolet absorption lines are in good agreement with the T e -based nebular abundances. We suspect that most of the disagreement with the strong-line abundances arises from uncertainties in the nebular models that are used to calibrate the "empirical" scale, and that strong-line abundances derived for H II regions and emission-line galaxies are as much as a factor of 2 higher than the actual oxygen abundances. However, other explanations, such as the effects of temperature fluctuations on the auroral line based abundances, cannot be completely ruled out. These results point to the need for direct abundance determinations of a larger sample of extragalactic H II regions, especially for objects more metal-rich than solar.
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