Spatially-Resolved O II Recombination Line Observations of the Ring Nebula, NGC 6720

We present spatially-resolved spectral of O II permitted lines and [O III] forbidden lines in the Ring Nebula NGC 6720. We find significant differences in the spatial distribution of the O II and [O III] lines. The [O III] emission follows the H-beta emission measure; however, the O II emission peaks closer to the central star. This suggests that radiative recombination may not be the primary mechanism for producing the O II lines. O+2 abundances derived from O II lines are 5-10 times larger than those derived from [O III] in the region within 20" of the central star, but agree to within 0.2-0.3 dex outside this region. The [O III] electron temperature rises smoothly from about 10,000 K in the outer shell to about 12,000 K in the center; we see no evidence for a temperature jump that would be associated with a shock. If temperature fluctuations are responsible for the discrepancy in O+2 abundances, the average temperature would have to be approximately 6,500 K in the He$^{+2}$ zone and about 9,000 K in the outer shell in order to force the [O III]-derived abundance to equal that derived from O II. We therefore argue that temperature fluctuations can not explain the abundance discrepancy. The O II emission does not peak at the locations of dusty knots, creating difficulties for models which explain the O II - [O III] discrepancy by density fluctuations. We examine the possibility high-temperature dielectronic recombination in a central hot bubble enhances the O II line strengths in the central nebula. However, comparison of recombination rates with collisional excitation rates shows that the increase in recombination emission due to dielectronic recombination at T ~ 10^5 K is not sufficient to overcome the increase in [O III] emission. (Abridged)