A Detailed Look at Chemical Abundances in Magellanic Cloud Planetary
  Nebulae. I. The Small Magellanic Cloud
  We present an analysis of elemental abundances of He, N, O, Ne, S, and Ar in
Magellanic Cloud planetary nebulae (PNe), and focus initially on 14 PNe in the
Small Magellanic Cloud (SMC). We derived the abundances from a combination of
deep, high dispersion optical spectra, as well as mid-infrared (IR) spectra
from the Spitzer Space Telescope. A detailed comparison with prior SMC PN
studies shows that significant variations among authors of relative emission
line flux determinations lead to systematic discrepancies in derived elemental
abundances between studies that are >~0.15 dex, in spite of similar analysis
methods. We used ionic abundances derived from IR emission lines, including
those from ionization stages not observable in the optical, to examine the
accuracy of some commonly used recipes for ionization correction factors
(ICFs). These ICFs, which were developed for ions observed in the optical and
ultraviolet, relate ionic abundances to total elemental abundances. We find
that most of these ICFs work very well even in the limit of substantially
sub-Solar metallicities, except for PNe with very high ionization. Our
abundance analysis shows enhancements of He and N that are predicted from prior
dredge-up processes of the progenitors on the AGB, as well as the well known
correlations among O, Ne, S, and Ar that are little affected by nucleosynthesis
in this mass range. We identified MG_8 as an interesting limiting case of a PN
central star with a ~3.5 M_sun progenitor in which hot-bottom burning did not
occur in its prior AGB evolution. We find no evidence for O depletion in the
progenitor AGB stars via the O-N cycle, which is consistent with predictions
for lower-mass stars. We also find low S/O ratios relative to SMC H_II regions,
with a deficit comparable to what has been found for Galactic PNe.
