Three dimensional geometries and the analysis of H II regions
  We compare emission line intensities from photoionization models of smooth
and fractal shell geometries for low density H II regions, with particular
focus on the low-ionization diagnostic diagram [N II]/H-alpha vs H-alpha.
Building on previously published models and observations of Barnard's Loop, we
show that the observed range of intensities and variations in the line
intensity ratios may be reproduced with a three dimensional shell geometry. Our
models adopt solar abundances throughout the model nebula, in contrast with
previous one dimensional modeling which suggested the variations in line
intensity ratios could only be reproduced if the heavy element abundances were
increased by a factor of 1.4. For spatially resolved H II regions, the multiple
sightlines that pierce and sample different ionization and temperature
conditions within smooth and fractal shells produce a range of line intensities
that are easily overlooked if only the total integrated intensities from the
entire nebula model are computed. Our conclusion is that inference of H II
region properties, such as elemental abundances, via photoionization models of
one dimensional geometries must be treated with caution and further tested
through three dimensional modeling.
