Modelling the emission line spectrum from a planetary nebula is often thought to be a relatively straightforward exercise, in that there is but one source of ionizing radiation, and the gas distribution is often fairly simple. Hyung, Aller, and Feibelman (1994, hereafter HAF) published a very thorough analysis of the young planetary nebula IC 418, which has a relatively simple ionization structure. Using a combination of IUE and ground-based echelle data, they inferred a rough physical and ionization structure from a dozen traditional diagnostic line ratios, which they used as a guide to construct a more complete photoionization model. We used the same data as HAF and constructed a nebular diagnostic diagram using the ntplot task, the output for which is shown in the upper portion of Figure 4 . This diagram is similar to that of HAF, but not identical, in that we include the [O I] and C III] diagnostic curves (HAF used C III] but did not plot it). There are also shifts of the [N II] and [S II] temperature and density curves, owing to our use of different (and in the case of [S II], more recent) atomic cross sections for these ions.
HAF noted that the nebular (i.e., density-sensitive) line ratios of [S II]
and [O II] do not give results in accord with those indicated by the
auroral/nebular
(i.e., temperature-sensitive) line ratios. (Nor do they agree with that
inferred from other ions.) They attributed these discrepancies to a genuine
physical effect: namely, that the ions of C III], N III, [O III],
[Cl III], and [Ar III] are formed in strata where T
K and N
cm
. The [S II] lines, they
argued, are emitted in regions where H is partly neutral, and the density is
cm.
The shift in the [S II] curves that came from using more recent atomic
cross-sections (Cai and Pradhan 1993) removed some of the discrepancy noted
by HAF in the T and
N as inferred from [S II] vs. other ions.
Still we found the disagreement between the [S II] and [O II]
temperature dignostics to be curious, especially since the trend of inferred
T
with ionization potential for
the other ions did not follow a simple relation. We noted that HAF used a
significantly lower value for the extinction constant, 
, than that
derived by most other observers: Cahn, Kaler, and Stanghellini (1992) quote
an average of 
. (This higher extinction value also brings HAF's
observed H
/H
ratio closer to the expected value of 2.85 for N=
and T
=.) When we used that higher extinction value and
replotted the results (which only involved changing the value of one number
in our input table), the T
diagnostics agreed to better than 500 K,
except for [S III] which HAF note is seriously affected by atmospheric
water vapor. The density diagnostics also agreed to within about 10%, except
for that of [S II], which is still 
% lower than the average
suggested from the other ions. While this effect could be real (S II has
the lowest ionization potential of the relevant N
diagnostics, after
all), we note that the ratio of 
is consistent with N
= 10,000 cm within the quoted errors. Given the quoted
uncertainties in the HAF data, the excellent agreement among many diagnostics
that span a large range in ionization potential, and our preference for simple
models in the absence of direct evidence to the contrary, we adopt
N
= 10,500 cm and
T
= 9700 K for all ions in our abundance analysis.
We compare in Table 8 the ionic abundances from HAF (their Table 6)
to those we derived with the nebular package. Actually, we offer two
comparisons: the column labelled ``ionic'' shows the abundances calculated
with the ionic task, using the same N, T, and extinction constant
used by HAF. Most of the values agree to within 
%, as would be
expected since the methods are essentially the same, and the atomic data are
mostly drawn from the same sources. Note, however, that the [O I]
abundance differs by 
%, which is harder to understand even if the
atomic cross sections were different. The differences in the abundances are
somewhat larger for values in the ``abund'' column, which were derived with
the abund task using the higher value for the extinction constant, and
the constant values of N and
T adopted above. Clearly the derived ionic
abundances are quite dependent upon the inferred physical model (i.e., the
variation of N and
T within the nebula). The major point of this
exercise was to demonstrate that the nebular package will give
essentially the same result as other published analyses, given the same input
data, but that it is much easier to infer a viable physical model (at
least to first order) using the utilities presented here.
