It is very desirable to make use of information from all the available
diagnostics in order to provide at least a simple context within which to
infer the range of electron temperatures and densities that are found
within a given nebula. The remaining tasks make use of the TABLES external
package in order to provide a simple and powerful data structure and
ancillary tools for access to the observed data and the derived results.
The input tables may contain line fluxes for many nebulae and/or many regions
within nebulae, one object/region per row. The flux(es) for a given emission
line (usually, but not necessarily, given relative to 
H
) are
placed in separate columns. The tasks locate particular emission line fluxes
or ratios of line fluxes via names of specific columns in the input table.
These columns have suggestive default names, but are entirely user-definable:
see Table 7: A and B .
Since it is very unlikely to find a complete set of diagnostic line ratios
for any given object (owing to limited signal-to-noise ratio, finite spectral
resolution, wavelength coverage, etc., of the observed spectra) the nebular tasks make maximum use of whatever information is available, and
derive missing information whenever possible. For example, one ordinarily
obtains from [O III] by forming the ratio of 
.
However, one can still derive if one has 
and either 
or 
, since the intensity ratio of the latter two lines (which come
from the same upper level) is set by the ratio of the transition
probabilities. If is missing altogether, then and/or
can still be used to calculate the O
abundance. Indeed, a
significant portion of the nebular source code is devoted to this sort
of exception handling.
Given an appropriate data structure, it remains to define what information
should be stored, particularly when the data may come from a variety of
observations of varying quality. For example, there are dozens of published
spectra of the planetary nebula NGC 7027, but only some of them resolve the
[O II] 3726+3729 Å doublet. Either line, or their sum, can be used to
derive the O
abundance (see § 3.3 ), but if both line fluxes
are known individually, their ratio can be used as a diagnostic for
N
(see §
2.2 ). Rather than store the fluxes of the individual lines,
it makes more sense to store the sum of the fluxes in the line pair, and
separately the ratio of the doublet. Nearly all density-sensitive doublets
can be stored both as a sum (
), and as a ratio
(
) for analysis with nebular.
The diagnostic line ratios are derived from the input line fluxes, and may
optionally be corrected for interstellar reddening. The reddening corrected
line flux 
is derived from the input line flux 
by:
where 
is the extinction constant (i.e. the logarithmic extinction
at H
, 4861.3 Å). The extinction function 
is taken
from one of a few possible extinction functions. The choices for Galactic
extinction are: Savage and Mathis (1979), Cardelli, Clayton, and Mathis (1989),
and the function of Kaler (1976) which is based on Whitford (1958). The
choices for extra-Galactic extinction laws are Howarth (1983) for the LMC,
and Prevot et al. (1984) for the SMC.
The simplest task that makes use of multiple diagnostics from many
ions at once is called ntplot. This task produces curves on a
- plot that are consistent with each of the available
diagnostics that can be derived from the input table
of fluxes. An example of the output for the planetary nebula
NGC 7027 is shown in Figure 3 , where each line style
denotes ions of roughly similar ionization potential.
This task can optionally produce a table containing each curve in a
separately named column, along with the reference T and N, for
more elaborate plotting with a presentation graphics application,
such as the igi task in the TABLES package.
