Certain emission line ratios in five-level atoms are very useful as diagnostics of electron temperature or density. The and ions have ground state configurations such that some transitions from upper levels have very different excitation energies; ratios of the resulting emission lines can serve as very effective temperature indicators because they are insensitive to density. Conversely, in ions some transitions to the ground state have upper levels with nearly the same excitation energy. Ratios of these lines can serve as very effective density indicators because the level populations are quite insensitive to temperature.
The available diagnostic line ratios for the nebular tasks are given
in Table 2 for N
, and in Table 3 for T. The tables
list the ion, the spectrum designation, the diagnostic line ratio, the
ionization potential of the ion (in eV), and the nebular ionization zone to
which they are attributed (see § 3.3 below). The line ratios are
given as , where and are
in units of Å; ratios involving sums of line strengths are given as
. Certain diagnostics noted
in the tables are not currently used in the 3-zone nebular model, described
in § 3.3 below.
The ionic abundances, relative to H, can be derived from the
observed ratio of a forbidden line intensity relative to H.
Aller (1984) provides a convenient fitting formula for the H
emissivity as computed by Brocklehurst (1971), which is accurate to within
about 4% for densities less than cm. The formula:
in units of (erg cm s), is used within the nebular
routines; here, K. The H emissivity is calculated
for the same temperature as the specified ion, and the ionic abundance
ratio is calculated from:
where H is the observed line ratio. Note that all
of the line emissivities output by the tasks in nebular are per unit
ion density per unit electron density. That is, the true volume
emissivity () is related to that computed by:
Transitions between any of the five levels can be used to derive the ionic
abundance for any of the ions, but the strongest lines that are typically
used in the nebular tasks are listed in Table 4 .
It should be noted that the nebular program gives line emissivities
and diagnostic ratios for metastable-level magnetic dipole or electric
quadrapole transitions under the assumption of pure statistical equilibrium
and does not account for radiation transfer effects such as self-absorption in
some levels. For some astrophysical situations such as giant H II
regions and AGN, the optical depths of the multiplet levels of and
ions such as [O III], [N II], and [Ne III] can become
significant (Rubin 1968, Rubin 1985), which will affect the observed
far-infrared line strengths for such objects compared to the program predictions.
While nebular does not currently make use of and diagnostics
from the far-infrared lines, the reader can use the program to do such in a
manner similar to that recently presented by Rubin et al. (1994) for
low-density H II regions and planetary nebulae. However, we advise
caution for such use on giant H II regions or dense, highly ionized
planetary nebulae for which the optical depth in the levels could become
important.
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