2.2 Nebular Diagnostics and Ionic Abundances   Next: OVERVIEW OF THE Up: CALCULATION OF THE Previous: Equations to be

## 2.2 Nebular Diagnostics and Ionic Abundances

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.   Next: OVERVIEW OF THE Up: CALCULATION OF THE Previous: Equations to be

Rocio Katsanis
Thu Aug 8 17:23:06 EDT 1996