TRACING ABUNDANCES IN GALAXIES WITH THE SPITZER ...

to the 3 P0 at 33.5 µm. Figure 1.3 (b) shows the predicted line flux ratio F([S III]
18.7 µm)/F([S III] 33.5 µm) as a function of the log of the electron density for sev-
eral values of the electron temperature. The electron density is best determined
by this ratio for values of the ratio between ∼1 and 11, corresponding to densities
between ∼10 3 and 10 5 cm −3 , and it only has a small dependence on Te. However,
other line ratios may also be used to determine Ne; for example, the ratio F([O II]
3729 ˚A)/F([O II] 3726 ˚A) which is more sensitive to slightly lower densities.
The electron temperature (Te) can be determined by ratios of fluxes of
pairs of emission lines emitted by a single ion from two upper levels which differ
significantly in excitation energy. This ensures that the relative population of the
levels depends on Te (Osterbrock, 1989). For example, the line flux ratio F([S III]
at 6312 ˚A)/F([S III] at 18.7 µm) may be used to determine Te. The [S III] line at
6312 ˚A comes from the upper 1 S level while the 18.7 µm line arises from one of
the lower 3 P levels (see Figure 1.3 (a)). The large difference in energy between the
1 S and 3 P levels leads to the relative rates of excitation of these levels depending
strongly on Te (the higher the temperature, the more the 1 S level is populated
relative to the 3 P levels), and thus it is possible to use the flux ratio of lines
emitted from these levels to determine Te (see Figure 1.3 (c)).
1.3.3 Abundances
Once the electron density and temperature are determined, it is possible to derive
abundances of ions and elements by number with respect to hydrogen. In order to
determine ionic abundances we take the ratio of an ionic line flux to the Hβ line
flux. Then, we sum the ionic abundances for all of its expected stages of ionization
to determine the total elemental abundance of an element. If an ionization stage
is unobserved but expected to be present, we adopt an ionization correction factor
15