1.3. Line intensitites

In conditions prevailing in PNe and H II regions the observed emission lines are optically thin, except for resonance lines such as H Ly, C IV1550, N V1240, Mg II2800, Si IV1400, and some helium lines. Also the fine structure IR lines could be optically thick in compact H II regions or giant H II regions (however, the velocity fields are generally such that this is not the case). The fact that most of the lines used for abundance determinations are optically thin makes their use robust and powerful.

The intensity ratios of recombination lines are almost independent of temperature. On the other hand, intensity ratios of optical and ultraviolet collisional lines are strongly dependent on electron temperature if the excitation levels differ.

Abundances of metals with respect to hydrogen are mostly derived using the intensity ratio of collisionally excited lines with H. It is instructive to understand the dependence of such emission line ratios with metallicity. Let us consider the [O III] 5007 / H line ratio and follow its behaviour as n(O) / n(H) decreases (from now on the notation n(O) / n(H) will be replaced by O/H). The temperature dependence of the [O III] 5007 and H lines implies that:

(1.22)

- At high metallicity (O/H around 10^-3 and above), cooling is efficient and T_e is low. Energy is mainly evacuated by the [OIII] 88µm line, whose excitation potential is 164 K. The cooling rate is then approximately given by

(1.23)

Eq. (1.21) implies that

(1.24)

Since T_e increases with decreasing O/H, Eq. (1.24) shows that [O III] 5007 / H increases. Note the value of [O III] 5007 / H depends on T , being larger for higher effective temperatures.

- At intermediate metallicities, (O/H of the order of 10^-3 - 210^-4), cooling is still mainly due to the oxygen lines, but the abundance of O/H being only moderate, T_e is higher, allowing collisional excitation of the [O III] 5007 line, which now becomes the dominant coolant. The cooling can then be roughly expressed by:

(1.25)

Eqs. (1.21) and (1.22) imply:

(1.26)

i.e. [O III] 5007 / H is proportional to T and independent of O/H.

- Finally, at low metallicity, when cooling is dominated by recombination and collisional excitation of hydrogen, T_e becomes independent of O/H. From Eq. (1.22), it follows that [O III] 5007 / H is proportional to O/H. It also depends on T and on the average population of neutral hydrogen inside the nebula.