3.6. The optical recombination lines mystery
It has been known for several decades that optical recombination lines in PNe and H II regions indicate higher abundances than collisionally excited lines (see Liu 2002 for a review). Most of the former studies concerned the carbon abundance as derived from C II 4267 and from C III] 1909, but more recent studies show that the same problem occurs with lines from O++, N++ and Ne++ (Liu et al. 1995b, 2000, 2001, Luo et al. 2001). The ORL abundances are higher than CEL abundances by factors of about 2 for most PNe, discrepancies over a factor 5 are found in about 5 % of the PNe and can reach factors as large as 20 (Liu 2002). For a given nebula, the discrepancies for the individual elements C, N, O, Ne are found to be approximately of the same magnitude.
The explanations most often invoked are: i) temperature fluctuations, ii) incorrect atomic data , iii) fluorescent excitation, iv) upward bias in the measurement of weak line intensities, v) blending with other lines, vi) abundance inhomogeneities. None of them is completely satisfactory, some are now definitely abandoned.
The completion of the OPACITY project has allowed accurate computation of effective recombination coefficients needed to analyze ORL data. The advent of high quantum efficiency, large dynamic range and large format CCDs now allows to obtain high quality measurements of many faint recombination lines for bright PNe, thus hypothesis iv) cannot be invoked anymore. In addition, Mathis & Liu (1999) have measured the weak [O III] 4931, whose intensity ratio with [O III] 5007 depends only on the ratio of transition probabilities from the upper levels. They found (4.15±0.11) 10-4 compared to the theoretical values 4.09 10-4 (Nussbaumer & Storey 1981), 4.15 10-4 (Froese Fisher & Saha 1985), 2.5 10-4 (Galavís et al. 1997). If, as expected, the latter computations give the more accurate results, the bias in the measurement of extremely weak lines could amount to 60%. This is far below what is needed to explain the ORL/CEL discrepancy. A large number of faint recombination lines have now been measured, and the observed relative intensities of permitted transitions from C++, N++, O++ and Ne++ are in agreement with the predictions of recombination theory, which goes against ii), iii), iv) and v). As mentioned in the previous subsection, the values of t2 derived from the comparison of temperatures from [O III] 4363/5007 and from the Balmer jump are too small to account for the large abundances derived from the ORL, therefore i) does not seem to be the good explanation. This is true even adopting a two-zone toy model instead of Peimbert's fluctuation scheme.
On the basis of detailed studies of several PNe, Liu (2002) notes that for a given nebula, the discrepancies for the individual elements C, N, O, Ne are found to be approximately of the same magnitude. The ORL/CEL abundance ratios correlate with the difference between the temperatures from [O III] 4363/5007 and from the Balmer jump. Liu et al. (2000) favour the hypothesis of an inhomogeneous composition, with clumps having He/H = 0.4 and C, N, O, Ne abundances around 400 times that in the diffuse gas in the case of NGC 6153. It is indeed possible to construct a photoionization model with components of different chemical composition that reproduces the observed integrated line ratios satisfactorily (Péquignot et al. 2002). However, such a model is difficult to reconcile with the present theories of element production in intermediate mass stars (e.g. Forestini & Charbonnel 1997). Also, such super metal rich knots are not in pressure equilibrium with the surroundings and should be short lived, unless they are very dense.
Spatial analyses of NGC 6153 (Liu et al. 2000) and of NGC 6720 (Garnett & Dinerstein 2001) show that the ORL/CEL discrepancy decreases with distance to the central star. A possible explanation for the large intensities of the recombination lines of C, N, O, Ne, mentioned by Liu et al. (2000), is high temperature dielectronic recombination for states with high quantum numbers, a process so far not included in the computations of the effective recombination coefficients. Then, the ORL would be preferentially emitted in regions of temperatures of (2 - 5) × 104 K. There remains to find a way to obtain such high temperature material in planetary nebulae. Apart from conduction and shock fronts, there is also the possibility of heating by dust grains (see Sect. 3.7.7).