There have been many reviews on the abundances of PN (e.g. Pottasch 1984; Peimbert 1990; Clegg 1993; Aller 1994). Harrington et al. (1982) have found from photoionization models of PN t2 values of 0.02 or less; in general, the lower the degree of ionization of the nebula the lower the t2 value.
From the comparison of Te(Bac / H ) with Te(4363/5007), Peimbert (1971) obtained < t2 > = 0.053 for three PN. From a similar comparison Liu & Danziger (1993) obtained a large spread in t2 values with a representative value of 0.03. Dinerstein, Lester & Werner (1985), determined T0, Ne and t2 for six PN from the [O III] lines at 4363, 5007, 52 µm and 88 µm and found < t2 > = 0.04.
Under the assumption that t2 = 0.00 the C++ abundances derived from the 3d2D - 4f2F0 4267 recombination line of C+ are in general higher than those derived from the [C III] 3s2 1S0 - 3s3p3 P2 1907 and C III] 3s2 1S0 - 3s3p3 P1 1909 collisionally excited lines, the difference can be as high as an order of magnitude. General discussions of this problem have been given in the literature (e.g. Torres-Peimbert, Peimbert & Daltabuit 1980; Barker 1982; French 1983; Kaler 1986; Peimbert 1989; Rola & Stasinska 1994). Three different ideas have been advanced to explain these differences: a) the presence of an unknown mechanism, like stellar continuum resonance fluorescence, strengthening 4267, however no evidence for the presence of an unknown mechanism has been found, b) an overestimation of the weak lines, when this occurs, in addition to the overestimation of 4267, the overestimate of the weak auroral lines produces a higher electron temperature that combined with the strong 1907, 1909 lines yields a low C++ abundance increasing the discrepancy between both determinations; this effect should not be present in observations of high quality, and c) the presence of spatial temperature variations.
Peimbert, Storey & Torres-Peimbert (1993) based on O+ recombination lines of multiplets 1, 2 and 10 derived for NGC 6572 an O++ / H+ abundance ratio a factor of 1.55 higher than that derived from the [O III] 4363 and 5007 lines, this result corresponds to t2 = 0.040 ± 0.025; the recombination coefficients were computed by Storey (1994) in LS coupling. Liu et al. (1994) based on O+ recombination lines of multiplets 1 and 2 in LS coupling and multiplets 10, 12, 19 and 20 in intermediate coupling derived for NGC 7009 an O++ / H+ ratio a factor of 4.7 higher than that derived from forbidden lines under the assumption of t2 = 0.00; to reconcile both O++ / H+ values, a t2 = 0.098 is needed. Similarly Liu et al. (1994) based on recombination lines derived abundances for C++, C+++, N++ and N+++ that give C/H and N/H ratios a factor of 6.1 and 4.1 times larger than those derived from collisionally excited lines implying t2 values of 0.086 and 0.072, respectively. Liu et al. (1995) derived for a group of six PN an < O/H > ratio which is a factor of 2.2 higher than the one derived from forbidden lines, this result corresponds to < t2 > ~ 0.05; the < O/H > value is in excellent agreement with the solar photospheric value. Kingsburgh & López (1995) from O+ recombination lines find for NGC 6543 an O++ / H+ ratio which is a factor of three higher than the one derived from collisionally excited lines, which implies that t2 = 0.08 and an O/H ratio two times higher than the solar one.
There are three possible explanations for the large t2 values observed: a) erroneous Te(4363/5007) and t2 determinations due to the presence of high density clumps (Viegas & Clegg 1994), b) the presence of chemical abundance inhomogeneities (Peimbert 1989) and c) the deposition of kinetic energy by shocks or by subsonic turbulence produced by mass loss from the central star.
Clumps with Ne 106 cm-3 embedded in a lower density medium with Ne ~ 104 cm-3, are needed for the first explanation. This possibility might work for some objects but not for all. A two orders of magnitude increase in the density is likely to produce a drop in the ionization degree and a high [O II] I(7320 + 7330) / I(3726 + 3729) ratio, which at least for NGC 7009 is not observed (Peimbert 1971). Moreover if this effect is present, it will also produce real temperature variations because the heating and cooling of these clumps will be different to that of the lower density medium.
There are some objects with C/H rich clumps like A30, A78 and NGC 4361 (e.g. Jacoby & Ford 1983; Torres-Peimbert, Peimbert & Peña 1990). For NGC 4361 Torres-Peimbert et al. have been able to compute a photoionization model with a large t2 value that reconciles the C abundances derived from recombination and collisionally excited lines.
Probably the most important explanation is the third one. The central stars of PN are loosing mass at velocities in the 1000 to 4000 km s-1 range. This stellar wind interacts with material that was ejected previously at about 20 km s-1 producing shocks (e.g. Kwok et al. 1978; Kahn 1989; Balick 1989, 1994; Cuesta, Phillips & Mampaso 1994).
Most PN show expansion velocities of the shell in the 20 to 30 km s-1 range. Type I PN show components, including outer lobes, expanding with velocities in the 70 to 800 km s-1 range (e.g. Webster 1978; Meaburn & Walsh 1980; Sabbadin, Capellaro & Turatto 1987, Weller & Heathcote 1989; López et al. 1991). Middlemass, Clegg & Walsh (1989, 1991) and Manchado & Pottasch (1989) have reported higher Te and lower O/H values for large faint halos relative to the brighter central part of several PN. Middlemass et al. interpret these results in terms of shocked filamentary regions, with the energy input coming from the winds produced by the central stars. The O/H differences could be due to different t2 values and not to real O/H differences.
Rowlands, Houck & Herter (1994) find that the highly ionized regions of NGC 6302 and NGC 6537 show higher Te values than those predicted by photoionization models, therefore they conclude that the difference is due to mechanical energy input produced by shocks. Balick et al. (1994) find fast low ionization emission regions, FLIERS, in several PN, among them NGC 7009; FLIERS show the ionization structure expected of bow shocks. Bohigas (1994) finds from line intensity ratios that there are regions of NGC 6302 dominated by shocks and regions dominated by photoionization.
Peimbert & Torres-Peimbert (1987a) find from 4267 a C++ / H+ ratio which is a factor of seven higher than that derived by Dufour (1984) for NGC 2818, a type I PN. This difference, again, probably is due to the adoption of t2 = 0.00, and implies that t2 for this object is large. Similar differences are found for other type I PN.
If the N/O abundance ratio is derived from the [N II]/[O II] line ratio and the O abundance from collisionally excited lines under the assumption that t2 = 0.00, the presence of large temperature variations would go in the direction of lowering O/H and increasing N/O. Therefore the low O/H values and the N/O versus O/H anticorrelation present in a group of type I PN, derived under the assumption that t2 = 0.00 (Peimbert & Torres-Peimbert 1983; Peimbert 1990 and references therein), could be due to increasing t2 values with decreasing O/H, without the need of invoking contamination of the nebulae due to ON cycling in the central stars.