Very deep spectroscopy of the bright Saturn Nebula NGC 7009 - II. Analysis of the rich optical recombination spectrum
[Abridged] We present a critical analysis of the rich optical recombination spectrum of NGC 7009, in the context of the bi-abundance nebular model proposed by Liu et al. (2000). The observed relative intensities are compared with the theoretical predictions based on high quality effective recombination coefficients, now available for the recombination line spectrum of a number of heavy element ions. The possibility of plasma diagnostics using the optical recombination lines (ORLs) of heavy element ions is discussed in detail. Plasma diagnostics based on the N II and O II recombination spectra both yield electron temperatures close to 1000 K, which is lower than those derived from the collisionally excited line (CEL) ratios by nearly one order of magnitude. The very low temperatures yielded by the O II and N II ORLs indicate that they originate from very cold regions. The C^{2+}/H^+, N^{2+}/H^+, O^{2+}/H^+ and Ne^{2+}/H^+ ionic abundance ratios derived from ORLs are consistently higher, by about a factor of 5, than the corresponding values derived from CELs. In calculating the ORL ionic abundance ratios, we have used the newly available high quality effective recombination coefficients, and adopted an electron temperature of 1000 K, as given by the ORL diagnostics and as a consequence presumably representing the physical conditions prevailing in the regions where the heavy element ORLs arise. A comparison of the results of plasma diagnostics and abundance determinations for NGC 7009 points to the existence of "cold", metal-rich (i.e. H-deficient) inclusions embedded in the hot, diffuse ionized gas, first postulated by Liu et al. (2000).