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Three-dimensional chemically homogeneous and bi-abundance photoionization models of the "super-metal-rich" planetary nebula NGC 6153

Deep spectroscopy of the planetary nebula (PN) NGC\,6153 shows that its heavy element abundances derived from optical recombination lines (ORLs) are ten times higher than those derived from collisionally excited lines (CELs), and points to the existence of H-deficient inclusions embedded in the diffuse nebula. In this study, we have constructed chemically homogeneous and bi-abundance three-dimensional photoionization models, using the Monte Carlo photoionization code {\sc mocassin}. We attempt to reproduce the multi-waveband spectroscopic and imaging observations of NGC\,6153, and investigate the nature and origin of the postulated H-deficient inclusions, as well as their impacts on the empirical nebular analyses assuming a uniform chemical composition. Our results show that chemically homogeneous models yield small electron temperature fluctuations and fail to reproduce the strengths of ORLs from C, N, O and Ne ions. In contrast, bi-abundance models incorporating a small amount of metal-rich inclusions ($\sim 1.3$ per cent of the total nebular mass) are able to match all the observations within the measurement uncertainties. The metal-rich clumps, cooled down to a very low temperature ($\sim 800$~K) by ionic infrared fine-structure lines, dominate the emission of heavy element ORLs, but contribute almost nil to the emission of most CELs. We find that the abundances of C, N, O and Ne derived empirically from CELs, assuming a uniform chemical composition, are about 30 per cent lower than the corresponding average values of the whole nebula, including the contribution from the H-deficient inclusions. Ironically, in the presence of H-deficient inclusions, the traditional standard analysis of the optical helium recombination lines, assuming a chemically homogeneous nebula, overestimates the helium abundance by 40 per cent.