5 Conclusions

Three photoionization models have been constructed for the planetary nebula PB8, a chemically homogeneous model, a bi-abundance model and a dusty bi-abundance model. Our intention was to construct a model that well reproduce the observed emission-lines and thermal structure determined from the plasma diagnostics. A powerlaw radial density profile was adopted for the spherical nebula distribution based on the radiation-hydrodynamics simulations. The density model parameters were adjusted to reproduce the total H$\beta$ intrinsic line flux of the nebula, and the mean electron density empirically derived from the CELs (García-Rojas et al., 2009). We have used the non-LTE model atmosphere derived by Todt et al. (2010) for temperature $T_{\rm eff}=52$kK and luminosity $L_{\rm\star}=6000$L$_{\odot}$. This ionizing source well reproduced the nebular observed H$\beta$ absolute flux, as well as the $[$OIII$]$ $\lambda$5007 line flux, at the distance of 4.9 kpc.

Our initial model reproduces the majority of CELs and the thermal structure, but large discrepancies exist in the observed ORLs from heavy element ions. It is found that a chemically homogeneous model cannot consistently explain the ORLs observed in the nebular spectrum. We therefore intended to address the cause of the heavily underestimated ORLs. Following the hypothesis of the bi-abundance model by Liu et al. (2000), a small fraction of metal-rich inclusions was introduced into the second model. The heavy element ORLs are mostly emitted from the metal-rich structures embedded in the dominant diffuse warm plasma of normal abundances. The agreement between the ORL intensities predicted by the model MC2 and the observations is better than the first model (MC1). The metal-rich inclusions occupying 5.6 percent of the total volume of the nebula, and are about 1.7 times cooler and denser than the normal composition nebula. The O/H and N/H abundance ratios in the metal-rich inclusions are $\sim$1.0 and 1.7dex larger than the diffuse warm nebula, respectively. The mean electron temperatures predicted by MC2 are lower than those from MC1, which is because of the cooling effects of the metal-rich inclusions. The results indicate that a bi-abundance model can naturally explain the heavily underestimated ORLs in the chemically homogeneous model. Therefore, the metal-rich inclusions may solve the problem of ORL/CEL abundance discrepancies. However, the model MC2 cannot explain the thermal SED of the nebula observed with the Spitzer spectrograph. In our final model, we have incorporated a dual dust chemistry consisting of two different grains, amorphous carbon and crystalline silicate, and discrete grain radii. It is found that a dust-to-gas ratio of 0.01 by mass for the whole nebula can roughly reproduce the observed IR continuum.

The PN PB8 shows moderate ADFs ($\sim$1.9-2.6; García-Rojas et al., 2009), which are typical of most PNe (see e.g. Liu, 2006). Previously, the bi-abundance model were only examined in two PNe with extremely large ADFs: Abell 30 (Ercolano et al., 2003b) and NGC 6153 (Yuan et al., 2011). In Abell 30, Ercolano et al. (2003b) used a metal-rich core whose density is about six times larger than the surrounding nebula. In NGC 6153, Yuan et al. (2011) used super-metal-rich knots distributed in the inner region of the nebula. In the present study, we adopted a bi-abundance model whose metal-rich knots are homogeneously distributed inside the diffuse warm nebula, and are associated with a gas-filling factors of 0.056. To reproduce the spectrum of PB8, it is not require to have extremely dense and super-metal-rich knots, since the ORLs do not correspond to very cold temperatures and extremely large ADFs such as Abell 30 and NGC 6153. We should mention that the stellar temperatures of Abell 30 ( $T_{\rm eff}=$130kK) and NGC 6153 ( $T_{\rm eff}=$90kK) are higher than that of PB8 ( $T_{\rm eff}=$52kK), so the central star of PB8 is likely in an early stage of its stellar evolution towards a white dwarf in comparison with Abell 30 and NGC 6153. Accordingly, the planetary nebula PB8 could be younger and less evolved than the PNe Abell 30 and NGC 6153. More recently, it has been found that PNe with ADFs larger than 10 mostly contain close-binary central stars (Wesson et al., 2017; Corradi et al., 2015; Jones et al., 2016). Currently, there is no evidence for a close-binary central star in PB8.

Our analysis showed that the bi-abundance hypothesis, which was previously tested in a few PNe with very large abundance discrepancies, could also be used to explain moderate discrepancies between ORL and CEL abundances in most of typical PNe (ADFs$\sim$1.6-3.2; Liu, 2006). It is unclear whether there is any link between the supposed metal-rich inclusions within the nebula and hydrogen-deficient stars. It has been suggested that a (very-) late thermal pulse is responsible for the formation of H-deficient central stars of planetary nebulae (see e.g. Werner & Herwig, 2006; Werner, 2001; Herwig, 2001; Blöcker, 2001). Thermal pulses normally occur during the AGB phase, when the helium-burning shell becomes thermally unstable. The (very-) late thermal pulse occurs when the star moves from the AGB phase towards the white dwarf. It returns the star to the AGB phase and makes a H-deficient stellar surface, so called born-again scenario. However, the metal-rich component with C/O $< 1$ predicted by our photoionization models is in disagreement with the products of a born-again event (Herwig, 2001; Werner & Herwig, 2006; Althaus et al., 2005).

It is also possible that the metal-rich inclusions were introduced by other mechanism such as the evaporation and destruction of planets by stars (Liu, 2003). Recently, Nicholls et al. (2012); Nicholls et al. (2013) proposed that a non-Maxwellian distribution of electron energies could explain the abundance discrepancy. However, Zhang et al. (2014) found that both the scenarios, bi-abundance models and non-Maxwellian distributed electrons, are adequately consistent with observations of four PNe with very large ADFs. It is unclear whether chemically inhomogeneous plasmas introduce non-Maxwell-Boltzmann equilibrium electrons to the nebula. Alternatively, the binarity characteristics such as the orbital separation and companion masses may have a leading role in forming different abundance discrepancies in those PNe with binary central stars (see e.g. Herwig, 2001; Althaus et al., 2005). Further studies are necessary to trace the origin of possible metal-rich knots within the nebula and the cause of various abundance discrepancies in planetary nebulae.