3.3 The nebular elemental abundances

We used a homogeneous chemical abundance distribution for the model MC1 consisting of 9 elements, including all the major contributors to the thermal balance of the nebula and those producing the density- and temperature-sensitive CELs. The abundances derived from the empirical analysis (García-Rojas et al., 2009) were chosen as starting values; these were iteratively modified to get a better fit to the CELs. The final abundance values are listed in Table 3, where they are given by number with respect to H.

A two-component elemental abundance distribution was used for the model MC2 that yields a better fit to the observed ORLs. The parameters of the metal-rich cells included in the bi-abundance model MC2 are summarized in Table 4. The metal-rich inclusions were constructed using 33 knots with the physical size of $ (0.35)^{3}$ arcsec$ ^{3}$. As shown in Figure4 (b), they are uniformly distributed inside the normal component model with the same geometry, but a filling factor of 0.056. The initial guesses at the elemental abundances of N and O in the the metal-rich component were taken from the ORL empirical results; they were successively increased to fit the observed N II and O II ORLs. Table 3 lists the final elemental abundances (with respect to H) derived for both components, normal and metal-rich. The final model, which provided a better fit to most of the observed ORLs, has a total metal-rich mass of about 6.3 percent of the ionized mass of the entire nebula.

The O/H and N/H abundance ratios in the metal-rich component are about 1.0 and 1.7 dex larger than those in the normal component. The C/O abundance ratio in the metal-rich component less than unity is in disagreement with the theoretical predictions of born-again stellar models (Althaus et al., 2005; Werner & Herwig, 2006; Herwig, 2001). As seen in Table 3, the ORL total abundances empirically derived were not similar to the elemental abundances chosen for the model metal-rich component. This is due to the fact that the ORL empirical abundances were derived from the ORLs, emitted mainly from metal-rich inclusion, over the H$ ^{+}$ flux of the entire nebula, emitted from both the diffuse gas and metal-rich inclusion. Hence, the empirical abundances of the ORLs are roughly similar to the mean total abundances of both the metal-rich and normal components.

As seen in Table 3, the elemental abundance for neon does not show a large abundance discrepancy similar to what we see for oxygen and nitrogen, which is unlike to the bi-abundance models of Abell 30 (Ercolano et al., 2003b) and NGC 6153 (Yuan et al., 2011). We note that the H-deficient knots of Abell 30 shows ADF(Ne$ ^{++}$) values in the range of 400-1000 (Wesson et al., 2003), and NGC 6153 has a ADF(Ne$ ^{++}$) of about 60 (Liu et al., 2000). Nevertheless, PB8 has ADF(Ne$ ^{++}$)=1.48 (García-Rojas et al., 2009). To reproduce the spectrum of Abell 30, Ercolano et al. (2003b) also assumed a bi-abundance model, in which the metal-rich core has a density of about six times higher than the surrounding normal envelope. Thus, both Abell 30 and NGC 6153 have extremely large ADFs, which are dissimilar to PB8. We should also include that the atomic data of the ORLs of Ne$ ^{++}$ ion (Kisielius et al., 1998) used by MOCASSIN do not have any recombination coefficients for the Ne II $ \lambda $4391.94 and $ \lambda $4409.30 lines, while García-Rojas et al. (2009) employed different atomic data (Kisielius & Storey; unpublished) to derive Ne$ ^{++}$ ion abundance from for Ne II ORLs.

It is worthwhile to mention that the AGB nucleosynthesis dramatically changes the composition of He, C and N (Karakas et al., 2009; Karakas & Lattanzio, 2003), but other elements such as Ne, S, Cl, and Ar are left untouched by the evolution and nucleosynthesis in low and intermediate-mass stars. In this typical PN with moderate ADFs, abundances of other elements heavier than oxygen such as neon in the metal-rich components seem to be the same as those in the normal component.

Table: Input parameters for the dust model of PB8.
Grain Species Weight Ref. for optical constants
Amorphous Carbon 1 Hanner (1988)
Crystalline Silicate 1 Jaeger et al. (1994)
Grain Radius ($ \mu $m) Weight
$ 0.16$ 50
$ 0.40$ 1

Ashkbiz Danehkar