5.3 The nebular elemental abundances

Figure: Non-LTE model atmosphere flux (solid line) calculated with the PoWR models for the surface abundances H:He:C:N:O = 10:85:0.3:5:0.6 by mass and the stellar temperature $T_{\rm eff}$=70kK, compared with a blackbody (dashed line) at the same temperature.

Figure 6: The density distribution based on the ISW models adopted for photoionization modelling of Abell 48. The cylinder has outer radius of $23\hbox {$^{\prime \prime }$}$ and thickness of $13\hbox {$^{\prime \prime }$}$. Axis units are arcsec, where 1 arcsec is equal to $9.30\times 10^{-3}$ pc based on the distance determined by our photoionization model.

Table 8 lists the nebular elemental abundances (with respect to H) used for the photoionization model. We used a homogeneous abundance distribution, since we do not have any direct observational evidence for the presence of chemical inhomogeneities. Initially, we used the abundances from empirical analysis as initial values for our modelling (see Section 4). They were successively modified to fit the optical emission-line spectrum through an iterative process. We obtain a C/O ratio of 21 for Abell48, indicating that it is predominantly C-rich. Furthermore, we find a helium abundance of 0.12. This can be an indicator of a large amount of mixing processing in the He-rich layers during the He-shell flash leading to an increase carbon abundance. The nebulae around H-deficient CSs typically have larger carbon abundances than those with H-rich CSs (see review by De Marco & Barlow, 2001). The ${\rm O}/{\rm H}$ we derive for Abell48 is lower than the solar value ( ${\rm O}/{\rm H}=4.57\times 10^{-4}$; Asplund et al., 2009). This may be due to that the progenitor has a sub-solar metallicity. The enrichment of carbon can be produced in a very intense mixing process in the He-shell flash (Herwig et al., 1997). Other elements seem to be also decreased compared to the solar values, such as sulphur and argon. Sulphur could be depleted on to dust grains (Sofia et al., 1994), but argon cannot have any strong depletion by dust formation (Sofia & Jenkins, 1998). We notice that the N/H ratio is about the solar value given by Asplund et al. (2009), but it can be produced by secondary conversion of initial carbon if we assume a sub-solar metallicity progenitor. The combined (C+N+O)/H ratio is by a factor of 3.9 larger than the solar value, which can be produced by multiple dredge-up episodes occurring in the AGB phase.

Figure 7: Top: electron density and temperature as a function of radius along the equatorial direction. Bottom: ionic stratification of the nebula. Ionization fractions are shown for helium, carbon, oxygen, argon (left-hand panel), nitrogen, neon and sulphur (right-hand panel).

Table: Fractional ionic abundances for Abell48 obtained from the photoionization model.

	Ion
Element	I	II	III	IV	V	VI	VII
H	3.84($-2$)	9.62($-1$)
He	3.37($-2$)	9.66($-1$)	1.95($-6$)
C	5.43($-4$)	1.73($-1$)	8.18($-1$)	8.93($-3$)	1.64($-15$)	1.00($-20$)	1.00($-20$)
N	1.75($-2$)	1.94($-1$)	7.79($-1$)	8.98($-3$)	2.72($-15$)	1.00($-20$)	1.00($-20$)
O	4.32($-2$)	2.60($-1$)	6.97($-1$)	1.18($-7$)	3.09($-20$)	1.00($-20$)	1.00($-20$)
Ne	9.94($-3$)	3.88($-1$)	6.03($-1$)	1.12($-13$)	1.00($-20$)	1.00($-20$)	1.00($-20$)
S	6.56($-5$)	8.67($-2$)	6.99($-1$)	2.12($-1$)	2.42($-3$)	1.66($-15$)	1.00($-20$)
Ar	2.81($-3$)	3.74($-2$)	8.43($-1$)	1.17($-1$)	1.02($-13$)	1.00($-20$)	1.00($-20$)