5 Ionic and total abundances

We derived ionic abundances for SuWt 2 using the observed CELs and the optical recombination lines (ORLs). We determined abundances for ionic species of N, O, Ne, S and Ar from CELs. In our determination, we adopted the mean $T_{\rm e}$([O III]) and the upper limit of $N_{\rm e}$([S II]) obtained from our empirical analysis in Table 4. Solving the equilibrium equations, using EQUIB, yields level populations and line sensitivities for given $T_{\rm e}$ and $N_{\rm e}$. Once the level population are solved, the ionic abundances, X${}^{i+}$/H${}^{+}$, can be derived from the observed line intensities of CELs. We determined ionic abundances for He from the measured intensities of ORLs using the effective recombination coefficients from Storey & Hummer (1995) and Smits (1996). We derived the total abundances from deduced ionic abundances using the ionization correction factor ($icf$) formulae given by Kingsburgh & Barlow (1994):

$$\footnotesize \frac{{\rm He}}{{\rm H}}=\left(\frac{{\rm He}^{+}}{... ...rm He}^{2+}}{{\rm H}^{+}}\right)\times {{icf}}({\rm He}),~~{{icf}}({\rm He})=1,$$ (2)

$$\footnotesize \frac{{\rm O}}{{\rm H}}=\left(\frac{{\rm O}^{+}}{{\... ...~~ {{icf}}({\rm O}) = \left(1+\frac{{\rm He}^{2+} }{{\rm He}^{+}}\right)^{2/3},$$ (3)

$$\footnotesize \frac{{\rm N}}{{\rm H}}=\left(\frac{{\rm N}^{+}}{{\... ... {{icf}}({\rm N}),~~{{icf}}({\rm N})= \left(\frac{{\rm O}}{{\rm O}^{+}}\right),$$ (4)

$$\footnotesize \frac{{\rm Ne}}{{\rm H}}= \left(\frac{{\rm Ne}^{2+}... ...icf}}({\rm Ne}),~~{{icf}}({\rm Ne})= \left(\frac{{\rm O}}{{\rm O}^{2+}}\right),$$ (5)

$$\footnotesize \frac{{\rm S}}{{\rm H}}=\left(\frac{{\rm S}^{+}}{{\rm H}^{+}} + \frac{{\rm S}^{2+}}{{\rm H}^{+}} \right) \times {{icf}}({\rm S}),$$ (6)

$$\footnotesize {{icf}}({\rm S})= \left[1-\left(1-\frac{{\rm O}^{+}}{{\rm O}}\right)^{3}\right]^{-1/3},$$ (7)

$$\footnotesize \frac{{\rm Ar}}{{\rm H}}= \left(\frac{{\rm Ar}^{2+}... ...\rm Ar}),~~{{icf}}({\rm Ar})= \left(1-\frac{{\rm N}^{+}}{{\rm N}}\right)^{-1} .$$ (8)

We derived the ionic and total helium abundances from the observed $\lambda$5876 and $\lambda$6678, and He II $\lambda$4686 ORLs. We assumed case B recombination for the singlet He I $\lambda$6678 line and case A for other He I $\lambda$5876 line (theoretical recombination models of Smits, 1996). The He${}^{+}$/H${}^{+}$ ionic abundances from the He I lines at $\lambda$5876 and $\lambda$6678 were averaged with weights of 3:1, roughly the intrinsic intensity ratios of the two lines. The He${}^{2+}$/H${}^{+}$ ionic abundances were derived from the He II $\lambda$4686 line using theoretical case B recombination rates from Storey & Hummer (1995). For high- and middle-EC PNe (E.C.$> 4$), the total He/H abundance ratio can be obtained by simply taking the sum of singly and doubly ionized helium abundances, and with an $icf$(He) equal or less than 1.0. For PNe with low levels of ionization it is more than 1.0. SuWt 2 is an intermediate-EC PN ( ${\rm EC}=6.6$; Dopita & Meatheringham, 1990), so we can use an $icf$(He) of 1.0. We determined the O${}^{+}$/H${}^{+}$ abundance ratio from the $[$O II$]$ $\lambda$3727 doublet, and the O${}^{2+}$/H${}^{+}$ abundance ratio from the $[$O III$]$ $\lambda$4959 and $\lambda$5007 lines. In optical spectra, only O${}^{+}$ and O${}^{2+}$ CELs are seen, so the singly and doubly ionized helium abundances deduced from ORLs are used to include the higher ionization stages of oxygen abundance.

Table 6: Parameters of the two best-fitting photoionization models. The initial mass, final mass, and Post-AGB age are obtained from the evolutionary tracks calculated for hydrogen- and helium-burning models by Blöcker (1995).

	Nebula abundances		Stellar parameters
Model 1	He/H	0.090	$T_{\rm eff}$(kK)	140
	C/H	4.00($-4$)	$L_{\star}\,({\rm L}_{\bigodot})$	700
	N/H	2.44($-4$)	$\log\,g$ (cgs)	$7.0$
	O/H	2.60($-4$)	H:He	8:2
	Ne/H	1.11($-4$)	$M_{\star}\,({\rm M}_{\bigodot})$	$\sim 0.605$
	S/H	1.57($-6$)	$M_{\rm\textsc{zams}}\, ({\rm M}_{\bigodot})$	3.0
	Ar/H	1.35($-6$)	$\tau _{\rm post-\textsc {agb}}$ (yr)	7500
Model 2	He/H	0.090	$T_{\rm eff}$(kK)	160
	C/H	4.00($-4$)	$L_{\star}\,({\rm L}_{\bigodot})$	600
	N/H	2.31($-4$)	$\log\,g$ (cgs)	$7.3$
	O/H	2.83($-4$)	He:C:N:O	33:50:2:15
	Ne/H	1.11($-4$)	$M_{\star}\,({\rm M}_{\bigodot})$	$\sim 0.64$
	S/H	1.57($-6$)	$M_{\rm\textsc{zams}}\, ({\rm M}_{\bigodot})$	3.0
	Ar/H	1.35($-6$)	$\tau _{\rm post-\textsc {agb}}$ (yr)	$25\,000$
	Nebula physical parameters
$M_{i}/{\rm M}_{\bigodot}$		0.21	$D$(pc)	2300
$N_{\rm torus}$		100cm${}^{-3}$	$\tau_{\rm true}$(yr)	$23\,400$-$26\,300$
$N_{\rm spheroid}$		50cm${}^{-3}$	$[{\rm Ar/H}]$	$-0.049$

We derived the ionic and total nitrogen abundances from $[$N II$]$ $\lambda$6548 and $\lambda$6584 CELs. For optical spectra, it is possible to derive only N${}^{+}$, which mostly comprises only a small fraction ($\sim10$-30%) of the total nitrogen abundance. Therefore, the oxygen abundances were used to correct the nitrogen abundances for unseen ionization stages of N${}^{2+}$ and N${}^{3+}$. Similarly, the total Ne/H abundance was corrected for undetermined Ne${}^{3+}$ by using the oxygen abundances. The $\lambda \lambda$6716,6731 lines usually detectable in PN are preferred to be used for the determination of S${}^{+}$/H${}^{+}$, since the $\lambda \lambda$4069,4076 lines are usually enhanced by recombination contribution, and also blended with O II lines. We notice that the $\lambda \lambda$6716,6731 doublet is affected by shock excitation of the ISM interaction, so the S${}^{+}$/H${}^{+}$ ionic abundance must be lower. When the observed S${}^{+}$ is not appropriately determined, it is possible to use the expression given by Kingsburgh & Barlow (1994) in the calculation, i.e. $({\rm S}^{2+}/{\rm S}^{+})=4.677+({\rm O}^{2+}/{\rm O}^{+})^{0.433}$.

Table 7: Model line fluxes for SuWt 2.

Line
3726 $[$O II$]$	$702$::	309.42	335.53
3729 $[$O II$]$	*	408.89	443.82
3869 $[$Ne III$]$	204.57::	208.88	199.96
4069 $[$S II$]$	1.71::	1.15	1.25
4076 $[$S II$]$	-	0.40	0.43
4102 H$\delta$	22.15:	26.11	26.10
4267 C II	-	0.27	0.26
4340 H$\gamma$	38.18:	47.12	47.10
4363 $[$O III$]$	6.15	10.13	9.55
4686 He II	43.76	42.50	41.38
4740 $[$Ar IV$]$	1.94	2.27	2.10
4861 H$\beta$	100.00	100.00	100.0
4959 $[$O III$]$	216.72	243.20	238.65
5007 $[$O III$]$	724.02	725.70	712.13
5412 He II	5.68	3.22	3.14
5755 $[$N II$]$	7.64	21.99	21.17
5876 He I	6.54	8.01	8.30
6548 $[$N II$]$	321.94	335.22	334.67
6563 H$\alpha$	286.00	281.83	282.20
6584 $[$N II$]$	1021.68	1023.78	1022.09
6678 He I	1.63	2.25	2.33
6716 $[$S II $]^{\rm\ast}$	70.36	9.17	10.21
6731 $[$S II $]^{\rm\ast}$	46.47	6.94	7.72
7065 He I	1.12	1.59	1.63
7136 $[$Ar III$]$	15.51	15.90	15.94
7320 $[$O II$]$	5.93	10.60	11.17
7330 $[$O II$]$	3.37	8.64	9.11
7751 $[$Ar III$]$	9.60	3.81	3.82
9069 $[$S III$]$	5.65	5.79	5.58
$I($H$\beta)$/10$^{-12}$ $\frac{\rm erg}{{\rm cm}^2{\rm s}}$	1.95	2.13	2.12

Note. $^{\rm\ast}$ The shock-excitation largely enhances the observed $[$S II$]$ doublet.

Figure: Spatial distribution maps of ionic nitrogen abundance ratio N${}^{+}$/H${}^{+}$ ( $\times 10^{-5}$) from $[$N II$]$ CELs (6548, 6584); ionic oxygen abundance ratio O${}^{++}$/H${}^{+}$ ( $\times 10^{-4}$) from $[$O III$]$ CELs (4959, 5007); and ionic Sulfur abundance ratio S${}^{+}$/H${}^{+}$ ( $\times 10^{-7}$) from $[$S II$]$ CELs (6716, 6731) for $T_{\rm e}=10\,000$K and $N_{\rm e}=100$cm$^{-3}$. White contour lines show the distribution of the narrow-band emission of H$\alpha$ and [NII] in arbitrary unit taken with the ESO 3.6-m telescope.

The total abundances of He, N, O, Ne, S, and Ar derived from our empirical analysis for selected regions of the nebula are given in Table 5. From Table 5 we see that SuWt 2 is a nitrogen-rich PN, which may be evolved from a massive progenitor ($M \geq 5$). However, the nebula's age (23400-26300 yr) cannot be associated with faster evolutionary time-scale of a massive progenitor, since the evolutionary time-scale of $7{\rm M}_{\bigodot}$ calculated by Blöcker (1995) implies a short time-scale (less than 8000yr) for the effective temperatures and the stellar luminosity (see Table2) that are required to ionize the surrounding nebula. So, another mixing mechanism occurred during AGB nucleosynthesis, which further increased the Nitrogen abundances in SuWt 2. Mass transfer to the two A-type companions may explain this typical abundance pattern.

Fig.7 shows the spatial distribution of ionic abundance ratio N${}^{+}$/H${}^{+}$, O${}^{++}$/H${}^{+}$ and S${}^{+}$/H${}^{+}$ derived for given $T_{\rm e}=10\,000$K and $N_{\rm e}=100$cm$^{-3}$. We notice that O${}^{++}$/H${}^{+}$ ionic abundance is very high in the inside shell; through the assumption of homogeneous electron temperature and density is not correct. The values in Table5 are obtained using the mean $T_{\rm e}$([O III]) and $N_{\rm e}$([S II]) listed in Table 4. We notice that O$^{2+}$/O$^{+}=5.9$ for the interior and O$^{2+}$/O$^{+}=0.6$ for the ring. Similarly, He$^{2+}$/He$^{+}=2.6$ for the interior and He$^{2+}$/He$^{+}=0.4$ for the ring. This means that there are many more ionizing photons in the inner region than in the outer region, which hints at the presence of a hot ionizing source in the centre of the nebula.