4 Plasma diagnostics

Figure: Flux ratio maps for field 2 (see Fig. 1) of the PN SuWt 2. From left to right: (a) flux ratio maps of the $[$O III$]$ $\lambda$5007Å to the H$\beta$ recombination line emission, (b) flux ratio map of the $[$N II$]$ $\lambda$6584 to the H$\alpha$ recombination line emission, (c) flux ratio map for the temperature-sensitive $[$N II$]$ $\lambda \lambda$5755, 6548, 6583 lines, and (d) for the density-sensitive $[$S II$]$ doublet. The black contour lines show the distribution of the narrow-band emission of H$\alpha$ and [NII] in arbitrary units taken with the ESO 3.6-m telescope observations.

(a) (b) (c) (d)

We derived the nebular electron temperatures $T_{\rm e}$ and densities $N_{\rm e}$ from the intensities of the collisionally excited lines (CELs) by solving the equilibrium equations for an $n$-level atom ( $\geqslant 5$) using EQUIB, a FORTRAN code originally developed by Howarth & Adams (1981). Recently, it has been converted to FORTRAN 90, and combined into simpler routines for NEAT (Wesson et al., 2012). The atomic data sets used for our plasma diagnostics, as well as for the CEL abundance determination in §5, are the same as those used by Wesson et al. (2012).

The diagnostics procedure was as follows: we assumed a representative initial electron temperature of 10000K in order to derive $N_{\rm e}([$S II$])$; then $T_{\rm e}([$N II$])$ was derived in conjunction with the mean density derived from $N_{\rm e}([$S II$])$. The calculations were iterated to give self-consistent results for $N_{\rm e}$ and $T_{\rm e}$. The correct choice of electron density and temperature is essential to determine ionic abundances.

Fig. 6 shows flux ratio maps for the density-sensitive $[$S II$]$ doublet. It indicates the electron density $N_{\rm e}$ of about $\lesssim 100$ cm${}^{-3}$ in the ring. We see that the interior region has a $[$S II$]$ $\lambda \lambda$ 6716/6731 flux ratio of more than 1.4, which means the inside of the ring has a very low density ( $N_{\rm e}\lesssim 50$ cm${}^{-3}$). Flux ratio maps for the temperature-sensitive $[$N II$]$ $\lambda \lambda$5755, 6548, 6583 lines indicate that the electron temperature $T_{\rm e}$ varies from 7000 to 14000 K. As shown in Fig. 6, the brightest part of the ring in $[$N II$]$ $\lambda$6584Å has an electron temperature of about 8000 K. The inside of the ring has a mean electron temperature of about 11800 K. We notice that Smith et al. (2007) found $N_{\rm e}=90$ cm${}^{-3}$ and $T_{\rm e}=11\,400$ K using the R-C Spectrograph ($R\sim6000$) on the CTIO 4-m telescope, though they obtained them from a $0.8$arcsec slit oriented along the major axis of the ring ( ${\rm PA}=135^{\circ}$).

Table 4 lists the electron density ($N_{\rm e}$) and the electron temperature ($T_{\rm e}$) of the different regions, together with the ionization potential required to create the emitting ions. We see that the east part of the ring has a mean electron density of $N_{\rm e}([$S II $])\lesssim 100$ cm${}^{-3}$ and mean temperatures of $T_{\rm e}([$N II$])=8\,140$ K and $T_{\rm e}([$O III $])=12\,390$ K, while the less dense region inside the ring shows a high mean temperature of $T_{\rm e}([$N II $])=11\,760$ K and $T_{\rm e}([$O III$])$ less than $20\,000$ K. We point out that the [S II] $\lambda \lambda$6716/6731 line ratio of more than 1.40 is associated with the low-density limit of $N_{\rm e}<100$ cm${}^{-3}$, and we cannot accurately determine the electron density less than this limit (see e.g. A39; Jacoby et al., 2001). Furthermore, we cannot resolve the [O II] $\lambda \lambda$3726,3729 doublet with our moderate spectral resolution ($R\sim3000$). Plasma diagnostics indicates that the interior region is much hotter than the ring region. This implies the presence of a hard ionizing source located at the centre. It is worth to mention that $T_{\rm e}([$N II$])$ is more appropriate for singly ionized species, while $T_{\rm e}([$O III$])$ is associated with doubly and more ionized species. Kingsburgh & Barlow (1994) found that $T_{\rm e}([$O III $])/T_{\rm e}([$N II$])=1.25$ for medium-excitation PNe and $T_{\rm e}([$O III $])/T_{\rm e}([$N II $])=1.15 + 0.0037 I(4686)$ for high-excitation PNe. Here, we notice that $T_{\rm e}([$O III $])/T_{\rm e}([$N II$])=1.52$ for the ring and $T_{\rm e}([$O III $])/T_{\rm e}([$N II$])=1.39$ for the total flux.

Table 4: Diagnostic ratios for the electron temperature, $T_{\rm e}$ and the electron density, $N_{\rm e}$.

Ion	Diagnostic	I.P.(eV)	Interior		Ring		Total
			Ratio	$T_{\rm e}(10^3{\rm K})$	Ratio	$T_{\rm e}(10^3{\rm K})$	Ratio	$T_{\rm e}(10^3{\rm K})$
$[$N II$]$	$\frac{\lambda6548+\lambda6584}{\lambda5755}$	14.53	63.71:	11.76:	161.33	8.14	175.78	7.92
$[$O III$]$	$\frac{\lambda4959+\lambda5007}{\lambda4363}$	35.12	35.41::	$\lesssim20.0$::	110.93	12.39	152.49	11.07
			Ratio	$N_{\rm e}({\rm cm}^{-3})$	Ratio	$N_{\rm e}({\rm cm}^{-3})$	Ratio	$N_{\rm e}({\rm cm}^{-3})$
$[$S II$]$	$\frac{\lambda6716}{\lambda6731}$	10.36	2.02	$\lesssim50.0$	1.46	$\lesssim100.0$	1.51	$\lesssim100.0$

Table 5: Ionic and total abundances deduced from empirical analysis of the observed fluxes across different nebula regions of SuWt 2.

$\lambda$(Å)	Abundance	Interior	Ring	Total
5876	He${}^{+}$/H${}^{+}$	-	0.066	0.049
6678	He${}^{+}$/H${}^{+}$	0.031	0.057	0.043
Mean	He${}^{+}$/H${}^{+}$	0.031	0.064	0.048
4686	He${}^{2+}$/H${}^{+}$	0.080	0.027	0.036
	$icf$(He)	1.0	1.0	1.0
	He/H	0.111	0.091	0.084
6548	N${}^{+}$/H${}^{+}$	7.932($-6$)	1.269($-4$)	1.284($-4$)
6584	N${}^{+}$/H${}^{+}$	1.024($-5$)	1.299($-4$)	1.334($-4$)
Mean	N${}^{+}$/H${}^{+}$	9.086($-6$)	1.284($-4$)	1.309($-4$)
	$icf$(N)	16.240	2.014	3.022
	N/H	1.476($-4$)	2.587($-4$)	3.956($-4$)
3727	O${}^{+}$/H${}^{+}$	1.109($-5$)	1.576($-4$)	1.597($-4$)
4959	O${}^{2+}$/H${}^{+}$	6.201($-5$)	8.881($-5$)	1.615($-4$)
5007	O${}^{2+}$/H${}^{+}$	6.998($-5$)	9.907($-5$)	1.808($-4$)
Mean	O${}^{2+}$/H${}^{+}$	6.599($-5$)	9.394($-5$)	1.711($-4$)
	$icf$(O)	2.336	1.262	1.459
	O/H	1.801($-4$)	3.175($-4$)	4.826($-4$)
3869	Ne${}^{2+}$/H${}^{+}$	2.635($-5$)	9.608($-5$)	1.504($-4$)
3968	Ne${}^{2+}$/H${}^{+}$	-	3.306($-5$)	-
Mean	Ne${}^{2+}$/H${}^{+}$	2.635($-5$)	6.457($-5$)	1.504($-4$)
	$icf$(Ne)	2.728	3.380	2.820
	Ne/H	7.191($-5$)	2.183($-4$)	4.241($-4$)
6716	S${}^{+}$/H${}^{+}$	3.307($-7$)	2.034($-6$)	2.179($-6$)
6731	S${}^{+}$/H${}^{+}$	2.189($-7$)	1.834($-6$)	1.903($-6$)
Mean	S${}^{+}$/H${}^{+}$	2.748($-7$)	1.934($-6$)	2.041($-6$)
6312	S${}^{2+}$/H${}^{+}$	-	3.292($-8$)	-
9069	S${}^{2+}$/H${}^{+}$	3.712($-7$)	1.198($-6$)	1.366($-6$)
Mean	S${}^{2+}$/H${}^{+}$	3.712($-7$)	6.155($-7$)	1.366($-6$)
	$icf$(S)	1.793	1.047	1.126
	S/H	1.158($-6$)	2.668($-6$)	3.836($-6$)
7136	Ar${}^{2+}$/H${}^{+}$	3.718($-7$)	8.756($-7$)	1.111($-6$)
4740	Ar${}^{3+}$/H${}^{+}$	-	-	4.747($-7$)
7005	Ar${}^{4+}$/H${}^{+}$	3.718($-7$)	-	-
	$icf$(Ar)	1.066	1.986	1.494
	Ar/H	5.230($-7$)	1.739($-6$)	2.370($-6$)