Table 5: Observational values of the line ratios used to constrain the photoionization models and model results in the form (model-observation)/(tolerance). The models are: [FS] Full Sphere; [HB] Hollow Bubble; [DD1] and [DD2] H $\beta$ constrained Density Distribution, 4.2 Myr spectrum; [DD2] H $\beta$ constrained Density Distribution, 3.6 Myr Spectrum; [DF] Density Fluctuations; [DG] Dust Grains. The geometric corrections for the models of Sect. 6 and further sections are also written. ^a Values are valid for the whole nebula; the other data are representative of the optical slit.
Diagnostics Observed [FS] [HB] [DD1] [DD2] [DDS] [DF] [DG]

Section 5.1 5.2 6.2 6.2 7.1 7.2 7.3

Density

[S II] $\lambda$ 6731/ $\lambda$ 6716 0.72 $\pm$ 7% -0.1 +0.0 -0.1 +0.0 +0.2 +0.1 +0.7

[O II] $\lambda$ 3726/ $\lambda$ 3729 0.78 $\pm$ 15% -2.1 -2.1 -2.1 -2.1 -2.0 -2.1 -1.9

[S III] $\lambda$ 19 $\mu$ m/ $\lambda$ 34 $\mu$ m^a 1.45 $\pm$ 37% -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8

Temperature

[O III] $\lambda$ 4363/ $\lambda$ 5007 0.0091 $\pm$ 5% -5.5 -4.9 -5.4 -1.6 +0.2 -1.6 +4.5

[O II] $\lambda$ 73(20+30)/ $\lambda$ 372(6+9) 0.0218 $\pm$ 17% -1.0 -1.1 -1.0 -0.4 -0.2 -0.4 -0.2

[S II] $\lambda$ 40(69+76)/ $\lambda$ 67(16+31) 0.0722 $\pm$ 11% -2.3 -2.3 -2.3 -1.7 -1.6 -1.8 -1.9

[N II] $\lambda$ 5755/ $\lambda$ 6583 0.0187 $\pm$ 16% -1.2 -1.3 -1.2 -0.3 -0.2 -0.5 -0.6

[O III] $\lambda$ 5007/ $\lambda$ 88 $\mu$ m^a 1.64 $\pm$ 23% +2.1 +2.3 +2.4 +3.9 +4.4 +3.3 +5.6

$T_{\rm opt}($ O III) (K) $11~140\pm180$ 10 080 10 210 10 100 10 840 11 850 10 850 11 950

T(O II) (K) $11~210\pm1180$ 10 130 9990 10 160 10 780 11 030 10 740 10 950

T(S II) (K) $9860\pm940$ 8060 8050 8070 8490 8630 8440 8390

T(N II) (K) $11~360\pm840$ 10 380 10 300 10 380 11 080 11 230 10 960 10 840

$T_{\rm IR}($ O III) (K)^a $8420\pm690$ 9470 9600 9640 10 320 10 550 10 080 11 090

Excitation

[O III] $\lambda$ 5007/[O II] $\lambda$ (3726+9) 2.86 $\pm$ 16% -1.7 -4.9 -0.4 +0.2 -0.2 -0.3 -0.3

[S III] $\lambda$ 6312/[S II] $\lambda$ (6716+31) 0.0631 $\pm$ 25% +2.0 -1.1 +6.3 +9.7 +4.9 +3.2 +1.5

[Ar IV] $\lambda$ (4711+41)/[Ar III] $\lambda$ 7135 0.074 $\pm$ 15% -3.9 -6.4 -3.9 -3.4 -1.2 -0.3 +2.9

[S IV] $\lambda$ 11 $\mu$ m/[S III] $\lambda$ (19+34) $\mu$ m^a 0.270 $\pm$ 37% -1.0 -2.4 -0.9 -0.9 -1.3 -0.8 +0.1

Abundances

He I $\lambda$ 5876/H $\beta$ 0.1193 $\pm$ 5% -0.7 -1.2 -0.1 +0.0 -0.1 +0.0 -0.3

[O III] $\lambda$ 5007/H $\beta$ 4.05 $\pm$ 4% -7.1 -13.3 -5.9 -0.8 +0.9 -1.5 +2.2

[N II] $\lambda$ 6563/[O II] $\lambda$ (3726+9) 0.075 $\pm$ 16% -0.1 +0.0 -0.4 -1.1 -1.0 -0.6 -0.3

[Ne III] $\lambda$ 3869/[O III] $\lambda$ 5007 0.0911 $\pm$ 5% -4.3 -6.0 -4.7 -4.0 -0.5 -0.2 +1.0

[Ar III] $\lambda$ 7135/H $\beta$ 0.0946 $\pm$ 5% +1.7 +1.7 +2.7 +6.9 +7.9 +5.6 +7.2

[O III] $\lambda$ 88 $\mu$ m/H $\beta^a$ 2.21 $\pm$ 25% -2.2 -2.8 -2.1 -2.0 -2.0 -1.9 -2.1

[Ne III] $\lambda$ 16 $\mu$ m/[O III] $\lambda$ 88 $\mu$ m^a 0.257 $\pm$ 33% +0.2 -0.1 +0.3 +0.3 +1.0 +0.9 +1.5

Other

[O I] $\lambda$ 6300/H $\beta$ 0.02 $\pm$ 50% -1.6 -1.0 -1.9 -2.0 -1.8 -1.7 -1.4

[O III] $\lambda$ 5007/H $\beta^a$ 3.52 $\pm$ 6% -5.4 -9.5 -4.6 -0.9 +0.8 -1.1 +1.8

Geometric corrections

A 1.07 1.07 1.40 1.75 1.35

K 1.48 1.48 0.52 0.52 0.12

B 0.58 0.58 1.45 3.31 1.15

**Table 5:** Observational values of the line ratios used to constrain the photoionization models and model results in the form (model-observation)/(tolerance). The models are: [FS] Full Sphere; [HB] Hollow Bubble; [DD1] and [DD2] H $\beta$ constrained Density Distribution, 4.2 Myr spectrum; [DD2] H $\beta$ constrained Density Distribution, 3.6 Myr Spectrum; [DF] Density Fluctuations; [DG] Dust Grains. The geometric corrections for the models of Sect. 6 and further sections are also written. ^a Values are valid for the whole nebula; the other data are representative of the optical slit.
Diagnostics	Observed	[FS]	[HB]	[DD1]	[DD2]	[DDS]	[DF]	[DG]
Section		5.1	5.2	6.2	6.2	7.1	7.2	7.3
Density
[S II] $\lambda$ 6731/ $\lambda$ 6716	0.72 $\pm$ 7%	-0.1	+0.0	-0.1	+0.0	+0.2	+0.1	+0.7
[O II] $\lambda$ 3726/ $\lambda$ 3729	0.78 $\pm$ 15%	-2.1	-2.1	-2.1	-2.1	-2.0	-2.1	-1.9
[S III] $\lambda$ 19 $\mu$ m/ $\lambda$ 34 $\mu$ m^a	1.45 $\pm$ 37%	-1.8	-1.8	-1.8	-1.8	-1.8	-1.8	-1.8
Temperature
[O III] $\lambda$ 4363/ $\lambda$ 5007	0.0091 $\pm$ 5%	-5.5	-4.9	-5.4	-1.6	+0.2	-1.6	+4.5
[O II] $\lambda$ 73(20+30)/ $\lambda$ 372(6+9)	0.0218 $\pm$ 17%	-1.0	-1.1	-1.0	-0.4	-0.2	-0.4	-0.2
[S II] $\lambda$ 40(69+76)/ $\lambda$ 67(16+31)	0.0722 $\pm$ 11%	-2.3	-2.3	-2.3	-1.7	-1.6	-1.8	-1.9
[N II] $\lambda$ 5755/ $\lambda$ 6583	0.0187 $\pm$ 16%	-1.2	-1.3	-1.2	-0.3	-0.2	-0.5	-0.6
[O III] $\lambda$ 5007/ $\lambda$ 88 $\mu$ m^a	1.64 $\pm$ 23%	+2.1	+2.3	+2.4	+3.9	+4.4	+3.3	+5.6
$T_{\rm opt}($ O III) (K)	$11~140\pm180$	10 080	10 210	10 100	10 840	11 850	10 850	11 950
T(O II) (K)	$11~210\pm1180$	10 130	9990	10 160	10 780	11 030	10 740	10 950
T(S II) (K)	$9860\pm940$	8060	8050	8070	8490	8630	8440	8390
T(N II) (K)	$11~360\pm840$	10 380	10 300	10 380	11 080	11 230	10 960	10 840
$T_{\rm IR}($ O III) (K)^a	$8420\pm690$	9470	9600	9640	10 320	10 550	10 080	11 090
Excitation
[O III] $\lambda$ 5007/[O II] $\lambda$ (3726+9)	2.86 $\pm$ 16%	-1.7	-4.9	-0.4	+0.2	-0.2	-0.3	-0.3
[S III] $\lambda$ 6312/[S II] $\lambda$ (6716+31)	0.0631 $\pm$ 25%	+2.0	-1.1	+6.3	+9.7	+4.9	+3.2	+1.5
[Ar IV] $\lambda$ (4711+41)/[Ar III] $\lambda$ 7135	0.074 $\pm$ 15%	-3.9	-6.4	-3.9	-3.4	-1.2	-0.3	+2.9
[S IV] $\lambda$ 11 $\mu$ m/[S III] $\lambda$ (19+34) $\mu$ m^a	0.270 $\pm$ 37%	-1.0	-2.4	-0.9	-0.9	-1.3	-0.8	+0.1
Abundances
He I $\lambda$ 5876/H $\beta$	0.1193 $\pm$ 5%	-0.7	-1.2	-0.1	+0.0	-0.1	+0.0	-0.3
[O III] $\lambda$ 5007/H $\beta$	4.05 $\pm$ 4%	-7.1	-13.3	-5.9	-0.8	+0.9	-1.5	+2.2
[N II] $\lambda$ 6563/[O II] $\lambda$ (3726+9)	0.075 $\pm$ 16%	-0.1	+0.0	-0.4	-1.1	-1.0	-0.6	-0.3
[Ne III] $\lambda$ 3869/[O III] $\lambda$ 5007	0.0911 $\pm$ 5%	-4.3	-6.0	-4.7	-4.0	-0.5	-0.2	+1.0
[Ar III] $\lambda$ 7135/H $\beta$	0.0946 $\pm$ 5%	+1.7	+1.7	+2.7	+6.9	+7.9	+5.6	+7.2
[O III] $\lambda$ 88 $\mu$ m/H $\beta^a$	2.21 $\pm$ 25%	-2.2	-2.8	-2.1	-2.0	-2.0	-1.9	-2.1
[Ne III] $\lambda$ 16 $\mu$ m/[O III] $\lambda$ 88 $\mu$ m^a	0.257 $\pm$ 33%	+0.2	-0.1	+0.3	+0.3	+1.0	+0.9	+1.5
Other
[O I] $\lambda$ 6300/H $\beta$	0.02 $\pm$ 50%	-1.6	-1.0	-1.9	-2.0	-1.8	-1.7	-1.4
[O III] $\lambda$ 5007/H $\beta^a$	3.52 $\pm$ 6%	-5.4	-9.5	-4.6	-0.9	+0.8	-1.1	+1.8
Geometric corrections
A				1.07	1.07	1.40	1.75	1.35
K				1.48	1.48	0.52	0.52	0.12
B				0.58	0.58	1.45	3.31	1.15

Source LaTeX | All tables | In the text

	1 Introduction
	2 Observational data and reduction
	3 Empirical diagnostics
	4 General strategy for model fitting
	5 Simple models
	6 Models with constrained density distribution
	7 Further refining of the models
	8 Sources of energy other than the ionizing flux
	9 Uncertainties in O/H and Ne/O
	10 Conclusion
	References
	Online Material
	Appendix A: Correction of Balmer lines used for dereddening
	Appendix B: Setting the geometric corrections A, B, and K