Physical Properties of the Very Young PN Hen3-1357 (Stingray Nebula) Based on Multiwavelength Observations

We measured the mid-IR flux densities for Bands 1-4 of the Spitzer/Infrared Array Camera (IRAC; Fazio et al. 2004), where the central wavelengths (${\lambda }_{{\rm{c}}}$) are 3.6, 4.5, 5.8, and 8.0 μm, respectively. We reduced the basic calibrated data (BCD, program ID: 50116, obs AORKEY: 25445376, PI: G. Fazio) using mosaicking and point-source extraction software (MOPEX)⁵ provided by the Spitzer Science Center (SSC) to create a mosaic image for each band. We subtracted artificial features seen in the images as best as possible. After we subtracted out surrounding stars by point-spread function fittings using the Digiphot photometry package in IRAF v.2.16,⁶ we performed aperture photometry. The results are summarized in Table 2.

Table 2.  Near- to Far-IR-Band Flux Densities of Hen3-1357

${\lambda }_{{\rm{c}}}$	Tele/Instr/Band	${F}_{\nu }$	${F}_{\lambda }$
(μm)		(mJy)	(erg s−1 cm−2 μm−1)
3.6	Spitzer/IRAC/Band1	1.09(+1) ± 5.22(−1)	2.58(−12) ± 1.24(−13)
4.5	Spitzer/IRAC/Band2	1.61(+1) ± 5.02(−2)	2.38(−12) ± 7.42(−15)
5.8	Spitzer/IRAC/Band3	1.08(+1) ± 1.68(−1)	9.87(−13) ± 1.53(−14)
8.0	Spitzer/IRAC/Band4	3.97(+1) ± 8.20(−1)	1.89(−12) ± 3.91(−14)
9.0	AKARI/IRC/S9W	8.87(+1) ± 8.62(0)	3.13(−12) ± 3.04(−13)
65.0	AKARI/FIS/N60	2.25(+3) ± 3.52(+2)	1.60(−12) ± 2.50(−13)
90.0	AKARI/FIS/WIDE-S	1.88(+3) ± 5.06(+1)	6.98(−13) ± 1.87(−14)
140.0	AKARI/FIS/WIDE-L	3.77(+2) ± 2.75(+2)	5.77(−14) ± 4.21(−14)

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To trace the amorphous silicate feature seen in the Spitzer/IRS spectrum, we used the AKARI Infrared Camera (IRC; Onaka et al. 2007) S9W (${\lambda }_{c}=9$ μm) and L18W (${\lambda }_{c}=18$ μm). We used the AKARI Far-Infrared Surveyor (FIS; Kawada et al. 2007) data as vital constraints to the warm–cold dust continuum in the SED modeling. For this end, we utilized the photometry measurements by Yamamura et al. (2010) for the IRC two bands and FIS Bright Source Catalog Ver.2 for the FIS-N60, WIDE-S, and WIDE-L bands at ${\lambda }_{c}=65$, 90, and 140 μm, respectively. These data were taken by the AKARI all-sky survey. We list these flux densities in Table 2, where A($-B$) means $A\times {10}^{-B}$ hereafter.

We secured the optical high-dispersion spectrum (3500–9200 Å) using the FEROS attached to the MPG ESO 2.2 m Telescope, La Silla, Chile (Prop.ID: 77.D-0478A, PI: M. Parthasarathy).

The weather condition was stable and clear throughout the night, and the seeing was 08–117 (average: 097) measured from the differential image motion monitor. FEROS's fibers use 20 apertures and provide simultaneously the object and sky spectra. The detector is the EEV CCD chip with 2048 × 4096 pixels of 15 × 15 μm square. We selected a 1 × 1 on-chip binning and low gain mode.⁷ The atmospheric dispersion corrector (ADC) was not used during the observation. The exposure time was a single 2100 sec at an airmass of 1.297–1.380. For the flux calibration and blaze function correction, we observed the standard star HR 3454 (Hamuy et al. 1992, 1994) at airmass ∼1.2. Since we did not use the ADC, a color-dependent displacement of the source from differential atmospheric refraction (DAR) might be present. However, we took the data of the Stingray nebula and HR 3454 to be at a similar airmass. Therefore, we believe that the DAR effect on the inferred extinction coefficients, the derived electron temperatures, and therefore on the derived ionic and elemental abundances would be largely reduced. We reduced the data with the echelle spectra reduction package Echelle in IRAF using a standard reduction manner including bias subtraction, removing scattered light, detector sensitivity correction, removing cosmic-ray hits, airmass extinction correction, flux-density calibration, and an all echelle order connection. Using the sky spectrum, we subtracted the sky lines from the Hen3-1357 spectrum. The average resolving power (λ/${\rm{\Delta }}\lambda$) is 44,950, which was measured from the average full width at half maximum (FWHM) of over 300 Th–Ar comparison lines obtained for the wavelength calibrations. The signal-to-noise ratios per pixel were ∼2–12 for the continuum.

The resultant FEROS spectrum is presented in Figure 1; the detected recombination lines (RLs) of O ii are shown in the lower panel. As far as we know, the N and O RLs such as N ii and O ii are detected in this PN for the first time.

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To investigate dust features and perform plasma diagnostics using fine-structure lines, we analyzed the mid-IR spectra taken by the Spitzer/Infrared Spectrograph (IRS; Houck et al. 2004) with the Short-Low (SL, 5.2–14.5 μm, the slit dimension: ∼36 × 57''), Short-High (SH, 9.9–19.6 μm, 47 × 113), and Long-High modules (LH, 18.7–37.2 μm, 111 × 223).

We processed the BCD (program ID: 3633, obs AORKEY: 11312640, PI: B. Matthew) using the data reduction packages SMART v.8.2.9 (Higdon et al. 2004) and IRSCLEAN v.2.1.1⁸ provided by the SSC. We scaled the flux density of the reduced LH spectrum to match with that of the reduced SH spectrum in the overlapping wavelength and we obtained the single 9.9–37.2 μm spectrum. Then, using a similar method, we combined this high-dispersion spectrum and the SL 5.2–14.5 μm spectrum into the single 5.2–37.2 μm spectrum.

We present the resultant spectrum in Figure 2. The intensity peak positions of the identified atomic lines are marked by the vertical lines. We detected Ne, S, and Ar fine-structure lines. The spectrum clearly shows two broad features (indicated by the horizontal red lines) attributed to amorphous silicate grains; the features centered at 9 μm and 18 μm are due to the Si-O stretching mode and the O-Si-O bending mode, respectively. Perea-Calderón et al. (2009) reported that this PN is an O-rich dust object. We did not identify any carbon-based dust grains and molecules in the Spitzer/IRS spectrum. Thus, we can conclude that Hen3-1357 has an O-rich dust nebula.

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We performed a correction to recover the loss of light from Hen3-1357 by the slit.

First, using the AKARI/IRC 9.0 μm band photometry listed in Table 2, we scaled the flux density of the spectrum by considering the AKARI/IRC 9.0 μm filter transmission curve by a constant scaling factor of 0.951. Next, using this scaled spectrum and the Spitzer/IRAC 8.0 μm filter transmission curve, we measured the Spitzer/IRAC 8.0 μm band flux density. The measured value 1.90(−12) erg s⁻¹ cm⁻² μm⁻¹is consistent with the IRAC 8.0 μm photometry result.

AKARI/IRC 9.0 μm and Spitzer/IRAC 8.0 μm bands include atomic lines of H, Ne, S, and Ar certainly contributing to these two bands. As noted in Section 3.4, we did not find a significant difference between optical nebular line intensities relative to the Hβ measured in 2006 and in 2011. This means that the ionization and elemental abundances of the nebula might not have changed between 2006 and 2011.

Our adopted scaling factor (0.951) indicates that the IR-band flux decreased by ∼5% between 2005 and 2009. Therefore, we assume that the mid-IR wavelength evolution had not dramatically changed between 2005 and 2009.

Taking into account these analyses, we scaled the flux density of the spectrum to match the AKARI/IRC 9.0 μm band flux density.

The Hβ flux of the entire nebula is necessary for setting the nebula's hydrogen density structure in our SED modeling as well as for calculating the ${\mathrm{Ne}}^{+,2+}$, ${{\rm{S}}}^{2+,3+}$, and ${\mathrm{Ar}}^{+,2+}$ to ${{\rm{H}}}^{+}$ number density ratios and electron density ${n}_{{\rm{e}}}$ and temperature ${T}_{{\rm{e}}}$ using mid-IR fine-structure lines of these ions.

Since the H i 7.46 μm line is in the longer wavelength edge of the SL2 spectrum (5.13–7.60 μm) and also in the shorter edge of the SL1 spectrum (7.46–14.29 μm), we did not employ this line for estimating the Hβ line flux of the entire nebula. Therefore, we obtained the Hβ line flux by utilizing the theoretical H i I(n = 7–6 and 11–8)/I(n = 4–2) intensity ratio calculated by Storey & Hummer (1995), where n is the principal quantum number. Note that a detected line at 12.37 μm (see Figure 2) indeed is composed of H i n = 7–6 at 12.37 μm and n = 11–8 at 12.38 μm. From the I(12.37 μm + 12.38 μm)/I(Hβ) = 1.04(−2) in the case of an ${n}_{{\rm{e}}}$ = 10⁴ cm⁻³ and a ${T}_{{\rm{e}}}$ = 10⁴ K (Storey & Hummer 1995), we estimated the Hβ flux of the entire nebula to be 9.83(−12) ± 7.33(−13) erg s⁻¹ cm⁻².

We measured the fluxes of the emission lines by Gaussian fittings and then corrected these fluxes using the formula

$$\begin{eqnarray}&&I(\lambda )=F(\lambda )\,\cdot \,{10}^{c({\rm{H}}\beta )(1+f(\lambda ))},\end{eqnarray} \tag{ 1 }$$

where I(λ) is the de-reddened line flux, F(λ) is the observed line flux, f(λ) is the interstellar extinction function at λ computed by the reddening law of Cardelli et al. (1989) with R_V = 3.1, and c(Hβ) is the reddening coefficient at Hβ.

We measured c(Hβ) values by comparing the observed 10 Balmer and Paschen line ratios to Hβ with the theoretical ratios of Storey & Hummer (1995) for a ${T}_{{\rm{e}}}$ = 10⁴ K and an ${n}_{{\rm{e}}}$ = 10⁴ cm⁻³ under the Case B assumption. To reduce the c(Hβ) estimation errors originated from the H i absorptions in the flux standard star HR 3454, we estimated c(Hβ) using different line ratios. The derived c(Hβ) values are listed in Table 3. Since the Hα line was saturated, we did not calculate c(Hβ) using the F(Hα)/F(Hβ) ratio. Finally, we adopted the average c(Hβ) = 8.27(−2) ± 3.47(−2). The scatter between the estimated c(Hβ) could be due to the H i absorptions' depth of HR 3454 measured by Hamuy et al. (1992, 1994). We did not correct interstellar extinction for the Spitzer/IRS spectrum because the extinction is negligibly small in the mid-IR wavelength.

Table 3.  Derived c(Hβ) Ratios

${\lambda }_{\mathrm{lab}.}$ (Å)	Line	c(Hβ)
3797.9	B10	8.25(−2) ± 6.43(−3)
3835.4	B9	3.25(−2) ± 5.17(−3)
3970.1	B7	7.39(−2) ± 2.95(−3)
4101.7	B6	4.38(−1) ± 3.56(−3)
4340.5	B5	1.34(−1) ± 5.16(−3)
8545.4	P15	2.03(−2) ± 1.04(−2)
8598.4	P14	3.84(−2) ± 2.54(−3)
8665.0	P13	7.49(−2) ± 2.48(−3)
8750.5	P12	6.64(−2) ± 1.98(−3)
9014.9	P10	1.18(−2) ± 2.25(−3)

Note.  For the interstellar reddening correction to the FEROS spectrum, we adopted the average c(Hβ) = 8.27(−2) ± 3.47(−2).

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For the year 2006, Reindl et al. (2014) reported $E(B-V)=0.11$, corresponding to c(Hβ) = 0.16. Although they did not give the uncertainty of $E(B-V)$, we assume $\delta \,E(B-V)=0.02$ from the fact that they measured $E(B-V)=0.14\pm 0.02$ in the year 1997. Thus, their c(Hβ) for the year 2006 is estimated to be 0.16 ± 0.03, which is consistent with ours.

In Table 13, we list 180 nebular lines detected in the FEROS spectrum. Since the [O iii] 5007 Å and Hα lines were saturated, we do not list their fluxes. We calculated the average heliocentric radial velocity 12.30 km s⁻¹ and local standard of rest (LSR) radial velocity 12.29 km s⁻¹ using all the identified lines in the FEROS spectrum (1σ uncertainty is 0.25 km s⁻¹). Our heliocentric radial velocity is in good agreement with Arkhipova et al. (2013, 12.6 ± 1.7 km s⁻¹).

In Table 14, we listed the fluxes of the identified 14 atomic gas emission lines detected in the flux-density scaled Spitzer/IRS spectrum, where the fluxes are normalized with respect to the Hβ flux of the entire nebula.

We investigated the possibility of temporal variations of the emission-line intensities by comparing our measurements with those of Arkhipova et al. (2013), who obtained the 3500–7200 Å low-resolution spectrum (FWHM = 4.5 Å) on 2011 June at the South African Astronomical Observatory (SAAO). In Table 15, we list their measured line intensities that overlapped with ours. In 2006–2011, the nebular line fluxes did not significantly change. Indeed, the I(λ) in 2006 are very similar to those in 2011 (I(2011)/I(2006) = 1.11 ± 0.02, correlation factor of 0.995). Thus, the ionization and elemental abundances of the nebula might not be largely changed in 2006–2011. Variation in the ${T}_{\mathrm{eff}}$ of the central star by 5000 K to 10,000 K in a 5- to 10-year interval might not immediately change the nebular morphology, parameters, and abundances in the same time period.

In forbidden line analysis, we employed the NEBULAR package by Shaw & Dufour (1995) and in recombination line analysis, we used private software. In both emission-line analyses, we adopted effective recombination coefficients, transition probabilities, and effective collision strengths listed in Otsuka et al. (2010, their Table 7).

We performed plasma diagnostics using collisionally excited lines (CELs) and RLs. We greatly increased the results compared to Parthasarathy et al. (1993), who obtained one ${n}_{{\rm{e}}}$ and two ${T}_{{\rm{e}}}$ using the optical spectrum taken in 1992, and Arkhipova et al. (2013), who deduced one ${n}_{{\rm{e}}}$ and four ${T}_{{\rm{e}}}$ based on the 3500–7200 Å spectrum taken in 2011. In Table 4, we list the diagnostic line ratios to derive ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$ and the resultant values. In Figure 3, we present the ${n}_{{\rm{e}}}$–${T}_{{\rm{e}}}$ diagram using the diagnostic CEL ratios. "opt" indicates the result from the optical forbidden line ratio; e.g., [S iii] I(9069 Å)/I(6312 Å) ratio. "ir/opt" means the result from the mid-IR fine-structure lines and optical forbidden line; e.g., [S iii] I(18.7/33.5 μm)/I(9067 Å) ratio. We note that CEL emissivities are in general sensitive to ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$, accordingly, CEL ionic abundances depend on a selection of ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$.

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Table 4.  Summary of Plasma Diagnostics

${n}_{{\rm{e}}}$-derivations (this work for the year 2006)					Arkhipova et al. (2013)
ID	Ion	Diagnostic line ratio	Ratio	Result (cm−3)	(cm−3)
(1)	[N i]	I(5197 Å)/I(5200 Å)	1.59(0) ± 3.16(−2)	1390 ± 90	⋯
(2)	[S ii]	I(6716 Å)/I(6731 Å)	3.23(−1) ± 7.30(−2)	5710 ± 1790	8740 ± 7701
(3)	[O ii]	I(3726/29 Å)/I(7320/30 Å)	4.37(0) ± 1.17(−1)	17,520 ± 530	⋯
(4)	[S iii]	I(18.7 μm)/I(33.5 μm)	3.94(0) ± 3.32(−1)	21,990 ± 4840	⋯
(5)	[Cl iii]	I(5517 Å)/I(5537 Å)	4.86(−1) ± 1.69(−2)	23,970 ± 3120	⋯
(6)	[Ne iii]	I(15.6 μm)/I(36.0 μm)	1.56(+1) ± 9.67(−1)	22,750 ± 5850	⋯
(7)	[Ar iv]	I(4711 Å)/I(4740 Å)	4.88(−1) ± 4.55(−2)	22,720 ± 4360	⋯
	H i	Paschen decrement		10,000 – 20,000	⋯
${T}_{{\rm{e}}}$-derivations (this work for the year 2006)					Arkhipova et al. (2013)
ID	Ion	Diagnostic line ratio	Ratio	Result (K)	(K)
(8)	[O i]	I(6300/63 Å)/I(5577 Å)	9.69(+1) ± 2.57(0)	8470 ± 70	⋯
(9)	[N ii]	I(6548/83 Å)/I(5755 Å)	6.38(+1) ± 1.55(0)	9280 ± 100	11,066 ± 1752
(10)	[S iii]	I(9069 Å)/I(6312 Å)	1.22(+1) ± 6.34(−1)	8880 ± 180	11,831 ± 2286
(11)	[S iii]	I(18.7/33.5 μm)/I(9069 Å)	1.38(0) ± 7.82(−2)	7430 ± 280	⋯
(12)	[Cl iii]	I(5517/37 Å)/I(8434/8501 Å)	2.03(+1) ± 4.54(0)	7490 ± 850	⋯
(13)	[Ar iii]	I(7135/7751 Å)/I(5191 Å)	2.09(+2) ± 1.14(+1)	8670 ± 150	⋯
(14)	[Ar iii]	I(9.01 μm)/I(7135/7751 Å)	9.70(−1) ± 4.27(−2)	8400 ± 310	⋯
(15)	[O iii]	I(4959 Å)/I(4363 Å)	5.91(+1) ± 7.27(−1)	9420 ± 40	11,553 ± 1579
(16)	[Ne iii]	I(15.6 μm)/I(3869/3968 Å)	1.92(0) ± 7.34(−2)	8560 ± 70	⋯
${T}_{{\rm{e}}}$(PJ)		(${I}_{\lambda }$(8194 Å)-${I}_{\lambda }$(8169 Å))/I(P11)	2.16(−2) ± 2.53(−3)	8090 ± 1680	⋯
${T}_{{\rm{e}}}$(He i)	He i	I(7281 Å)/I(6678 Å)	1.83(−1) ± 7.38(−3)	8340 ± 330	⋯
${T}_{{\rm{e}}}$(He i)	He i	I(7281 Å)/I(5876 Å)	4.95(−2) ± 1.80(−3)	7980 ± 360	⋯

Note.  For a comparison, the results from Arkhipova et al. (2013, for the year 2011) are listed in the last column.

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First, we calculated ${n}_{{\rm{e}}}$ using CELs. The ${n}_{{\rm{e}}}$–${T}_{{\rm{e}}}$ diagram indicates that the average ${n}_{{\rm{e}}}$ is in the range from ∼2000 cm⁻³ in neutral gas regions (by the ${n}_{{\rm{e}}}$([N i]) curve, ID(1)) and ∼20,000 cm⁻³ in highly ionized gas regions (by the ${n}_{{\rm{e}}}$([Ar iv]) curve, ID(7)) and the average ${T}_{{\rm{e}}}$ is ∼8000–10,000 K. We derived all ${n}_{{\rm{e}}}$ by adopting a constant ${T}_{{\rm{e}}}$ = 9000 K.

Next, we calculated ${T}_{{\rm{e}}}$([O i]) by adopting ${n}_{{\rm{e}}}$([N i]), ${T}_{{\rm{e}}}$([Ar iii]) by the average ${n}_{{\rm{e}}}$ = 22,980 cm⁻³ between ${n}_{{\rm{e}}}$([S iii]) and ${n}_{{\rm{e}}}$([Cl iii]), ${T}_{{\rm{e}}}$([S iii]) by ${n}_{{\rm{e}}}$([S iii]), ${T}_{{\rm{e}}}$([Cl iii]) by ${n}_{{\rm{e}}}$([Cl iii]), and both ${T}_{{\rm{e}}}$([O iii]) and ${T}_{{\rm{e}}}$([Ne iii]) by adopting ${n}_{{\rm{e}}}$([Ne iii]), respectively.

To obtain ${T}_{{\rm{e}}}$([O ii]), ${n}_{{\rm{e}}}$([O ii], and ${T}_{{\rm{e}}}$([N ii]), which are representative ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$ in lower ionization regions, we subtracted respective contributions from ${{\rm{O}}}^{2+}$ and N²⁺ recombination to the [O ii] 7320/30 Å lines and the [N ii] 5755 Å line. We calculated the contributions to these lines, ${I}_{{\rm{R}}}$([O ii] 7320/30 Å) and ${I}_{{\rm{R}}}$([N ii]5755 Å), using the following equations from Liu et al. (2000):

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{{\rm{R}}}([{\rm{O}}\,{\rm{}}\ \mathrm{II}]\,7320/30\,\mathring{\rm A} )}{I({\rm{H}}\beta )}=9.36{\left(\displaystyle \frac{{T}_{{\rm{e}}}}{{10}^{4}}\right)}^{0.44}\displaystyle \frac{n({{\rm{O}}}^{2+})}{n({{\rm{H}}}^{+})},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{{\rm{R}}}([{\rm{N}}\,{\rm{}}\ \mathrm{II}]\,5755\,\mathring{\rm A} )}{I({\rm{H}}\beta )}=3.19{\left(\displaystyle \frac{{T}_{{\rm{e}}}}{{10}^{4}}\right)}^{0.33}\displaystyle \frac{n({{\rm{N}}}^{2+})}{n({{\rm{H}}}^{+})}.\end{eqnarray} \tag{ 3 }$$

Here, n(O²⁺)/n(H⁺) and n(N²⁺)/n(H⁺) are the number density ratios of the O² and ${{\rm{N}}}^{+}$ with respect to the ${{\rm{H}}}^{+}$, respectively.

We adopted the CEL O²⁺ = 1.87(−4) ± 1.39(−6) (see Section 3.6) in order to obtain the ${I}_{{\rm{R}}}$([O ii] 7320/30 Å) = 0.16 ± 0.01, where I(Hβ) = 100. Based on the result that the CEL ${{\rm{O}}}^{2+}$ is consistent with the RL ${{\rm{O}}}^{2+}$, we assumed that the CEL ${{\rm{N}}}^{2+}$ could be very close to the RL ${{\rm{N}}}^{2+}$. Here, we adopted the RL N²⁺ = 6.97(−5) ± 3.17(−5) (see Section 3.6) to calculate the ${I}_{{\rm{R}}}$([N ii] 5755 Å) of 0.33 ± 0.05.

The [O ii] I(3726 Å)/I(3729 Å) ratio is an ${n}_{{\rm{e}}}$ indicator and the I(3726/29 Å)/I(7320/30 Å) ratio is sensitive to both ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$. In Hen3-1357, ${n}_{{\rm{e}}}$ exceeds the critical density of the [O ii]3726/29 Å lines, so the I(3726 Å)/I(3729 Å) ratio could not give reliable ${n}_{{\rm{e}}}$. Therefore, we used the I(3726/29 Å)/I(7320/30 Å) ratio to derive an ${n}_{{\rm{e}}}$ required for the ${{\rm{N}}}^{+}$, ${{\rm{O}}}^{+}$, Cl⁺, Ar⁺, and Fe²⁺ calculations. We obtained ${n}_{{\rm{e}}}$([O ii]) by adopting a constant ${T}_{{\rm{e}}}$ = 9000 K and then obtained ${T}_{{\rm{e}}}$([N ii]) using ${n}_{{\rm{e}}}$([O ii]) = 17,520 cm⁻³.

We found the discrepancy between two ${T}_{{\rm{e}}}$([S iii]) values (IDs 10 and 11). This might be due to the underestimated [S iii] 9069 Å that appeared in the red wavelength edge of the FEROS spectrum because the ionic ${{\rm{S}}}^{2+}$ abundance from this line is ∼14% smaller than that from the fine-structure [S iii] lines, which are insensitive to ${T}_{{\rm{e}}}$ (see Table 5). As we explained in Section, 2.2, the differential atmospheric refraction (DAR) effect might have affected [S iii] 9069 Å, although we cannot exactly estimate how much light was lost from the [S iii] 9069 Å line. The DAR effect might affect widely separated diagnostic line intensity ratios. However, for the ${{\rm{S}}}^{2+}$ abundance estimate, we adopted the average ${T}_{{\rm{e}}}$ between two ${T}_{{\rm{e}}}$([S iii]), thus, reducing the effects by inconsistency between these two ${T}_{{\rm{e}}}$([S iii]).

Table 5.  The Ionic Abundances Derived Using CELs

Elem.	Ion	${\lambda }_{\mathrm{lab}.}$	I(λ)	n(Xm+)/n(H+)	Elem.	Ion	${\lambda }_{\mathrm{lab}.}$	I(λ)	n(X${}^{{\rm{m}}+}$)/n(H+)
(X)	(X${}^{{\rm{m}}+}$)		(I(Hβ) = 100)		(X)	(X${}^{{\rm{m}}+}$)		(I(Hβ) = 100)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
N(CEL)	N0	5197.90 Å	3.63(−1) ± 4.38(−3)	1.11(−6) ± 3.46(−8)	S	${{\rm{S}}}^{+}$	4068.60 Å	4.47(0) ± 8.61(−2)	1.13(−6) ± 1.37(−7)
		5200.26 Å	2.28(−1) ± 3.59(−3)	1.07(−6) ± 1.82(−8)			4076.35 Å	1.51(0) ± 2.90(−2)	1.17(−6) ± 1.43(−7)
			Average	1.09(−6) ± 2.83(−8)			6716.44 Å	6.07(0) ± 1.54(−1)	9.55(−7) ± 1.57(−7)
	${{\rm{N}}}^{+}$	5754.64 Å	2.55(0) ± 3.87(−2)	3.61(−5) ± 2.41(−6)			6730.81 Å	1.25(+1) ± 3.19(−1)	1.07(−6) ± 1.13(−7)
		6548.04 Å	4.10(+1) ± 9.67(−1)	3.60(−5) ± 1.24(−6)				Average	1.06(−6) ± 1.30(−7)
		6583.46 Å	1.21(+2) ± 2.91(0)	3.60(−5) ± 1.25(−6)		${{\rm{S}}}^{2+}$	6312.10 Å	1.03(0) ± 2.19(−2)	6.19(−6) ± 9.21(−7)
			Average	3.60(−5) ± 1.27(−6)			9068.60 Å	1.26(+1) ± 5.96(−1)	4.90(−6) ± 3.88(−7)
			ICF(N(CEL))	3.09 ± 0.17			18.71 μm	1.39(+1) ± 4.65(−1)	5.60(−6) ± 8.07(−7)
				1.11(−4) ± 7.39(−6)			33.48 μm	3.52(0) ± 2.72(−1)	5.63(−6) ± 1.31(−6)
O(CEL)	O0	5577.34 Å	2.19(−1) ± 4.49(−3)	6.06(−5) ± 3.96(−6)				Average	5.34(−6) ± 6.98(−7)
		6300.30 Å	1.61(+1) ± 3.39(−1)	6.06(−5) ± 2.48(−6)		${{\rm{S}}}^{3+}$	10.51 μm	7.76(0) ± 2.66(−1)	4.18(−7) ± 6.52(−8)
		6363.78 Å	5.10(0) ± 1.11(−1)	6.00(−5) ± 2.46(−6)				ICF(S)	1.00
			Average	6.05(−5) ± 2.49(−6)					6.82(−6) ± 7.13(−7)
	${{\rm{O}}}^{+}$	3726.03 Å	1.01(+2) ± 2.62(0)	2.67(−4) ± 1.08(−5)	Ar	Ar+	6.99 μm	7.43(0) ± 2.53(−1)	7.15(−7) ± 2.48(−8)
		3728.81 Å	3.76(+1) ± 9.79(−1)	2.56(−4) ± 9.88(−6)		Ar2+	5191.82 Å	6.41(−2) ± 3.11(−3)	1.94(−6) ± 3.27(−7)
		7320/7330 Å	3.18(+1) ± 5.56(−1)	2.98(−4) ± 2.32(−5)			7135.80 Å	1.08(+1) ± 3.22(−1)	1.47(−6) ± 1.16(−7)
			Average	2.70(−4) ± 1.29(−5)			7751.10 Å	2.63(0) ± 9.57(−2)	1.50(−6) ± 1.23(−7)
	${{\rm{O}}}^{2+}$	4363.21 Å	2.46(0) ± 2.96(−2)	1.88(−4) ± 9.02(−6)			9.01 μm	1.30(+1) ± 4.71(−1)	1.70(−6) ± 6.56(−8)
		4931.23 Å	5.46(−2) ± 2.92(−3)	1.80(−4) ± 9.67(−6)				Average	1.59(−6) ± 9.25(−8)
		4958.91 Å	1.46(+2) ± 3.80(−1)	1.87(−4) ± 1.26(−6)		Ar3+	4711.37 Å	3.39(−2) ± 3.05(−3)	2.12(−8) ± 2.29(−9)
			Average	1.87(−4) ± 1.39(−6)			4740.16 Å	6.95(−2) ± 1.72(−3)	2.09(−8) ± 8.27(−10)
			ICF(O(CEL))	1.00				Average	2.10(−8) ± 1.31(−9)
				4.57(−4) ± 1.30(−5)				ICF(Ar)	1.00
Ne	Ne+	12.81 μm	4.67(+1) ± 1.55(0)	7.23(−5) ± 2.45(−6)					2.32(−6) ± 9.57(−8)
	Ne2+	3869.06 Å	4.03(+1) ± 9.46(−1)	8.77(−5) ± 4.07(−6)	Fe	Fe2+	4658.05 Å	1.11(−1) ± 2.50(−3)	6.71(−8) ± 2.80(−9)
		3967.79 Å	1.00(+1) ± 2.16(−1)	7.22(−5) ± 3.29(−6)			4701.53 Å	4.65(−2) ± 3.17(−3)	7.17(−8) ± 5.65(−9)
		15.56 μm	9.67(+1) ± 3.19(0)	8.38(−5) ± 4.54(−6)			4733.91 Å	2.58(−2) ± 2.74(−3)	8.82(−8) ± 1.01(−8)
		36.02 μm	6.18(0) ± 3.23(−1)	8.57(−5) ± 1.01(−5)			4754.69 Å	2.86(−2) ± 3.64(−3)	9.18(−8) ± 1.21(−8)
			Average	8.41(−5) ± 4.56(−6)			5270.40 Å	5.89(−2) ± 2.40(−3)	6.76(−8) ± 3.48(−9)
			ICF(Ne)	1.00				Average	7.26(−8) ± 5.11(−9)
				1.56(−4) ± 4.77(−6)				ICF(Fe)	2.30 ± 0.14
Cl	Cl+	8578.69 Å	3.04(−1) ± 1.35(−2)	1.64(−8) ± 8.17(−10)					1.67(−7) ± 1.57(−8)
		9123.60 Å	1.03(−1) ± 5.46(−3)	2.12(−8) ± 1.23(−9)
			Average	1.76(−8) ± 9.22(−10)
	Cl2+	5517.72 Å	1.17(−1) ± 3.39(−3)	1.02(−7) ± 3.71(−8)
		5537.89 Å	2.40(−1) ± 4.59(−3)	1.02(−7) ± 3.93(−8)
		8434.00 Å	7.76(−3) ± 1.23(−3)	1.18(−7) ± 7.51(−8)
		8500.20 Å	9.76(−3) ± 3.70(−3)	1.18(−7) ± 8.55(−8)
			Average	1.03(−7) ± 4.06(−8)
			ICF(Cl)	1.01 ± 0.06
				1.21(−7) ± 4.16(−8)

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Similarly, if we underestimate the [O ii] 7320/30 Å intensity by ∼14%, which is an expected value from the above analysis for the ${{\rm{S}}}^{2+}$ abundance, we obtain ${n}_{{\rm{e}}}$([O ii]) = 20 300 cm⁻³. Then, using ${n}_{{\rm{e}}}$([O ii]), we obtain ${T}_{{\rm{e}}}$([N ii]) = 9010 K. Under ${n}_{{\rm{e}}}$([O ii]) and ${T}_{{\rm{e}}}$([N ii]), the ${{\rm{N}}}^{+}$, O⁺, Cl⁺, and Fe²⁺ abundances⁹ would increase by ∼12%. Even if the DAR effect is present in our FEROS spectrum, the potential error of c(Hβ), ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$, and ionic/elemental abundances caused by the DAR effect would be ∼15% or less. Hence, our conclusion on these physical parameters derived from the CELs and the RLs does not change.

Finally, we calculated ${T}_{{\rm{e}}}$ and ${n}_{{\rm{e}}}$ using He i lines and H i Paschen series. We calculated ${T}_{{\rm{e}}}$(He i) using He i I(7281 Å)/I(6678 Å) and I(7281 Å)/I(5876 Å) ratios using the recombination coefficients in a constant ${n}_{{\rm{e}}}$ = 10⁴ cm⁻³ provided by Benjamin et al. (1999). We calculated the Paschen jump ${T}_{{\rm{e}}}$(PJ) using Equation (7) of Fang & Liu (2011). The H i P11 line is in an echelle order gap. Therefore, we obtained the expected I(P11) using the observed H i P12 line and the theoretical I(P11)/I(P12) ratio of 1.30 in ${n}_{{\rm{e}}}$ ∼ 10²–10⁵ cm⁻³ and ${T}_{{\rm{e}}}$ ∼ 5000–15,000 K (Storey & Hummer 1995). Thus, we obtained ${n}_{{\rm{e}}}$ ∼10,000–20,000 cm⁻³ by comparing the observed I(Pn)/I(P10) ratios (n is from 12 to 42) and the theoretical calculations under the Case B assumption and ${T}_{{\rm{e}}}$(PJ) = 8090 K by Storey & Hummer (1995).

As a comparison, the results from Arkhipova et al. (2013, for the year 2011) are listed in the last column. Arkhipova et al. (2013) reported ${T}_{{\rm{e}}}$([O iii]) = 11,553 ± 1579 K, ${T}_{{\rm{e}}}$([O ii]) = 11,983 ± 770 K,¹⁰ ${T}_{{\rm{e}}}$([N ii]) = 11,066 ± 1752 K, ${T}_{{\rm{e}}}$([S iii]) = 11,831 ± 2286 K,¹¹ and ${n}_{{\rm{e}}}$([S ii]) = 8740 ± 7701 cm⁻³. The difference between their ${T}_{{\rm{e}}}$([O iii]) and ours is due to the [O iii] 4363 Å intensity (see Table 15). Under a constant ${n}_{{\rm{e}}}$, the ${T}_{{\rm{e}}}$([O iii]) becomes higher as the [O iii] I(4959/5007 Å)/I(4363 Å) ratio becomes lower. The [N ii] ${n}_{{\rm{e}}}$–${T}_{{\rm{e}}}$ curve in Figure 3 suggests that the discrepancy in ${T}_{{\rm{e}}}$([N ii]) could be due to the difference in adopted ${n}_{{\rm{e}}}$.

In Table 16, we list ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$ adopted for calculating each ionic abundance. We determined these values by referring to the ${n}_{{\rm{e}}}$–${T}_{{\rm{e}}}$ diagram and taking the ionization potential (IP) of the targeting ion into account. We calculated the CEL ionic abundances by solving an equation of population at multiple energy levels (from two energy levels for Ne⁺ and Ar⁺ and 33 levels for Fe²⁺) under the listed ${n}_{{\rm{e}}}$ and ${T}_{{\rm{e}}}$. We adopted a constant ${n}_{{\rm{e}}}$ = 10⁴ cm⁻³ and the average ${T}_{{\rm{e}}}$(He i) = 8160 K to calculate He⁺. For the RL ${{\rm{C}}}^{2+}$, ${{\rm{N}}}^{2+}$, and ${{\rm{O}}}^{2+}$, we adopted ${n}_{{\rm{e}}}$ = 10⁴ cm⁻³ and ${T}_{{\rm{e}}}$(PJ).

We summarize the resultant CEL and RL ionic abundances in Tables 5 and 6, respectively. When we detected two or more lines of a target ion, we derived each ionic abundance using each line intensity. Then, we adopted the weight-average value as the representative ionic abundance as listed in the last line of each ion by boldface. We give the 1σ uncertainty of each ionic abundance, which accounts for the uncertainties of line fluxes (including c(Hβ) uncertainty), ${T}_{{\rm{e}}}$, and ${n}_{{\rm{e}}}$.

Table 6.  The Ionic Abundances Derived Using RLs

Elem.	Ion	${\lambda }_{\mathrm{lab}.}$	I(λ)	n(${{\rm{X}}}^{{\rm{m}}+}$)/n(H+)
(X)	(${{\rm{X}}}^{{\rm{m}}+}$)	(Å)	(I(Hβ) = 100)
He	He+	4120.81	1.77(−1) ± 4.80(−3)	9.95(−2) ± 5.32(−3)
		4387.93	4.39(−1) ± 6.42(−3)	7.18(−2) ± 4.73(−3)
		4437.55	6.64(−2) ± 4.31(−3)	8.53(−2) ± 6.61(−3)
		4471.47	4.63(0) ± 4.85(−2)	9.34(−2) ± 5.22(−3)
		4713.22	6.68(−1) ± 6.70(−3)	1.14(−1) ± 9.20(−3)
		4921.93	1.21(0) ± 4.45(−3)	9.05(−2) ± 4.65(−3)
		5015.68	2.16(0) ± 1.19(−2)	7.69(−2) ± 3.63(−3)
		5047.74	1.68(−1) ± 3.09(−3)	8.24(−2) ± 4.52(−3)
		5875.60	1.47(+1) ± 2.62(−1)	1.02(−1) ± 6.54(−3)
		6678.15	3.97(0) ± 9.94(−2)	9.79(−2) ± 5.74(−3)
		7281.35	7.26(−1) ± 2.30(−2)	8.37(−2) ± 4.43(−3)
			Average	9.69(−2) ± 5.88(−3)
			ICF(He)	1.00
				9.69(−2) ± 5.88(−3)
C(RL)	${{\rm{C}}}^{2+}$	4267.18	1.03(−1) ± 4.54(−3)	9.66(−5) ± 3.06(−5)
		6578.05	5.05(−2) ± 3.71(−3)	9.84(−5) ± 3.88(−5)
			Average	9.72(−5) ± 3.33(−5)
			ICF(C(RL))	1.48 ± 0.22
				1.44(−4)  ± 5.38(−5)
N(RL)	${{\rm{N}}}^{2+}$	4630.54	2.02(−2) ± 2.59(−3)	9.27(−5) ± 4.21(−5)
		5679.56	1.69(−2) ± 2.30(−3)	4.23(−5) ± 1.93(−5)
			Average	6.97(−5) ± 3.17(−5)
			ICF(N(RL))	1.48 ± 0.22
				1.03(−4) ± 4.94(−5)
O(RL)	${{\rm{O}}}^{2+}$	4069.62	2.65(−2) ± 3.24(−3)	2.78(−4) ± 7.04(−5)
		4069.88	3.84(−2) ± 4.55(−3)	2.52(−4) ± 6.61(−5)
		4072.15	5.68(−2) ± 2.51(−3)	2.34(−4) ± 5.45(−5)
		4075.86	7.55(−2) ± 5.04(−3)	2.26(−4) ± 5.34(−5)
		4104.99	4.05(−2) ± 4.28(−3)	3.64(−4) ± 9.07(−5)
		4153.30	3.10(−2) ± 1.60(−3)	4.04(−4) ± 9.69(−5)
		4349.43	3.34(−2) ± 2.39(−3)	1.70(−4) ± 3.92(−5)
		4366.90	3.41(−2) ± 2.60(−3)	4.48(−4) ± 1.07(−4)
		4638.86	3.44(−2) ± 3.53(−3)	3.06(−4) ± 7.73(−5)
		4641.81	6.37(−2) ± 2.21(−3)	2.38(−4) ± 5.35(−5)
		4649.13	1.03(−1) ± 2.72(−3)	2.13(−4) ± 4.79(−5)
		4650.84	3.42(−2) ± 1.93(−3)	3.28(−4) ± 7.57(−5)
		4661.63	4.79(−2) ± 2.17(−3)	3.83(−4) ± 8.68(−5)
		4676.23	3.19(−2) ± 5.12(−3)	3.34(−4) ± 9.09(−5)
			Average	2.82(−4) ± 6.73(−5)
			ICF(O(RL))	2.45 ± 0.07
				6.89(−4) ± 1.66(−4)

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The CEL abundances calculated using the optical lines are well consistent with ones using mid-IR fine-structure lines, indicating that the calculated CEL ionic abundances are the result of the proper selection of ${T}_{{\rm{e}}}$, in particular, and of accurate scaling flux of the Spitzer/IRS spectrum.

We obtained the RL ${{\rm{N}}}^{2+}$ and ${{\rm{O}}}^{2+}$ in this PN for the first time. The higher multiplet lines are in general insensitive to Case A or Case B assumptions and reliable because these lines are less affected by both resonance fluorescence by starlight and recombination from higher terms. The consistency between the RL ${{\rm{C}}}^{2+}$ abundance by the multiple V6 4267.18 Å line and by the V2 6578.05 Å line indicates that the RL ${{\rm{C}}}^{2+}$ from both lines can be reliable. We can have the similar conclusion for the RL O²⁺ and ${{\rm{N}}}^{2+}$ abundances. The RL ${{\rm{O}}}^{2+}$ abundances are well consistent among the O ii V1 4638/42/49/51/62/76 Å, V2 4349/67 Å, V10 4069.6/69.9/72/76 Å, V19 4153 Å, and V20 4105 Å lines. The RL ${{\rm{N}}}^{2+}$ abundances are derived using the V3 5679 Å and 4631 Å lines.

As is compared in Table 7, our ionic abundances agree with Arkhipova et al. (2013). However, we found obvious discrepancies in Ne²⁺ and ${{\rm{S}}}^{2+}$. Their ${{\rm{S}}}^{2+}$ seems to be derived using the auroral line [S iii] 6312 Å. Although they did not report the detection of any [Ne iii] lines in their spectrum taken in 2011, we assume that they derived the Ne²⁺ using nebular [Ne iii] lines. The Ne²⁺ and ${{\rm{S}}}^{2+}$ differences between Arkhipova et al. (2013) and us are due to the adopted ${T}_{{\rm{e}}}$. We stress that our adopted ${T}_{{\rm{e}}}$ for the Ne²⁺ and ${{\rm{S}}}^{2+}$ is determined using the [Ne iii] and [S iii] fine-structure, nebular, and auroral lines. For instance, if we adopt their ${T}_{{\rm{e}}}$([O iii]) = 11,553 K to calculate the Ne²⁺ using the nebular [Ne iii] lines, the volume emissivities of these [Ne iii] lines become 2.66 times higher than those in our adopted ${T}_{{\rm{e}}}$ = 8560 K. Accordingly, the Ne²⁺ is down to 3.18(−5), which is consistent with Arkhipova et al. (2013). However, since the emissivities of the fine-structure [Ne iii] lines do not largely change, even in both 8560 K by ours and 11,553 K by Arkhipova et al. (2013), the Ne²⁺ abundances using the fine-structure [Ne iii] lines keep 8.38(−5) (from the [Ne iii] 15.56 μm line) and 8.57(−5) (from the [Ne iii] 36.02 μm line). That is, we find out the spurious Ne²⁺ derivation discrepancy between the nebular and the fine-structure lines. We confirmed that a similar conclusion can apply for S²⁺. Thus, if the nebula condition is in a steady state and had not dramatically changed between 2006 and 2011, we can conclude that our Ne²⁺ and S²⁺ are more reliable.

Table 7.  Comparison of the Ionic Abundances in 2006 by Us and in 2011 by Arkhipova et al. (2013)

Ion (X${}^{{\rm{m}}+}$)	n(X${}^{{\rm{m}}+}$)/n(H+) in 2006	n(X${}^{{\rm{m}}+}$)/n(H+) in 2011
He+	9.69(−2) ± 5.88(−3)	9.70(−2) ± 8.00(−3)
N+	3.60(−5) ± 1.27(−6)	5.81(−5) ± 2.31(−5)
O+	2.70(−4) ± 1.29(−5)	9.10(−5) ± 7.16(−5)
O2+(CEL)	1.87(−4) ± 1.39(−6)	1.01(−4) ± 4.26(−5)
Ne2+	8.41(−5) ± 4.56(−6)	3.46(−5) ± 1.76(−5)
S+	1.06(−6) ± 1.30(−7)	9.34(−7) ± 5.70(−7)
S2+	5.34(−6) ± 6.98(−7)	1.43(−6) ± 1.13(−6)
Ar2+	1.59(−6) ± 9.25(−8)	1.00(−6) ± 4.26(−7)

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By introducing the ionization correction factor (ICF), we inferred the nebular abundances from their ionic abundances. We calculated these ICF(X) derived based on the fraction of the observed ionic abundances with similar ionization potentials to the target element. The ICF(X) of element X is listed in the last line of each element of Tables 5 and 6. The abundance of the element X n(X)/n(H) corresponds to the value derived from the ICF(X) · ${{\rm{\Sigma }}}_{{\rm{m}}=1}$n(X${}^{{\rm{m}}+}$)/n(H⁺). We will compare these ICF(X) based on IPs with those calculated by Cloudy photoionization model later.

As shown in Section 3.6, we obtained the O(CEL), Ne, S, and Ar ionic abundances in various ionization stages. Thus, for these elements, we can adopt ICF(X) = 1.0. We adopted ICF(He) = 1.0 because we did not detect the nebular He ii lines. Assuming that N corresponds to the sum of the ${{\rm{N}}}^{+}$ and ${{\rm{N}}}^{2+}$, we recovered the unobserved ${{\rm{N}}}^{2+}$(CEL) using the ICF(N) proposed by Delgado-Inglada et al. (2014). Then, using ICF(N) for N(CEL), we determined ICF(N(RL)). Since the IPs in both C and N ions are similar, we assumed that ICF(C(RL)) is as same as ICF(N(RL)). ICF(O(RL)) corresponds to O(CEL)/O²⁺(CEL). ICF(Cl) corresponds to the Ar/(Ar⁺ + Ar²⁺) ratio. For ICF(Fe), we adopted Equation (3) of Delgado-Inglada & Rodríguez (2014).

In Table 8, we summarize the resultant elemental abundances derived by introducing the ICFs. The value (X) in the third column is 12 + log₁₀n(X)/n(H). The value in the last column is the relative abundance to the Sun. We referred to the solar abundance by Asplund et al. (2009). Our work improved nebular elemental abundances calculated by the pioneering work of Parthasarathy et al. (1993) and a recent comprehensive study of Arkhipova et al. (2013).

Table 8.  Elemental Abundances

Elem. (X)	n(X)/n(H)	(X)	[X/H]
He	9.69(−2) ± 5.88(−3)	10.99 ± 0.03	+0.06 ± 0.03
C(RL)	1.44(−4) ± 5.38(−5)	8.16 ± 0.16	−0.23 ± 0.17
C(CEL)	9.54(−5) ± 4.26(−5)	7.98 ± 0.19	−0.40 ± 0.20
N(RL)	1.03(−4) ± 7.39(−6)	8.01 ± 0.03	+0.15 ± 0.12
N(CEL)	1.11(−4) ± 7.39(−6)	8.05 ± 0.03	+0.19 ± 0.12
O(RL)	6.89(−4) ± 1.66(−4)	8.84 ± 0.10	+0.11 ± 0.13
O(CEL)	4.57(−4) ± 1.30(−5)	8.66 ± 0.01	−0.07 ± 0.07
Ne	1.56(−4) ± 4.77(−6)	8.19 ± 0.01	+0.14 ± 0.10
S	6.82(−6) ± 7.13(−7)	6.83 ± 0.05	−0.33 ± 0.05
Cl	1.21(−7) ± 4.16(−8)	5.08 ± 0.15	−0.17 ± 0.16
Ar	2.32(−6) ± 9.57(−8)	6.37 ± 0.02	−0.13 ± 0.10
Fe	1.67(−7) ± 1.57(−8)	5.22 ± 0.04	−2.24 ± 0.09

Note.  C(CEL) is an expected value estimated by adopting the RL C/O ratio.

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Using the RL C, N, and O, we derived the C/O and the N/O ratios using the same type of emission lines, i.e., RLs. These ratios are important proofs of the initial mass of the central star. In Table 8, we list an expected C(CEL) based on the assumption that the RL C/O ratio (0.21 ± 0.09) is consistent with the CEL C/O ratio.

The RL C/O ratio indicates that Hen3-1357 is an O-rich PN, which is also supported by the detection of the amorphous silicate features. The average of the logarithmic difference between the nebular and solar abundances of S, Cl, and Ar $\langle [{\rm{S}},\mathrm{Cl},\mathrm{Ar}/{\rm{H}}]\rangle \,=-0.21\pm 0.10$ indicates that this PN is about a half of a solar metallicity (0.6 Z_☉). In the Milky Way chemical evolution of such a metallicity, [Fe/H] should be comparable to [α/H]. The expected [Fe/H] is –0.23 from the average [S,Ar/H] ∼ –0.23 if all of the Fe atoms are in the gas phase and are not captured by any dust grains. However, the observed [Fe/H] is much smaller than the expected [Fe/H] value. Thus, the largely depleted [Fe/H] suggests that over 99% of the Fe atoms in the nebula would be locked within silicate grains.

One of the long-standing problems in PN abundances is that the RL C, N, O, and Ne ionic abundances are in general larger than the CEL ones. Several explanations for the abundance discrepancy have been proposed, e.g., temperature fluctuation, high-density clumps, and cold hydrogen-deficient components (see, e.g., a review by Liu 2006). There might be a possible link between the binary central star and the abundance discrepancy, as was recently proposed by Jones et al. (2016). In Hen3-1357, the abundance discrepancy factor (ADF) defined as the ratio of the RL to the CEL ionic abundance is 1.51 ± 0.36 in ${{\rm{O}}}^{2+}$, which is lower than a typical value ∼2.0 (Liu 2006). Such a degree of the ${{\rm{O}}}^{2+}$ discrepancy can be explained by introducing the temperature fluctuation model proposed by Peimbert (1967).

Parthasarathy et al. (1993) and Feibelman (1995) showed the IUE UV spectrum taken on 1992 April 23 (IUE Program ID: NA108, PI: S.R. Pottasch, Data-ID: 44459). From there, we can see the CEL C iii] 1906/09 Å and N iii] 1744-54 Å lines. Although Parthasarathy et al. (1995) gave these line fluxes, the CEL ${{\rm{C}}}^{2+}$ and N²⁺ have never been calculated so far. It would be of interest to estimate the ADF(C²⁺) because the RL ${{\rm{C}}}^{2+}$ of 6.91(−5) ± 1.48(−6) using the C ii 4267 Å line detected in the spectrum taken in 1992 was calculated by Arkhipova et al. (2013). We download the processed SWP44459 data set from the Multimission Archive at STScI (MAST), we measured the fluxes of the C iii] 1906/09 Å and N iii] 1744-54 Å lines, and calculated the CEL C²⁺ = 9.53(−5) ± 1.19(−6) and the CEL N²⁺ = 5.49(−5) ± 5.32(−6) using the F(Hβ), E(B-V), ${T}_{{\rm{e}}}$, and ${n}_{{\rm{e}}}$ reported by Parthasarathy et al. (1993). The ADF(C²⁺) of 1.24 ± 0.27 in 1992 is similar to our ADF(O) measured in 2006. This might be applied even for ADF(N); the ratio of the RL ${{\rm{N}}}^{2+}$ in 2006 to the CEL N² in 1992 is 1.27 ± 0.59.

Based on our analysis, we conclude that the ADF(C/N/O) would be < 2.

The He/C/N/O/Ne/S abundances are close to the AGB star nucleosynthesis model predictions by Karakas (2010) for initially 1.0, 1.25, and 1.5 M${}_{\odot }$ stars with Z = 0.008 (0.4 Z_☉). The 1.0 M_☉ model predicts (He):10.99, (C):8.09, (N):7.81, (O):8.53, (Ne):7.69, and (S):7.00. The differences among these models are (C) and (N); (C):8.04 and (N):7.90 in the 1.25 M_☉ model, and (C):8.12 and (N):7.95 in the 1.5 M_☉ model. The predicted final core mass is 0.58 M_☉ in an initially 1.0 M_☉ star to 0.63 M_☉ in a 1.5 M_☉ star.

According to current stellar models for low-mass AGB stars, partial mixing of the bottom of the H-rich convective envelope into the outermost region of the ¹²C-rich intershell layer leads to the synthesis of extra ¹³C and ¹⁴N at the end of each third dredge-up (TDU). During He-burning, ¹⁴N captures two α particles and ²²Ne are produced. ²⁰Ne is the most abundant and it is not altered significantly by H or He burning. The (Ne) discrepancy between the observation (8.19) and the model prediction (7.69) might be due to an increase of ²²Ne. The models for the 1.0, 1.25, and 1.5 M_☉ stars with Z = 0.008 by Karakas (2010) do not predict TDUs and do not include such partial mixing zone (PMZ). Note that the PMZ is not well justified yet. The Ne abundance in Hen3-1357 suggests that the progenitor might have formed a PMZ and extra ²²Ne and Ne might be conveyed to the stellar surface by unexpected mechanisms, e.g., very few TDUs or LTPs. Otherwise, we might interpret that the (Ne) discrepancy between the observation and the model prediction is due to the errors in the atomic data of ${\mathrm{Ne}}^{+,2+}$.

From chemical abundance analysis, we can conclude that the progenitor mass could be 1.0–1.5 M_☉ if Hen3-1357 had evolved from a star with the initial Z ∼ 0.008.

First, we investigated the SED of the CSPN using the FEROS spectrum, which is the sum of the nebular emission lines and continuum and the CSPN spectrum. For this end, we need to subtract the nebular continuum from the FEROS spectrum. We used the Nebcont code in the Dispo package of STARLINK v.2015A¹² to generate the nebular continuum. For the calculation, we adopted the Hβ flux of the entire nebula 9.83(−12) erg s⁻¹ cm⁻², n(He⁺/H⁺) = 9.69(−2), ${T}_{{\rm{e}}}$ = 8090 K, and ${n}_{{\rm{e}}}$ = 22,860 cm⁻³, which is the average among ${n}_{{\rm{e}}}$([S iii]), ${n}_{{\rm{e}}}$([Cl iii]), ${n}_{{\rm{e}}}$([Ne iii]), and ${n}_{{\rm{e}}}$([Ar iv]).

In the upper panel of Figure 4, we show the synthesized nebular continuum. The discontinuity around 8200 Å indicates the Paschen jump. After we scaled the de-reddened FEROS spectrum up to match with the Hβ line flux of the entire nebula, we manually removed gas emission lines to the extent possible. This gas emission-line-free FEROS spectrum is presented in the same panel. In the lower panel, we show the resultant spectrum generated by subtracting the synthesis nebular continuum spectrum from the gas emission-line-free and flux-density-scaled FEROS spectrum. Note that the residual spectrum coincides with the spectrum of the CSPN. A spike feature around 8200 Å is from the residuals of Paschen and Bracket continuum between the observed and the model. If we can subtract this continuum around the Paschen jump from the observed spectrum, the spike feature will be gone. This spike feature does not affect the Ic-band magnitude measurement. Using this residual spectrum, we measured flux densities for BVRIc bands by taking filter transmission curves of each band, as summarized in Table 9.

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Table 9.  BVRIc Band De-reddened Flux Densities of the CSPN's SED Derived from the Residual FEROS Spectrum

${\lambda }_{c}$ (Å)	Band	${F}_{\lambda }$ (erg s−1 cm−2 Å−1)
4378.1	Johnson-B	1.21(−14) ± 1.14(−15)
5466.1	Johnson-V	5.69(−15) ± 8.76(−16)
6358.0	Cousins-R	3.58(−15) ± 8.66(−16)
7829.2	Cousins-I	1.63(−15) ± 7.08(−16)

Note.  The extinction-free V-band magnitude (m_V) is 14.51 ± 0.17, where ${F}_{\lambda }$(m_V = 0) is 3.631(−9) erg s⁻¹ cm⁻² Å⁻¹.

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Reindl et al. (2014) performed spectral synthesis fitting of the spectrum of the CSPN taken using Far Ultraviolet Spectroscopic Explorer (FUSE) in 2006 and obtained ${T}_{\mathrm{eff}}=\mathrm{55,000}$ K and log g = 6.0 ± 0.5 cm s⁻². However, in our Cloudy model with this ${T}_{\mathrm{eff}}$ and the measured de-reddened m_V of the CSPN (14.51, see Section 4.1) determining the luminosity, we overproduced the fluxes of higher IP ions such as [Ne iii] and [O iii] lines.¹³

It might be because the nebula ionization structure is not yet fully changed by the recent very fast post-AGB evolution of the CSPN. Although we firmly believe the results of Reindl et al. (2014), we needed to adopt a SED of the CSPN with a lower ${T}_{\mathrm{eff}}$ to reproduce the overall observed nebular line fluxes. For instance, we estimated ${T}_{\mathrm{eff}}$ to be 50,560 ± 2710 K using the [O iii]/Hβ line ratio and the formula established among PNe in the Large Magellanic Cloud by Dopita & Meatheringham (1991).

Therefore, we utilized the non-local thermodynamic equilibrium (non-LTE) stellar atmospheres modeling code Tlusty (Hubeny 1988)¹⁴ to obtain the SED of the CSPN for our Cloudy model. Using Tlusty, we constructed line-blanketed, plane-parallel, and hydrostatic stellar atmosphere, where we considered the He, C, N, O, Ne, Si, P, S, and Fe abundances. We run a grid model to cover ${T}_{\mathrm{eff}}$ from 43,000 to 53,000 K in a constant 1000 K steps. Here, we adopted the observed nebular (He), (N(CEL)), (O(CEL)), (Ne), and (S). We adopted the expected (C(CEL)) = 7.98 (see Table 8). As Reindl et al. (2014) reported, there is no significant difference between the nebular and stellar He, C, N, O, S abundances. We adopted stellar (Si) = 7.52 and (P) = 4.42 derived by Reindl et al. (2014). From the nebular $\langle [{\rm{S}},\mathrm{Ar}/{\rm{H}}]\rangle =-0.23$, we adopted (Fe) = 7.23. We interpret that 99% of the Fe atoms in the stellar atmosphere are eventually locked as dust grains in the nebula. We set the microturbulent velocity to 10 km s⁻¹ and the rotational velocity to 20 km s⁻¹.

Based on Reindl et al. (2014, 2017), Parthasarathy et al. (1993), and Karakas (2010), the core mass of the CSPN (m_*) is ∼0.53–0.6 M_☉. Referring to the theoretical post-AGB evolution tracks presented in Figure 4 of Reindl et al. (2017), we adopted $\mathrm{log}\,g=5.25$ cm s⁻² and the distance D = 2.5 kpc to obtain m_* ∼ 0.53–0.6 M_☉. D has been determined in the range between 826 pc (see Reindl et al. 2017, reference therein) and 5.85 kpc (Frew et al. 2016) thus far. When we adopt D = 826 pc, we have to set a very small inner radius of the nebula to reproduce the observed Hβ flux and by doing so, we overproduced fluxes of higher IP lines and obtained hotter dust temperatures, accordingly causing lower dust continuum fluxes. If D is 5.0 kpc, the situation would become better than the case of D = 826 pc, and we can then reproduce the observed line fluxes. However, we must set $\mathrm{log}\,g$ ∼ 4.5 cm s⁻² in order to obtain a value above the m_* range, and Hen3-1357 would be classified as a halo PN not a thin disk PN.

We verified our adopted D of 2.5 kpc. Following Quireza et al. (2007), we can classify Hen3-1357 into a Type II or III PN based on the observed (He) and N/O ratio. Hen3-1357 would be a thin disk population. Quireza et al. (2007) reported that the average peculiar velocity relative to the Galaxy rotation (ΔV) is ∼23 km s⁻¹ for Type IIb and ∼70 km s⁻¹ for Type III and the average height from the Galactic plane ($| z|$) is ∼0.225 kpc for Type IIa and ∼0.686 kpc for Type III, respectively. From the constraint on $| z|$, we obtained a range of D toward Hen3-1357 between 1.07 and 3.27 kpc. Maciel & Lago (2005) calculated the rotation velocities at the nebula Galactocentric positions calculated for a Galaxy disk rotation curve based on four distance scales. Using their established Galaxy rotation velocity based on the distance scale of Cahn et al. (1992), van de Steene & Zijlstra (1995), and Zhang (1995), Equation (3) of Quireza et al. (2007), and our measured LSR radial velocity 12.29 km s⁻¹ (see Section 3.3), we obtained a D versus ΔV plot. Using this plot and the constraint on ΔV, we got another range of D between 1.63 and 4.92 kpc. Thus, we obtained D = 1.63–3.27 kpc, with 2.5 kpc in the middle value of this distance range. From the above discussion, we adopted D = 2.5 kpc and the absolute V-band magnitude of the CSPN M_V = 2.555.

Finally, we obtained the synthesized spectra using SYNSPEC, ¹⁵ as displayed in Figure 5.

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4.3.1. Nebular Elemental Abundances

4.3.2. Nebula Geometry, Boundary Conditions, and Gas Filling Factors

4.3.3. Dust Grains and Size Distribution

To find the best-fit model, we varied ${T}_{\mathrm{eff}}$, the inner radius of the nebula ${r}_{\mathrm{in}}$, ${n}_{{\rm{H}}}$, (He/C/N/O/Ne/S/Cl/Ar/Fe), the dust mass fraction, and f within a given range using the optimize command available in Cloudy.

García-Hernández et al. (2002) found that the distribution of molecular hydrogen H₂ v = 1-0 S(1) at 2.122 μm and v = 2-1S (1) at 2.248 μm is quite homogeneous and extends well beyond the distribution of the H i Brγ line. This suggests that Hen3-1357 has large neutral regions.

Thus, we went to deep neutral gas regions in our model; we continued calculation until any of the model's predicted flux densities at AKARI/FIS 65/90/140 μm bands reached or exceeded the relevant observed values. The Cloudy model predicted ${r}_{\mathrm{ib}}=1\buildrel{\prime\prime}\over{.} 48$ where ${T}_{{\rm{e}}}$ drops below 4000 K. We stopped our model calculation at the outer radius (${r}_{\mathrm{out}}$) of 3.4(−2) pc (277). The goodness of fit was determined by the reduced ${\chi }^{2}$ value calculated from the following observational constraints: 17 broadband fluxes, 5 broadband flux densities, 104 gas emission fluxes, ${r}_{\mathrm{ib}}$, de-redden F(Hβ) of the entire nebula. Table 10 summarizes the parameters of the best-fit model, where the reduced ${\chi }^{2}$ is 33.5.

Table 10.  The Best-fit Cloudy Model Parameters of Hen3-1357

Parameters of the CSPN	Value
L*/${T}_{\mathrm{eff}}$/$\mathrm{log}\,g$/D	330 L☉/45,550 K/5.25 cm s−2/2.5 kpc
MV	2.555
R*	0.291 R☉
m*	0.550 M☉
Parameters of the Nebula	Value
(X)	He:10.97, C:8.18, N:7.89, O:8.58, Ne:8.20
	Mg:5.86, Si:5.84, S:6.74, Cl:4.73, Ar:6.25
	Fe:5.23, Others: Karakas (2010)
Geometry	Spherical symmetry
Shell size	${r}_{\mathrm{in}}$:044 (0.005 pc), ${r}_{\mathrm{out}}$:277 (0.034 pc)
Ionization boundary	148 (0.018 pc)
radius (${r}_{\mathrm{ib}}$)
Filling factor (f)	0.58
${n}_{{\rm{H}}}$	11 610 cm−3
F(Hβ)	9.84(−12) erg s−1 cm−2 (de-reddened)
mg	3.81(−2)M☉
Parameters of the Dust	Value
Grain size	0.01–0.50 μm
Td	40–150 K
md	1.98(−4)M☉
md/mg (DGR)	5.20(−3)

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The SED of the best-fit model, in comparison with the observational data, is presented in Figure 6. From the model result we confirmed that the gas-emission contribution to Spitzer/IRAC 8.0 μm and AKARI/IRC 9.0/18 μm bands is 51.8%, 19.1%, and 3.9%, respectively. Thus, the disagreement at the Spitzer/IRAC 8.0 μm band between the observed photometry and the predicted SED can be explained by considering the gas-emission contribution to the relevant band.

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The observed and model-predicted line fluxes, band fluxes, and band flux densities are summarized in Table 18. The intensity of the O ii 4075 Å and 4651 Å is the sum of the multiplet V10 and V1 O ii lines, respectively. It is noteworthy that we simultaneously reproduced both the observed RL/CEL N and O line fluxes.

The predicted ICF(X) by Cloudy listed in Table 11 is in excellent agreement with the ICF(X) derived in Section 3.7, indicating that our Cloudy model succeeded in explaining the ionization nebula structure and the ICF(X) based on IP is the proper value.

As described in Section 4.2, under the constraints of the CSPN at D = 2.5 kpc, we need ${T}_{\mathrm{eff}}=\mathrm{45,550}$ K and L_* = 330 L_⊙ in order to explain the observed quantities. With D, L_*, and $\mathrm{log}\,g$, we derived m_* = 0.55 M_⊙.

The gas mass (m_g) = 3.81(−2) M_☉ is the sum of the ionized and neutral gas masses. The ionized gas mass is 5.38(−3) M_☉ and the remaining is the neutral gas mass. Our derived m_g is close to the ejected mass, which equals 8.9(−2) M_⊙ in initially 1.5 M_⊙ stars with Z = 0.008 during the last thermal pulse AGB, predicted by Karakas & Lattanzio (2007). We obtained a dust mass (m_d) of 1.98(−4) M_☉.

It is of interest to know how far-IR data impact gas and dust mass estimates in our model. When we stopped model calculations at ${r}_{\mathrm{ib}}$, we obtained m_g = 4.61(−3) M_☉ and m_d = 3.79(−5) M_☉. This model did not well fit any AKARI far-IR fluxes. To fit the observed far-IR data, we need a larger ${r}_{\mathrm{out}}$. With the AKARI far-IR data, we obviously obtained much greater m_g and m_d. About 80% of the total dust mass is from warm–cold dust components beyond the ionization front. From the model results, we confirmed that the gas-emission contribution to AKARI65/90/140 μm bands is 1.4%, 1.08%, and 2.58%, respectively. AKARI far-IR data would be thermal emission from warm–cold dust.

Cox et al. (2011) derived an upper limit of the sum of m_d and m_g = 0.16 M_☉ within a 3 pc radius using the AKARI/90 μm and a constant dust-to-gas mass ratio (DGR) = 6.25(−3) for O-rich dust, although the measured dust temperature (T_d) is unknown. Using their results, we calculated an upper limit m_g = 0.159 M_☉ and m_d = 9.94(−4) M_☉, respectively.

Umana et al. (2008) derived the total ionized mass of ∼5.7(−2) M_☉ using the radio data in 2002, assuming D = 5.6 kpc, inner/outer radii = 065/13 shallow shell geometry, and f = 1.0. Using the IRAS data, they derived T_d = 137 ± 2 K and m_d = 2(−4) M_☉using the 60 μm flux density in the case of the silicate. Based on the results and assumptions of Umana et al. (2008), ionized gas and co-existing dust would be ∼6.6(−3) M_☉ and ∼4.0(−5) M_☉, respectively, if we adopt D = 2.5 kpc and f = 0.58. These estimated values are consistent with our derived m_g and m_d when we stopped the model at ${r}_{\mathrm{ib}}$. On the dust, Cox et al. (2011) found that the AKARI far-IR flux densities are a factor two lower than predicted from the IRAS data. They interpreted that the far-IR variability in its infrared flux might occur due to recent mass-loss event(s) or evolution of the CSPN. Following the report of Cox et al. (2011) and the dust mass ∼4.0(−5) M_☉ co-existing with the ionized gas by the IRAS data in 1980s, we estimate the dust mass to be ≲2(−5) M_☉ in 2006–2007, which is comparable to our derived dust mass of 3.79(−5) M_☉ within the ionized gas.