Chemical Abundances of Planetary Nebulae in the Substructures of M31. II. The Extended Sample and a Comparison Study with the Outer-disk Group^*

Before introducing target selection, we briefly give some definitions in terms of boundaries in the M31 structure. We adopted the M31 bulge radius (∼3.4 kpc) from the surface brightness fitting by Irwin et al. (2005). The inner disk of M31 is defined at R₂₅ (=95'; de Vaucouleurs et al. 1991), which corresponds to 21.7 kpc at the distance of M31; this radius well encompasses the optical disk of M31. Beyond R₂₅ lies the extended disk that stretches to 40 kpc, with detections as far as ∼70 kpc (Ibata et al. 2005). In the current paper, all M31 PNe beyond R₂₅ but with kinematics consistent with the extended disk are dubbed the outer-disk PNe. Previous spectroscopic observations of Kwitter et al. (2012), Balick et al. (2013), and Corradi et al. (2015) all focused on the outer-disk PNe in M31.

In Papers I and II, we targeted the PNe in the Northern Spur and the Giant Stream substructures. Since our targets kinematically deviate from the extended disk of M31 and are mostly located in the halo, hereafter we call them the halo PNe to avoid possible confusion with the outer-disk PNe. For the new GTC observations, we selected a sample that covers not only the substructures but also more extended areas in the M31 system such as the eastern and the southeastern halo regions and the dwarf satellite M32. The locations/hosts of our targets are given in Table 1, where other properties such as target positions (right ascension—R.A., declination—decl.), visual magnitudes in [O iii] λ5007 (${m}_{\lambda 5007}$), heliocentric velocities ${v}_{\mathrm{helio}}$ (in km s⁻¹), angular distances to the center of M31, and the sky-projected galactocentric distances (in kpc) are also presented. The spatial locations of our targets, including those studied in Papers I and II, are shown in Figure 1. Our halo nebulae are mostly outside R₂₅.

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Table 1.  Observing Log and Properties of PNe

PN ID a	R.A.	Decl.	${m}_{\lambda 5007}$ b	${v}_{\mathrm{helio}}$ c	ξ	η	${R}_{\mathrm{gal}}$ d	Location e	GTC Obs.
	(J2000.0)	(J2000.0)		(km s−1)	(°)	(°)	(kpc)		Grism	Expos.
PN8 (M2430)	00:47:25.9	+42:58:59.7	21.32	−135.1	0.858	1.720	26.3	Northern Spur	R1000B	2 × 2400 s
PN9 (M2449)	00:46:13.8	+42:40:28.5	20.88	−70.6	0.642	1.408	21.2	Northern Spur	R1000B	4 × 1200 s
									R1000R	2 × 1200 s
PN10 (LAMOST)	00:44:03.1	+42:27:46.6	20.74	−234.0	0.242	1.194	16.7	Northern Spur	R1000B	4 × 1200 s
PN11 (M2432)	00:47:30.3	+43:03:40.9	20.69	−411.0	0.871	1.798	27.4	Giant Stream	R1000B	4 × 1200 s
									R1000R	2 × 1200 s
PN12 (M2466)	00:49:08.0	+42:28:44.3	21.96	−392.3	1.179	1.220	23.3	Giant Stream	R1000B	4 × 2400 s
PN13 (LAMOST)	00:49:55.2	+38:32:49.0	21.91	−362.0	1.404	−2.707	41.8	SE Halo	R1000B	4 × 2400 s
									R1000R	2 × 1890 s
PN14 (M2507)f	00:48:27.2	+39:55:34.3	21.23	−146.9	1.095	−1.334	23.7	Giant Stream	R1000B	4 × 2400 s
PN15 (M2512)	00:45:58.5	+39:13:25.4	21.10	−318.2	0.627	−2.042	29.3	SE Halo	R1000B	8 × 1200 s
PN16 (M2895)	00:42:42.2	+40:51:39.8	20.78	−193.3	−0.007	−0.408	5.59	M32	R1000B	6 × 1200 s
PN17 (LAMOST)	00:53:38.6	+41:09:32.1	21.15	−437.0	2.052	−0.078	28.1	Eastern Halo g	R1000B	5 × 2100 s
									R1000R	2 × 1800 s
PN18 (M2234)	00:42:42.3	+40:51:49.5	20.13	−147.3	−0.006	−0.405	5.56	M32	R1000B	6 × 1000 s

Notes. PN18 was discarded from the analysis because no nebular emission lines were detected in its spectrum.

^aNumber in the bracket is the ID from Merrett et al. (2006), except PN10, PN13, and PN17, which were discovered and identified in the LAMOST survey (Yuan et al. 2010). ^bFrom Merrett et al. (2006), except PN10, PN13, and PN17, the ${m}_{\lambda 5007}$ of which are adopted from Yuan et al. (2010). ^cFrom Merrett et al. (2006), except PN10, PN13, and PN17, the ${v}_{\mathrm{helio}}$ of which are adopted from Yuan et al. (2010). ^dSky-projected galactocentric distance estimated at a distance of 785 kpc to M31 (McConnachie et al. 2005). ^eHere, "Halo" means that the PN belongs to the outer halo or is associated with some substructure. ^fPN nature confirmed by the LAMOST survey (Yuan et al. 2010). ^gMight be associated with the NE Shelf, as explained in Section 4.4.

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We selected eight PNe from the catalog of Merrett et al. (2006) and three from that of Yuan et al. (2010); the latter is based on a spectroscopic survey at the Large Sky Area Multi-Object Fiber Spectroscopic Telescope¹⁷ (LAMOST; Su et al. 1998; Cui et al. 2004, 2010, 2012; Zhao et al. 2012). These new targets were named PN8–PN18 (see Table 1 and Figure 1), following the target naming (PN1–PN7) in Paper II. According to their locations in M31, our GTC samples PN1–PN17 are highlighted with different colors in Figure 1, where PN16 and PN18 are too close to each other and visually indistinguishable. The [O iii] brightnesses of the new sample are ${m}_{\lambda 5007}\sim 20.48\mbox{--}21.96$, extending down to nearly 1.8 mag from the bright-end cutoff of the planetary nebula luminosity function (PNLF) of M31 (Ciardullo et al. 1989; Merrett et al. 2006; Ciardullo 2010).

Yuan et al. (2010) did not assign their newly discovered PNe to any locations (i.e., the substructure or the extended disk). We identified the locations of the three LAMOST targets (PN10, PN13, and PN17) according to their kinematics shown in Figure 2, which also presents the distribution of the line-of-sight velocity with respect to the center of M31, ${v}_{\mathrm{los}}$, versus distance along the major and minor axes of M31. The kinematics of PN10 obviously deviates from the extended disk of M31 and is somewhat close to the Northern Spur sample identified by Merrett et al. (2006, Figure 32 therein). We thus identified PN10 as a possible Northern Spur object. PN13 visually resides on the southeast (SE) extension of the Giant Stream; PN15 also seems to be on the stream. However, the velocities of these two PNe, although both deviating from the kinematics of the extended disk, are inconsistent with the stellar orbit of Merrett et al. (2003). PN17 is located in the eastern halo, 205 from the center of M31. Its velocity differs significantly from the disk, and its location seems to be very close to the NE Shelf (Ferguson et al. 2005). We temporarily assign PN13, PN15, and PN17 to be the halo nebulae; a detailed discussion is given in Section 4. The PN nature of PN14 (ID 2507 in Merrett et al. 2006) was confirmed in the LAMOST survey; it might be associated with the Giant Stream. For the other targets selected from Merrett et al. (2006), we adopted their locations identified by the authors (Table 1).

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Deep spectroscopy of M31 PNe was carried out with the Optical System for Imaging and low-intermediate-Resolution Integrated Spectroscopy (OSIRIS) spectrograph on the 10.4 m Gran Telescopio Canarias (GTC) at Observatorio de El Roque de los Muchachos (ORM, La Palma). These observations were obtained from 2016 September 2 to 2016 September 11 for GTC program No. GTC25-16B (PI: X. Fang) in service mode. The OSIRIS grism R1000B (1000 lines mm⁻¹), which covers ∼3630–7850 Å, and a long slit with 10 width were used. The OSIRIS detector is a combination of two 2048 × 4096 CCDs. The pixel size is 15 μm, corresponding to 0127 in angular size. We adopted the standard observing mode where the output images were binned by 2 × 2. The above instrument setup produces a spectral resolution of ∼5.5 Å (FWHM) in the blue part of the spectrum and 6.4 Å in the red, at a dispersion of ∼2.072 Å pixel⁻¹. The ideal observing conditions at the ORM provided photometric and clear nights, and excellent seeing (06–08) for most of the observations. The Moon was also close to dark during the observations. Throughout the observations, the long slit was placed along the parallactic angles to minimize light loss due to atmospheric diffraction. The typical physical sizes of PNe are ≲0.5 pc (e.g., Frew et al. 2016), corresponding to ≲013 in angular size at the distance of M31. This is smaller than the binned CCD pixel size (0254) of OSIRIS, and thus our targets are all point sources and supposed to be well accommodated within the GTC 1'' wide long slit.

In order to remove cosmic rays and to avoid saturation of strong emission lines, multiple exposures were made for each target PN. These exposures are summarized in Table 1. In total, 30 hr observations were completed at the GTC for 11 targets. Thanks to the large light-collecting area of the GTC, we could clearly see almost all of the PNe in the direct acquisition CCD image with an exposure of a few seconds (e.g., Figure 3) and then placed the GTC long slit on the targets. Blind offset was utilized only for the two PNe in M32 due to their close proximity (∼74 and 154) to the center of M32. Exposures of the spectrophotometric standard stars Ross 640 and G191-B2B (Oke 1974, 1990) were made each night to calibrate the fluxes for the target spectra, using a slit width of 252. The HgAr and neon arc line images were obtained (with both 10 and 252 slit widths) for wavelength calibration and geometric rectification. Other basic calibration files, such as bias and spectral flats, were also obtained for both the target PN and the standard spectrophotometric star in each night.

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We also obtained long-slit spectroscopy of four PNe (PN9, PN11, PN13, and PN17) using the GTC OSIRIS red grism R1000R that covers ∼5080–10370 Å. These observations were obtained on 2016 August 23–24 for program No. GTC66-16A (PI: X. Fang). Slit width was 10, and spectral resolution FWHM ∼ 6.7 Å in the blue region and 8.5 Å in the red, with a dispersion of 2.59 Å pixel⁻¹. The R1000R exposures are summarized in Table 1. The HgAr, neon, and xenon arc lines were used for wavelength calibration. Spectrophotometric standard stars for flux calibration were the same as in the R1000B spectroscopy. Data were obtained under photometric conditions, with seeing ∼08–10.

The GTC OSIRIS long-slit spectra were reduced using iraf¹⁸ v2.16. Data reduction generally followed the standard procedure, similar to what has been described in Fang et al. (2015). The raw PN spectral images were first bias-subtracted and corrected for flat-field. We then performed wavelength calibration using HgAr arc lines for the PN spectra obtained with the R1000B grism and HgAr+Xe for the R1000R spectra. Although geometry distortion along the long slit does not affect the nebular emission lines of our targets, which are point sources on the CCD, such distortion of the sky lines must be corrected for so that background subtraction can be properly done. During the wavelength calibration, we rectified the geometry distortion by fitting the arc lines using third-order polynomial functions in the two-dimensional (2D) spectrogram. This geometry rectification "straightened" the sky lines along the slit.

We subtracted the background from each single exposure of the target frame by fitting the background emission along the slit direction using high-order cubic spline functions (see more details in Fang et al. 2015). We then combined the background-subtracted 2D frames of the same PN to remove the cosmic rays. We then used the FILTER/COSMIC task in the software midas¹⁹ v13SEPpl1.2 to further eliminate any possible cosmic residuals in the CCD images. The above procedures produced a well "cleaned" spectral image for each PN, which was then flux-calibrated (and also corrected for the atmospheric extinction) using the spectrum of spectrophotometric standards.

We extracted a 1D spectrum in the fully calibrated 2D frame of each PN for spectral analysis. As an example, Figure 4 shows the 1D spectra for PN12 and PN17 in our sample. In the common wavelength region (5080–7850 Å) covered by the R1000B and R1000R grisms, differences in the fluxes of emission lines (He i λλ5876, 6678, 7065, [N ii] λλ6548, 6583, Hα, [S ii] λλ6716, 6731, [Ar iii] λ7136, [O ii] λλ7320, 7330) detected in both spectra of PN9, PN11, PN13, and PN17 are mostly less than 5%. We corrected for the effect of second-order contamination in the red part of the R1000B spectrum (Figure 4, top) following the method of Fang et al. (2015). For the R1000R grism, the second-order contamination exists beyond 9200 Å (Figure 4, bottom). Fortunately, this contamination only affects the [S iii] λ9531 emission line. The [S iii] λ9069 nebular line was unaffected.

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Despite careful data reduction, the detection of emission lines in one (target PN18) of the two PNe in M32 failed due to its close proximity (74) to the bright nucleus of M32, although this target is the brightest in our sample. The other M32 PN (PN16) is 154 from M32's center and has good data quality. We thus analyzed 10 PNe (PN8–PN17; Table 1) in this paper.

The emission line fluxes were measured from the extracted 1D spectra by integrating over line profiles. The observed line fluxes of all targets, normalized to F(Hβ) = 100, are presented in Table 2, where the observed Hβ fluxes (in erg cm⁻² s⁻¹) are also presented. The R1000R spectrum was scaled according to the Hα line flux in the R1000B spectrum. We derived the logarithmic extinction parameter, c(Hβ), by comparing the observed and theoretical ratios of hydrogen Balmer lines, Hα/Hβ and Hγ/Hβ. The theoretical Case B H i line ratios were adopted from Storey & Hummer (1995) at an electron temperature of 10,000 K and a density of 10⁴ cm⁻³. The c(Hβ) values of our PNe are small (0.08–0.25) and are presented in Table 2. The observed line fluxes were then dereddened using the formula

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

where f(λ) is the extinction curve of Cardelli et al. (1989) with a total-to-selective extinction ratio R_V = 3.1. The extinction-corrected line intensities, all normalized to I(Hβ) = 100, along with the measurement errors, are presented in Table 2. Given the excellent observing conditions (seeing <10) and the slit width (10), light loss in strong emission lines is expected to be negligible.

Table 2.  Fluxes and Intensities

Ion	λ	Transition	PN8		PN9		PN10		PN11		PN12
	(Å)		F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)
[O ii]	3727a	2p3 4So–2p3 2Do	19.6	22.4 ± 2.5	50.3	57.3 ± 5.2	29.3	35.1 ± 3.9	32.9	39.4 ± 4.3	59.7	68.2 ± 5.5
H i	3798	2p2Po–10d2D	⋯	⋯	3.72	4.22 ± 0.94	3.34	3.96 ± 0.90	3.15	3.74 ± 0.83	4.55	5.17 ± 1.05
H i	3835	2p2Po–9d2D	3.12	3.53 ± 1.00	5.74	6.48 ± 1.83	4.78	5.65 ± 1.60	6.24	7.38 ± 2.01	4.93	5.58 ± 1.17
[Ne iii]	3868	2p4 3P2–2p4 1D2	107	120 ± 8	82.4	92.8 ± 6.2	76.5	90.0 ± 6.0	100	117 ± 8	29.2	33.0 ± 2.2
H i	3889b	2p2Po–8d2D	5.75	6.48 ± 0.97	15.5	17.4 ± 2.6	12.4	14.6 ± 2.20	15.1	17.8 ± 2.6	14.4	16.2 ± 2.4
[Ne iii]	3967c	2p4 3P1–2p4 1D2	46.2	51.6 ± 4.0	38.5	43.0 ± 3.3	36.0	41.8 ± 3.2	50.0	58.2 ± 4.5	27.7	31.0 ± 2.3
He i	4026	2p3Po–5d3D	1.48	1.64 ± 0.85	2.53	2.79 ± 1.45	1.50	1.73 ± 0.89	0.46	0.53 ± :	2.21	2.45 ± 1.27
[S ii]	4068d	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${P}_{3/2}^{{\rm{o}}}$	9.05	10.0 ± 1.5	2.73	3.01 ± 0.45	1.91	2.18 ± 0.33	4.88	5.58 ± 0.83	5.32	5.88 ± 0.87
H i	4101	2p2Po–6d2D	27.0	29.8 ± 3.1	23.0	25.2 ± 2.6	22.8	25.9 ± 2.7	29.4	33.5 ± 3.4	27.5	30.3 ± 3.1
C ii	4267	3d2D–4f2Fo	⋯	⋯	⋯	⋯	⋯	⋯	1.38	1.52 ± 0.27	0.79	0.85 ± 0.31
H i	4340e	2p2Po–5d2D	42.5	45.3 ± 3.3	43.5	46.4 ± 3.5	42.0	45.7 ± 3.3	40.1	43.7 ± 3.1	42.2	45.0 ± 3.2
[O iii]	4363	2p2 1D2–2p2 1S0	9.43	10.0 ± 1.2	8.20	8.71 ± 1.04	8.19	8.90 ± 1.07	12.4	13.5 ± 1.6	4.20	4.47 ± 0.53
He i	4388	2p1${P}_{1}^{{\rm{o}}}$–5d1D2	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.13	1.20 ± 0.54
He i	4471	2p3Po–4d3D	5.61	5.88 ± 0.82	4.38	4.59 ± 0.74	4.47	4.76 ± 0.66	4.88	5.21 ± 0.84	5.47	5.74 ± 0.82
N iii	4641f	3p2${P}_{3/2}^{{\rm{o}}}$–3d2${D}_{5/2}$	⋯	⋯	⋯	⋯	⋯	⋯	3.44	3.57 ± 0.72	⋯	⋯
C iii	4649g	3s3S–3p3Po	⋯	⋯	1.46	1.50 ± 0.67	⋯	⋯	⋯	⋯	⋯	⋯
He ii	4686	3d2D–4f2Fo	1.21	1.23 ± 0.40	1.52	1.55 ± 0.50	⋯	⋯	13.0	13.2 ± 1.1	0.87	0.89 ± 0.18
[Ar iv]	4711h	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{5/2}^{{\rm{o}}}$	1.72	1.75 ± 0.53	1.14	1.16 ± 0.35	1.34	1.37 ± 0.41	4.28	4.38 ± 0.66	0.81	0.83 ± 0.20
[Ar iv]	4740	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${{\rm{D}}}_{3/2}^{{\rm{o}}}$	2.87	2.91 ± 0.55	1.38	1.40 ± 0.26	1.18	1.20 ± 0.35	4.32	4.40 ± 0.82	⋯	⋯
H i	4861e	2p2Po–4d2D	100	100	100	100	100	100	100	100	100	100
He i	4922	2p1${P}_{1}^{{\rm{o}}}$–4d1D2	0.74	0.73 ± :	0.72	0.71 ± :	1.16	1.15 ± 0.63	1.03	1.02 ± 0.61	1.49	1.48 ± 0.67
[O iii]	4959	2p2 1P1–2p2 1D2	438	433 ± 17	425	420 ± 16	354	349 ± 13	474.1	467 ± 18	189	187 ± 7
[O iii]	5007	2p2 1P2–2p2 1D2	1307	1286 ± 25	1286	1266 ± 24	1068	1046 ± 20	1450	1420 ± 26	569	560 ± 11
[N i]	5198i	2p3 4${S}_{3/2}^{{\rm{o}}}$–2p3 2${D}_{3/2}^{{\rm{o}}}$	0.77	0.74 ± :	⋯	⋯	0.56	0.53 ± :	⋯	⋯	⋯	⋯
He ii	5411	4f2Fo–7g2G	⋯	⋯	⋯	⋯	⋯	⋯	1.47	1.37 ± 0.36	⋯	⋯
[Cl iii]	5537	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{3/2}^{{\rm{o}}}$	1.71	1.60 ± 0.47	⋯	⋯	⋯	⋯	0.55	0.51 ± 0.28	0.58	0.54 ± 0.31
[N ii]	5755	2p2 1D2–2p2 1S0	2.42	2.24 ± 0.49	1.46	1.36 ± 0.30	1.10	1.00 ± 0.22	1.04	0.94 ± 0.20	1.47	1.36 ± 0.26
C iv	5805	3s2S–3p2Po	⋯	⋯	9.29	8.59 ± 0.95	⋯	⋯	⋯	⋯	⋯	⋯
He i	5876	2p3Po–3d3D	17.5	16.1 ± 1.8	18.5	17.1 ± 1.8	15.6	14.0 ± 1.2	16.4	14.6 ± 1.3	17.2	15.8 ± 1.7
[O i]	6300	2p4 3P2–2p4 1D2	4.22	3.78 ± 1.24	7.19	6.46 ± 2.12	5.12	4.42 ± 1.45	2.38	2.05 ± 0.67	2.38	2.13 ± 0.50
[S iii]	6312j	3p2 1D2–3p2 1S0	2.87	2.57 ± 0.64	1.25	1.13 ± 0.41	1.31	1.13 ± 0.41	1.75	1.50 ± 0.54	1.45	1.30 ± 0.47
[O i]	6363	2p4 3P1–2p4 1D2	1.60	1.43 ± 1.20	1.52	1.36 ± 1.14	1.64	1.41 ± 1.18	0.62	0.53 ± 0.44	0.51	0.46 ± 0.40
[N ii]	6548	2p2 3-2p2 1D2	15.8	14.0 ± 1.5	19.8	17.5 ± 2.0	10.2	8.65 ± 0.92	13.0	11.0 ± 1.2	23.6	20.9 ± 2.4
H i	6563e	2p2Po–3d2D	304	284 ± 13	322	285 ± 15	287	283 ± 12	293	283 ± 13	301	284 ± 14
[N ii]	6583	2p2 3P2–2p2 1D2	53.7	47.4 ± 4.2	62.0	55.0 ± 4.9	29.8	25.2 ± 2.2	39.8	33.6 ± 2.9	73.0	64.4 ± 5.7
He i	6678k	2p1${P}_{1}^{{\rm{o}}}$–3d1D2	5.26	4.62 ± 0.65	4.73	4.17 ± 0.58	4.00	3.36 ± 0.47	4.35	3.65 ± 0.50	4.64	4.07 ± 0.56
[S ii]	6716	3p3 4${{\rm{S}}}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{5/2}^{{\rm{o}}}$	1.87	1.64 ± 0.34	2.42	2.13 ± 0.44	1.03	0.86 ± 0.20	2.23	1.86 ± 0.38	2.38	2.10 ± 0.43
[S ii]	6731	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{3/2}^{{\rm{o}}}$	2.31	2.02 ± 0.38	4.23	3.71 ± 0.50	1.68	1.41 ± 0.26	4.24	3.54 ± 0.42	4.98	4.36 ± 0.44
He i	7065	2p3Po–3s3S	9.96	8.55 ± 1.03	11.5	9.93 ± 1.20	10.7	8.76 ± 1.05	8.25	6.72 ± 0.81	10.7	9.23 ± 1.11
[Ar iii]	7136	3p4 3P2–3p4 1D2	19.3	16.5 ± 1.6	14.8	12.7 ± 1.23	12.3	10.0 ± 1.10	18.0	14.5 ± 1.4	17.1	14.7 ± 1.4
He i	7281	2p1${P}_{1}^{{\rm{o}}}$–3s1S0	⋯	⋯	0.43	0.36 ± :	⋯	⋯	0.44	0.36 ± :	0.34	0.29 ± :
[O ii]	7320	2p3 2${D}_{5/2}^{{\rm{o}}}$–2p3 2${P}_{3/2}^{{\rm{o}}}$	10.1	8.59 ± 1.11	6.88	5.84 ± 0.75	7.91	6.33 ± 0.82	2.36	1.88 ± 0.24	6.55	5.55 ± 0.71
[O ii]	7330	2p3 2${D}_{3/2}^{{\rm{o}}}$–2p3 2${P}_{3/2}^{{\rm{o}}}$	8.54	7.23 ± 1.10	5.78	4.91 ± 0.74	6.19	4.95 ± 0.75	1.83	1.46 ± 0.22	7.20	6.10 ± 0.91
[Ar iii]	7751	3p4 3P1–3p4 1D2	3.05	2.52 ± 0.63	2.24	1.86 ± 0.46	2.24	1.74 ± 0.78	3.89	3.00 ± 0.74	2.96	2.45 ± 0.60
H i	8750	3d2D–12f2Fo	⋯	⋯	1.72	1.36 ± 0.41	⋯	⋯	1.57	1.14 ± 0.34	⋯	⋯
H i	9015	3d2D–10f2Fo	⋯	⋯	1.85	1.45 ± 0.43	⋯	⋯	1.31	0.94 ± 0.27	⋯	⋯
[S iii]	9069	3p2 3P1–3p2 1D2	⋯	⋯	21.5	17.0 ± 1.4	⋯	⋯	22.7	16.2 ± 1.3	⋯	⋯
H i	9229	3d2D–9f2Fo	⋯	⋯	2.26	1.76 ± 0.62	⋯	⋯	7.52	5.34 ± 1.88	⋯	⋯
He ii	9345	5g2G–8h2Ho	⋯	⋯	5.14	4.00 ± 1.3	⋯	⋯	3.55	2.51 ± 0.81	⋯	⋯
[S iii]	9531l	3p2 3P1–3p2 1D2	⋯	⋯	17.4	13.5 ± 1.6	⋯	⋯	14.4	10.1 ± 1.2	⋯	⋯
c(Hβ)			0.181		0.177		0.243		0.245		0.180
log F(Hβ)m			−15.29		−15.09		−14.92		−15.04		−15.09

Ion	λ	Transition	PN13		PN14		PN15		PN16		PN17
	(Å)		F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)	F(λ)	I(λ)
[O ii]	3727a	2p3 4So–2p3 2Do	44.1	50.1 ± 5.8	24.2	27.5 ± 3.0	63.2	74.4 ± 8.2	71.5	76.3 ± 9.2	23.5	27.1 ± 2.4
H i	3798	2p2Po–10d2D	⋯	⋯	5.68	6.44 ± 1.43	⋯	⋯	13.0	13.8 ± 2.8	4.21	4.83 ± 1.01
H i	3835	2p2Po–9d2D	3.72	4.19 ± 1.10	3.82	4.32 ± 1.00	3.07	3.57 ± 0.91	⋯	⋯	5.63	6.44 ± 1.14
[Ne iii]	3868	2p4 3P2–2p4 1D2	43.0	48.1 ± 3.1	40.2	45.2 ± 2.8	80.5	93.2 ± 4.7	122	130 ± 10.4	93.0	106 ± 8
H i	3889b	2p2Po–8d2D	12.6	14.1 ± 2.0	13.3	15.0 ± 2.1	12.3	14.2 ± 1.9	3.87	4.10 ± 2.1	16.4	18.6 ± 2.6
[Ne iii]	3967c	2p4 3P1–2p4 1D2	28.2	31.3 ± 2.4	27.3	30.4 ± 2.5	41.3	47.2 ± 2.8	60.2	63.5 ± 6.4	51.2	57.7 ± 4.7
He i	4026	2p3Po–5d3D	1.73	1.91 ± 0.78	1.89	2.09 ± 0.85	1.03	1.17 ± 0.67	⋯	⋯	3.18	3.56 ± 0.64
[S ii]	4068d	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${{\rm{P}}}_{3/2}^{{\rm{o}}}$	2.56	2.81 ± 0.62	5.57	6.14 ± 0.91	4.10	4.61 ± 0.86	8.41	8.82 ± 1.06	2.40	2.67 ± 0.53
H i	4101	2p2Po–6d2D	22.8	25.0 ± 2.4	24.9	27.4 ± 2.8	24.4	27.4 ± 2.0	25.2	26.4 ± 3.7	28.0	31.1 ± 2.2
C iii	4187	4f 1${F}_{3}^{{\rm{o}}}$–5g1G4	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.03	1.13 ± 0.24
He ii	4199	4f2Fo–11g2G	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.05	1.15 ± 0.27
H i	4340e	2p2Po–5d2D	42.0	44.5 ± 3.2	40.8	43.5 ± 3.0	39.3	42.5 ± 3.1	60.2	62.1 ± 6.5	41.2	44.2 ± 3.2
[O iii]	4363	2p2 1D2–2p2 1S0	4.02	4.26 ± 0.51	5.62	5.97 ± 0.67	5.31	5.73 ± 0.68	11.0	11.4 ± 1.3	15.6	16.7 ± 1.7
He i	4388	2p1${P}_{1}^{{\rm{o}}}$–5d1D2	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.27	1.36 ± 0.31
He i	4471	2p3Po–4d3D	5.23	5.47 ± 0.88	4.31	4.52 ± 0.70	4.45	4.72 ± 0.76	4.91	5.02 ± 0.71	4.03	4.24 ± 0.68
N iii	4641f	3p2${P}_{3/2}^{{\rm{o}}}$–3d2${D}_{5/2}$	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	2.63	2.71 ± 0.52
C iv	4658	5g2G–6h2Ho	⋯	⋯	⋯	⋯	1.52	1.57 ± 0.22	⋯	⋯	⋯	⋯
He ii	4686	3d2D–4f2Fo	⋯	⋯	⋯	⋯	2.03	2.08 ± 0.24	21.5	21.7 ± 2.3	26.0	26.6 ± 2.4
[Ar iv]	4711h	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{5/2}^{{\rm{o}}}$	0.94	0.96 ± 0.17	⋯	⋯	1.06	1.10 ± 0.17	⋯	⋯	4.95	5.05 ± 0.90
[Ar iv]	4740	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{3/2}^{{\rm{o}}}$	⋯	⋯	⋯	⋯	1.40	1.43 ± 0.20	⋯	⋯	4.76	4.83 ± 0.91
H i	4861e	2p2Po–4d2D	100	100	100	100	100	100	100	100	100	100
He i	4922	2p1${P}_{1}^{{\rm{o}}}$–4d1D2	1.48	1.47 ± 0.87	0.73	0.73 ± 0.43	1.96	1.94 ± 0.64	⋯	⋯	1.01	1.00 ± 0.40
[O iii]	4959	2p2 1P1–2p2 1D2	295	292 ± 11	232	230 ± 9	427	421 ± 16	564	561 ± 28	497	491 ± 18
[O iii]	5007	2p2 1P2–2p2 1D2	891	878 ± 16	710	699 ± 13	1275	1250 ± 23	1693	1680 ± 31	1519	1493 ± 27
[N i]	5198i	2p3 4${S}_{3/2}^{{\rm{o}}}$–2p3 2${D}_{3/2}^{{\rm{o}}}$	⋯	⋯	0.65	0.63 ± :	⋯	⋯	⋯	⋯	⋯	⋯
He ii	5411	4f2Fo–7g2G	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.95	1.85 ± 0.33
[Cl iii]	5517	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{5/2}^{{\rm{o}}}$	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.46	0.43 ± :
[Cl iii]	5537	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{3/2}^{{\rm{o}}}$	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.57	0.53 ± 0.26
[N ii]	5755	2p2 1D2–2p2 1S0	0.43	0.40 ± :	1.12	1.04 ± 0.22	1.26	1.15 ± 0.21	⋯	⋯	0.34	0.31 ± :
C iv	5805	3s2S–3p2Po	⋯	⋯	⋯	⋯	16.1	14.6 ± 1.6	⋯	⋯	⋯	⋯
He i	5876	2p3Po–3d3D	15.0	13.8 ± 1.2	16.1	14.8 ± 1.4	17.0	15.3 ± 1.3	15.5	15.0 ± 1.4	14.8	13.5 ± 1.2
[O i]	6300	2p4 3P2–2p4 1D2	3.42	3.08 ± 0.61	1.49	1.34 ± 0.30	3.75	3.28 ± 0.65	⋯	⋯	1.54	1.37 ± 0.27
[S iii]	6312j	3p2 1D2–3p2 1S0	1.97	1.78 ± 0.38	1.38	1.24 ± 0.34	2.53	2.22 ± 0.52	⋯	⋯	0.92	0.82 ± 0.26
[O i]	6363	2p4 3P1–2p4 1D2	1.27	1.14 ± 0.54	0.39	0.35 ± 0.18	1.25	1.09 ± 0.53	⋯	⋯	0.48	0.43 ± :
[N ii]	6548	2p2 3P1–2p2 1D2	10.8	9.62 ± 1.05	8.77	7.77 ± 0.95	22.0	18.9 ± 2.1	72.3	68.1 ± 7.4	4.25	3.72 ± 0.40
H i	6563e	2p2Po–3d2D	290	286 ± 13	256	284 ± 12	281	287 ± 12	290	285 ± 14	299	282 ± 13
[N ii]	6583	2p2 3P2–2p2 1D2	30.8	27.3 ± 2.0	24.6	21.8 ± 1.8	63.8	54.7 ± 4.0	255	240 ± 18	11.4	9.93 ± 0.72
He i	6678k	2p1${P}_{1}^{{\rm{o}}}$–3d1D2	4.08	3.60 ± 0.49	4.26	3.75 ± 0.58	4.24	3.61 ± 0.49	⋯	⋯	4.15	3.60 ± 0.49
[S ii]	6716	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{5/2}^{{\rm{o}}}$	2.12	1.87 ± 0.34	1.00	0.87 ± 0.18	3.23	2.74 ± 0.50	12.1	11.3 ± 2.0	0.90	0.78 ± 0.14
[S ii]	6731	3p3 4${S}_{3/2}^{{\rm{o}}}$–3p3 2${D}_{3/2}^{{\rm{o}}}$	4.40	3.87 ± 0.52	1.45	1.27 ± 0.19	5.29	4.49 ± 0.60	16.8	15.8 ± 2.1	1.53	1.32 ± 0.17
[Ar v]	7005	3p2 3P2–3p2 1D2	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.44	0.38 ± :
He i	7065	2p3Po–3s3S	9.04	7.82 ± 1.17	10.2	8.81 ± 1.40	8.83	7.34 ± 1.10	⋯	⋯	6.70	5.68 ± 0.85
[Ar iii]	7136	3p4 3P2–3p4 1D2	12.8	11.1 ± 1.10	9.00	7.72 ± 0.90	19.8	16.4 ± 1.7	13.7	12.7 ± 1.6	8.10	6.84 ± 0.68
He i	7281	2p1${P}_{1}^{{\rm{o}}}$–3s1S0	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.57	0.47 ± :
[O ii]	7320	2p3 2${D}_{5/2}^{{\rm{o}}}$–2p3 2${P}_{3/2}^{{\rm{o}}}$	6.76	5.78 ± 0.74	8.39	7.13 ± 1.05	3.65	2.98 ± 0.38	6.84	6.31 ± 0.82	1.92	1.60 ± 0.20
[O ii]	7330	2p3 2${D}_{3/2}^{{\rm{o}}}$–2p3 2${P}_{3/2}^{{\rm{o}}}$	5.75	4.90 ± 0.73	8.16	6.94 ± 1.21	3.58	2.92 ± 0.44	11.2	10.3 ± 1.5	1.44	1.20 ± 0.17
[Ar iii]	7751	3p4 3P1–3p4 1D2	2.08	1.73 ± 0.43	1.18	0.98 ± 0.30	3.63	2.88 ± 0.72	6.07	5.53 ± 1.37	1.17	0.96 ± 0.23
H i	8750	3d2D–12f2Fo	1.57	1.25 ± 0.37	⋯	⋯	⋯	⋯	⋯	⋯	1.63	1.25 ± 0.37
H i	9015	3d2D–10f2Fo	4.54	3.59 ± 1.03	⋯	⋯	⋯	⋯	⋯	⋯	1.48	1.13 ± 0.32
[S iii]	9069	3p2 3P1–3p2 1D2	37.8	30.0 ± 2.4	⋯	⋯	⋯	⋯	⋯	⋯	13.0	9.86 ± 0.78
H i	9229	3d2D–9f2Fo	2.84	2.23 ± 0.78	⋯	⋯	⋯	⋯	⋯	⋯	2.15	1.64 ± 0.57
He ii	9345	5g2G–8h2Ho	6.81	5.34 ± 1.72	⋯	⋯	⋯	⋯	⋯	⋯	4.98	3.77 ± 1.21
[S iii]	9531l	3p2 3P1–3p2 1D2	55.4	43.3 ± 6.1	⋯	⋯	⋯	⋯	⋯	⋯	12.2	9.22 ± 1.20
c(Hβ)			0.172		0.177		0.220		0.087		0.196
log F(Hβ)m			−15.34		−15.07		−15.45		−15.29		−15.21

Notes. Fluxes and intensities are normalized such that Hβ = 100. A colon ":" indicates that the uncertainty in line intensity is large (>100%).

^aA blend of the O ii λ3726 (2p^{3 4}${S}_{3/2}^{{\rm{o}}}$–2p^{3 2}${D}_{3/2}^{{\rm{o}}}$) and λ3729 (2p^{3 4}${S}_{3/2}^{{\rm{o}}}$–2p^{3 2}${D}_{5/2}^{{\rm{o}}}$) doublet. ^bBlended with the He i λ3888 (2s³S–3p $3$ P^o) line. ^cBlended with H i λ3970 (2p²P^o–7d²D) and He i λ3965 (2s¹S–4p¹P^o). ^dBlended with [S ii] λ4076; probably also blended with the weak O ii M10 3p⁴${D}^{{\rm{o}}}$–3d⁴F and C iii M16 4f³${F}^{{\rm{o}}}$–5g³G lines. ^eCorrected for the flux from the blended He ii line. ^fBlended with the N iii λλ4634, 4642 lines; probably also blended with O ii M1 λλ4639, 4642. ^gBlended with the O ii M2 3s⁴P–3p⁴D^o lines. ^hCorrected for the flux from the blended He iλ4713 (2p³P^o–4s³S) line. ⁱBlended with [N i] λ5200 (2p^{3 4}${S}_{3/2}^{{\rm{o}}}$–2p^{3 2}${D}_{5/2}^{{\rm{o}}}$). ^jCorrected for the flux from the blended He ii λ6311 (5g²G–16h²H^o) line. ^kCorrected for the flux from the blended He ii λ6683 (5g²G–13h²H^o) line. ^lFlux underestimated due to the second-order contamination beyond 9200 Å. ^mIn units of erg cm⁻² s⁻¹, as measured in the extracted spectrum.

Download table as:  ASCIITypeset images: 1 2 3

We carried out plasma diagnostics of PNe using the ratios of the extinction-corrected fluxes of the collisionally excited lines (CELs; also often called forbidden lines) of heavy elements in Table 2. The [S ii] λ6716/λ6731 ratio is a common density diagnostic. Where available, the intensity ratio of the fainter [Ar iv] λλ4711, 4740 lines was also used to derive the electron density; here the flux of the blended He i λ4713 line was corrected for using the theoretical He i line ratios calculated by Porter et al. (2012). The electron temperature was derived from the [O iii] (λ4959 + λ5007)/λ4363 nebular-to-auroral line ratio. The [N ii] temperature was also determined whenever the [N ii] λ5755 line was detected. References for the atomic data utilized in plasma diagnostics as well as the ionic-abundance determinations (in Section 3.3) are summarized in Table 3, where the sources of the effective recombination coefficients for the optical recombination lines (ORLs) analyzed in the paper are also given. The results of plasma diagnostics are presented in Table 4.

Only in two PNe (PN12 and PN13) did we find that ${T}_{{\rm{e}}}$([N ii]) is reasonably lower than ${T}_{{\rm{e}}}$([O iii]). In the other targets (except PN16), ${T}_{{\rm{e}}}$([N ii]) > ${T}_{{\rm{e}}}$ ([O iii]). This might be due to high-density clumps in PNe (Morisset 2017): at high densities (${N}_{{\rm{e}}}\gtrsim {10}^{5}$ cm⁻³), emission of the [N ii] λλ6548, 6583 nebular lines can be suppressed due to collisional de-excitation (while emission of the λ5755 auroral line is unaffected), and consequently the [N ii] temperature is overestimated. Results of the plasma diagnostics based on the CELs are visually demonstrated in Figure 5, where the diagnostic curves of the different forbidden-line ratios are plotted for each PN. The fortran code equib, which was originally developed by Howarth & Adams (1981) to solve the statistical equilibrium equations of multi-level atoms to derive level populations and line emissivities under given nebular physical conditions, was used for the plasma diagnostics.

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Other temperature-sensitive ratios are [O ii] λ3727/(λ7320 + λ7330) and [S ii] (λ6716+λ6731)/λ4072, where λ3727 is a blend of the [O ii] λλ3726, 3729 doublet and λ4072 is a blend of [S ii] λλ4068, 4076. However, we did not detect these faint auroral lines all PNe to a desired S/N. For the four PNe for which the OSIRIS R1000R spectroscopy was obtained, we also derived the temperature using the [S iii] (λ9069+λ9531)/λ6312 line ratio. Since the [S iii] λ9531 nebular line was affected by the second-order contamination (see Section 2.3), we assumed a theoretical ratio λ9531/λ9069 = 2.48 (Mendoza & Zeippen 1982a; Mendoza 1983) to derive the intrinsic flux of this [S iii] line. Besides the traditional CEL diagnostics, we also determined the electron temperatures using the He i ORLs. These He i temperatures were generally lower than those derived from the CELs (Table 4), consistent with Paper II. The principles of PN plasma diagnostics based on the He i ORLs are described in Zhang et al. (2005).

Uncertainties in the electron temperatures and densities presented in Table 4 were estimated based on the measurement errors of emission line fluxes through propagation. Weaker lines generally have larger measurement errors as a result of introducing larger uncertainties in temperatures/densities. A typical example is [N ii] λ5755, the intensity of which is 10%–30% that of [O iii] λ4363 for most targets in our sample. Errors in the [N ii] temperatures are systematically higher that those in the [O iii] temperatures, which are thus best measured.

Using the relative intensities of emission lines in Table 2 and the electron temperatures and densities in Table 4, we calculated the ionic abundances of our PNe. The equib program was used to calculate the ionic abundances of He, C, N, O, Ne, S, Cl, and Ar relative to hydrogen, which are presented in Table 5. The deep GTC spectroscopy enabled the detection of several faint diagnostic lines, including the [O iii] λ4363, [N ii] λ5755, and [S iii] λ6312 auroral lines. It is thus possible to consider multiple ionization zones within a nebula, i.e., to assign different temperatures/densities when calculating the abundances of ionic species with different ionization stages (i.e., the ionization potentials). This is a more realistic paradigm of nebular analysis and reduces the uncertainties in the resultant abundances that may arise from the temperatures assumed.

Table 5.  Ionic Abundances

Ion	Line	Abundance (${{\rm{X}}}^{i+}$/H+)
	(Å)	PN8	PN9	PN10	PN11	PN12
He+	4471	0.105 ± 0.016	0.087 ± 0.014	0.090 ± 0.013	0.099 ± 0.016	0.109 ± 0.015
	5876	0.104 ± 0.012	0.111 ± 0.012	0.090 ± 0.010	0.095 ± 0.008	0.102 ± 0.011
	6678	0.113 ± 0.016	0.102 ± 0.014	0.082 ± 0.011	0.089 ± 0.012	0.100 ± 0.014
Adopteda		0.104 ± 0.012	0.111 ± 0.012	0.090 ± 0.010	0.095 ± 0.008	0.102 ± 0.011
He2+	5411	⋯	⋯	⋯	1.47(±0.40) × 10−2	⋯
	4686	1.02(±0.28) × 10−3	1.28(±0.41) × 10−3	⋯	1.10(±0.10) × 10−2	0.74(±0.15) × 10−3
C2+	4267	⋯	⋯	⋯	1.47(±0.26) × 10−3	8.17(±2.98) × 10−4
N+	5755	2.26(±0.50) × 10−5	1.53(±0.34) × 10−5	8.30(±1.83) × 10−6	6.09(±1.30) × 10−6	1.02(±0.20) × 10−5
	6548	6.89(±0.74) × 10−6	1.01(±0.12) × 10−5	4.12(±0.44) × 10−6	5.05(±0.54) × 10−6	1.32(±0.15) × 10−5
	6583	7.95(±0.70) × 10−6	1.08(±0.10) × 10−5	4.08(±0.36) × 10−6	5.29(±0.46) × 10−6	1.39(±0.12) × 10−5
Adoptedb		7.95(±0.70) × 10−6	1.08(±0.10) × 10−5	4.08(±0.36) × 10−6	5.29(±0.46) × 10−6	1.39(±0.12) × 10−5
O+	3727	2.15(±0.24) × 10−5	3.58(±0.32) × 10−5	1.47(±0.16) × 10−5	1.46(±0.18) × 10−5	5.82(±0.47) × 10−5
	7320	5.54(±0.77) × 10−5	5.01(±0.64) × 10−5	3.40(±0.44) × 10−5	1.30(±0.20) × 10−5	4.23(±0.54) × 10−5
	7330	5.69(±0.86) × 10−5	5.14(±0.75) × 10−5	3.24(±0.49) × 10−5	1.24(±0.20) × 10−5	5.67(±0.64) × 10−5
	7325	5.61(±0.86) × 10−5	5.07(±0.75) × 10−5	3.33(±0.49) × 10−5	1.27(±0.20) × 10−5	4.88(±0.64) × 10−5
Adoptedc		3.58(±0.42) × 10−5	3.82(±0.45) × 10−5	1.92(±0.25) × 10−5	1.45(±0.20) × 10−5	5.68(±0.68) × 10−5
O2+	4363	3.60(±0.43) × 10−4	4.09(±0.50) × 10−4	2.68(±0.32) × 10−4	3.30(±0.39) × 10−4	1.69(±0.20) × 10−4
	4959	3.53(±0.14) × 10−4	3.96(±0.15) × 10−4	2.61(±0.10) × 10−4	3.17(±0.12) × 10−4	1.65(±0.06) × 10−4
	5007	3.63(±0.10) × 10−4	4.13(±0.10) × 10−4	2.71(±0.06) × 10−4	3.34(±0.06) × 10−4	1.71(±0.05) × 10−4
Adoptedd		3.63(±0.10) × 10−4	4.13(±0.10) × 10−4	2.71(±0.06) × 10−4	3.34(±0.06) × 10−4	1.71(±0.05) × 10−4
Ne2+	3868	9.40(±0.63) × 10−5	8.60(±0.57) × 10−5	6.37(±0.43) × 10−5	7.34(±0.50) × 10−5	2.74(±0.20) × 10−5
	3967	9.25(±0.72) × 10−5	8.29(±0.64) × 10−5	6.07(±0.46) × 10−5	8.76(±0.68) × 10−5	4.12(±0.31) × 10−5
Adoptede		9.40(±0.63) × 10−5	8.60(±0.57) × 10−5	6.37(±0.43) × 10−5	7.34(±0.50) × 10−5	2.74(±0.20) × 10−5
S+	6716	9.00(±1.86) × 10−8	2.43(±0.50) × 10−7	7.10(±1.65) × 10−8	2.32(±0.47) × 10−7	1.39(±0.28) × 10−7
	6731	8.99(±1.69) × 10−8	2.43(±0.32) × 10−7	7.10(±1.11) × 10−8	2.33(±0.28) × 10−7	2.10(±0.21) × 10−7
Adopted		8.99(±1.69) × 10−8	2.43(±0.32) × 10−7	7.10(±1.12) × 10−8	2.33(±0.30) × 10−7	2.10(±0.22) × 10−7
S2+	6312	4.69(±1.17) × 10−6	2.39(±0.44) × 10−6	1.82(±0.50) × 10−6	2.03(±0.46) × 10−6	2.38(±0.38) × 10−6
	9069	⋯	3.65(±0.30) × 10−6	⋯	2.59(±0.21) × 10−6	⋯
	9531	⋯	5.28(±0.78) × 10−7	⋯	2.94(±0.41) × 10−7	⋯
Adoptedf		4.69(±1.17) × 10−6	3.57(±0.31) × 10−6	1.82(±0.50) × 10−6	2.54(±0.22) × 10−6	2.38(±0.38) × 10−6
Cl2+	5537	1.83(±0.46) × 10−7	⋯	⋯	4.57(±1.80) × 10−8	6.69(±2.72) × 10−8
Ar2+	7136	1.30(±0.12) × 10−6	1.11(±0.13) × 10−6	7.46(±0.77) × 10−7	1.01(±0.13) × 10−6	1.20(±0.11) × 10−6
	7751	8.32(±2.07) × 10−7	6.79(±2.01) × 10−7	5.40(±1.35) × 10−7	8.70(±2.16) × 10−7	8.35(±2.00) × 10−7
Adoptedg		1.30(±0.12) × 10−6	1.11(±0.13) × 10−6	7.46(±0.77) × 10−7	1.01(±0.13) × 10−6	1.20(±0.11) × 10−6
Ar3+	4711	2.35(±0.58) × 10−7	2.10(±0.63) × 10−7	1.81(±0.41) × 10−7	5.52(±0.83) × 10−7	⋯
	4740	4.90(±0.60) × 10−7	2.39(±0.44) × 10−7	1.81(±0.38) × 10−7	5.36(±0.88) × 10−7	⋯
Adopted		4.90(±0.60) × 10−7	2.39(±0.44) × 10−7	1.81(±0.38) × 10−7	5.36(±0.88) × 10−7	⋯
	(Å)	PN13	PN14	PN15	PN16	PN17
He+	4471	0.104 ± 0.015	0.086 ± 0.013	0.090 ± 0.013	0.095 ± 0.013	0.081 ± 0.012
	5876	0.089 ± 0.008	0.096 ± 0.010	0.099 ± 0.008	0.096 ± 0.012	0.088 ± 0.008
	6678	0.088 ± 0.013	0.092 ± 0.014	0.089 ± 0.013	⋯	0.088 ± 0.011
Adopteda		0.089 ± 0.008	0.096 ± 0.010	0.099 ± 0.008	0.096 ± 0.012	0.088 ± 0.008
He2+	5411	⋯	⋯	⋯	⋯	2.00(±0.36) × 10−2
	4686	⋯	⋯	1.73(±0.20) × 10−3	1.80(±0.22) × 10−2	2.21(±0.20) × 10−2
N+	5755	6.21(±:) × 10−6	8.82(±1.87) × 10−6	2.47(±0.45) × 10−5	⋯	1.65(±:) × 10−6
	6548	8.91(±0.97) × 10−6	3.61(±0.44) × 10−6	1.48(±0.16) × 10−5	3.81(±0.41) × 10−5	1.42(±0.15) × 10−6
	6583	8.61(±0.63) × 10−6	3.43(±0.28) × 10−6	1.45(±0.11) × 10−5	4.57(±0.40) × 10−5	1.29(±0.10) × 10−6
Adoptedb		8.61(±0.63) × 10−6	3.43(±0.28) × 10−6	1.45(±0.11) × 10−5	4.57(±0.40) × 10−5	1.29(±0.10) × 10−6
O+	3727	1.13(±0.13) × 10−4	9.96(±1.10) × 10−6	4.08(±0.45) × 10−5	3.57(±0.48) × 10−5	1.25(±0.11) × 10−5
	7320	9.55(±1.22) × 10−5	3.74(±0.55) × 10−5	2.94(±0.37) × 10−5	5.10(±0.66) × 10−5	1.20(±0.15) × 10−5
	7330	9.89(±1.27) × 10−5	4.43(±0.61) × 10−5	3.52(±0.43) × 10−5	1.02(±0.15) × 10−4	1.10(±0.16) × 10−5
	7325	9.70(±1.25) × 10−5	4.05(±0.60) × 10−5	3.20(±0.43) × 10−5	7.39(±1.05) × 10−5	1.16(±0.17) × 10−5
Adoptedc		1.10(±0.14) × 10−4	2.03(±0.33) × 10−5	4.01(±0.45) × 10−5	4.25(±0.76) × 10−5	1.24(±0.12) × 10−5
O2+	4363	4.31(±0.52) × 10−4	1.76(±0.20) × 10−4	6.07(±0.72) × 10−4	5.47(±0.86) × 10−4	2.84(±0.30) × 10−4
	4959	4.23(±0.16) × 10−4	1.70(±0.07) × 10−4	6.00(±0.23) × 10−4	5.32(±0.30) × 10−4	2.73(±0.10) × 10−4
	5007	4.40(±0.08) × 10−4	1.79(±0.04) × 10−4	6.15(±0.11) × 10−4	5.52(±0.13) × 10−4	2.88(±0.05) × 10−4
Adoptedd		4.40(±0.10) × 10−4	1.79(±0.05) × 10−4	6.15(±0.12) × 10−4	5.52(±0.15) × 10−4	2.88(±0.05) × 10−4
Ne2+	3868	7.25(±0.47) × 10−5	3.15(±0.20) × 10−5	1.41(±0.10) × 10−4	1.22(±0.13) × 10−4	5.29(±0.40) × 10−5
	3967	7.70(±0.60) × 10−5	3.34(±0.27) × 10−5	1.58(±0.10) × 10−4	1.48(±0.15) × 10−4	6.90(±0.56) × 10−5
Adoptede		7.25(±0.47) × 10−5	3.15(±0.20) × 10−5	1.41(±0.10) × 10−4	1.22(±0.13) × 10−4	5.29(±0.40) × 10−5
S+	6716	7.26(±1.32) × 10−7	5.75(±1.19) × 10−8	3.52(±0.64) × 10−7	8.16(±1.95) × 10−7	5.78(±1.03) × 10−8
	6731	7.26(±1.10) × 10−7	5.75(±0.86) × 10−8	3.52(±0.47) × 10−7	8.16(±1.62) × 10−7	5.78(±0.85) × 10−8
Adopted		7.26(±1.20) × 10−7	5.75(±0.90) × 10−8	3.52(±0.56) × 10−7	8.16(±1.95) × 10−7	5.78(±0.94) × 10−8

Ion	Line	Abundance (${{\rm{X}}}^{i+}$/H+)
	(Å)	PN13	PN14	PN15	PN16	PN17
S2+	6312	6.05(±1.32) × 10−6	1.98(±0.54) × 10−6	7.89(±1.85) × 10−6	⋯	1.07(±0.23) × 10−6
	9069	7.40(±0.60) × 10−6	⋯	⋯	⋯	1.75(±0.16) × 10−6
	9531	1.94(±0.27) × 10−6	⋯	⋯	⋯	2.96(±0.38) × 10−7
Adoptedf		7.32(±1.10) × 10−6	1.98(±0.54) × 10−6	7.89(±1.85) × 10−6	⋯	1.70(±1.25) × 10−6
Cl2+	5517	⋯	⋯	⋯	⋯	4.06(±4.05) × 10−8
	5537	⋯	⋯	⋯	⋯	4.06(±1.92) × 10−8
Ar2+	7136	1.28(±0.15) × 10−6	5.71(±0.67) × 10−7	1.90(±0.20) × 10−6	1.11(±0.16) × 10−6	4.16(±0.42) × 10−7
	7751	8.34(±2.07) × 10−7	3.03(±0.93) × 10−7	1.39(±0.35) × 10−6	2.03(±0.64) × 10−6	2.43(±0.58) × 10−7
Adoptedg		1.28(±0.15) × 10−6	5.71(±0.67) × 10−7	1.90(±0.20) × 10−6	1.11(±0.16) × 10−6	4.16(±0.42) × 10−7
Ar3+	4711	⋯	⋯	2.75(±0.43) × 10−7	⋯	4.94(±0.88) × 10−7
	4740	⋯	⋯	3.35(±0.54) × 10−7	⋯	5.35(±1.01) × 10−7
Adopted		⋯	⋯	3.35(±0.54) × 10−7	⋯	5.35(±1.01) × 10−7
Ar4+	7005	⋯	⋯	⋯	⋯	4.59(±:) × 10−8

Notes.

^aThe He⁺/H⁺ abundance ratio derived from the He i λ5876 line is adopted. ^bThe ${{\rm{N}}}^{+}$/H⁺ abundance ratio derived from [N ii] λ6583 is adopted. ^cA weighted average value of the ${{\rm{O}}}^{+}$/H⁺ ratios derived from the [O ii] λ3727 nebular and λ7325 (=λ7320+λ7330) auroral lines are adopted, with the assigned weights proportional to the intensities of these two lines. See the text for details. ^dThe ${{\rm{O}}}^{2+}$/H⁺ ratio derived from [O iii] λ5007 is adopted. ^eThe Ne²⁺/H⁺ ratio derived from [Ne iii] λ3868 is adopted. ^fFor PN9, PN11, PN13, and PN17, where both λ6312 and λ9069 lines are observed, a weighted average of the ${{\rm{S}}}^{2+}$/H⁺ ratios derived from these two [S iii] lines is adopted, with the weights proportional to the dereddened line fluxes. ^gThe Ar²⁺/H⁺ ratio derived from [Ar iii] λ7136 is adopted, because measurements of this line are much better than that of [Ar iii] λ7751 lying at the red end of R1000B grism.

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The [O iii] temperature was used to derive ${{\rm{O}}}^{2+}$/H⁺, Ne²⁺/H⁺, Ar²⁺/H⁺, Ar³⁺/H⁺, and Cl²⁺/H⁺. We adopted the [N ii] temperature to calculate ${{\rm{N}}}^{+}$/H⁺ and ${{\rm{O}}}^{+}$/H⁺ for PN12 and PN13, where we found that the [N ii] temperature is lower than that derived from the [O iii] line ratio. For the other PNe, we considered the recipe of Dufour et al. (2015, also Kwitter & Henry 2001) for the electron temperature in the low-ionization region: if He ii λ4686 was detected, we adopted an [N ii] temperature of 10,300 K derived by Kaler (1986); otherwise, we assumed a temperature of 10,000 K.

The [S iii] temperature derived for the four PNe (PN9, PN11, PN13, and PN17) is in general meaningfully different from the [O iii] temperature and thus was used to calculate the S²⁺/H⁺ ratio. For the other PNe, we adopted the electron temperature that was used to calculate the ${{\rm{N}}}^{+}$/H⁺ ratio to derive ${{\rm{S}}}^{2+}$/H⁺. In the calculations of ${{\rm{S}}}^{+}$/H⁺, we adopted the [S ii] temperature (9200 K) for PN12; for the other targets, we adopted the temperature that was used to calculate the ${{\rm{N}}}^{+}$/H⁺ ratio. Although temperatures (or the lower limits) were also derived from the [O ii] λ3727/(λ7320+λ7330) line ratio, they were much too different from the [S iii] temperatures (Table 4), given that the ionization potential of O⁺ (35.12 eV) is close to that of ${{\rm{S}}}^{2+}$ (34.83 eV); the differences between the [O ii] temperatures and those derived from the [O iii] lines are also questionable. The only exception is PN17, the [O ii] temperature of which seems reasonable compared to those derived from the [O iii] and [S iii] line ratios. We adopted the electron density derived from the [S ii] λ6716/λ6731 ratio for the ionic-abundance calculations of the low-ionization species. Where available, the density yielded by [Ar iv] λ4711/λ4740 was assumed for the high-ionization species, otherwise the [S ii] density was used. For PN17, the density derived from [Cl iii] λ5517/λ5537 was used to derive Cl²⁺/H⁺.

Care must be taken when deriving the ${{\rm{O}}}^{+}$/H⁺ ratio, although ${{\rm{O}}}^{+}$ is not the dominant ionization stage of oxygen in PNe. We noticed that the [O ii] λ3727 (a blend of λλ3726, 3729) nebular line yielded a very different ${{\rm{O}}}^{+}$/H⁺ ratio from that derived from the [O ii] λλ7320,7330 auroral lines, if the same electron density was assumed. Such difference in ${{\rm{O}}}^{+}$/H⁺ even reached one order of magnitude for some PNe in our sample. This might be because λ3727 and λλ7320, 7330 actually come from regions with very different densities. Besides its dependence on temperature, the [O ii] λ3727/(λ7320 +λ7330) line ratio also has a non-negligible dependence on the density, as can be seen in Figure 5. If these two [O ii] lines come from different nebular regions, the diagnosed temperature can be unrealistically high.

If we adopt the [S ii] density for [O ii] λ3727 and assumed a higher density (e.g., 20,000 cm⁻³; Table 4) for λ7325 (=λ7320 + λ7330), the two ${{\rm{O}}}^{+}$/H⁺ ratios derived can be brought to the same level (Table 5). Thus, the electron densities (or the lower limit; see Table 4) yielded by the [O ii] diagnostic ratio was assumed for the λ7325 line. We then derived a weighted average from the two ${{\rm{O}}}^{+}$/H⁺ ratios, with the weights proportional to the intensities of the λ3727 and λ7325 lines. The averaged ${{\rm{O}}}^{+}$/H⁺ ratio was adopted and then used for the determination of elemental abundances.

Ne²⁺/H⁺ derived from [Ne iii] λ3868 was adopted; the other [Ne iii] nebular line, λ3967, is blended with H i λ3970. For the four PNe (PN9, PN11, PN13, and PN17) where both λ6312 and λ9069 of [S iii] were detected, a line intensity-weighted average of the ${{\rm{S}}}^{2+}$/H⁺ ratios derived from the two [S iii] lines was adopted. For the other PNe in our sample, ${{\rm{S}}}^{2+}$/H⁺ derived from λ6312 was adopted. The total intensity of the [Ar iv] λλ4711, 4740 doublet was used to derive Ar³⁺/H⁺. The flux of [Ar iv] λ4711 was corrected for the blended He i λ4713 line. The effective recombination coefficients of the He i lines calculated by Porter et al. (2012) were used to derive the He⁺/H⁺ ratios. The He²⁺/H⁺ ratio was derived from He ii λ4686 using the hydrogenic effective recombination coefficients from Storey & Hummer (1995). We also detected C ii λ4267 (M6 3d ²D–4f ²F^o) in the spectra of PN11 and PN12, and the ${{\rm{C}}}^{2+}$/H⁺ ratio was derived using this line (Table 5). The Case B effective recombination coefficients of the C ii lines were adopted from Davey et al. (2000), and an electron temperature of 10,000 K and a density of 10⁴ cm⁻³ were assumed.

The uncertainties in ionic abundances (in the brackets in Table 5) were estimated from the measurement errors in the line fluxes. Extra errors in abundances could be introduced by the electron temperatures and densities adopted in the abundance determinations, although we have considered multiple ionization zones by deriving the abundances of low- and high-ionization species using different temperatures/densities. However, these errors in general have a minor contribution to the total uncertainty budget and were not included in the final uncertainties of the ionic abundances. In Paper II, we have estimated that errors in the [O iii] temperature typically introduce ∼10% uncertainties in the resultant ionic abundances, while in this work such errors are probably even lower. It is evident that the ORLs of heavy elements (C ii, O ii, N ii and Ne ii) observed in PNe could be emitted by nebular regions as cold as ≲1000 K (e.g., Liu 2012; Fang & Liu 2013; McNabb et al. 2013). For an ORL (like C ii λ4267) excited by radiative recombination, its emissivity (i.e., effective recombination coefficient) generally decreases with the electron temperature (e.g., Osterbrock & Ferland 2006; Fang & Liu 2013). Thus, the ${{\rm{C}}}^{2+}$/H⁺ derived here could be overestimated due to the temperature (10,000 K) assumed. According to the calculations of Davey et al. (2000), the effective recombination coefficient of the C ii λ4267 line decreases by a factor of 9.4 as the temperature increases from 1000 K to 10,000 K.

The total elemental abundances (relative to hydrogen) were derived based on the ionic abundances presented in Table 5. The helium abundance is a sum of the ionic ratios, He/H = He⁺/H⁺ + He²⁺/H⁺. For heavy elements, the total abundances were derived mostly using the ionization correction factors (ICFs) of Kingsburgh & Barlow (1994). Elemental abundances are presented in Table 6, and the ICFs used to correct for the unseen ions are presented in Table 7.

In the cases where both ${{\rm{S}}}^{+}$/H⁺ and ${{\rm{S}}}^{2+}$/H⁺ were derived, S/H = ICF(S) × (S⁺/H⁺ + ${{\rm{S}}}^{2+}$/H⁺) was used, where ICF(S) was adopted from Kingsburgh & Barlow (1994, Equation A36 therein). For PN16, where only ${{\rm{S}}}^{+}$/H⁺ was obtainable, the empirical fitting formula of Kingsburgh & Barlow (1994, Equation A38 therein) was used to derive ${{\rm{S}}}^{2+}$/H⁺. If both Ar²⁺ and Ar³⁺ were observed, we used Ar/H = ICF(Ar) × (Ar²⁺/H⁺ + Ar³⁺/H⁺), where ICF(Ar) is from Kingsburgh & Barlow (1994, Equation A30 therein). In typical physical conditions of PNe, the concentration of argon in Ar⁴⁺ is supposed to be negligible compared to that in Ar²⁺ and Ar³⁺. If only Ar²⁺ was observed (in PN12, PN13, PN14, and PN16 in our sample), Equation A32 in Kingsburgh & Barlow (1994) was used to derive ICF(Ar). Only Cl²⁺ was observed in our spectra (of PN8, PN11, PN12, and PN17), and we assumed Cl/Cl²⁺ ≈ S/S²⁺ as in Wang & Liu (2007), according to the similarity in ionization potentials. C/H was derived for two PNe in our sample assuming ICF(C) = O/O²⁺ (Table 6). Delgado-Inglada et al. (2014) developed a new set of formulae for the ICFs of PNe by computing a large grid of photoionization models. These ICFs have validity application ranges defined by the ionic fractions of helium, He²⁺/(He⁺ + He²⁺), and oxygen, ${{\rm{O}}}^{2+}$/(O⁺ + O²⁺). We expect that these ICFs are adequate estimates of elemental abundances in PNe. However, not all of our targets have their helium or oxygen ionic fractions located within these validity ranges. Besides, the new ICFs do not differ much from the classical methods of Kingsburgh & Barlow (1994) for most of the elements (García-Rojas et al. 2016). In particular, adopting the new ICFs of Delgado-Inglada et al. (2014) did not eliminate the "sulfur anomaly" in PNe, which is discussed in Section 4.1.

The uncertainties in the brackets following the elemental abundances in Table 6 were estimated from the errors in ionic abundances (Table 5) through propagation. The possible errors brought about by ionization corrections were not considered, although they could be significant for some heavy elements. The dominant ionization stage of helium in PNe is He⁺, and thus the error in He/H mainly comes from He⁺/H⁺. The [O ii] and [O iii] nebular lines are among the best observed in the optical spectrum of a PN. Although determination of ${{\rm{O}}}^{+}$/H⁺ is usually less accurate than ${{\rm{O}}}^{2+}$/H⁺ due to the detection sensitivity of instruments in the optical wavelength region, the concentration of oxygen in ${{\rm{O}}}^{2+}$ is much higher than in ${{\rm{O}}}^{+}$. Besides, ICF(O) is always close to unity (Table 7). He/H and O/H thus are the most accurate among all elements analyzed in this paper. N/H and Ne/H were derived based on the ionic and elemental abundances of oxygen and are expected to be reliable. Determinations of S/H in this work were improved for some PNe by using the strong [S iii] λ9069 nebular line and adopting the [S iii] temperatures. Errors in S/H and Ar/H introduced by the ICFs are non-negligible but difficult to quantify. Thus, they were not considered in the error estimation. The uncertainty in Cl/H is large because only Cl²⁺ was observed. The uncertainty in carbon is also considerable since only the weak C ii λ4267 line was observed in our GTC spectrum.

We detected the C iv λ5805 (a blend of the λλ5801.33, 5811.98 doublet²⁰ ) broad emission in the spectra of PN9 and PN15 (Figure 6). Including target PN2 in Paper II, we have now observed this C iv line in three PNe in our GTC sample. In PN9, we also detected C iii λ4649 (a blend of the λλ4647.42, 4650.25, 4651.47 of M1 2s3s³S–2s3p³P^o multiplet), the observed flux of which is 2.2 × 10⁻¹⁷ erg cm⁻² s⁻¹ and line width is ∼15 Å. This C iii line is probably also blended with the faint O ii λλ4649.13, 4650.84 ORLs of the M1 2p² 3s⁴P–2p² 3p⁴D^o multiplet, because we found a nearby narrow emission feature that could be due to the λ4661.63 of the same multiplet of O ii. Line fluxes and widths of C iv λ5805 of the three PNe are presented in Table 8.

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The broad C iii and C iv lines observed in PN2, PN9, and PN15 are from their central stars, which are probably of Wolf-Rayet ([WR]) type. The intensity ratio and FWHM of C iii λ4649 and C iv λ5805 indicate that PN9 has a [WC4] central star, according to the classification of Acker & Neiner (2003, also Crowther et al. 1998). The estimated stellar temperature of PN9 seems to be slightly higher than the temperature range (∼55,000–91,000 K; Acker & Neiner 2003) covered by the [WC4]-type stars. C iii λ4649 was not observed in the other two PNe. Previous GTC spectroscopy have found [WC4]-type central stars in two outer-disk PNe (Balick et al. 2013; PN ID 174 and 2496 in Merrett et al. 2006).

How these [WC] central stars formed is not well-understood, although a significant fraction of Galactic PNe have been observed to harbor such type of stars. The five M31 PNe with unambiguous detection of broad [WC] features are all bright in [O iii], <0.9 mag from the PNLF bright cutoff, indicating that He-burning cores might produce visible PNe. This may help to constrain the post-AGB evolutionary models of He burners. As suggested by Balick et al. (2013), an AGB final thermal pulse, or a late thermal pulse early in post-AGB, might be the channel to these [WC] central stars.

PN14 in our sample was also observed at the GTC by Corradi et al. (2015; PN ID M2507), who also used the OSIRIS R1000B grism but with a slit width of 08. Our observing conditions are better (seeing ∼08 and clear nights). The logarithmic extinction parameters c(Hβ) derived from the two observations are also quite similar. Although the extinction laws adopted are different (Cardelli et al. 1989 in this work, and Savage & Mathis 1979 in Corradi et al. 2015), it has been proven that in the wavelength range covered by the OSIRIS R1000B grism, line fluxes corrected using different extinction laws differ very little. Our observed Hβ flux of PN14 is only 4.6% lower than that given by Corradi et al. (2015) by 4.6%. The dereddened fluxes of the [O ii] λ3727 and [O iii] λ5007 nebular lines of PN14 differ from the observations of Corradi et al. (2015) by ∼1% and 2%, respectively. However, the dereddened fluxes of the [O iii] λ4363 differ by ∼10%. Our O/H ratio (2.00(±0.23) × 10⁻⁴) of PN14 agrees with that of Corradi et al. (2015, 1.73(±0.44) × 10⁻⁴) within the errors.

The abundances of α-elements (O, Ne, S, Ar, etc.) of a PN reflect the metallicity (Z) of the interstellar medium (ISM) from which the progenitor star of the PN formed. The He/H and N/O ratios are also indicative of progenitor masses: Type I PNe tend to have higher abundance ratios, while Type II PNe generally exhibit low N/O and less massive progenitors (Peimbert 1978; Maciel 1992; Kingsburgh & Barlow 1994). The α-elements of PNe also help to constrain the theory of stellar models and probe into the evolution of low- to intermediate-mass stars and consequently the chemical evolution of galaxies (e.g., Kwitter & Henry 2001; Milingo et al. 2002a, 2002b; Kwitter et al. 2003; Henry et al. 2004). Although the exact mechanism(s) is (are) still unclear, previous studies of Galactic and Magellanic Cloud PNe have established that PN morphology is a useful indicator of stellar populations (Peimbert & Torres-Peimbert 1983; Manchado et al. 2000; Shaw et al. 2001; Stanghellini et al. 2002a, 2002b, 2003, 2006). At the distance of M31, all PNe are spatially unresolved, and their central stars cannot be directly observed. The stellar population of PNe can be inferred from the elemental abundances of the nebulae.

Following the discussion in Paper II, in this section we made a correlation study of the abundances of He, N, O, and α-elements for our extended halo sample (see Figures 7–11). The M31 outer-disk PNe observed by Kwitter et al. (2012), Balick et al. (2013), and Corradi et al. (2015) ²¹ using large telescopes (Gemini-North and the GTC) were included and henceforth mentioned as the disk sample (or the disk PNe) in this paper. Also considered in the study were previous observations of PNe and H ii regions in M31, including the bulge and disk PNe from Jacoby & Ciardullo (1999), and the nine H ii regions from Zurita & Bresolin (2012) where the temperature-diagnostic auroral lines were observed. The solar abundances from Asplund et al. (2009) and the abundances of the Orion Nebula from Esteban et al. (2004) were used as benchmarks.

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Figure 7 shows the N/O abundance ratio versus He/H (left) and O/H (right) in logarithm. Our sample (the color-filled circles in Figure 7), including the PNe studied in Papers I and II, all have low N/O (<0.5) except PN16, a PN associated with M32 and the N/O (∼1.07 ± 0.24) of which is higher than the other targets and hints at the possibility of a Type I nature. Its He/H (=0.114), however, is normal compared to others. Our targets and the disk sample show no obvious trend in N/O versus He/H or O/H and are clearly separated from the Galactic Type I objects of Milingo et al. (2010), whose N/O seems to be correlated with He/H and anticorrelated with O/H. Among the M31 disk sample, there are two outliers and one of them has N/O close to 1.0. Most of the M31 PNe have higher N/O ratios than H ii regions (including the Orion Nebula), but there are three PNe in our sample with very low N/O. Within our sample, the PNe associated with the Northern Spur, the Giant Stream, and the outer halo generally cannot be distinguished from each other in abundance ratios, although the halo target PN13 has the lowest N/O ratio.

All M31 PNe show positive correlation between neon and oxygen (Figure 8), consistent with the previous observations of PNe in the Galaxy, the Large and Small Magellanic Clouds, and M31 (Henry 1989). One outlier is from Jacoby & Ciardullo (1999). This neon–oxygen positive correlation was defined by the samples of H ii regions and metal-poor blue compact galaxies analyzed by Izotov & Thuan (1999), Izotov et al. (2012), and Kennicutt et al. (2003). We noticed that 12+log(Ne/H) of the Sun (7.93 ± 0.10, Asplund et al. 2009) is slightly lower than, although still agrees within the errors with, what is expected from the neon–oxygen correlation, indicating that the current solar neon might be underestimated. This problem was investigated through a comparison study of PNe and H ii regions by Wang & Liu (2008).

The argon in our targets is generally correlated with oxygen, although the scatter is noticeable (Figure 9). Our sample also seems to have slightly lower argon than what is expected from the argon–oxygen correlation defined by the H ii regions and metal-poor blue compact galaxies, but this deficiency is more obvious in the outer-disk sample, especially in the PNe with lower oxygen [12+log(O/H) < 8.45]. As discussed in Paper II, sulfur abundances of M31 PNe are all lower than what is expected from the sulfur–oxygen correlation. Although the GTC spectra of four PNe (PN9, PN11, PN13m and PN17) in our sample have covered the [S iii] λλ9069, 9531 lines, their 12+log(S/H) are still underabundant by ∼0.24–0.39 dex. This deficiency in sulfur, known as the "sulfur anomaly", was previously noticed in Galactic PNe (Henry et al. 2004; Milingo et al. 2010). So far, the most plausible explanation seems to be the inadequacy in ICF used to correct for the sulfur ions (e.g., ${{\rm{S}}}^{3+}$ and higher ionization stages) unobserved in the optical but detectable in the IR, although taking into account the IR observations of ${{\rm{S}}}^{3+}$ has alleviated, but could not eliminate, this deficiency (Henry et al. 2012). Theoretical studies show that sulfur is unlikely destroyed by the nucleosynthetic processes in low- to intermediate-mass stars (Shingles & Karakas 2013). On the other hand, the M31 H ii regions of Zurita & Bresolin (2012) generally agree with the sulfur–oxygen correlation (Figure 10).

Although strictly speaking chlorine cannot be classified as an α-element because its two stable isotopes, ³⁵Cl and ³⁷Cl, are not formed through α-processes but produced during both hydrostatic and explosive oxygen burning (Woosley & Weaver 1995), it is a secondary product during oxygen burning and created from the isotopes of sulfur and argon (Clayton 2003). Cl/H was derived for five objects in our GTC sample using the [Cl iii] λλ5517, 5537 doublet (Table 6). It has also been derived for three outer-disk PNe. Together with the Galactic samples from Henry et al. (2004, 2010) and Milingo et al. (2010), chlorine exhibits a loose correlation with oxygen (Figure 11). The chlorine–oxygen relation among the M31 PNe alone has large scatter, probably much affected by large uncer-tainties, given the weakness of the [Cl iii] lines. Using the Galactic H ii regions from Esteban et al. (2015, including the Orion Nebula) as a baseline for correlation, we found that not all M31 PNe are located along this relation within the errors.

In this section, we study the stellar populations of our sample by constraining the central star parameters, which, again, were estimated from the observed nebular spectra. In a PN spectrum, the intensities of nebular emission lines, such as [O iii] λ5007 and He ii λ4686, relative to the Hβ, are to some extent representative of the central star temperature (${T}_{\mathrm{eff}}$). For an optically thick PN, at a given ${T}_{\mathrm{eff}}$, the central star luminosity (L_*) can be determined from the nebular Hβ luminosity (e.g., Osterbrock & Ferland 2006). Based on the photoionization models of a large sample of optically thick PNe in the Large and Small Magellanic Clouds (hereafter LMC and SMC), Dopita & Meatheringham (1991, also Meatheringham & Dopita 1991) derived empirical relationships between ${T}_{\mathrm{eff}}$ and L_* and the excitation class (EC) in the form of polynomials (Equations (3.1) and (3.2) in Dopita & Meatheringham 1991). These empirical relations work equivalently to the transformation between the observed Hertzsprung–Russell (H–R) diagram, $\mathrm{log}L({\rm{H}}\beta )$ versus EC, and the true H–R diagram, $\mathrm{log}({L}_{* }/{L}_{\odot })$ versus $\mathrm{log}{T}_{\mathrm{eff}}$. The EC parameter was defined in terms of the λ5007/Hβ and λ4686/Hβ nebular line ratios. However, we were aware that these relationships were based on the models of the optically thick PNe in the Clouds, which are both metal poor (Z = 0.008 in the LMC and 0.004 in the SMC), while previous and our current spectroscopic observations have demonstrated that the bright PNe in the outer disk and the halo of M31 are all metal rich (Kwitter et al. 2012; Balick et al. 2013; Fang et al. 2013, 2015; Corradi et al. 2015). The relationships given by Dopita & Meatheringham (1991) could be metallicity dependent (Dopita et al. 1992), although the [O iii]/Hβ line ratio is less dependent than other lines. Thus, whether they are applicable to the PNe in M31 might be questionable.

In order to assess the applicability of the relationship of Dopita & Meatheringham (1991), we derived the ${T}_{\mathrm{eff}}$ for the M31 disk PNe studied by Kwitter et al. (2012) and Balick et al. (2013) using the relation and compared them with the cloudy model results presented in these two papers. The differences in $\mathrm{log}{T}_{\mathrm{eff}}$ are mostly less than 0.06 dex. We made the same comparison for the L_* of the same disk sample and found that the differences in $\mathrm{log}({L}_{* }/{L}_{\odot })$ are mostly less than 0.05 dex. The disk sample contains the brightest PNe in M31 with ${m}_{\lambda 5007}\sim 20.4\mbox{--}20.9$. This comparison study between the two sets of ${T}_{\mathrm{eff}}$ and L_* thus confirms our anticipation that the brightest PNe in M31, those within two magnitudes from the bright cutoff of the PNLF, should not be quite evolved and probably still optically thick (A. A. Zijlstra 2017, private communication). We noticed that the empirically derived L_* of three less bright PNe (with ${m}_{\lambda 5007}=20.72$, 20.88, and 20.89) are lower than their corresponding cloudy models by ∼0.2 dex. This difference might be due to a possibility that the empirical relationship of Dopita & Meatheringham (1991) underestimates the stellar luminosities of fainter PNe, which might no longer be optically thick. We made a similar comparison study of the stellar parameters for the M31 bulge and disk PNe of Jacoby & Ciardullo (1999), which are systematically fainter (${m}_{\lambda 5007}\sim 20.73\mbox{--}23.16$), and found that the empirically derived $\mathrm{log}({L}_{* }/{L}_{\odot })$ are lower than the photoionization models by 0.2 dex in average (although the scatter in the sample of Jacoby & Ciardullo 1999 is largely due to the faintness of the targets). The largest difference in both $\mathrm{log}{T}_{\mathrm{eff}}$ and $\mathrm{log}({L}_{* }/{L}_{\odot })$ is found in the brightest PN of Balick et al. (2013; PN ID M2496, ${m}_{\lambda 5007}=20.42$).

The EC of our target PNe is mostly between ∼3 and 7.6. We derived their central star temperatures and luminosities using the relationships of Dopita & Meatheringham (1991). Despite the applicability of these relationships assessed above, the stellar luminosity thus derived might still be underestimated for (1) bright, young (and thus probably dusty) PNe due to the absorption of a large fraction of stellar flux by dust and (2) the PNe that are optically thin to the ionizing radiation of the central stars. Since the extinction of our targets are low (Section 3.1), the first possibility could be discounted. The relatively faint PNe in M31 might not be optically thick, and their stellar luminosities derived using the empirical relationship might be underestimated. According to the discussion above, we revised up the $\mathrm{log}({L}_{* }/{L}_{\odot })$ of the fainter targets (${m}_{\lambda 5007}\geqslant 21$) in our sample by 0.2 dex to compensate for the possible underestimation. The stellar temperatures and luminosities of our PNe are presented in Table 9 (the second and third columns).

Table 9.  Estimated Properties of PN Central Stars and the Progenitors^a

		Z = 0.016 b			Z = 0.01 c			Z = 0.02 c
ID	$\mathrm{log}{T}_{\mathrm{eff}}$	$\mathrm{log}({L}_{* }/{L}_{\odot })$	${M}_{\mathrm{fin}}$	${M}_{\mathrm{ini}}$	${t}_{\mathrm{ms}}$	${M}_{\mathrm{fin}}$	${M}_{\mathrm{ini}}$	${t}_{\mathrm{ms}}$	${M}_{\mathrm{fin}}$	${M}_{\mathrm{ini}}$	${t}_{\mathrm{ms}}$
PN1	4.971	3.657	0.597	1.82	1.43	0.563	1.53	1.77	0.565	1.55	2.32
			⋯	1.75	1.61	⋯	1.40	2.31	⋯	1.42	3.05
PN2	5.077	3.464	0.594	1.80	1.49	0.556	1.47	1.99	0.554	1.45	2.82
			⋯	1.72	1.69	⋯	1.32	2.71	⋯	1.30	3.99
PN3	5.126	3.696	0.618	2.00	1.10	0.583	1.70	1.31	0.579	1.67	1.85
			⋯	1.97	1.15	⋯	1.60	1.55	⋯	1.56	2.25
PN4	4.932	3.525	0.576	1.64	1.94	0.550	1.42	2.20	0.545	1.38	3.35
			⋯	1.53	2.40	⋯	1.26	3.13	⋯	1.21	5.08
PN5	5.052	3.702	0.606	1.90	1.27	0.576	1.64	1.44	0.577	1.65	1.91
			⋯	1.84	1.38	⋯	1.53	1.76	⋯	1.54	2.34
PN6	4.989	3.448	0.597	1.82	1.43	0.563	1.53	1.77	0.565	1.55	2.32
			⋯	1.75	1.61	⋯	1.40	2.31	⋯	1.42	3.05
PN7	4.967	3.445	0.570	1.59	2.14	0.545	1.38	2.41	0.539	1.32	3.78
			⋯	1.47	2.73	⋯	1.21	3.55	⋯	1.15	6.04
PN8	5.082	3.310	0.585	1.72	1.69	0.559	1.50	1.89	0.559	1.50	2.57
			⋯	1.62	2.00	⋯	1.35	2.53	⋯	1.35	3.52
PN9	5.073	3.501	0.589	1.76	1.60	0.558	1.49	1.92	0.558	1.49	2.62
			⋯	1.67	1.85	⋯	1.34	2.59	⋯	1.34	3.61
PN10	4.980	3.687	0.602	1.87	1.34	0.567	1.56	1.66	0.570	1.59	2.13
			⋯	1.80	1.47	⋯	1.44	2.12	⋯	1.47	2.72
PN11	5.137	3.662	0.611	1.94	1.20	0.583	1.70	1.31	0.578	1.66	1.88
			⋯	1.90	1.28	⋯	1.60	1.55	⋯	1.55	2.29
PN12	4.761	3.639	0.584	1.71	1.72	0.554	1.45	2.06	0.553	1.44	2.87
			⋯	1.61	2.04	⋯	1.30	2.84	⋯	1.29	4.10
PN13	4.906	3.423	0.567	1.57	2.24	0.536	1.30	2.86	0.530	1.25	4.58
			⋯	1.44	2.92	⋯	1.11	4.52	⋯	1.05	7.96
PN14	4.825	3.643	0.588	1.75	1.62	0.556	1.47	1.98	0.555	1.46	2.76
			⋯	1.66	1.89	⋯	1.32	2.71	⋯	1.31	3.89
PN15	5.067	3.380	0.580	1.68	1.83	0.551	1.43	2.16	0.546	1.38	3.28
			⋯	1.57	2.21	⋯	1.27	3.05	⋯	1.22	4.94
PN16	5.240	3.331	0.633	2.13	0.93	0.583	1.70	1.31	0.579	1.67	1.85
			⋯	2.12	0.94	⋯	1.60	1.54	⋯	1.56	2.25
PN17	5.166	3.464	0.610	1.93	1.21	0.574	1.62	1.49	0.576	1.64	1.94
			⋯	1.88	1.30	⋯	1.51	1.84	⋯	1.53	2.39

Notes. All masses are in units of solar mass (M_☉) and ages are in gigayears (Gyr).

^aFor each PN, ${M}_{\mathrm{ini}}$ values in the first and second lines were derived using Equations (1) and (2) of the linear initial–final mass relations of Catalán et al. (2008), respectively. ${t}_{\mathrm{ms}}$ was derived based on the model grids computed by Schaller et al. (1992). ^b ${M}_{\mathrm{fin}}$ were interpolated from the post-AGB model tracks of Vassiliadis & Wood (1994). ^c ${M}_{\mathrm{fin}}$ were interpolated from the post-AGB model tracks of Miller Bertolami (2016).

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The model-based $\mathrm{log}({L}_{* }/{L}_{\odot })$ versus EC relation of Dopita & Meatheringham (1991) is actually similar to the method of Zijlstra & Pottasch (1989), who derived the central star luminosities of PNe using the Hβ flux only. With the assumption that PNe are optically thick to the ionizing stellar radiation, the methodology of Zijlstra & Pottasch (1989) is analogous to the Zanstra method for determining stellar temperatures (Zanstra 1931). This assumption is justified by the very high optical depth of the H i Lyman emission lines: each recombination of hydrogen (H⁺ + ${{\rm{e}}}^{-}$) eventually results in the emission of Balmer lines and the Lyα photon (Osterbrock & Ferland 2006). Following the method of Zijlstra & Pottasch (1989) and the tabulation of ${T}_{\mathrm{eff}}$ versus L_* in Pottasch (1984, p. 169), we derived the stellar luminosities that are close to those derived using the empirical relationship of Dopita & Meatheringham (1991).

The $\mathrm{log}{T}_{\mathrm{eff}}$ versus EC relation of Dopita & Meatheringham (1991) is dependent on the spectral energy distribution (SED) of the ionizing source. Blackbodies (i.e., the Planck function), as assumed in the photoionization models of Dopita & Meatheringham (1991), can result in $\mathrm{log}{T}_{\mathrm{eff}}$ versus EC relations different from the cases where more realistic models (like those of Rauch 2003) are used. At a given intensity ratio of two nebular lines, e.g., I(He ii λ4686)/I(Hβ), the stellar atmospheres of Rauch (2003) can predict higher ${T}_{\mathrm{eff}}$ than a blackbody. In this regard, we tried to constrain the central star temperatures and luminosities by fitting the observed line ratios (including λ4363/λ5007, He i/He ii, [O ii]/[O iii], [Ar iii]/[Ar iv], [Ne iii]/[O iii], and [S ii]/[S iii]) to those predicted by the photoionization models calculated at a huge number of grids, the Mexican Million Models dataBase (3MdB; Morisset et al. 2015). The 3MdB models were computed with the cloudy program (Ferland et al. 2013) and include both the radiation- and the matter-bounded cases as well as the stellar SEDs of both blackbody and Rauch atmospheres. The tolerance of fitting was set to be ≤20% for all line ratios. Using the 3MdB, we managed to obtain ${T}_{\mathrm{eff}}$ for nine objects in our sample, and they generally agree within the errors with the corresponding values derived using the empirical relationship of Dopita & Meatheringham (1991). However, no optimum constraint on stellar luminosity was achieved.

The emergent spectrum of a PN can be affected by many factors, including central star parameters (${T}_{\mathrm{eff}}$, L_*, $\mathrm{log}g$), density profile of the nebular shell, nebular abundances, nebular radius, and filling factor; fixing other parameters and varying only ${T}_{\mathrm{eff}}$ and L_*, as was usually done with cloudy for extragalactic PNe, could be unrealistic and the derived parameters problematic. In particular, determining the central star luminosity without knowing the exact covering factor (≤1) of the nebula may underestimate L_*, not mentioning the case where the nebula is optically thin.

The central star locations of our PNe in the H–R diagram are shown in Figure 12, along with the new model tracks of the H-burning post-asymptotic giant branch (post-AGB) evolutionary sequences calculated by Miller Bertolami (2015, 2016) at two metallicities, Z = 0.01 and 0.02, for various initial masses.²² These two metallicities were chosen for analysis because they bracket the solar metallicity (${Z}_{\odot }\sim 0.013\mbox{--}0.018$; Grevesse et al. 1993; Grevesse & Sauval 1998; Lodders 2003; Asplund et al. 2009) and thus are probably suitable for the metallicity environment of M31 (as discussed in Section 4.3, the O/H ratios of the total sample of M31 PNe are mostly located between the AGB models with Z = 0.007 and 0.019). Also overplotted in the H–R diagram are the 18 M31 disk PNe observed by Kwitter et al. (2012; 16 PNe) and Balick et al. (2013; two PNe). Our targets are located between the model tracks with final masses of 0.53–0.58 M_☉, while the disk sample are mostly 0.56–0.657 M_☉, with a few objects extending to <0.56 M_☉ (Figure 12, bottom). The 15 disk and bulge PNe from Jacoby & Ciardullo (1999) are also presented in Figure 12, but with large scatter in stellar luminosity. In order to make a contrast study, we also placed all samples in Figure 13 where the classical/old post-AGB evolutionary model tracks of Vassiliadis & Wood (1994) are presented.

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The final core masses (${M}_{\mathrm{fin}}$) of our targets and the M31 disk sample were interpolated from the model tracks. Our targets, as constrained by the new post-AGB models, are in the range 0.536–0.583 M_☉ (Table 9) with an average mass of 0.562(±0.015) M_☉, while the disk sample are mostly in the range 0.550–0.602 M_☉ with an average of 0.571(±0.016) M_☉. Based on the old models, the core masses of our sample are 0.567–0.633 M_☉, and the disk PNe are ∼0.583–0.660 M_☉. The initial masses (${M}_{\mathrm{ini}}$) were then derived using the semi-empirical initial–final mass relation (IFMR) of white dwarfs given by Catalán et al. (2008). A comparison between the core masses derived for the two samples using the two sets of post-AGB models is presented in Figure 14 (left).