THE DETECTION OF C60 IN THE WELL-CHARACTERIZED PLANETARY NEBULA M1-11

We obtained optical spectra of M1-11 using the High-Dispersion Spectrograph (HDS; Noguchi et al. 2002) attached to one of the two Nasmyth foci of the 8.2 m Subaru telescope on 2008 October 6 (program ID: S08B-110, PI: M. Otsuka) and 2005 October 18 (PI: A. Tajitsu). The spectra were taken in two wavelength ranges: 3600–5400 Å (the blue spectra, taken in 2008) and 4600–7500 Å (the red spectra, taken in 2005).

When we obtained the blue spectra, an atmospheric dispersion corrector (ADC) was used to minimize the differential atmospheric dispersion over the broad wavelength region. We used a slit width of 12 (0.6 mm) and a 2 × 2 on-chip binning. We set the slit length to be 8'' (4.0 mm), which fitted the nebula well and allowed us to directly subtract sky background from the object frames. The slit position angle (P.A.) was ∼225°. The CCD sampling pitch along the slit length projected on the sky was ∼0276 per binned pixel. The resolving power reached around R > 33,000, which is derived from the mean of the full width at half-maximum (FWHM) of narrow Th–Ar and night sky lines. The total exposure time was 600 s (=300 s ×2 frames). For the flux calibration, blaze function correction, and airmass correction, we observed G192B2B as a standard star.

For the red spectra, we used the red image de-rotator and set it to P.A. = 90°. We set the slit width to 06 and the slit length to 7'' and selected a 1 (wavelength dispersion)×2 (spatial direction) on-chip binning. The resulting spectral resolution R is >65,000. We used an exposure time of 300 s and observed G192B2B as a standard star.

For both sets of observations, we took several bias, instrumental flat lamp, and Th–Ar comparison lamp frames. We are interested in detecting weak C, N, and O RLs. The peak intensities of these lines are typically ∼10%–20% higher than the local continuum, and therefore a high signal-to-noise ratio (S/N) of the continuum is necessary. The resulting S/N after subtraction of the sky background was found to range from ∼5 at ∼3700 Å to ∼30 at ∼5200 Å in the blue spectrum, and from ∼5 at ∼4800 Å to 15 at ∼6700 Å in the red one.

Data reduction of the Subaru/HDS spectra and analysis of the emission lines was done with the long-slit reduction package noao.twodspec available in IRAF,⁷ and was performed in the same manner as described by Otsuka et al. (2010). When measuring the fluxes of the emission lines, we assumed that the line profiles were Gaussian and we applied a multiple Gaussian fitting technique.

The line fluxes were dereddened using

$$\begin{equation} \log _{10}\left[\frac{I(\lambda)}{I{\rm (H\beta)}}\right] = \log _{10}\left[\frac{F(\lambda)}{F{\rm (H\beta)}}\right] + c({\rm H\beta })f(\lambda), \end{equation} \tag{ 1 }$$

where I(λ) and F(λ) are the dereddened and the observed fluxes at λ, respectively, and f(λ) is the interstellar extinction parameter at λ, from the reddening law of Cardelli et al. (1989) with R_V = 3.1. The interstellar reddening correction was performed using the reddening coefficient c(Hβ) at Hβ. We compared the observed Balmer line ratios of Hγ (blue spectrum) or Hα (red spectrum) with Hβ to the theoretical ratio computed by Storey & Hummer (1995) assuming the electron temperature T_e = 10⁴ K, the electron density n_e = 10⁴ cm⁻³, and that the nebula is optically thick in Lyα (Case B of Baker & Menzel 1938). We derived c(Hβ) = 1.677 ± 0.008 for the blue and 1.218 ± 0.017 for the red spectra.

The flux scaling was performed using all emission lines detected in the overlap region between the blue and the red spectra. The dereddened relative intensities I(λ) detected in both spectra are consistent within 10% of each other. The combined dereddened spectrum is presented in Figure 1, and the detected lines are listed in Appendix Table 16. We have detected over 160 emission lines, thus exceeding the number of detections by Henry et al. (2010), who report more than 70 lines in the 3700–9600 Å spectra. Our measurements of the line intensities I(λ) are in agreement with the results from Henry et al. (2010) within a ∼14% error.

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Specifically, we detected C ii, N ii, and O ii RLs, and highly excited lines due to He ii, C iii, and N iii. These high excitation lines show a relatively broad FWHM (∼0.8–1.6 Å) compared to typical nebular lines (∼0.2–0.5 Å). It is possible that the He ii, C iii, and N iii lines are not of nebular origin but of stellar origin because the effective temperature of the central star (29,300 K; Phillips 2003) is not high enough for species with an ionization potential (IP) ≳40 eV to exist in the nebula. For example, we did not detect any nebular lines from species with an IP ≳40 eV, such as [Ne iii] λλ3876/3967 (IP>41 eV) and [Ar iv] λ4711/40 (>40.7 eV). The IPs of He ii, C iii, and N iii are 54.4, 47.9, and 47.5 eV, respectively.

For our analysis, we also used the emission-line fluxes in the 7700–9300 Å range measured by Henry et al. (2010), scaled in such a way that the shorter wavelength part of their spectrum matches our HDS observations.

We downloaded archival HST/WFPC2 photometry in the F656N (6564 Å/28 Å) filter (PI: R. Sahai; PID: 8345), which traces the Hα emission. We reduced the photometric data using the standard HST pipeline with MultiDrizzle and present the drizzled M1-11 F656N image in Figure 2. The plate scale is 0025 pixel⁻¹. The image shows that M1-11 is an elongated nebula; the dimensions of the bright rim are ∼08 along P.A. = −27° and ∼05 along P.A. = +63°.

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2.2.1. The Total Hα and Hβ Fluxes

2.2.2. The Hydrogen Density Profile

In Figure 3(a), we present the radial profile from A toward B indicated in Figure 2. Based on this radial profile, we examined the ionized hydrogen density n(H⁺) as a function of the distance from the central star R. When we restrict the integration to the optional portion of the nebula, the dereddened observed Hα flux using c(Hβ) = 1.218 and the reddening law of Cardelli et al. (1989) with R_V = 3.1, I_l(Hα) in erg s⁻¹ cm⁻² is given by

$$\begin{equation} 4\pi D^2 I_{l}({\rm H}\alpha) = \int 4{\pi }j({\rm H}\alpha){\epsilon } dV_{l}, \end{equation} \tag{ 2 }$$

where D is the distance to M1-11 from us, j(Hα) is the emission coefficient, and is the filling factor, which is the fraction of the nebular volume filled by ionized gas. V_l is the volume of the nebula. In Case B,

$$\begin{equation} \frac{4{\pi }j({\rm H}\alpha)}{n({\rm H}^{+})n_{\rm e}} \simeq 3.856\times 10^{-25}\left(\frac{10^{4}}{T_{\rm e}}\right)^{-1.077}, \end{equation} \tag{ 3 }$$

with T_e = 5400 K derived from the Balmer jump (see Section 3.2), D = 2.1 kpc (Tajitsu & Tamura 1998), and assuming n_e ≃ n(H⁺), n(H⁺) can be written as a function of the distance from the central star R in cm as

$$\begin{equation} n({\rm H}^{+}) \simeq 3.74\times 10^{19}\left(\frac{I_{l}({\rm H}\alpha)}{\epsilon R}\right)^{0.5}. \end{equation} \tag{ 4 }$$

The resulting n(H⁺) profile from A toward B with different values for is presented in Figure 3(b). If we assume that the ionized gas is concentrated within R = 10 and that the density has a constant value of 10⁵ cm⁻³ obtained from Balmer decrements, then we find that is around 0.2. We used these n(H⁺) profiles with different values for in the SED modeling (see Section 4.1).

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We obtained J- and Ks-band medium-resolution (R ∼ 2500) spectra using the near-infrared imager and spectrograph ISLE (Yanagisawa et al. 2006, 2008) attached to the Cassegrain focus of the 1.88 m telescope at the Okayama Astrophysical Observatory (OAO). The observations were done in ISLE engineering time in 2008 March (Ks) and 2010 January (J). The detector of ISLE is a 1 K × 1 K HgCdTe HAWAII array. We used a science grade detector for the J-band observations and an engineering grade detector for the Ks-band observations. The entrance slit width was 1'' for both sets of observations. We fixed the P.A. at 90° during the observations. The sampling pitches in wavelength were ∼1.68 × 10⁻⁴ and ∼3.4 × 10⁻⁴ μm pixel⁻¹ in the J and Ks spectra, respectively, while the sampling pitch in the space direction was 025 pixel⁻¹ for both spectra. We observed standard stars HIP35132 (A0V) and HIP35180 (A1V) for the J-band and HIP31900 (F0V) for the Ks-band spectra at different airmasses to calibrate the flux levels, and correct for telluric absorption and airmass extinction. We observed M1-11 in a series of 120 s exposures in both observing modes. The total exposure times were 3600 s for the J-band spectra and 3480 s for the Ks-band spectra, respectively. Dark frames with the same science exposure time, Ar and Xe lamp frames, and on- and off-dome flat frames were also taken. For further wavelength calibration and distortion correction, OH lines recorded in the object frames were used. The data reduction was performed in a standard manner using IRAF. The interstellar reddening corrected spectra are presented in Figures 4(a) and (b). For this correction, we adopted the c(Hβ) applied in the HDS red spectrum. The resulting S/Ns are >40 in the J-band and >30 in Ks-band spectra at the continuum level.

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We detected more than 50 lines in these spectra, including a series of vibration–rotation excited lines of molecular hydrogen (H₂), as listed in Appendix Table 17. The line fluxes were normalized such that I(Paβ) = 100 in the J-band and I(Brγ) = 100 in the Ks-band spectra.

Figure 5 shows the spatial profiles of Brγ and H₂ 1–0 S(1)/2–1 S(1) lines in the K-band spectrum. In both of the spectra, the H₂ lines are easily distinguished from other ionic lines by their spatial spread of up to ∼ 16'' in diameter. The ratio of H₂ 1–0 S(1)/2–1 S(1) is a traditional shock indicator (e.g., Hora & Latter 1994, 1996; Kelly & Hrivnak 2005). The ratio in M1-11 is ∼4.5 at the center of the nebula, and it decreases up to ∼1.0 outside of the ionized region. The ratio of H₂ 1–0 S(1)/2–1 S(1) = 4.5 along the optical nebula (≲6'' in diameter) indicates a mix of UV and shock excitation (this is usual in PPNe; e.g., Kelly & Hrivnak 2005). Furthermore, the detection of a series of H₂ lines with upper vibrational level (v ⩾ 3) in the J band indicates that these lines are excited by fluorescence through the absorption of UV photons from the central star in the photodissociation region (PDR).

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The excitation diagram of H₂ lines for the entire slit of the spectra is shown in Figure 6. An ortho-to-para ratio of three is assumed. It clearly shows that the vibrational excitation temperature (T_vib) exceeds the rotation excitation temperature (T_rot), indicating fluorescence emission (see Shupe et al. 1998 for BD+30° 3639; Hora & Latter 1994 for M2-9). The difference in excitation temperature between different rotation levels (T_rot ∼ 2150 K for v = 1 and T_rot ∼ 1000 K for v ⩾ 2) indicates that H₂ lines are collisionally (shock) excited in a part (the center) of the nebula. However, it is evident that the UV excitation in PDR is still dominant for most of the H₂ emission in M1-11.

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The lines at 1.15 and 1.19 μm are identified with [P ii] (in the ³P₁–¹D₂ and ³P₂–¹D₂ transitions, respectively), representing the discovery of these lines in M1-11. Adopting the transition probabilities of Mendoza & Zeippen (1982), the collisional impacts of Tayal (2004a), and the level energy listed in Atomic Line List v2.05b12,⁸ the expected [P ii] I(1.19 μm)/I(1.15 μm) ratio is 2.63 in T_e = 10,000 K and n_e = 5 × 10⁴ cm⁻³. The observed line ratio (2.79 ± 0.44) agrees well with the theoretical value, which confirms the identification of the [P ii] 1.15/1.19 μm lines. Our measurement of the I([Kr iii] 2.19 μm)/I(Brγ) ratio of 3.44 ± 0.23 also agrees with Sterling & Dinerstein (2008; 3.22 ± 0.26).

The N^{2 +} abundance can be estimated from the N iii] λ1750 line, present in archival IUE spectra that we retrieved from the Multi-mission Archive at the STScI (MAST). We collected low-resolution IUE spectra taken by the short-wavelength prime (SWP) and long-wavelength prime (LWP) cameras (file IDs: SWP25846, LWP05896, and LWP05897), all of which were made using the large aperture (10.3 × 23 arcsec²). In these spectra, we identified the He ii λ1640 and N iii] λ1750 lines. We determined that c(Hβ) = 0.67 ± 0.12, by comparing the theoretical ratio of He ii I(λ1640)/(λ4686) = 6.56 to the observed value, in the case of T_e = 10⁴ K and n_e = 10⁴ cm⁻³ as given by Storey & Hummer (1995). The interstellar extinction correction was made using Equation (1). The flux measurements of the detected lines along with the normalized values are listed in Table 1. While we did not detect the C iii] λλ1906/09 lines in the SWP and LWP spectra, Kingsburgh & Barlow (1994) show I(C iii]λλ1906/09) to be six with an uncertainty greater than a factor of two.

We analyzed the 2.5–5.5 μm prism spectra of M1-11 taken with the Infrared Camera (IRC) spectrograph (Onaka et al. 2007) on board of the AKARI satellite (Murakami et al. 2007). The data were obtained as part of a mission program, PNSPEC (data ID: 3460037, PI: T. Onaka), on 2009 April 11. The used observing window was 1' × 1'. For the data reduction, we used the IRC Spectroscopy Toolkit for the Phase 3 data version. Figure 7 shows the IRC spectrum with the local dust continuum subtracted. The S/N is >30 for the dust continuum. Several prominent lines are visible, and their central wavelengths are indicated by dotted lines. The line fluxes are listed in Table 2. For the IRC spectra, we derived c(Hβ) = 1.40 ± 0.03 by comparing the observed intensity ratios of H i 4–5 (Brα 4.051 μm), 4–6 (Brβ 2.625 μm), and 5–7 (Pfβ 4.653 μm) to Hβ and the theoretical values of Storey & Hummer (1995) for the case of 10⁴ K and 10⁴ cm⁻³. To correct for interstellar reddening, we used the ratio of the extinction at each wavelength to the B − V color excess, A_λ/E(B − V), given by Fluks et al. (1994), in combination with the correlation between Hβ and the color excess, c(Hβ) = 1.47E(B − V), from Seaton (1979).

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In the AKARI spectra, we also found an emission band at 3.2–3.6 μm, which may be due to aromatic and aliphatic hydrocarbon species. A similar feature is seen in PN NGC 7027 and PPN IRAS 21282+5050, the latter of which has a [WC11] central star. ISO/SWS archival spectra of NGC 7027 and IRAS 21282+5050 are shown for reference in Figure 7. The resonance at 3.3 μm is attributed to vibrational transitions in PAHs (e.g., Draine 2011). We also recognize the 6.2, 7.7, and 11.3 μm resonances due to PAHs in the spectra of M1-11. In particular, the 11.3 μm C–H out-of-plane bending mode is seen in the Spitzer/IRS spectrum (see next section). Cohen et al. (1986) already detected the 6.2, 6.7, 7.7, and 8.6 μm resonances in M1-11. The 3.3 μm band profile of M1-11 is similar to the ones seen in NGC 7027 and IRAS 2152+5050, and thus we assume that the emission seen in M1-11 is also due to PAHs. Indeed, the 3.3 μm feature was first detected by Allen et al. (1982), who also measured its flux. Using the theoretical intensity ratio of H i I(5–9) to I(5–11) = 1.86 in the case of T_e = 10⁴ K and n_e = 10⁴ cm⁻³, we removed the contribution from H i n = 5–9 to the 3.3 μm feature and estimated the flux due to PAHs I(PAH 3.3 μm) to be 7.63(−12) erg s⁻¹ cm⁻², which is about twice as large as the measurement by Allen et al. (1982; 3.1(−12) erg s⁻¹ cm⁻²). Any pure rotational H₂ lines in Spitzer/IRS are not detected (see Table 2).

M1-11 was observed by Spitzer on 2006 November 10 with the 9.9–19.6 μm (SH) and 18.7–37.2 μm (LH) modes on the Infrared Spectrograph (IRS; Houck et al. 2004) as part of program ID 30430 (PI: H. Dinerstein; AORKEY: 19903232). We downloaded the archival spectral images, and after masking bad pixels using IRSCLEAN, we extracted the one-dimensional spectra using SPICE. The S/N is >30 for the dust continuum.

In the spectrum of Cohen et al. (1986), very weak and tentative features are seen around 7.0 and 8.5 μm that may arise at least partially from fullerene C₆₀, with possible blending from the PAH 8.5 μm band. However, the quality of their data is insufficient to be confident in these features. To check the presence of the C₆₀ 8.5 μm feature, we downloaded the 7.7–13.3 μm archival spectral data obtained using the VLT spectrometer and imager for the mid-infrared (VISIR) at ESO VLT UT3 (ID: 084.D-0868A; PI: E. Lagadec). We reduced the raw data using ESO gasgano. To compare the VISIR data with the Spitzer spectra of other C₆₀ PNe and also to combine it with M1-11's Spitzer spectrum, we degraded the original VISIR spectral resolving power of ∼400 down to 90 by using a Gaussian convolution technique. The S/N of the convoluted VISIR spectrum is >70.

The IRS and VISIR combined 7.7–37.2 μm spectrum, which is shown in Figure 8, reveals the solid-state/molecular features and atomic lines on the dust continuum thermal emission. The detected lines are listed in Table 2. The emission around 8.5 μm is the complex of C₆₀ 8.5 μm and PAH 8.6 μm. We measured the flux density of C₆₀ 8.5 μm by using multiple Gaussian fittings to separate its flux from the PAH 8.6 μm feature (see Section 2.6.3). We performed the interstellar reddening correction in a manner similar to that described in Section 2.5. By comparing the observed intensity ratios H i F(n = 6–7)/F(Hβ) and F(n = 8–11)/F(Hβ) to the theoretical values of Storey & Hummer (1995) for the Case B assumption in T_e = 10⁴ K and n_e = 10⁴ cm⁻³, we determined that c(Hβ) = 1.63 ± 0.02.

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2.6.1. Broad Spectral Features at 10–13 and 16–22 μm

2.6.2. 30 μm Broad Feature

The carrier of the 30 μm feature remains somewhat of a mystery. While MgS has been proposed and often used as the carrier of this feature (Hony et al. 2003), recent work has cast doubt on its identification with MgS (see, e.g., Zhang et al. 2009; García-Hernández et al. 2010; Zhang & Kwok 2011). Nevertheless, we consider MgS as a possible dust component in M1-11 to explain the 30 μm feature in the spectrum.

Other potential carriers, in particular hydrogenated amorphous carbon (HAC; see Grishko et al. 2001; Hony et al. 2003), should also be considered. In the SED model for PPN HD 56126, Hony et al. (2003) showed that broad emission features around 7–9 μm and 10–13 μm are partly due to HACs, making the identification of the 30 μm band with HACs (Grishko et al. 2001) a possibility. We examined whether HAC can be the main contributor to the 10–13 and 30 μm broad features by applying a modified blackbody model to the IRS spectrum, including both MgS and HACs.

The observed flux density F_λ due to thermal emission from dust grains is given by

$$\begin{equation} F_{\lambda } = \sum _{i}\left(\frac{4}{3}\pi a_{i}\rho _{i} D^{2}\right)^{-1} m_{d,i}Q_{\lambda ,i}\pi B_{\lambda }(T_{d,i}), \end{equation} \tag{ 5 }$$

where a_i is the grain radius of component i, ρ_i is the dust density, m_{d, i} is the dust mass, Q_{λ, i} is the absorption efficiency, and B_λ(T_{d, i}) is the Planck function for a dust temperature T_{d, i}. We adopt a distance D = 2.1 kpc (Tajitsu & Tamura 1998). In Table 4, we list the optical constants that we use for each of the dust species considered. For MgS, we used the optical constants of nearly pure MgS, e.g., Mg_0.9Fe_0.1S, from Begemann et al. (1994). For the HACs, we adopt the Q_λ of HAC in the case of H/(H+C) = 0.3 calculated by Hony et al. (2003). In two models, we consider different compositions, consisting of combinations of PAHs, amorphous carbon (AC), SiC, MgS, and HAC (Figure 9). We considered the 9.9–37.2 μm Spitzer spectrum and AKARI FIS 65/90 μm photometry data, except for the 16–22 μm broadband. We assume spherically shaped grains with a radius of a = 0.5 μm for AC, SiC, and HACs, and we excluded PAHs. To reproduce the broad 30 μm emission using MgS, as discussed in Hony et al. (2003), we considered a continuous distribution of ellipsoids (CDEs; e.g., Bohren & Huffman 1983; Fabian et al. 2001; Min et al. 2003) and calculated the Q_λ of CDE MgS using Equation (18) given by Min et al. (2003). To simplify, we assume that the value of each ellipsoid MgS grain is ≃4πa³/3, where a is 0.5 μm.

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Table 4. Adopted Optical Constants for Each Model Dust Component

Dust Species	Data Source
SiC	Pegourie (1988)
Amorphous carbon (AC)	Rouleau & Martin (1991)
MgS	Begemann et al. (1994)
HAC	Hony et al. (2003)

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The results of the modified blackbody fitting are shown in Figure 9, and the derived T_{d, i}, m_{d, i}, and mass fraction for each dust component are summarized in Table 5. Model 1 with AC, SiC, and MgS can explain the observed spectrum reasonably well, while model 2 with HAC instead of MgS predicts an unseen broad emission feature around 20 μm. However, we should keep in mind that it is extremely difficult to characterize carbon compounds with a mixed aromatic and aliphatic content—such as HACs—in the laboratory because these optical constants are strongly variable for different chemical and physical conditions. Jones (2012) presents HAC theoretical models that show the extreme variability of HAC spectra depending on parameters such as hydrogen-content, grain size, etc. In any case, the 20 μm feature is much weaker than the 30 μm feature (see Grishko et al. 2001) and one could detect the 30 μm features while not detecting the 20 μm feature. Currently, therefore, we do not completely rule out HACs as a carrier of the 30 μm broad feature.

Table 5. Results from the Modified Blackbody Fitting to the Spitzer/IRS Spectrum

Models	Dust	Td	md
	Component	(K)	(M☉)
Model 1	SiC	160	2.85(−5)
(Figure 9(a))	AC	120	2.97(−4)
	MgS	220	3.17(−6)
Model 2	SiC	170	1.75(−5)
(Figure 9(b))	AC	120	1.77(−4)
	HAC	80	0.11

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In this paper, therefore, we assume that SiC and MgS are the main contributors to the 10–13 and 30 μm broad features, respectively. In the remainder of our analysis, we will only consider PAHs, SiC, AC, and MgS to model the dust emission in the SED.

2.6.3. 8.5, 17.3, and 18.9 μm Emission due to C₆₀ Fullerenes

In the VISIR and Spitzer combined spectrum of M1-11, we see infrared features at 8.5 (although blended with the PAH 8.6 μm, see below), 17.3, and 18.9 μm, most likely due to the fullerene C₆₀.

In our own Milky Way, these C₆₀ infrared features were recently detected in five PNe, including Tc1, M1-12, M1-20, K3-54, and M1-60 (Cami et al. 2010; García-Hernández et al. 2010, 2012), a C-rich PPN (IRAS 01005+7910; Zhang & Kwok 2011), and two O-rich post-AGB stars (IRAS 06338+5333 and HD52961; Gielen et al. 2011). In Figure 8, we show the IRS spectrum of M1-12 compared to M1-11. The C₆₀ 17.3 and 18.9 μm features seem to be present in M1-11, although they are much weaker than those in M1-12. The spectrum of M1-12 shows spectral features due to PAHs, SiC, AC, MgS, and a very weak 16–22 μm feature, which resembles that of M1-11. The 16–22 μm feature is not seen in Tc1, M1-20, K3-54, and M1-60. Some other PNe with fullerenes in the Magellanic Clouds exhibit the 16–22 μm feature (García-Hernández et al. 2011a, 2012). In the inset of Figure 8, the ∼16–20 μm spectra of M1-11 and M1-12 are shown with a local dust continuum subtracted. The wavelength positions of the intensity peak and the line widths of the C₆₀ 17.3 and 18.9 μm lines in M1-11 are almost coincident with those in M1-12. In addition, the complex line around 8.5–8.6 μm—which turns out to be a blend of PAH 8.6 μm and C₆₀ 8.5 μm—in M1-11 is very similar to that in M1-12, as shown in Figure 10. These comparisons with M1-12 support the identification of this feature as a C₆₀+PAH blend.

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To quantify the excitation temperature and the total number of C₆₀, we need to separate the flux of C₆₀ 8.5 μm from the PAH 8.6 μm band. Cami et al. (2010) reported that the FWHM of C₆₀ 8.5 μm in the PN Tc1 is 0.15 μm by Gaussian fitting. Tc1 shows strong C₆₀ lines but very weak PAH bands. Assuming that the FWHM of C₆₀ 8.5 μm is ∼0.15 μm in M1-11 and M1-12, we fit the broad line at 8.6 μm with multiple Gaussians. The line at 8.6 μm in M1-11 can be represented by three plus one Gaussian components, as shown in Figure 10(a). We assume that the profile of the PAH 8.6 μm line is represented by the sum of two Gaussians at the peak wavelengths of ∼8.7 and ∼8.8 μm. The FWHM of the PAH 8.6 μm represented by the sum of these two Gaussians is 0.2 μm, which is consistent with NGC 7027 (0.23 μm in ISO/SWS spectrum shown in Figure 7). The FWHM of the C₆₀ 8.5 μm line indicated by the blue line is 0.17 μm. The FWHM of the C₆₀ and PAH complex is 0.3 μm. The resultant Gaussian fitting for M1-12 is presented in Figure 10(b). The PAH 8.6 μm is represented by the sum of two Gaussians at ∼8.6 and ∼8.7 μm. The FWHMs of the C₆₀ and the PAHs for M1-12 are the same as those of M1-11. The measured fluxes of the C₆₀ 8.5 μm and PAH 8.6 μm lines in M1-11 are listed in Table 2.

The excitation temperature and the number of C₆₀ were derived by creating a vibration excitation diagram as shown in Figure 10(c). We followed the method of Cami et al. (2010). N_u is the number of C₆₀ molecules in the upper vibrational levels. N_u is written by

$$\begin{equation} N_{u} = \frac{4 \pi I(C_{60}) D^{2}}{A} \frac{\lambda }{hc}, \end{equation} \tag{ 6 }$$

where I(C₆₀) is the fluxes of the C₆₀ lines in erg s⁻¹ cm⁻², D is the distance to M1-11 (2.1 kpc; Tajitsu & Tamura 1998), A is the transition probabilities (4.2, 1.1, and 1.9 s⁻¹ for C₆₀ 8.5, 17.3, and 18.9 μm, respectively, from García-Hernández et al. 2011b), h is Planck's constant, and c is the speed of light. The vibrational degeneracy is given by g_u. In thermal equilibrium, the Boltzmann equation relates the N_u to the excitation temperature T_ext:

$$\begin{equation} N_{u} \propto g_{u}\exp (-E_{u}/kT_{{\rm ext}}), \end{equation} \tag{ 7 }$$

where E_u and k are the energy of the excited level and the Boltzmann constant, respectively. We confirmed that our measured excitation temperature, T_ext of 338 ± 9 K, in Tc 1 using Equations (6) and (7) is consistent with Cami et al. (2010; 332 K). Accordingly, we obtained a T_ext of 399 ± 36 K and a N(C₆₀) of 4.57 ± 1.23(+46). The total mass of C₆₀ m_C60 is 2.75(−8) M_☉.

Our estimated T_ext, N(C₆₀), and m_C60 in M1-12 are 345 ± 35 K, 5.30 ± 1.23(+46), and 3.18(−8) M_☉, respectively, adopting a D of 3.9 kpc (Tajitsu & Tamura 1998). García-Hernández et al. (2010) measured a T_ext in M1-12 of 546 K. Their measured FWHM of C₆₀ 8.5 μm is 0.237 μm. The T_ext discrepancy between these is due to the differences in the measured line flux of this line.

We determined the electron temperatures T_e and densities n_e using 11 diagnostic CELs, and listed the results in Table 6.

For [N ii] λ5755 and [O ii]λλ7320/30, we subtracted the recombination contamination from both lines using

$$\begin{equation} \frac{I_{R}([{\rm N\,\scriptsize{II}}]\lambda 5755)}{I(\rm H\beta)} = 3.19\left(\frac{T_{\rm e}}{10^4}\right)^{0.33}\times \frac{\rm N^{2+}}{\rm H^{+}}, \end{equation} \tag{ 8 }$$

and

$$\begin{equation} \frac{I_{R}([{\rm O\,\scriptsize{II}}]\lambda \lambda 7320/30)}{I(\rm H\beta)} = 9.36\left(\frac{T_{\rm e}}{10^4}\right)^{0.44}\times \frac{\rm O^{2+}}{\rm H^{+}}, \end{equation} \tag{ 9 }$$

given by Liu et al. (2000). Adopting N^{2 +} and O^{2 +} ionic abundances derived from N ii and O ii lines (see Section 3.4), we determined that I_R([N ii] λ5755) = 0.12 and I_R([O ii] λλ7320/30) = 2.11. The recombination contamination is ∼2% in [N ii] λ5755 and ∼8% in [O ii], respectively.

The resulting n_e–T_e diagnostic diagram is shown in Figure 11. The solid lines indicate diagnostic lines for the electron temperatures, while the broken lines are electron density diagnostics. Since the gas in M1-11 has a much higher density than the critical densities of the density-sensitive lines [O ii] λλ3726/29 and [S ii] λλ6717/31, the ratios of [O ii] I(λλ3726/29)/I(λλ7320/30) and [S ii] I(λλ6717/31)/I(λλ4069/76) are density sensitive rather than temperature sensitive. The critical densities at T_e = 10,000 K for [O ii] λλ3726/29 are ∼4500 and ∼980 cm⁻³, respectively, and those of [S ii] λλ6717/31 are ∼1400 and ∼3600 cm⁻³, respectively. The densities derived from the [O ii] λλ3726/29 and [S ii] λλ6717/31 ratios might be the value for the thin shell region, while those from the [O ii] I(λλ3726/29)/I(λλ7320/30) and [S ii] I(λλ6717/31)/I(λλ4069/76) would be the values for the bright rim. To determine n_e, we adopted T_e = 10,000 K for all of the density-diagnostic lines. T_e([N ii]) was calculated using n_e = 36,490 cm⁻³, which is the average between n_e([O ii]) derived from I(λλ3726/29)/I(λλ7320/30) (n_e([O ii]_n/a) hereafter) and n_e([S iii]). For T_e([S iii]), T_e([O iii]), and T_e([Ar iii]), we adopted n_e([S iii]). For T_e([O i]), we adopted n_e([N i]). Our estimates for T_e([N ii]), T_e([O iii]), and T_e([S iii]) are in excellent agreement with those by Henry et al. (2010), who estimated 10,720, 9996, and 9100 K, respectively. The estimates for n_e and T_e are summarized in Table 6.

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To calculate the CEL ionic abundances, we adopt a three-zone model based on the n_e–T_e diagram. The T_e and n_e combinations for each ion are listed in Table 7. For the N⁰ and O⁰ abundances, we adopted T_e([O i]) and n_e([N i]) (zone 1). The averaged n_e is from n_e([O ii]_n/a) and n_e([S iii]), and T_e([N ii]) is for ions with 0 eV < IP ≲ 13.6 eV (zone 2). n_e([S iii]) and the averaged temperature among T_e([O iii]), T_e([S iii]), and T_e([Ar iii]) are for ions with IP=14.4–35.5 eV (zone 3).

We calculate the He, C, N, and O abundances using the RLs of these elements by adopting the T_e derived from the Balmer discontinuity together with He i line ratios and the n_e from the Balmer decrements, listed in Table 6. The Balmer discontinuity temperature T_e(BJ) was determined using the method described by Liu et al. (2001), which we used to obtain the C^{2 +}, N^{2 +}, and O^{2 +} abundances from RLs.

The He i electron temperatures T_e(He i) were derived from the ratios of He i I(λ7281)/I(λ6678), I(λ7281)/I(λ5876), and I(λ6678)/I(λ5876) assuming a constant electron density of 10⁶ cm⁻³, estimated from the Balmer decrements (see below). We adopted the emissivities of He i provided by Benjamin et al. (1999). The T_e(He i) derived from three different line ratio combinations is 3980–6980 K. We adopted T_e(He i) derived from He i I(λ7281)/I(λ6678) for the He⁺ abundance calculations. The reason why this T_e(He i) is the most reliable was discussed in Otsuka et al. (2010).

The intensity ratios of the high-order Balmer lines Hn (n: the principal quantum number of the upper level) to a lower Balmer line, e.g., Hβ, are also sensitive to the electron density. In Figure 12, we plot the ratios of higher-order Balmer lines to Hβ compared to the theoretical values by Storey & Hummer (1995) for T_e(BJ) and a n_e of 10⁵, 5 × 10⁵, and 10⁶ cm⁻³. The electron density in the RL emitting regions seems to be >10⁵ cm. Care when dealing with this value is necessary because it apparently has large scatter.

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The derived ionic abundances are listed in Table 8. In the last line of the transition series for each ion, we present the adopted ionic abundance in bold face. The adopted values represent the line-intensity-weighted mean in case two or more lines are detected. For reference, the results by Sterling & Dinerstein (2008; for Kr) and Henry et al. (2010; for the others) are also listed in the last column. This is the first time the Ne⁺, P⁺, and Fe^{2 +} abundances are derived for M1-11. In total, 15 ionic abundances are determined by solving for a >5 level atomic model, with the exception of Ne⁺, for which the abundance was calculated using a two-level energy model. We adopted the same collisional strengths and transition probabilities used in Otsuka et al. (2010, 2011), except for Cl⁺ for which we adopted the transition probabilities from the CHIANTI atomic database,⁹ the collisional impacts of Tayal (2004b), and the level energy listed in Atomic Line List v2.05b12. We subtracted the recombination contamination in the [N ii]λ5755 and [O ii]λλ7320/30 lines to derive the N⁺ and O⁺ abundances.

In general, our derived abundances are comparable to the values of Henry et al. (2010) and Sterling & Dinerstein (2008). The discrepancies between our N⁺, O⁺, and S⁺ abundances and the results by Henry et al. (2010) are mainly due to adopted electron temperature; Henry et al. adopted 10,200 K. Note that they employed three different T_es and a constant n_e = 20,000 cm⁻³ in their models. With their T_es, we would find N⁺, O⁺, and S⁺ abundances comparable to their results. Lastly, a minor discrepancy for the N⁺ and O⁺ abundances must be due to the recombination contamination in the [N ii]λ5755 and [O ii]λλ7320/30 lines, respectively.

Our values for the ionic abundances derived from RLs are listed in Table 9. In general, the Case B assumption applies to lines from levels having the same spin as the ground state, and the Case A assumption applies to lines of other multiplicities. In the last of the line series of each ion, we present the adopted ionic abundance and the error estimated from the line-intensity-weighted mean in bold face. Effective recombination coefficients for the lines' parent multiplet are the same as those used by Otsuka et al. (2010). The RL ionic abundances are insensitive to the electron density under ≲10⁸ cm⁻³ (Zhang & Liu 2003). For the ionic abundance calculations, we therefore adopted the effective recombination coefficients in case of n_e = 10⁴ cm⁻³ for C^{2 +} and N^{2 +}. For He⁺ and O^{2 +} calculations, we adopted n_e = 10⁶ cm⁻³ and 10⁴ cm⁻³, respectively. Since He ii, C iii, C iv, N iii, and O iii appeared to be of stellar origin, we did not estimate the abundances of these ions.

The He⁺ abundances are determined by using six electron density insensitive He i lines to reduce intensity enhancement by collisional excitation from the He⁰ 2s³S level. For the C^{2 +} abundances, the V6 and V17.06 lines, which have higher angular momentum as upper levels, seem to be unaffected by both resonance fluorescence by starlight and recombination from excited ²S and ²D terms. Comparison of the C^{2 +} abundances derived from V6 and V17.06 lines indicated that the observed C ii lines would have less population enhancement mechanisms. Our estimated He⁺ and C^{2 +} abundances are consistent with Henry et al. (2010; 3.56(−2), 4.48(−4)).

We estimated the O^{2 +} abundances by using the O ii lines showing the least contamination from other ionic transitions. We excluded the O ii 4676.23 Å line when determining O^{2 +} abundance because this line is much stronger than the other V1 lines.

The abundance discrepancy factor (ADF), which is the ratio of RL to CEL abundances, is 19.5 ± 8.4 for O^{2 +} and 15.3 ± 13.6 for N^{2 +}. The large uncertainty of ADF(N^{2 +}) is due to the large uncertainty in the CEL N^{2 +} abundance. ADF(O^{2 +}) in M1-11 is comparable to that of high-density PN M2-24 (namely, 17; Zhang & Liu 2003). The density structure for M1-11 is similar to that of M2-24, showing a large density contrast of n_e = 10^{3 − 6} cm⁻³.

The elemental abundances are estimated using an ionization correction factor, ICF(X), based on the IP. ICFs(X) for each element are listed in Table 10. The He abundance is the sum of the He⁺ and He^{0 +} abundances, and we allowed for the unseen He⁰ abundance. The C abundance is the sum of the C⁺ and C^{2 +} abundances, and we added the unseen C⁺ using ICF(C). Henry et al. (2010) used ICF(C) = O/O^{2 +}. Since the IPs of C^{+, 2 +} (11.3 and 24.4 eV) are close to those of N^{+, 2 +} (14.5 and 29.6 eV), we instead adopted ICF(C) = N/N^{2 +}. The N abundance is the sum of N⁺ and N^{2 +}. For the RL N abundance, we corrected for the unseen N⁺ by assuming (N/N^{2 +})_CEL = (N/N^{2 +})_RL. The O abundance is the sum of the O⁺ and O^{2 +} abundances. For the RL O abundance, we assume (O^{2 +}/O)_RLs = (O^{2 +}/O)_CELs. The Ne abundance is equal to the Ne⁺ abundance. The P abundance is the sum of the P⁺ and P^{2 +} abundances. We assumed that P/P⁺ = S/S⁺ and considered the P^{2 +} abundance. The S abundance is the sum of the S⁺, S^{2 +}, and S^{3 +} abundances. We corrected for the unseen S^{3 +} abundance by using the CEL O and O⁺ abundances. We assume that the Cl abundance is the sum of Cl⁺ and Cl^{2 +}. The Ar abundance is the sum of the Ar⁺ and Ar^{2 +} abundances, and we corrected for the unseen Ar⁺. The Fe abundance is the sum of the Fe^{2 +} and Fe^{3 +} abundances, and we corrected for the unseen Fe^{3 +}. The Kr abundance is the sum of the Kr⁺, Kr^{2 +} and Kr^{3 +} abundances, and we corrected for the unseen Kr⁺ and Kr^{3 +}.

The resulting elemental abundances are listed in Table 11. The types of emission lines used for the abundance estimations are specified in the second column. The number densities of each element relative to hydrogen are listed in the third column, and the subsequent two columns are the number densities in the form of log₁₀(X/H), where H is 12, and the number densities relative to the solar value. The last columns are the measurements by Sterling & Dinerstein (2008) for Kr and Henry et al. (2010) for the others. Our estimated abundances are in agreement with the values given by these authors except for C, N, and O. The C discrepancy between Henry et al. (2010) and ours is due to the different ICF(C). When we assume ICF(C) = O/O^{2 +}, we find that the C abundance is 10.45 ± 0.22. The N and O discrepancies are due to the N⁺ and O⁺ discrepancies caused by the differently adopted T_e s.

We attempted to estimate the carbon abundance from CELs by correlating ADF(C^{2 +}) with ADF(O^{2 +}). We found a tight correlation, ADF(C^{2 +}) = 0.997 ×ADF(O^{2 +}), among 56 Galactic PNe from Wang & Liu (2007), Wesson et al. (2005), Liu et al. (2004), and Tsamis et al. (2004). When we consider only the 18 PNe with ADF(O^{2 +})>5, there seems to be no correlation between ADF(C^{2 +}) and ADF(O^{2 +}). For these 18 PNe, ADF(C^{2 +}) is 7.65 ± 1.97. When we adopt this value for ADF(C^{2 +}), the C^{2 +} abundance derived from CELs is 7.31(−5) ± 3.56(−5) and the I(C iii]λ1906/09) is 33.8 ± 16.5. The CEL C abundance and the CEL C/O ratio are 8.46 ± 0.34 dex and −0.14 ± 0.34 dex, respectively. The CEL C/O ratio derived from CELs agrees well with the value derived from RLs, which is −0.57 ± 0.37 dex, although there is a large uncertainty.

We should keep in mind that the >9 dex C abundances derived from both the CELs and the RLs are confirmed in many PNe and can also be theoretically explained by AGB nucleosynthesis if we assume a small minimum H-envelope mass for the third dredge-up (∼0.5 M_☉; Straniero et al. 1997 for solar metallicity). However, for stars with a main-sequence mass of ∼1–3 M_☉ and an initial metallicity of Z = 0.004, O abundances of >9 dex are not expected to occur. For example, we present the predicted abundances for initially 1.5 M_☉ stars within Table 12. In M1-11, we adopt the observed N and O abundances derived from CELs, while for the C abundances we used CEL predictions and observed values for the RLs. Karakas (2010) adopted scaled-solar abundances as the initial composition. The accuracy of the predicted abundances is within 0.3 dex. The model-predicted C and O abundances are close to the predicted CEL C and the observed CEL O abundances. The model could also explain the observed abundance of Ne and P, which are He-rich intershell products that are brought up to the stellar surface by the third dredge-up in late AGB phase.

Comparison of the model of Karakas (2010) and our observation suggests that the CEL O abundance would be more reliable in M1-11 relative to the RL O. This would also be applied to the N abundance. Therefore, we consider the CEL CNO abundances to represent the gas-phase abundances of these elements in M1-11. If the CEL C/O ratio is correct, then M1-11 might be a C-rich or O-rich PN. In the next section, we verify the C and O abundances through gas+dust SED modeling.

We investigate the fractional ionization, the evolutionary stage of the central star, and the physical conditions of the ionized gas and dust grains by constructing an SED model based on the PI code Cloudy c08.00 and modified blackbody fitting. Through SED modeling, we derive the ionized gas mass m_g, dust mass m_d, and dust temperature T_d in the nebula, as well as the total luminosity L_* and the effective stellar temperature T_eff. We verify CEL C and O abundances through our model.

4.2.1. Model Approach

Using Cloudy and modified blackbody fitting, we attempted to fit the observed SED from ∼0.1 to 90 μm, assuming that the dust in M1-11 is composed of PAHs, AC, SiC, and MgS grains. We excluded the broad 16–22 μm feature in the fitting procedure.

Since there are no optical constants of MgS available for the UV, we could not include MgS in the Cloudy modeling. Instead, we fitted the MgS feature using single temperature thermal emission applied to the infrared opacity. For MgS, we assumed CDE, while for all other dust species we used spherical grains. Unfortunately, Cloudy does not allow CDE grains, providing a second reason to model the MgS contribution separately. Indeed, at present, there are no publicly available PI codes that can handle CDE grain shapes.

We assume that the observed SEDs can be expressed as the sum of the calculated SED from the Cloudy model and the modified blackbody fit to the MgS emission. First, we fitted the SED in the range from ∼0.1 to 22.5 μm and 65–90 μm using Cloudy. Then, we fitted a modified blackbody to the difference between the observations and the fitted SED from Cloudy, to account for the contribution from MgS. In both the Cloudy model and the MgS modified blackbody fitting, we adopted a distance D to M1-11 of 2.1 kpc.

In the Cloudy calculations, we used Tlusty's non-LTE theoretical atmosphere model¹⁰ with [Z/H] = −0.81, which is consistent with the observed [Ar/H]. McCarthy et al. (1997) found that the effective temperature T_eff = 29,000 K, the surface gravity log  g = 3.0, and the core mass M_* = 0.74 M_☉ for the central star, using their non-LTE model based on Keck/HIRES spectra. However, they adopted a distance D of 4.6 kpc. Guided by their results, we used a series of theoretical atmosphere models with T_eff in the range from 27,500 to 35,000 K and log  g values of 3.0, 3.25, 3.50, 3.75, and 4.0 to describe the SED of the central star. We found that T_eff = 31,950 K, log  g = 3.5, and a total luminosity L_* = 4510 L_☉ can accommodate the observations well.

For the gas-phase elemental abundances X/H, we adopted the observed values listed in Table 11 as a first guess and varied these to match observations, except for C. For C, we varied the C abundance to match the predicted value: I(C iii]λ1906/09) = 33.8 ± 16.5. We did not fit the He ii, C iii, or N iii lines because these lines would be of stellar wind origin. For the N abundances, we adopted the CEL value. Treating the collisional impacts of [P ii] as a function of electron temperature and solving the five-level energy model for this ion is not included in Cloudy c08.00, leading to an overestimate of the P abundance (log₁₀P/H + 12 > 6). We adapted the code to perform this analysis correctly and to obtain a better estimate of the P abundance. We also revised the C iii], [N ii], [O ii, iii], [Ne ii], [S iii], and [Ar iii] line-calculation programs in Cloudy. The abundance of elements that were not observed was fixed at [X/H] = −0.81. Reliable dielectric recombination (DR) rate measurements do not exist for the low stages of ionization of S at photoionization temperatures (Cloudy c08 manual), and thus we adopted the scaled DR of oxygen for sulfur line calculations to match the observed [S ii].

We adopted the hydrogen density profile as presented in Figure 3(b). Based on the HST image shown in Figure 2, we fixed the outer radius R_out at 26 (0.026 pc) and varied the inner radius R_in and filling factor to match the observed SED. The best-fit R_in and are ∼08 (0.008 pc) and 0.25–0.3, respectively, assuming that the gas and dust co-exist in the same sized nebula.

We assumed that amorphous carbon and SiC are present in the form of spherical dust grains with a radius a = 0.5 μm. To calculate the opacities for these species, we used the optical constants listed in Table 4. Zhang & Kwok (1990) observed a near-IR excess, also shown in the SED of Figure 13, arising from both the PAH and the small dust grain emission. To explain the excess, we also included small carbonaceous grains with a grain size of a = 0.005 μm, as well as PAHs. We adopted the optical data of Desert et al. (1990), Schutte et al. (1993), and Bregman et al. (1989). To explain the MgS feature around 30 μm, we performed a modified blackbody fitting with a single dust temperature T_d and CDE-shaped grains with a characteristic size of a = 0.5 μm, as we mentioned in Section 2.6.2.

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To verify the degree of modeling accuracy, we evaluated the gas emission line strengths and the broadband fluxes in the features of interest, including three AKARI/FIS and two Wide-field Infrared Survey Explorer (WISE) photometry bands; and we fitted the overall SED shape with the adopted elemental abundances. We will discuss the resulting elemental abundance and the ionization correction factors.

4.2.2. Results of SED Modeling

The derived physical quantities are listed in Tables 13 and 14, which can be compared with the flux levels in the 13 spectral features of interest. In Table 14, we compare the predicted emission line and band fluxes with the observed values, where I(Hβ) is 100 and the intrinsic log  I(Hβ) is −10.22 erg s⁻¹ cm⁻². Columns 4 and 5 list the observed values and the values predicted by Cloudy modeling. The type of emission is indicated in Column 3.

Table 13. The Derived Properties of the Central Star, Ionized Nebula, and Dust by the SED Model

Parameters	Central Star
L*	4710 L☉
Teff	31 830 K
log  g	3.5 cm s−2
[Z]	−0.81
M*	∼0.6 M☉
Progenitor	1–1.5 M☉
Age	>1000 yr
Distance	2.1 kpc
	Nebula
Abundances	He:11.11, C:8.49, N:7.89, O:8.30,
(log X/H+12)	Ne:7.67, P:5.21, S:6.15, Cl:4.20,
	Ar:5.95, Fe:5.01, Others:[X/H] = −0.81
Geometry	Spherical
Shell size	Rin = 08(0.008 pc)/Rout = 26(0.027 pc)
Input density profile	See Figure 3(b)
	0.25
log F(Hβ)	−10.22 erg s−1 cm−2 (deredden)
mg(Cloudy)	0.023 M☉
	Dust in Nebula
Composition	PAHs, AC, SiC, MgS
Grain size	0.5 and 0.005 μm (see the text for detail)
Grain shape	CDE for MgS, spherical for the others
Td(Cloudy)a	90–267 K (see the text)
Td(BB fitting)b	160–200 K
md(Cloudy)a	3.44(−4) M☉
md(BB fitting)b	4.81(−6)–9.27(−6) M☉
md(Tot.)c	3.49(−4)–3.53(−4) M☉
md/mg(Cloudy)	1.52(−2)

Notes. The accuracy of log (X/H) + 12 is 0.3 dex. AC stands for amorphous carbon. ^aThe temperature and total mass of PAHs, AC, and SiC grains derived by Cloudy. ^bThe temperature and mass of MgS grains derived by the modified blackbody fitting. ^cThe total mass of PAHs, AC, SiC, and MgS grains.

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Table 14. The Predicted Relative Fluxes by the Cloudy Models

Ions	λlab	Type	I(λ)obs	I(λ)cloudy
He+	4387.93 Å	RL	2.38(−1)	2.69(−1)
	4471.47 Å	RL	1.72(0)	2.22(0)
	4921.93 Å	RL	4.64(−1)	5.84(−1)
	5876.66 Å	RL	6.16(0)	6.76(0)
	6678.16 Å	RL	1.60(0)	1.74(0)
	7281.35 Å	RL	3.19(−1)	4.70(−1)
C2 +	1906/09 Å	CEL	<5.03(+1)	4.52(+1)
N+	5754.64 Å	CEL	5.87(0)	6.92(0)
	6548.04 Å	CEL	5.89(+1)	6.77(+1)
	6583.46 Å	CEL	1.90(+2)	2.00(+2)
N2 +	1750 Å	CEL	1.41(0)	1.04(0)
O+	3726.03 Å	CEL	5.54(+1)	6.97(+1)
	3728.81 Å	CEL	1.97(+1)	2.94(+1)
	7320/30 Å	CEL	2.58(+1)	4.39(+1)
O2 +	4361.21 Å	CEL	1.37(−1)	1.80(−1)
	4958.91 Å	CEL	6.44(0)	6.07(0)
	5006.84 Å	CEL	1.85(+1)	1.83(+1)
Ne+	12.81 μm	CEL	3.09(+1)	3.18(+1)
P+	1.15 μm	CEL	1.22(−1)	1.31(−1)
	1.19 μm	CEL	3.41(−1)	3.93(−1)
S+	4068.60 Å	CEL	1.79(0)	1.27(0)
	4076.35 Å	CEL	6.34(−1)	4.07(−1)
	6716.44 Å	CEL	4.42(−1)	4.56(−1)
	6730.81 Å	CEL	1.08(0)	9.08(−1)
S2 +	6312.10 Å	CEL	3.23(−1)	5.50(−1)
	9068.60 Å	CEL	3.22(0)	3.89(0)
	18.71 μm	CEL	1.40(0)	3.65(0)
Cl+	8578.69 Å	CEL	1.19(−1)	5.94(−2)
	9123.60 Å	CEL	7.76(−2)	1.57(−2)
Cl2 +	5517.66 Å	CEL	2.88(−2)	3.24(−2)
	5537.60 Å	CEL	7.22(−2)	7.62(−2)
Ar2 +	5191.82 Å	CEL	1.86(−2)	2.62(−2)
	7135.80 Å	CEL	2.46(0)	3.04(0)
	8.99 μm	CEL	3.06(0)	1.91(0)
Fe2 +	4701.53 Å	CEL	6.89(−2)	6.62(−2)
	4754.69 Å	CEL	3.86(−2)	2.70(−2)
	4769.43 Å	CEL	5.32(−2)	2.22(−2)
	4881.00 Å	CEL	4.93(−2)	7.07(−2)
	5270.40 Å	CEL	7.06(−2)	8.85(−2)
Bands	λcenter	Δλ	I(λ)obs	I(λ)cloudy
B	0.40 μm	0.300 μm	4.05(+2)	4.36(+2)
J	1.24 μm	0.162 μm	1.14(+2)	1.24(+2)
H	1.66 μm	0.251 μm	9.21(+1)	1.12(+2)
Ks	2.16 μm	0.262 μm	8.36(+1)	8.01(+1)
WISE1	3.353 μm	0.663 μm	1.15(+2)	1.32(+1)
WISE2	4.603 μm	1.042 μm	1.43(+2)	1.27(+2)
AKARI1	9.22 μm	4.104 μm	1.62(+3)	1.01(+3)
IRS1	10.30 μm	1.000 μm	2.21(+2)	2.18(+2)
IRS2	11.30 μm	1.000 μm	6.54(+2)	6.81(+2)
IRS3	12.50 μm	1.000 μm	5.14(+2)	5.14(+2)
IRS4	13.50 μm	0.600 μm	2.08(+2)	2.56(+2)
AKARI2	66.70 μm	20.2 μm	4.49(+2)	5.04(+2)
AKARI3	89.20 μm	39.9 μm	3.70(+2)	3.47(+2)

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The predicted CEL C and O abundances are close to the model results by Karakas (2010). The predicted CEL C/O ratio (+0.19 dex) suggests that M1-11 could be a normal low-mass, C-rich PN slowly evolving toward higher effective temperatures. The elemental abundances predicted by Cloudy are comparable with the observation and are in excellent agreement with the model prediction by Karakas (2010).

In Figure 13, we present the calculated SED from Cloudy (dots), the MgS modified blackbody fitting (broken line), and the sum of those two components (thick line). The gray lines and circles represent the observations including the IUE spectra, 2MASS JHKs (Ramos-Larios & Phillips 2005), the AKARI 9/18/65/90 μm, and the WISE 3 and 4 μm photometry. In the inset, we focus on the ∼10–40 μm part of the SED. The predicted SED matches the data in the UV to mid-IR range well, except for the PAH emission, in particular the 13.6 μm feature due to the C–H out of plane bending mode (quartet).

The temperatures of the 0.5 μm sized amorphous carbon, SiC, and MgS are 91, 102 (by Cloudy), and 160–200 K (by blackbody fitting), respectively. The temperature of the 0.005 μm sized amorphous carbon grains and PAHs are 177 K and 267 K, respectively. The gas C mass within 26 predicted by Cloudy is 4.68(−5) M_☉. Most of the C in the nebula exists as grains. The mass of pure C₆₀ in the nebula is only ∼0.008% of the total C dust.

Assuming a distance of 2.1 kpc, the initial mass of the progenitor is estimated to be 1–1.5 M_☉ based on the location of M1-11 with respect to the post-AGB H-burning evolutionary tracks with Z = 0.004 (Vassiliadis & Wood 1994), as shown in Figure 14. The age is >1000 yr after leaving the AGB phase.

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Since the discovery of fullerenes C₆₀ and C₇₀ in a C-rich PN Tc1 (Cami et al. 2010), the number of detections of these lines are increasing (García-Hernández et al. 2010, 2011a; Zhang & Kwok 2011); however, the formation process of fullerenes in evolved stars and in the ISM is under debate. At present, three explanations for fullerene formation are proposed.

4.3.1. Destruction of HAC

4.3.2. Destruction of PAH Clusters

4.3.3. Photochemical Process of PAH Clusters

4.3.4. Comparison between C₆₀ PNe