INFRARED STUDY OF FULLERENE PLANETARY NEBULAE

The C₆₀ fullerene molecule displays four infrared features located at ∼7.0, 8.5, 17.4, and 18.9 μm (e.g., Kratschmer et al. 1990; Iglesias-Groth et al. 2011). In order to better isolate these spectral features, we performed a careful subtraction of the dust continuum emission between 5 and 25 μm in the spectra of the 263 PNe mentioned above. To do so, the dust continuum emission was represented by 3–7 order polynomials fitted at spectral locations that we believed to be free from any dust or gas feature; for example, the spectral points at 6, 9, 14, and 24 μm are not affected by dust emission at 6–9, 9–13, 15–20, and 25–35 μm. Note that we preferred to exclude the 25–38 μm spectral region from the dust continuum subtraction because the 25–35 μm emission sometimes extends well beyond 38 μm, which made determining the location of the continuum difficult. Then, by inspecting the dust continuum subtracted or residual spectra, we searched for emission features at the four spectral positions corresponding to the bands that may be attributed to C₆₀ fullerenes (see Figure 1). To illustrate the technique, in Figure 1, we show examples of the dust continuum subtracted spectra of the PNe Tc 1 and K 3−54. Tc 1 (see the left panel in Figure 1) was observed at high resolution and displays some of the strongest fullerene features in our sample. On the other hand, PN K 3−54 (see the right panel in Figure 1) was observed at low resolution and displays much weaker fullerene bands than Tc 1.

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We found obvious fullerene features in 16 objects out of the 263 PNe analyzed. They are distributed as follows: seven SMC PNe (six from program 20443 and one from program 103), four LMC PNe (three from program 20443 and one from program 103), and five Galactic PNe (three from program GO 3633 and two from program GO 50261). Most of these detections have already been published: three Galactic targets and one SMC target in García-Hernández et al. (2010); the 10 detections of fullerenes in PNe of the MCs in García-Hernández et al. (2011a); and the first fullerene detection in Tc 1 in Cami et al. (2010). In this paper, we report the detection of fullerenes in a new source, the Galactic PN M 1−60, and provide an overall and detailed analysis of the whole sample of PNe with fullerenes.

In a previous work, we presented some basic CLOUDY models (Ferland et al. 1998) for the fullerene PNe in the MCs (García-Hernández et al. 2011a). We were only interested in doing some general and basic model predictions to explore the possible origins of the 7.0 μm emission and the usually low [Ne iii]/[Ne ii] ratios observed in fullerene PNe. To do so, we adopted the stellar ionizing continuum blackbodies (BBs) and stellar spectra from Rauch (2003) and concluded that the 7.0 μm emission in fullerene PNe cannot be attributed solely to [Ar ii] 6.99 μm but also to a combination of C₆₀ and C₇₀. Furthermore, the fact that those models were unable to explain the low [Ne iii]/[Ne ii] ratios by photoionization, and given that fast stellar winds from the central stars are ubiquitous in PNe (and the associated shocks), lead us to the suggestion of a possible shock-excited origin for the [Ne ii] 12.8 μm emission in fullerene PNe (see García-Hernández et al. 2011a for more details). We did not contemplate the possibility, however, that the observed [Ne iii]/[Ne ii] ratios also might be explained by using model atmospheres with line (and wind) blanketing (C. Morisset 2011, private communication; see also Morriset et al. 2004 and references therein). Here, we present new radiation transfer modeling exploring this option.

We used version C08.01 of the photoionization code CLOUDY to model the nebular emission in our fullerene sources. For the model atmosphere of the central star, we used the grid of models provided by Pauldrach et al. (2001), which are available in CLOUDY, identified as tables WMBasic. These models include non-LTE, line- and wind-blanketed model, atmospheres for OB stars with solar and sub-solar metallicities. For all models, we have assumed a constant luminosity of 10⁴ L_☉ of the star and a fixed distance to the nebula of 0.1 pc (inner radius). Variations of luminosity and/or inner radius closely mimic variations of the temperature of the central star. Thus, our sequences (varying central star temperature) represent the locus of a given model for any combination of luminosity, distance, and temperature. We computed models using solar and sub-solar metallicities for the atmosphere of the central star, but there are no large differences in the resulting line ratios. We assumed for the abundances of the nebula those for the prototype fullerene PN Tc 1 and quoted by Pottasch et al. (2011) in Table 15. We considered a spherical geometry for the nebula with a density of 1800 cm⁻³ at the inner radius, and a dependency with the distance to central ionizing source as r⁻². The chemical abundances of the photoionized gas are also those quoted by Pottasch et al. (2011) in their Table 15.

In Figure 6, we display our model predictions compared to the observed line ratios ([Ar ii]/H i versus [Ar iii]/H i and [S iv]/[S iii] versus [Ne iii]/[Ne ii]) in the fullerene PNe of our sample. In the right panel, we present a combination of line ratios ([S iv]/[S iii] versus [Ne iii]/[Ne ii]), which permits determination of the effective temperature (T_eff) of the central star, independently of the nebular abundances. It can clearly be seen that model atmospheres with line and wind blanketing can explain many of the observed [Ne iii]/[Ne ii] ratios. In addition, all fullerene sources show a rather narrow range in effective temperature (T_eff ∼ 30, 000–45,000 K).

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The fact that line and wind blanketing can explain many of the observed [Ne iii]/[Ne ii] ratios weakens the hypothesis of a shock-excited origin for the [Ne ii] 12.8 μm emission. Unfortunately, the shock hypothesis cannot be directly tested with the present data.

It should be noted that the observed central star effective temperatures determinations in the literature (listed in Table 2) came mostly from hydrogen Zanstra analysis, and thus, although more reliable for optically thick PNe, they should always be used as lower limits for optically thin targets (see also Section 4.1). Moreover, none of the temperature determinations available are free from model assumptions. Indeed, from our CLOUDY modeling (see Figure 6), we infer effective temperatures higher than the hydrogen Zanstra temperatures (although always lower than 45,000 K) for all of these MC PNe. The only exception is LMC 02 for which the [S iv]/[S iii] ratio is somewhat lower than expected for its T_eff (39,000 K as derived from FUSE data; we attribute this difference to a contamination by C₇₀ of the observed 18.7 μm emission. From Figure 6, it is also evident that for Galactic PNe M 1−20 and M 1−60 the models indicate T_eff ∼ 40,000–45,000 K,¹⁴ whereas for Tc 1 T_eff ≃ 35,000 K. Note that the Galactic PNe M 1−12 and K 3−54 are not shown in this diagram because they only present [Ne ii] 12.8 μm and [S iv] 10.5 μm emission, respectively. An anomalous high value of [Ne ii] 12.8 μm emission (e.g., as a consequence of strong shocks) in these sources cannot be discarded.

In the left panel of Figure 6 ([Ar ii]/H i versus [Ar iii]/H i), we illustrate how varying the abundance of Ar noticeably affects the line ratios involving these lines. It can be seen that the observed values of [Ar iii]/H i can be explained with the model effective temperature, consistent with the values derived from the [S iv]/[S iii] versus [Ne iii]/[Ne ii] diagram shown in the right panel of Figure 6. However, none of the models can explain (even taking into account maximum errors of 40% in the observed line intensity ratios) the high observed values of the [Ar ii]6.99 μm/H i line flux ratio. For example, in the case of Tc 1 and M 1−12, the expected ratios are around 1, whereas in the case of M 1−20 and M 1−60 those are around 0.1. Note that PN K 3−54 does not appear in this diagram because the H i 7.5 μm line is blended with the much stronger 7.7 μm AIB. Thus, the new CLOUDY modeling confirms that the 7.0 μm emission in fullerene PNe cannot be attributed uniquely to [Ar ii] 6.99 μm, and the C₆₀ and C₇₀ emission contributions have to be taken into account.

Our previous work indicates that the fullerene emission in PNe of the MCs likely originates from solid-phase fullerene molecules, which are formed on the surface of pre-existing VSGs (or HACs) (García-Hernández et al. 2011a; Duley & Hu 2012). This conclusion was based on the fact that the observed C₆₀ 7.0/18.9, 8.5/18.9, and 17.4/18.9 intensity ratios differ from the theoretical predictions for UV-excited gas-phase C₆₀ molecules given by Sellgren et al. (2010). Here, we determined the fluxes of the 7 and 8.5 μm C₆₀ transitions (which are actually only due to C₆₀) in the Galactic PNe M 1−20, M 1−12, M 1−60, and K 3−54¹⁵ and we constructed the corresponding Boltzmann excitation diagrams (see below for more details) for these Galactic PNe.

In Table 3, we list the C₆₀ intensity ratios in fullerene PNe of our Galaxy in comparison with the values derived for fullerene PNe in the MCs. Note that the listed C₆₀ F(7.0)/F(18.9) flux ratios are obtained by correcting the observed emission fluxes at 7 μm by the C₆₀ contribution factors (f_C60) derived from the Boltzmann excitation diagrams (see below) and also listed in Table 3. In addition, the listed C₆₀ F(8.5)/F(18.9) intensity ratios in a few sample PNe (see above) were corrected by their corresponding contribution factors at 8.5 μm (not shown in Table 3). From the results obtained, we can reach a similar conclusion about the fullerene excitation mechanism for the subsample of fullerene-detected PNe in our Galaxy (see Table 3). In particular, the C₆₀ 7.0/18.9 and 8.5/18.9 ratios indicate photon energies of less than 5 eV, regardless of the central star temperatures (between ∼30,000 K and 45,000 K). In addition, the C₆₀ 17.4/18.9 intensity ratio strongly varies from source to source (from 0.21 to 1.13), while this ratio is predicted to be insensitive to the energy of the absorbed UV photons (a C₆₀ 17.4/18.9 ratio of 0.28–0.38 is predicted by Sellgren et al. 2010) for gas-phase fullerene molecules. It should be noted that our conclusion is different from that very recently drawn by Bernard-Salas et al. (2012). However, the other fullerene C₇₀ also contributes to the observed 7 μm flux (Iglesias-Groth et al. 2011; García-Hernández et al. 2011a)—e.g., in Tc 1, the C₇₀ flux contribution (40%) is even higher than that for C₆₀ (25%). Our conclusion is supported by the fact that the same temperatures (within the errors) are needed to explain both the 7.0 and 8.5 μm C₆₀ band strengths. Finally, we note that taking into account the uncertainties of flux measurements and Einstein coefficients, our average intensity C₆₀F(7.0)/F(18.9) (=0.28), F(8.5)/F(18.9) (=0.35), and F(17.4)/F(18.9) (=0.56) ratios would be more consistent with the C₆₀ intrinsic strengths reported by Fabian (1996) and Iglesias-Groth et al. (2011). Thus, in the following, we will assume that the fullerene emission in PNe is originated from solid-state fullerenes.

We can determine the fullerene excitation temperature for each PN from the flux measurements of the C₆₀ and C₇₀ transitions (see Table 1) and the absorptivity measurements recently obtained by Iglesias-Groth et al. (2011). Absorptivity for each transition led to an f-value from which the Einstein coefficient A_ij, is derived which provides a relation between the emitted flux and the number of molecules populating the energy level associated with the transition (see, e.g., Cami et al. 2010 for more details).

We adopted the temperature dependence of the absorptivity for each C₆₀ and C₇₀ transition given in Iglesias-Groth et al. (2011) and developed an iterative process to find the best possible correlation coefficient in the plane ln(N_u/g_u) versus E_u/k independently for each fullerene. A thermal distribution over the excited states will be indicated by collinear data points in the Boltzmann excitation diagram. In this case, the slope and the intercept of the linear relation determines the temperature and total number of emitting fullerene molecules. The initial temperatures for this iterative process were assumed in the range from 100 to 1000 K and only a few iterations were required for a quick convergence. The temperature values for C₆₀ and C₇₀ derived this way are listed in Table 3. The four mid-IR transitions of C₆₀ were considered, allowing the fraction of the flux of the 7 μm transition—which is actually due to C₆₀—to be a free parameter because of the possible contamination with C₇₀ and the [Ar ii] nebular line. The best linear fit is sensitive to this fraction, and thus we also iterated on this parameter in order to explore the full range of possible values (from 0 to 1). In the case of C₇₀, we considered the three or four (depending on the source and the signal-to-noise ratio (S/N) of the spectrum; see Table 1 for the C₇₀ features used for each source) mid-infrared transitions less contaminated by other species, iterating also on the fraction of the 7 μm flux that may be due to C₇₀. We generally found very good correlation coefficients that are always higher than 0.89. Figure 7 illustrates examples of the Boltzmann excitation diagrams for the C₆₀ (left panel) and C₇₀ (right panel) fullerene emission detected in the MC PNe SMC 16 and LMC 02, respectively.

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The fullerene PNe in the MCs were previously studied by us in García-Hernández et al. (2011a). The sources in the MCs offer a more reliable estimation of the C₆₀ and C₇₀ abundances in PNe than in their Galactic counterparts. This is because the distances to the MCs (48.5 and 61 kpc for the LMC and SMC, respectively) are accurately known and reliable C abundances are also available in the literature (García-Hernández et al. 2011a). However, this is not the case for the five fullerene PNe in our Galaxy—in addition, only Tc 1 has a reliable C abundance in the literature (Table 2). For consistency, we decided to assume the recent statistical distances by Stanghellini & Haywood (2010) for four of the Galactic sources: M 1−20 (8.0 kpc), M 1−12 (9.2 kpc), M 1−60 (9.5 kpc), and K 3−54 (23.4 kpc). The only exception is Tc 1¹⁶, for which we assumed a distance of 2 kpc for comparison with Cami et al. (2010). Following Milanova & Kholtygin (2009), we may assign a PN type (i.e., type I, IIa, IIb, III, and IV)¹⁷ and an average carbon abundance (A(C) = log(C/H)+12) to each Galactic PN from the height above the Galactic plane z. Therefore, we assume a type IIa and A(C) = 8.55 for M 1−20 (z = 0.492 kpc) and K 3−54 (z = 0.547 kpc) as well as a type IIb and A(C) = 8.83 for M 1−12 (z = 0.258 kpc) and M 1−60 (z = 0.290 kpc). The IIab PN types of the Galactic fullerene PNe, as derived by this very rough and limited method, seem to be consistent with that of Tc 1, which is identified as a slowly evolving low-mass type II PN (García-Hernández et al. 2010). In addition, as we will see in Section 4.1, all fullerene PNe are likely of low mass and are slowly evolving toward the white dwarf stage. Table 2 lists all relevant information (e.g., H_β flux, C abundance, electron temperature and density, and total hydrogen and carbon masses of the nebula) as well as the source of information used in each case from the literature for all fullerene PNe in our sample.

By using the above distances, the number of C₆₀ and C₇₀ molecules (or masses of pure C₆₀ and C₇₀) was estimated for all sources in our sample, and the C₆₀/C and C₇₀/C abundances listed in Table 3 were derived from the total carbon and hydrogen mass of the nebula. The total H mass of the nebula is obtained from the electronic temperature and density and the observed H_β flux, while the total carbon mass is obtained from the total H mass and C abundance of the nebula. The corresponding C₇₀/C₆₀ ratios are also given in Table 3. We find C₆₀/C ∼0.01%–0.05% (average of 0.03%) and T_C60 = 260–660 K for the four Galactic fullerene PNe studied for the first time in this paper. The formal error of our fullerene abundance estimations are difficult to evaluate because we used different literature sources for the C abundance, electron density, etc. However, it should be noted that by giving the C₆₀/C and C₇₀/C abundance ratios, the distance dependence is canceled. Thus, the main sources of error are the electronic density and carbon abundance. We estimate that the errors of our fullerene abundances in MC PNe are certainly lower than 50% (likely much lower for most of the MC PNe sample), but the maximum error in the C₆₀/C ratio for the Galactic PNe (with the exception of Tc 1 for which the C abundance is more accurately known) may be a factor two or three. Taking into account all assumptions made regarding the Galactic objects, our individual and average C₆₀/C abundances as well as the C₆₀ temperatures for these sources are very similar to the C₆₀ abundances obtained in the MCs (see Table 3). Finally, note that we estimate C₆₀/C = 0.04% and C₇₀/C = 0.005% in Tc 1, which are a factor of 40 and 300, respectively, lower than the ∼1.5% estimates for both species by Cami et al. (2010).

The temperature and luminosity of central stars of PNe are important parameters in order to determine the evolutionary status of the nebula. Central star temperatures are available for a sizable number of objects in the sample of PNe with fullerenes (nine PNe). However, most of the temperature determinations of the objects at hand rely on widely used indirect methods: either Zanstra (Zanstra 1931) or the Energy Balance (Stoy 1933), with only one exception, LMC 02, obtained from FUSE data (Herald & Bianchi 2004). Moreover, for those PNe for which Zanstra temperatures have been obtained (SMC 13, SMC 24, SMC 27, and LMC 25), only hydrogen Zanstra temperatures could be determined, for which the optically thick nature of the nebulae to all the photons above the Lyman limit of H is not assured. An indication that the effective temperature of these stars cannot be much higher than ≈50,000  K is provided by the lack of detection of He ii 4686 Å nebular line flux and confirmed by our new CLOUDY modeling (see Section 3.1).

Although not definitive, conclusions can be drawn given the small number of objects and the uncertainties; the available data show that all the PNe with fullerenes have central stars with low effective temperatures in the range between ∼30,000 and 45,000 K. Given the paths that these stars follow in the H-R diagram, a low temperature can imply a very old or a very young star, therefore a second parameter, stellar luminosity (or mass), is needed in order to understand their evolutionary status. Unfortunately, central star luminosity determinations rely on the availability of the distances accurately determined for a handful of objects in the Galaxy and none of the fullerene-containing PNe are among them. The situation is quite different for the PNe located at the known distances of the MCs. In this case, determinations of the central star luminosities are possible with great accuracy provided that the central star flux is measured. Out of the 11 PNe in the clouds, only 3 of them have measured luminosities (see Villaver et al. 2003, 2004); the reasons are either the objects were not observed with the appropriate instrumentation in order to measure the stellar flux (six PNe), the star was saturated (LMC 25), or the central star was below the nebular level and thus not detected (SMC 13).

PNe SMC 24, SMC 27, and LMC 02 are the only ones that we can analyze in full given that they have both luminosities and effective temperatures available (Villaver et al. 2004; Herald & Bianchi 2004). Although conclusions from three objects cannot be extrapolated to the full sample, we find it meaningful that these three have luminosities that locate them in the horizontal part of the post-AGB tracks for central stars of PNe. Together with their low effective temperatures, this indicates that at least these three objects are truly unevolved stars for which less than ≈10,000  yr (central star time according to Vassiliadis & Wood 1994) could have passed since the moment the star left the AGB phase. Moreover, all three objects have central stars in the low-mass range: 0.59 M_☉ for SMC 24, 0.60 M_☉ for SMC 27, and 0.56 M_☉ for LMC 02, implying that the three of them descend from a low-mass progenitor with a main-sequence mass <1.5 M_☉. It is important to note that the masses of fullerene systems in the SMC are within the average mass of central stars of PNe in the SMC, 0.63 M_☉ (Villaver et al. 2004), while the LMC object is significantly less massive than the average (0.65 M_☉ central star mass) (Villaver et al. 2003, 2007).

The central star and nebular gas are interdependent systems, that is, the evolution of the nebulae is governed by the energetics provided by the central star mostly through the stellar wind and ionizing radiation field. In that sense, the physical radius of the PNe can provide an indirect way of evaluating the evolutionary status of the systems provided that for the objects in the MCs this quantity is available. If we take the photometric radius of the nebulae¹⁸ from Hubble Space Telescope (HST) data in Stanghellini et al. (2003) and Shaw et al. (2006) and then adopt a distance to the SMC of 61 kpc and to the LMC of 48.5 kpc, we obtain the physical radius of the PNe in the MCs. With only one exception, LMC 99 (with a physical radius of 0.1  pc), all the radii are <0.06  pc. The average radius of all the PNe in the MCs that contain fullerenes is 0.058  pc (or 0.054 pc if we exclude LMC 99). The majority of the PNe in the HST samples have small sizes; they were selected to avoid entangled lines in the STIS spectroscopic observations. They have a median photometric radius of 0.10 pc in the LMC and 0.08 pc in the SMC (see Shaw et al. 2006). The samples of MC PNe that contain fullerenes have physical sizes even smaller (most of them <0.06 pc) than the average values. Irrespective of the mechanism, whether at the expense of the energy provided by the hot bubble (the high-velocity wind producing an adiabatic shock) or by the propagation of the ionization front, shell growth is expected to increase with time (see Villaver et al. 2002b). Thus, if we accept physical size as an indicator of the evolutionary status of the nebulae, then the fullerene PNe in the MCs seem to be young (non-evolved) systems, as suggested by their small physical radii that are smaller than the average value of a full sample.

Interestingly, the fraction of fullerene-detected PNe increases with decreasing metallicity (∼5% in the Galactic disk versus ∼31% in the MCs). This fraction goes from ∼5% in the Galactic disk (two detections from 39 C-rich compact (<4'') and young PNe; Stanghellini et al. 2012) to ∼20% in the LMC (four detections from 20 C-rich LMC PNe) and ∼44% in the SMC (seven detections from 16 C-rich SMC PNe). In addition, the Spitzer/IRS spectra reveal that dust processing is very limited in the low-metallicity environments of the MCs. The size of the dust grains remains small (e.g., Stanghellini et al. 2012) and the formation of PAHs (as indicated by the presence of AIBs) is more difficult at low metallicities (Stanghellini et al. 2007). This indicates that the dust grains are less processed in low-metallicity PNe than in their Galactic counterparts, likely because of the probability of forming big carbon dust aggregates around the central star, which may be affected by the posterior PN evolution—i.e., the quickly changing UV radiation field and/or the post-AGB shocks from the strong stellar winds. This probability decreases with decreasing metallicity.

Although we find meaningful that the fraction of fullerene PNe probably depends upon the metallicity of the host environment, it is worth noting here that selection effects in the Spitzer PN samples may play a potentially significant role in the statistics mentioned above. None of these MC PN samples are complete, though the surface brightness was high enough to be included in an HST or Spitzer sample. However, our estimation of the detection rate of fullerenes (∼5%) in our own Galaxy comes from the sample of 157 compact and young PNe in the Galactic disk (Stanghellini et al. 2012). This Galactic fullerene detection rate may be considered as an upper limit for environments of roughly similar solar metallicity. This is because Stanghellini et al.'s (2012) PNe sample is sampling the early stages of PN evolution and dust processing (see below), when the detection rate of fullerenes is expected to be maximized; the fullerenes are not too cold (e.g., T_{C60, C70} < 100 K) to escape detection at mid-infrared wavelengths.

In short, the high detection rate of fullerenes in MC PNe seems to be strongly linked to the limited dust processing (or the general presence of small dust grains) in low-metallicity circumstellar envelopes. This is consistent with the observational finding that the still unidentified 21 μm feature (Kwok et al. 2001; see also García-Hernández 2012 for a recent review) is much more common in post-AGB stars of the MCs than in our own Galaxy (Volk et al. 2011). This suggests that the 21 μm feature is possibly also related with the formation of fullerenes and its carrier may be a fragile intermediate product from the decomposition of HAC or a similar material (see below).

As we have mentioned before, dust processing seems to depend on metallicity. For example, MC PNe display infrared spectra, which are similar to many Galactic post-AGB stars, where dust evolution is still in its early stages, and/or still taking place. However, in galactic post-AGB stars, we already can see huge 25–35 μm features (e.g., Hrivnak et al. 2000) and very little 6–9, 9–13, and 15–20 μm features, contrary to what we observe in the MCs. It seems that it is now well established that the carrier of unidentified infrared emission (UIE)—both discrete and broad features—observed from ∼3 to 20 μm in C-rich evolved stars should be carbon nanoparticles with mixed aliphatic and aromatic structures similar to that of HAC dust (Kwok et al. 2001; Kwok & Zhang 2011). Note that instead of HAC nanoparticles, other organic matter with a complex mix of aliphatic and aromatic structures (e.g., coal, petroleum fractions, quenched carbonaceous compounds, etc.) may be present in the circumstellar envelopes of evolved stars and might be responsible for the UIE (e.g., Kwok et al. 2001). For example, coal and petroleum fractions may explain a diverse set of aromatic and aliphatic features seen in proto-PNe (e.g., Cataldo et al. 2002). In this context, our Spitzer spectra of fullerene PNe also show that a complex mixture of aliphatic and aromatic species (e.g., HACs, PAH clusters, fullerenes, and small dehydrogenated carbon clusters) is present in their circumstellar envelopes.

Our interpretation is that the broad infrared features at 6–9, 9–13, 15–20, and 25–35 μm are intimately related with the formation of fullerenes in PNe, being likely produced by a carbonaceous compound with a mixture of aromatic and aliphatic structures (e.g., HAC) and/or their decomposition products (e.g., fullerene precursors or intermediate products). It should be noted that Kwok et al. (2001) were the first to suggest that the broad 6–9 and 9–13 μm features seen in proto-PNe may be due to a carbonaceous compound with a mixed aromatic/aliphatic structure. The 6–9 and 15–20 μm features, which are almost exclusively seen in low-metallicity MC PNe (Figures 3 and 4), may be due to small dust grains (e.g., HAC nanoparticles), while the 9–13 and 25–35 μm that are seen in all metallicity environments (Figures 2–4) would be produced by big dust grains (e.g., HAC aggregates). The broad 6–9 μm feature may be due to HACs, PAH clusters, or VSGs (see, e.g., Tielens 2008), while the 15–20 μm emission may be identified with the C–C–C bending modes of relatively large PAHs or PAH clusters (Van Kerckhoven et al. 2000). On the other hand, although the broad 9–13 and 25–35 μm features are usually attributed to SiC (the so-called 11.5 μm feature; e.g., Speck et al. 2009) and MgS (e.g., Hony et al. 2002), respectively, these features may be due to bigger dust grains (e.g., HAC aggregates). García-Hernández (2012) argued against the SiC and MgS identification of these features in fullerene PNe and it will not be repeated here. Basically, the 25–35 μm feature may be explained by HACs (see Grishko et al. 2001; García-Hernández et al. 2010), and the spectral characteristics (position and shape; see also Table 4) of the 9–13 μm emission differ from those of the SiC 11.5 μm feature.

In this section, we study the fullerene emission in our sample of fullerene PNe versus other solid-state/molecular infrared features. The flux emitted in the C₆₀ 18.9 μm feature is roughly correlated with the fullerene content (or C₆₀/C abundance values in Table 3; see also Figure 8) and can be taken as representative of the fullerene emission. Almost all fullerene PNe in our sample show some emission in the broad 9–13 μm feature¹⁹ and in the 11.3 μm PAH feature. However, not all PNe in our sample display evident AIB emissions at ∼6.2 and 7.7 μm or in the very broad 6–9 and 25–35 μm features, which complicates the exploration of any possible relation between the fullerene emission, the carriers of the latter emission features. In particular, we prefer to exclude (on a quantitative basis; see below) the very broad 6–9 and 25–35 μm features from our study. This is because very few fullerene PNe display the 6–9 μm emission, the sensitivity of Infrared Spectrograph (IRS) drops dramatically for λ ⩾ 36 μm, and previous Infrared Space Observatory observations of PNe show that the 25–35 μm feature may go up to wavelengths longer than 40 μm (Hony et al. 2002). The central wavelengths and integrated fluxes of the AIBs (usually attributed to PAHs) at ∼6.2, 7.7, and 11.3 μm, as well as the broad 9–13 and 15–20 μm features, are given in Table 4.

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Figure 8 displays the flux ratio C₆₀ 18.9 μm/9–13 μm versus the fullerene abundances (in percentage), where we include the propagated error bars corresponding to an individual flux error estimation of ∼15%. Note that we do not include the error bars of the fullerene abundances in order to avoid dulling Figure 8. The formal error in our estimation of the fullerene abundances is difficult to calculate (e.g., there are different literature sources for the C abundance, electron density, etc.), but it should be lower than 50% in the MC sources and likely higher in the Galactic PNe (see Section 3.2). Although most of the sources are concentrated in the lower left corner of the diagram displayed in Figure 8, we find that the flux ratio C₆₀ 18.9 μm/9–13 μm seems tentatively to increase with increasing fullerene abundances. Also, two apparent outliers in Figure 8 seem to be PNe Tc 1 and SMC 15. If real, the position of Tc 1 in this diagram may involve a steeper correlation at the highest Galactic metallicities. However, Tc 1's Spitzer spectrum only covers the inner nebula, while the Spitzer apertures cover the full nebula in the rest of fullerene PNe displayed in Figure 8. On the other hand, SMC 15 displays the highest electron density (N_e = 7500 cm⁻³) among the PNe in the SMC (with an average N_e of ∼3500 cm⁻³; see Table 2). It should be noted that by using the average electron density for SMC 15 (3500 cm⁻³), a lower C₆₀/C abundance of ∼0.03% is obtained. Thus, if we do not take into account Tc 1 and SMC 15, then Figure 8 would show an even tighter trend between the C₆₀ 18.9 μm/9–13 μm flux ratio and fullerene abundances in fullerene PNe. In summary, we conclude that there is a tentative observed trend in Figure 8, but more detections of fullerenes in PNe are needed in order to reach a definitive conclusion.

More interesting is that Figure 8 may also be interpreted as a consequence of the destruction of the carrier of the 9–13 μm feature in those PNe dominated by the fullerene emission. This would be expected if the carrier of the broad 9–13 μm feature is a precursor of the fullerene molecules²⁰ and if it is intimately related with the fullerene formation process, as we have just interpreted in the previous section. As we have already mentioned in the Introduction, the strong variability of the broad 9–13 μm emission from source to source (see Table 4) is more consistent with an HAC identification.

Figure 9 compares the fullerene emission with the AIB emission at 6.2 and 11.3 μm (e.g., the C₆₀ 18.9 μm/AIB 11.3 μm flux ratio versus the AIB 6.2 μm/AIB 11.3 μm flux ratio). We find two different groups in Figure 9. A first group composed of three PNe (Tc 1, LMC 02, and SMC 24),²¹ which are dominated by the fullerene emission (C₆₀ 18.9 μm/AIB 11.3 μm >8) and show very weak AIB emission at 6.2 and 11.3 μm (AIB 6.2 μm/AIB 11.3 μm  <  0.75). These fullerene-dominated PNe are also characterized by the weakness of the broad 9–13 μm feature compared to the fullerene emission. This suggests that these three fullerene-dominated PNe may have a mix of aliphatic and aromatic hydrocarbon materials of similar chemical composition (e.g., size and degree of hydrogenation) and/or are under approximate physical conditions (e.g., the intensity of the UV radiation field) in their circumstellar envelopes. A second group in Figure 9, however, is formed by the rest of PNe in our sample that display similar levels of fullerene emission but covering a wide range of AIB 6.2 μm/AIB 11.3 μm flux ratios, likely reflecting quickly changing physical conditions (e.g., UV radiation field and/or the post-AGB shocks) and/or chemical composition. The latter is consistent with the relative strengths of the IR features of amorphous organic nanoparticles with mixed aliphatic and aromatic structures (e.g., HACs), which are known to be strongly dependent on physical conditions and chemical composition (e.g., Scott et al. 1997; Grishko et al. 2001). A similar result is obtained from Figure 10, where we display the C₆₀ 18.9 μm/AIB 11.3 μm flux ratio versus the AIB 7.7 μm/AIB 11.3 μm flux ratio. Again, the same three fullerene-dominated PNe (although Tc 1 does not show the 7.7 μm AIB) form a separate group in this latter diagram, while the rest of objects show a wide range of AIB 7.7 μm/AIB 11.3 μm intensity ratios.

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Finally, a few MC PNe (LMC 25 and 48 in Figure 3 and SMC 13, 15, 18, and 20 in Figure 4) show a broad 15–20 μm emission (see also Table 4). This broad emission feature is usually attributed to the C–C–C bending modes of relatively large PAHs or PAH clusters (e.g., Van Kerckhoven et al. 2000). The 15–20 μm/11.3 μm and 15–20 μm/6.2 μm flux ratios are displayed in Figure 11 and they may be used to estimate the size (number of C atoms) of the grains/PAH clusters responsible for this emission (see, e.g., Van Kerckhoven et al. 2000; Tappe et al. 2006, 2012 for more details). All members of the 15–20 μm subgroup of MC PNe, with the exception of SMC 20, show AIB 11.3 μm/15–20 μm and AIB 6.2 μm/15–20 μm ratios lower than ∼0.1 and 0.2, respectively, suggesting relatively large grains/PAHs clusters of more than 4000 C atoms (see Tappe et al. 2006, 2012, and references therein). Curiously, the observed characteristics of the 15–20 μm emission in these sources—shape, integrated strength relative to the 6.2 and 11.3 μm AIBs, and complete lack of the discrete emission features at 16.4, 17.0, and 17.8 μm—are very similar to the 15–20 μm bump observed in the shock-induced dust processing environment of the supernova remnant N132D (Tappe et al. 2006, 2012). Our interpretation is that these PAH clusters/amorphous carbon nanoparticles survive the harsh conditions in the circumstellar envelope long enough to be detected only in the low-metallicity environments of MC PNe. In our own Galaxy, however, the usual lack of PAH cluster-like 15–20 μm emission in fullerene PNe indicates that these PAH clusters/amorphous carbon nanoparticles are quickly destroyed.

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Some advances in our understanding of the fullerene formation process in PNe have been made since the discovery of C₆₀ and C₇₀ fullerenes in the PN Tc 1 by Cami et al. (2010). From the observational point of view, our recent detections of fullerenes and graphene precursors (possible planar C₂₄) in PNe have challenged our previous understanding on the formation of these complex molecules, showing that they can form in H-rich circumstellar environments and that they may coexist with PAH-like molecules (García-Hernández et al. 2010, 2011a). The coexistence of a great diversity of aromatic and aliphatic species in PNe with fullerenes supports the idea that fullerenes may form from the photochemical processing (e.g., as a consequence of UV irradiation or shocks) of small solid particles similar to that of HAC, the so-called HAC fullerene formation scenario. The prevailing view was that the H-poor RCBs, resembling the experimental conditions on Earth (Kroto et al. 1985), would be the ideal astrophysical environments for fullerene formation. However, Spitzer observations of RCB stars (García-Hernández et al. 2011b, 2011c) have shown that fullerene formation is inefficient in the highly hydrogen-deficient circumstellar environment of most RCBs. Fullerenes are seen in conjunction with strong PAH-like features in the two least H-deficient RCB stars DY Cen and V854 Cen. In addition, the V854 Cen's IR spectrum evolved from HACs to AIBs (e.g., from PAHs) and C₆₀ in a timescale of only 10 years, supporting the "HAC fullerene formation scenario." The fact that previous CLOUDY photoionization models, using BB and Rauch (2003) stellar atmospheres as ionizing continuum, could not explain the low [Ne iii]/[Ne ii] ratios observed in fullerene MC PNe with fast stellar winds (e.g., shocks) prompted the speculation that fullerenes may be formed by the shock-induced decomposition of HAC material. This interpretation was consistent with the low effective temperatures (<25,000 K) found in the other astronomical environments, such as the proto-PN IRAS 01005+7910, post-AGB and RCB stars, and reflection nebulae, where fullerenes have been found so far (see below). The UV radiation field in the latter astrophysical environments is likely not intense enough for the photochemical processing of HAC (see discussion in García-Hernández et al. 2011b). Indeed, the PAH cluster-like 15–20 μm emission observed in fullerene PNe show a resemblance to that observed in the shock-induced dust processing environment of the supernova remnant N132D (Tappe et al. 2006, 2012).

However, the new CLOUDY models presented in this paper (Section 3.1) show that many of the observed [Ne iii]/[Ne ii] ratios may be explained by photoionization when using model atmospheres with line and wind blanketing. This result weakens the hypothesis of a shock-excited origin for the [Ne ii] 12.8 μm emission. Although fast stellar winds (e.g., shocks) are generally present in fullerene PNe²², the shock hypothesis cannot be directly tested with the actual data. Furthermore, the winds of central stars of PNe are radiation driven (Pauldrach et al. 1986) and, as such, the wind velocity is expected to increase with the central star temperature, allowing the development of wind-driven shock regions when only the central star is sufficiently evolved (Villaver et al. 2002b). Weaker shocks are also expected to be associated with the propagation of the ionization front within the nebula. Figure 6 suggests that the UV radiation from the central star can explain the low [Ne iii]/[Ne ii] ratios observed in many fullerene PNe, putting some doubt on the suggestion of the fullerenes being formed by the shock-induced HAC's decomposition. In summary, this result, together with the narrow range of T_eff (∼30,000–45,000 K) displayed by our sample sources in Figure 6, indicates common fullerene formation conditions in PNe and suggests that perhaps the UV irradiation is photochemically processing the small solid particles with mixed aromatic and aliphatic structures similar to that of HAC dust and this process may form the fullerenes. This interpretation is consistent with the early suggestion by Kwok et al. (2001), who emphasizes the important role of photochemistry in the evolution from proto-PNe to PNe.

From the experimental point of view, we would like to emphasize the recent finding by Duley & Hu (2012) that HAC nanoparticles prepared under a variety of conditions can show IR features coincident with the four C₆₀ IR features, which may be attributed to fullerene precursors or proto-fullerenes. The presence of proto-fullerenes takes place in conjunction with the 16.4 μm feature. This feature is usually present in the proto-PN IRAS 01005+7910, post-AGB and RCB stars, and reflection nebulae (all of them with T_eff < 30, 000 K), likely indicating the presence of proto-fullerenes (García-Hernández et al. 2012) as a previous stage in the evolution and dehydrogenation of UV irradiated HAC dust in fullerene PNe. More recently, Dunk et al. (2012) propose a Closed Network Growth (CNG) mechanism of fullerenes, where larger fullerenes may grow from pre-existing C₆₀ molecules and this formation route can work under the presence of hydrogen. CNG of fullerenes would be consistent with the "HAC fullerene formation scenario" and it may work in the complex circumstellar environments of fullerene PNe. In this context, the smaller C₅₀, C₆₀, and C₇₀ would be supplied by the photochemical processing of HAC dust.