A MOLECULAR LINE SURVEY OF THE CARBON-RICH PROTOPLANETARY NEBULA AFGL 2688 IN THE 3 mm AND 1.3 mm WINDOWS

Circumstellar envelopes (CSEs) created by stellar winds from stars on the asymptotic giant branch (AGB) stage are active sites of molecular synthesis. Thus far, more than 70 molecular species have been detected in CSEs (Cernicharo et al. 2011 and references therein). During the post-AGB evolution, the effective temperatures of the central stars steeply increase, while at the same time, the remnants of the CSE expand and disperse. The increasing ultraviolet (UV) radiation fields gradually dissociate the molecules, and finally ionize the envelopes, leading to the formation of planetary nebulae (PNs). The protoplanetary nebula (PPN) is a rapid (∼10³ yr) transition phase between the AGB and PN phases (Kwok 1993). The chemical processes during the evolution from the AGB to PN phases, however, are far from fully understood. Different carbon-to-oxygen abundance ratio sets up different reaction routes. Although the molecular species in carbon-rich environments is generally thought to be more abundant than that in oxygen-rich environments, Ziurys et al. (2007) recently found unexpected complexity in the chemistry of oxygen-rich environments. Unbiased spectral line survey is the best way to globally investigate the physical conditions and molecular composition in CSEs (see Cernicharo et al. 2011 for a recent review). Most of the work, however, has been focused on the brightest carbon star IRC+10216 (see, e.g., Kawaguchi et al. 1995; Cernicharo et al. 2000, 2010; Patel et al. 2011, etc.). In order to better understand the processes involved in circumstellar chemistry, it would be useful to study objects at different stages of evolution, especially in the post-AGB and PN phases.

In order to understand the interactions between the molecular processes, stellar evolution, and chemical environment, our research group has undertaken a long-term project devoted to systematic molecular line surveys of a sample of evolved stars over a wide frequency range. We have reported the observations of carbon-rich AGB stars IRC+10216, CIT 6, and AFGL 3068, and a young PN NGC 7027 in 1.3 mm, 2 mm, 3 mm, and 7 mm bands (He et al. 2008; Zhang et al. 2008, 2009a, 2009b; Chau et al. 2012). Since the same instrumental settings were used, the systematic uncertainties in the study of circumstellar chemistry are minimized. Our results demonstrate that the evolved stars in the AGB stage have similar chemical compositions and the differences in the abundance of long carbon-chain and Si-bearing molecules can be explained by slightly different evolutionary status and carbon abundances. In the PN stage, the chemical composition changes dramatically with the enhancement of ionized species and the destruction of long-chain molecules, implying the considerable influence of UV radiation field and/or shock waves on the circumstellar chemistry. The present paper is the sixth part of this series. We present a 3 mm and 1.3 mm spectral line survey toward the carbon-rich PPN AFGL 2688, with the goal of investigating the chemical transition in the short evolutionary timescale between the AGB and PN stages.

AFGL 2688 (CRL 2688, V1610 Cyg, and the Egg Nebula) is a bipolar PPN whose visible appearance consists of a pair of bipolar lobes, a dark equatorial lane, and a large number of roughly concentric arcs (Sahai et al. 1998b). The dark equatorial lane exhibits strong emission from H₂ and CO (Sahai et al. 1998a; Cox et al. 2000), suggesting the presence of molecular matter. Details of the stellar wind history and the nebular structures have been thoroughly discussed by Balick et al. (2012), who obtained an expansion velocity of 15–18 km s⁻¹. The dynamical age of the nebula and mass-loss rate were estimated to be ∼350 yr and 3 × 10⁻⁵ M_☉ yr⁻¹, respectively (Ueta et al. 2006; Lo & Bechis 1976). The central star of AFGL 2688 is a completely obscured F-type supergiant with an effective temperature of about 7250 K and enhanced abundances of carbon, nitrogen, neon, and yttrium (Ishigaki et al. 2012). The distance to this PPN is highly uncertain. Ney et al. (1975) and Cohen & Kuhi (1977) estimated a distance of 1–1.5 kpc, while a smaller value (0.3–0.42 kpc) was obtained by Ueta et al. (2006) and Balick et al. (2012) based on the expansion velocity. Lacking of an accurate determination, we have adopted the commonly used value of 1 kpc (Sahai et al. 1998b).

Because of their brightness in the infrared and strong molecular emissions, AFGL 618 and AFGL 2688 are two of the most well-studied PPNs, and are therefore suitable for spectral line surveys at millimeter wavelengths. In terms of morphology, both objects are bipolar nebulae and Woods et al. (2005) suggested that the molecular richness observed in the two PPNs is due to the presence of dense and optically thick equatorial tori separating the bipolar lobes. Based on the spectral type (B0) of the central star, AFGL 618 is more evolved than AFGL 2688 and is closer to becoming a PN. A line survey of AFGL 618 has been performed by Pardo et al. (2007) with the IRAM 30 m telescope in the frequency range of 80–276 GHz. For AFGL 2688, most of previous observations were limited to specific molecular lines. Park et al. (2008) surveyed this object in the frequency range of 85–116 GHz. Recently, Wesson et al. (2010) reported the Herschel/SPIRE FTS spectra of AFGL 618 and AFGL 2688 in the wavelength range from 195 to 670 μm, which trace the warm inner regions of the CSEs. Differing from AFGL 618, AFGL 2688 does not show emission from ionized species, suggesting that its cool central star has not yet provided enough UV photons to alter the chemistry of the CSE.

A comparison between the chemical compositions of the two PPNs can inform us about the efficiency of chemical processes in PPN stage. For this purpose, a spectral line survey of AFGL 2688 over a wider frequency range and with higher sensitivity is desirable. As of 2013, the reported detected and tentatively detected molecules in AFGL 2688 include C₂, C₃, C₄, CO, CN, CS, C₂S, C₂H, C₄H, C₅H, C₆H, C₄H₂, C₆H₂, C₃N, HCN, HNC, HC₃N, HC₅N, HC₇N, HC₉N, HCP, PH₃, PN, NH₃, SiS, SiO, SiC₂, H₂, H₂O, NaCN, MgNC, AlF, and NaCl (see Cernicharo et al. 2001, 2011; Highberger et al. 2001, 2003; Tenenbaum & Ziurys 2008; Milam et al. 2008; Park et al. 2008; Ishigaki et al. 2012; Wesson et al. 2010, and references therein).

The spectra of AFGL 2688 presented in this paper represent the most complete line survey of this object to date. In Section 2, we describe the observations and the data reduction. In Section 3, we present the detected molecular lines, intensity measurements, rotation-diagram analysis, and calculations of molecular abundances, as well as isotopic ratios. In Section 4, we discuss the implication of our observations on circumstellar chemistry. Finally, the conclusions are summarized in Section 5.

The spectral line survey at the 3 mm and 1.3 mm windows were performed during the period from 2005 April and 2006 September with the Arizona Radio Observatory (ARO) 12 m telescope at Kitt Peak and the Heinrich Hertz Submillimeter Telescope (SMT) 10 m telescope at Mt. Graham. The observations were conducted in beam switching mode, with an azimuth beam throw of 2'. Pointing and focus were checked every 2 hr using nearby planets. We obtained the spectra of AFGL 2688 in the frequency ranges of 71–111 GHz, 157–160 GHz,³ and 218–267 GHz, with an on-source integration time of around 1 hr for each frequency setting. The dual-channel SIS receivers were employed in single-sideband dual polarization mode. The system temperatures were 150–400 K and 400–700 K for the 3 mm and 1.3 mm bands, respectively. The image rejection ratio was typically better than 20 dB. The half-power beamwidths (HPBWs) of the ARO 12 m telescope and the SMT are 86''–38'' and 32''–28'' over the frequency ranges 71–160 GHz and 218–267 GHz, respectively. For the 3 mm observations, the receiver back ends were equipped with two 256 channel filter banks with spectral resolutions of 500 kHz and 1 MHz and a millimeter autocorrelator with 3072 channels and 195 kHz resolution. The 3 mm data were calibrated to the $T^*_R$ temperature scale, which was corrected for atmospheric attenuation, radiative loss, and rearward and forward scattering and spillover by the chopper-wheel method. The main-beam brightness temperature was derived using $T_{R}=T^*_{R}/\eta ^*_m$, where $\eta ^*_m$ is the corrected beam efficiency (0.94–0.71 over the frequency range 71–161 GHz). For the 1.3 mm observations, the spectrometers used were a 2048 channel acousto-optical spectrometer with a spectral resolution of 500 kHz per channel and 1024 channel Forbes Filterbanks with a spectral resolution of 1 MHz per channel. The temperature scale was given in terms of $T^*_A$, which was corrected for atmospheric attenuation. The main-beam temperature was derived using $T_{R}=T^*_A/\eta _{{\rm mb}}$, where the main-beam efficiency, η_mb, is ∼0.7. The conversion factors are 32.5–29.1 Jy K⁻¹ and 35 Jy K⁻¹ for 3 mm and 1.3 mm observations, respectively.

The spectra were reduced using the CLASS software package in GILDAS, which is developed and distributed by the Observatorie de Grenoble and IRAM. The scans due to bad atmospheric conditions and receiver instabilities were discarded, and the calibrated spectral data were co-added using the rms noise of each spectrum as weights. Spectral baselines were subtracted by fitting the line-free spectral regions to the low-order polynomial. The 3 mm and 1.3 mm spectra were smoothed and rebinned to a frequency resolution of 1 MHz and 3 MHz, respectively. This led to a typical rms noise level of <8 mK in the main-beam temperature unit for both spectra.

The 3 mm and 1.3 mm overall spectra are shown in Figure 1 with the strong lines identified. More detailed spectra with expanded frequency scales for the 3 mm and 1.3 mm observations are shown in Figures 2 and 3, respectively, with identified lines marked in the spectra. Complete data of the spectra are available in the online journal. Figure 4 shows the individual line profiles in velocity units. Including uncertain detections, we detected a total of 143 lines (or groups of lines) belonging to 19 different molecular species and 13 isotopologues. For the line detections, we have carefully examined the spectra to eliminate artifacts near the band edge. Although some lines are faint (with intensities lower than 3σ noise level), we still consider them to be real or tentative detections because other transitions from the same species are clearly detected in this object or they have been commonly observed in other evolved stars. Most lines lie well within ±20 km s⁻¹ of the central velocity. Unlike AFGL 618, no line is found to show P Cygni profiles. Except SiS and SiO, all the observed molecules contain carbon. The line density is about 1.6 lines GHz⁻¹ for both spectra. Figure 5 shows the cumulative number of detected lines exceeding a given main-beam temperature. For comparison, we have also included the results from Park et al. (2008) in Figure 5. We can see that many more lines are detected in the present work because of higher sensitivity and/or wider frequency range coverage. The line identifications were made using the JPL (Pickett et al. 1998), CDMS (Müller et al. 2001, 2005), and LOVAS (Lovas 1992) spectral line databases. To confirm our identifications, we checked the presence of other transitions of the same species at other frequencies, and compared the identifications with those from previous observations of other sources (Cernicharo et al. 2000; Pardo et al. 2007; He et al. 2008). We can confidently identify all the features, except two lines at 233.938 GHz and 264.191 GHz. Although these lines are close to the HC¹³CCCCN (J = 85–84) line at 223.937 GHz and the Si¹³CC (15_{1, 14}–15_{1, 15}) line at 264.190 GHz, we do not make the association as the other transitions of HC¹³CCCCN and Si¹³CC are not detected. Table 1 lists the line identification as well as the integrated line intensities (∫T_Rdv). The overall spectral properties are similar to that of IRC+10216. No new species are detected in AFGL 2688 beyond those seen in IRC+10216 and most of the non-detections could be due to the larger distance of AFGL 2688 compared to IRC+10216.

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3.1. Individual Molecules

3.2. Comparison with Park et al. (2008)

The λ3 mm spectral line survey of Park et al. (2008) resulted in the detections of eight molecules in AFGL 2688. As illustrated in Figure 5, our spectra are about one order of magnitude deeper and are therefore able to reveal ∼5 times more lines than theirs. There is an overlapping frequency range (85–111 GHz) between the survey of Park et al. (2008) and ours. In Figure 6, we compare the integrated intensities of the lines detected in the overlapping region. Because the beam sizes of the two observations are similar, we do not correct for the effect of beam dilution. Inspection of Figure 6 shows that the intensities of the lines detected in the two observations are in excellent agreement. Our observations detected all the species in those of Park et al. (2008), except C₂S (shown in red). There are 14 molecules detected in our survey (shown in blue) that were not detected by Park et al. (2008).

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Park et al. (2008) claimed the first detection of C₂S in AFGL 2688 through one transition (J = 8–7). The intensity of this C₂S line given by Park et al. (2008) is well above our detection limit. However, we did not detect this line with a 3σ upper limit of 0.01 K. Furthermore, Park et al. (2008) did not detect the J = 7–6 and J = 9–8 transitions of C₂S which also lie in the frequency range of their survey and have comparable strengths to the J = 8–7 line in IRC+10216 (Cernicharo et al. 1987). Therefore, we suspect that this detection is not real, and C₂S cannot be detected in this object at the present sensitivity level.

3.3. Rotation Temperatures, Column Densities, and Fractional Abundances

We have applied the rotation-diagram technique to derive the excitation temperatures (T_ex) and column densities (N) of the molecules detected in our spectra, assuming LTE, optically thin conditions, and negligible background temperature. In Figure 7, we have plotted the populations of the upper levels (N_u) against the corresponding excitation energies (E_u) in the transitions, using the equation,

$$\begin{equation} \ln \frac{N_u}{g_u}=\ln \frac{3k\int T_s dv}{8\pi ^3\nu S\mu ^2}= \ln \frac{N}{Q(T_{\rm ex})}-\frac{E_u}{kT_{\rm ex}}, \end{equation} \tag{ 1 }$$

where g_u is the degeneracy of the upper level, S is the line strength, μ is the dipole moment, ν is the line frequency, Q is the rotational partition function, and k is the Boltzmann constant. Assuming that the surface brightness has a Gaussian distribution, the source brightness temperature T_s is given by $T_s=T_{R}(\theta ^2_b+\theta ^2_s)/\theta ^2_s$, where θ_b is the antenna HPBW and θ_s is source size. The θ_s value may be different for different molecules, and is poorly known for most of the species. We followed the assumption by Park et al. (2008) as well as Fukasaku et al. (1994) and took a uniform θ_s of 20'' for all the species. This assumption leads to a factor-of-two uncertainty in T_s. If a given molecule has more than one transition detected, its T_ex and N can be deduced using a straight-line fit to N_u/g_u versus E_u/kT_ex. When more transitions are detected, the results are more reliable. Departure from the linear relation may imply non-LTE excitation, different excitation mechanisms, effect of optical thickness, misidentification, and/or line blending. The effects of saturation and subthermal excitation on the rotation diagram have been extensively discussed by Goldsmith & Langer (1999). Since our present survey covers a wide frequency range and our detections include molecular transitions arising from energy levels over a wide energy range, the rotational diagram analysis can be particularly useful.

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The rotation diagrams for 10 molecules detected in our survey are shown in Figure 7. The derived values of T_ex and N are given in Table 2, together with the results by Fukasaku et al. (1994) and those of IRC+10216 (He et al. 2008) for comparison. T_ex may be different from species to species. Generally, there are good linear relationships between N_u/g_u and E_u/kT_ex. Nevertheless, some molecules (i.e., SiC₂, HC₃N, and CH₃CN) appear to arise from regions with temperature variations. The average T_ex of HC₃N is 46.1 K, higher than the 25.8 K value obtained by Park et al. (2008) using only λ3 mm data. Figure 7 clearly shows that the higher-J transitions of HC₃N have a higher T_ex. HC₅N transitions were detected only in the 3 mm band and have a low T_ex value of 27.8 K, in good agreement with the that of HC₃N deduced by Park et al. (2008). This implies that the cyanopolyynes coexist in the same regions. The deduced column densities are in order-of-magnitude agreement with the results of Fukasaku et al. (1994). Goldsmith & Langer (1999) suggested that finite optical depth τ can cause deviations of the points from a straight line on the rotation diagram, and an optical correction factor C_τ = τ/(1 − e^−τ) should be introduced in the rotation diagram. However, using the "population diagram" technique presented by Goldsmith & Langer (1999), we found that the ln C_τ values for all the species in Figure 7 are too small (<0.02) to affect our results.

Table 2. Excitation Temperatures, Column Densities, and Molecular Abundances

Species	Texa	N (cm−2)			fX		$f_X/f_{\rm HC_3N}$
	(K)	This Paperb	F94c	IRC+10216d	This Paperb	IRC+10216e	This Paperb	AFGL 618f
CN	⋅⋅⋅	4.10 × 1014	⋅⋅⋅	⋅⋅⋅	8.67 × 10−6	2.18 × 10−6	21.49	3.03
13CN	⋅⋅⋅	2.38 × 1013	⋅⋅⋅	⋅⋅⋅	2.85 × 10−6	7.60 × 10−8	7.06	0.07
CO	⋅⋅⋅	3.45 × 1017	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	100
13CO	⋅⋅⋅	2.45 × 1016	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	2.5
C17O	⋅⋅⋅	2.47 × 1015	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.29
C18O	⋅⋅⋅	2.18 × 1015	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	0.20
CS	⋅⋅⋅	2.88 × 1016	⋅⋅⋅	⋅⋅⋅	7.04 × 10−8	1.10 × 10−6	0.17	0.13
13CS	⋅⋅⋅	8.70 × 1014	⋅⋅⋅	⋅⋅⋅	1.69 × 10−8	2.20 × 10−8	0.04	⋅⋅⋅
C33S	⋅⋅⋅	2.63 × 1014	⋅⋅⋅	⋅⋅⋅	3.58 × 10−9	⋅⋅⋅	0.01	⋅⋅⋅
C34S	⋅⋅⋅	3.22 × 1015	⋅⋅⋅	⋅⋅⋅	5.40 × 10−8	3.70 × 10−8	0.13	⋅⋅⋅
SiO	25.1	7.11 × 1012	⋅⋅⋅	⋅⋅⋅	9.07 × 10−9	1.30 × 10−7	0.02	0.01
SiS	36.4	5.24 × 1013	4.5 × 1013	⋅⋅⋅	1.40 × 10−7	1.05 × 10−6	0.35	⋅⋅⋅
C2H	6.6	3.10 × 1015	⋅⋅⋅	⋅⋅⋅	1.22 × 10−6	2.80 × 10−6	3.03	0.50
HCN	⋅⋅⋅	1.21 × 1015	4.32 × 1015	⋅⋅⋅	6.17 × 10−7	1.40 × 10−5	1.53	1.49
HC15N	⋅⋅⋅	1.45 × 1013	⋅⋅⋅	⋅⋅⋅	2.91 × 10−8	⋅⋅⋅	0.07	⋅⋅⋅
H13CN	⋅⋅⋅	1.52 × 1014	⋅⋅⋅	⋅⋅⋅	5.34 × 10−7	3.10 × 10−7	1.32	0.03
HNC	⋅⋅⋅	5.03 × 1013	2.0 × 1014	⋅⋅⋅	5.71 × 10−7	7.20 × 10−8	1.42	0.17
HN13C	⋅⋅⋅	1.60 × 1012	⋅⋅⋅	⋅⋅⋅	4.79 × 10−9	1.90 × 10−9	0.01	0.004
SiC2	95.3	4.94 × 1013	⋅⋅⋅	2.9 × 1015	2.67 × 10−7	2.40 × 10−7	0.66	⋅⋅⋅
C3H	51.1	9.43 × 1013	⋅⋅⋅	1.32 × 1014	4.05 × 10−7	5.50 × 10−8	1.00	0.02
C3N	⋅⋅⋅	1.08 × 1014	⋅⋅⋅	4.54 × 1014	5.36 × 10−7	3.00 × 10−7	1.32	0.12
C4H	12.8	1.91 × 1015	2.91 × 1015	8.1 × 1015	3.95 × 10−6	3.20 × 10−7	9.79	1.0
C5H	⋅⋅⋅	1.32 × 1015	⋅⋅⋅	⋅⋅⋅	2.47 × 10−7	⋅⋅⋅	0.61	0.005
HCO+	⋅⋅⋅	1.67: × 1013	⋅⋅⋅	⋅⋅⋅	2.57: × 10−8	⋅⋅⋅	0.06	0.10
H2CO	⋅⋅⋅	2.64 × 1013	⋅⋅⋅	⋅⋅⋅	3.05 × 10−8	⋅⋅⋅	0.08	0.13
H2CS	⋅⋅⋅	1.63: × 1013	⋅⋅⋅	⋅⋅⋅	1.87: × 10−8	⋅⋅⋅	0.05	⋅⋅⋅
HC3N	46.1	3.90 × 1014	7.27 × 1014	8.0 × 1014	3.83 × 10−7	1.25 × 10−6	1.0	1.0
H13CCCN	32.4	2.37 × 1013	⋅⋅⋅	2.0 × 1013	3.20 × 10−8	⋅⋅⋅	0.08	⋅⋅⋅
HC5N	27.8	2.06 × 1014	2.05 × 1014	⋅⋅⋅	8.47 × 10−8	7.03 × 10−6	0.21	⋅⋅⋅
CH3CN	28.0	5.85 × 1013	⋅⋅⋅	2.6 × 1013	7.60 × 10−8	6.60 × 10−8	0.19	0.03

Notes. ^aA constant excitation temperature of 40 K was assumed for the species for which the rotation diagrams cannot be obtained. ^bFor the species with optically thick emission, this gives the low limits. ^cFrom Fukasaku et al. (1994). ^dFrom He et al. (2008). ^eFrom Woods et al. (2003). ^fThose of the circumstellar shell in AFGL 618; from Pardo & Cernicharo (2007).

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We also calculated the fractional abundances (f_X) of the detected molecules relative to H₂ using the formula proposed by Olofsson (1996). A detailed explanation of the method can be found in Zhang et al. (2009b). The deduced f_X values and those normalized to HC₃N are given by Table 2, where the results for IRC+10216 and AFGL 618 (Woods et al. 2003; Pardo & Cernicharo 2007) are listed for comparison. It should bear in mind that the calculations were based on assumed mass-loss rate, distance, and geometry of the shell, which are not well known. We estimate that the error of f_X amounts to a factor of five. Nevertheless, when comparing the relative f_X between detected molecules, the uncertainties invoked by these assumed parameters can be greatly reduced.

3.4. Isotopic Ratios

The CSEs of evolved stars are constantly replenished by products of nucleosynthesis in the stellar interior. As a star evolves, changes of nuclear process lead to changing isotopic compositions, which are eventually reflected in the composition of the CSE. The isotopic ratios in the CSE of IRC+10216 have been obtained by several groups (i.e., Wannier et al. 1991; Kahane et al. 2000). These studies suggest that the ¹²C/¹³C, ¹⁶O/¹⁷O, and ¹⁸O/¹⁷O ratios are lower compared to the solar values, while the ¹⁴N/¹⁵N ratio is more than 10 times larger than solar. The ¹⁶O/¹⁸O ratio and those of heavier elements are consistent with the solar values. We have determined the isotopic ratios of C, N, O, and S in AFGL 2688 through the same J transitions of molecules and their isotopologues. The calculations are based on the assumptions that the main and isotopic lines are optically thin and the lines are under the same excitation conditions. The results, along with those of IRC+10216 and the Sun, are presented in Table 3. The main lines of CO, HCN, and CS are optically thick, and thus only give the lower limits of the corresponding isotopic ratios.

Table 3. Isotopic Abundance Ratios

Isotopic Ratio	AFGL 2688		IRC+10216a	Solarb
	Species	Value
12C/13C	12C34S/13C32S	61 ± 30c	45±3	89
	H12C3N/H13CCCN	23 ± 14
	12CO/13CO	>4.1
	12CS/13CS	>18.3
	H12CN/H13CN	>3.3
14N/15N	HC14N/HC15N	>24	>4400	272
	H13C14N/H12C15N	<751d
16O/17O	C16O/C17O	>37	840 ± 200	2681
	13C16O/12C17O	<810d
18O/17O	C18O/C17O	0.8 ± 0.2	0.7 ± 0.3	5.37
32S/34S	C32S/C34S	>6.7	21.8 ± 2.6	22.5
33S/34S	C33S/C34S	0.1:	0.18 ± 0.1	0.18

Notes. ^aFrom the references in Kahane et al. (2000). ^bFrom Lodders (2003). ^cAssuming that the ³⁴S/³²S ratio is solar. ^dAssuming that the ¹²C/¹³C ratio is smaller than the solar value.

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We have detected the rare species ¹²C³⁴S and ¹³C³²S. The ¹²C³⁴S/¹³C³²S ratio is 2.7 ± 1.3. Assuming that the ³²S/³⁴S ratio is solar, we obtained ¹²C/¹³C=61 ± 30. ¹²C/¹³C can also be obtained through the HC₃N and isotopic lines which are likely to be optically thin. A comparison of the two results suggests a ¹²C/¹³C ratio of ∼31–37, slightly lower than that of IRC+10216 and significantly lower than the solar value. We note that the results obtained by previous authors scatter over a wide range of 20–66 (see Milam et al. 2009). The low ¹²C/¹³C ratio is typical for carbon-rich CSEs and is suggestive of the existence of a nonstandard mixing mechanism (or cool bottom processing; e.g., Charbonnel 1995) during the red giant phase of low-mass AGB stars. A more detailed discussion about the implications of ¹²C/¹³C for AGB nucleosynthesis can be found in Milam et al. (2009).

Although not strictly true, the derived ¹⁶O/¹⁷O abundance ratio is expected to be positively correlated with that of ¹²C/¹³C since both ¹³C and ¹⁷O are produced by ¹²C and ¹⁶O through (p, γ) reactions followed by β decay. Assuming that the ¹³CO and C¹⁶O lines are optically thin and the ¹²C/¹³C ratio is smaller than the solar value, we derive a ¹⁶O/¹⁷O ratio of <810 in AFGL 2688, or at least three times smaller than the solar value.

From the J = 2–1 transitions of C¹⁸O and C¹⁷O, we obtain an ¹⁸O/¹⁷O ratio of 0.8 ± 0.2, a value consistent with that in IRC+10216 and significantly lower than the solar value, suggesting that ¹⁷O in this object has been substantially enhanced. Combining the present data with those of other CSEs previously reported by us (He et al. 2008; Zhang et al. 2009a, 2009b), we can clearly see a positive correlation between ¹⁶O/¹⁷O and ¹²C/¹³C ratios (Figure 8).

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On the other hand, ¹³C and ¹⁷O can be destroyed by the reactions ¹³C(p, γ)¹⁴N and ¹⁷O(p, α)¹⁴N. Both paths lead to the overproduction of ¹⁴N. The enhancement of ¹⁴N in carbon-rich CSEs has been confirmed by the observations of Wannier et al. (1991), who obtained a lower limit of 544 for the ¹⁴N/¹⁵N ratio in AFGL 2688, about twice higher than the solar value. Assuming that the J = 3–2 transitions of H¹²C¹⁴N and H¹³C¹⁵N are optically thin and the ¹²C/¹³C is smaller than the solar value, we obtained an upper limit for ¹⁴N/¹⁵N of 751, about six times lower than the lower limit in IRC+10216. The lower ¹⁴N/¹⁵N value in AFGL 2688 may be related to the slightly lower ¹²C/¹³C and ¹⁶O/¹⁷O ratios than those in IRC+10216 (Figure 8), suggesting that the two objects probably have different intrinsic properties, such as metallicity and mass.

The nucleosynthesis of sulfur isotopes ³³S and ³⁴S requires relatively high temperatures, which are unlikely to be achieved in the interior of intermediate- and low-mass stars. This is supported by our results that no discrepancy between the S isotopic ratios in AFGL 2688 and the solar values is found.

In order to investigate the chemical evolution of CSEs during the AGB–PPN–PN transitions, we have plotted the integrated-intensity ratios of the molecular lines in AFGL 2688, IRC+10216, and NGC 7027 in Figures 9 and 10, respectively. The I_int(AFGL 2688)/I_int(IRC+10216) and I_int(NGC 7027)/I_int(AFGL 2688) ratios of the lines from the molecular species X (respectively, represented as R₁(X) and R₂(X) hereafter) can, to some extent, reflect the relative abundance of X in these objects. Although line intensity ratios can be affected by factors in addition to molecular abundance, such as different excitation conditions and optical depths, these effects can be substantially reduced by comparing lines arising from different levels. Therefore, our observations covering a wide frequency range are particularly suited for such a study. Our results show that R₁(X) ranges from 0.02 to 2.89 with a mean value of 0.41, while R₂(X) ranges from 0.02 to 20.2 with a mean value of 1.64. Generally, the chemical pattern of AFGL 2688 is more similar to that of IRC+10216 compared to NGC 7027, suggesting that the radiation field from the central star plays an important role on circumstellar chemistry and can alter chemical composition over a short timescale.

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IRC+10216 is the closest carbon-rich star (d ∼120 pc; Loup et al. 1993). NGC 7027 has a similar distance (∼880 pc; Masson 1989) to AFGL 2688. If the three objects had nearly identical intrinsic brightness, the line intensities should be proportional to $(1+\theta _b^2/\theta _s^2)^{-1}d^{-2}$, as denoted by the dashed lines in Figures 9 and 10. We can infer from Figures 9 and 10 that the intrinsic molecular line strengths in AFGL 2688 and NGC 7027 are consistently at least one order of magnitude higher than those in IRC+10216 if they are at the same distance from the Earth. This suggests that the detection of abundant molecular species in IRC+10216 is not so much because of its unique chemical nature, but its proximity. Furthermore, the degree of chemical activity has increased, not decreased, since the end of AGB.

Nevertheless, there are some differences in the molecular abundance of IRC+10216 and AFGL 2688. As shown in Figure 9, the abundance of CN-bearing molecules, such as HC₃N and CH₃CN, is enhanced in AFGL 2688. CN-bearing molecules have a chemical link with NH₃, a molecule formed near the central star. Nguyen-Q-Rieu et al. (1984) found that the NH₃ lines in AFGL 2688 are stronger than those in IRC+10216 by a factor of >2. Therefore, it can be inferred that the injection of NH₃ during the AGB-to-PPN evolution enhances the production of CN-bearing molecules in AFGL 2688 through subsequent reactions. Figure 9 also indicates that Si-bearing molecules (SiS, SiO, and SiC₂) appear to be depleted in AFGL 2688 with respect to IRC+10216, suggesting that the refractory species have partly condensed into dust grains. SiS appears to be more depleted than SiO and SiC₂. This can be attributed to the fact that SiS has been converted into other silicon species in the outer envelope through gas-phase photochemical reactions. Detailed discussions about the chemistry of SiS and SiO in CSEs have been given by other authors (e.g., Bachiller et al. 1997b; Schöier et al. 2006, 2007).

We also found that the H₂CO line in AFGL 2688 is much stronger than that in IRC+10216. H₂CO is known to be formed through the reaction between CO and H on grain surface, and can be further transformed into methanol. The H₂CO line has a broader profile (see Figure 4) than the other molecular lines, probably implying that it originates from an extended dust region. The detection of H₂CO, therefore, suggests that grain surface chemistry may be actively processing molecular gas in this PPN. Based on their 3 mm observations, Lucas et al. (1986) found that the C₄H radical seems enhanced in AFGL 2688 with respect to IRC+10216. However, this is not supported by our 1.3 mm observations, which do not reveal C₄H lines (Figure 9). The strengths of C₄H lines suggest that this species is located at a very cool region so that the low-N transitions are strengthened whereas the high-N transitions are strongly suppressed.

The central-star temperature of NGC 7027 is about 30 times higher than that of AFGL 2688. Figure 10 shows that most of neutral carbon chain molecules are destroyed during the evolution from PPN to PN, while HCO⁺ is enhanced by a factor of >10. This is consistent with previous findings (e.g., Cernicharo et al. 2011) and can be attributed to the chemistry activated by UV photons from the central star. The ¹²CO/¹³CO line ratios in NGC 7027 are larger than those in AFGL 2688, which can be attributed to decreasing optical depth as the result of nebular expansion.

Using the ARO 12 m and SMT 10 m telescopes, we have carried out a molecular line survey of the PPN AFGL 2688 at the 3 mm and 1.3 mm windows. A total of 143 spectral lines corresponding to 32 molecular species and isotopologues were detected. Only two faint lines remain unidentified. Five molecules, namely, C₃H, CH₃CN, H₂CO, H₂CS, and HCO⁺, are new detections in this object. The sensitive spectra show no evidence for the presence of C₂S in AFGL 2688, contrary to the result of Park et al. (2008). We calculated the rotation temperature, the column densities, and fractional abundances (or their lower limits) of the identified molecules.

Using the observed line ratios of several molecules, we are able to determine the isotopic abundance ratios of several elements. The ¹²C/¹³C and ¹⁶O/¹⁷O ratios are typical of CSEs of evolved stars, and are considerably lower than the solar values. The ¹⁴N/¹⁵N ratio in AFGL 2688 significantly differs from that in IRC+10216, probably reflecting different metallicities or/and masses of their progenitor stars.

By comparing the chemical compositions of AFGL 2688 with those of the AGB star IRC+10216 and the PN NGC 7027, we have come to the conclusion that AFGL 2688 and NGC 7027 have thicker molecular envelopes than IRC+10216. While the chemical patterns of AFGL 2688 and IRC+10216 are generally similar, we note that the chemistry in NGC 7027 is different, probably as the result of a drastically different radiation environment and photochemistry. Nevertheless, we do note that there are slight differences between the molecular line strengths in AFGL 2688 and IRC+10216, providing evidence for chemical evolution during the AGB-to-PPN transition. Specially, CN-containing molecules are enhanced and refractory molecules are depleted as the result of stellar evolution.

While we are able to come to some useful conclusions on chemical evolution in the circumstellar environment, we do wish to note that the origin of chemical diversity in CSEs can be complicated by a number of factors. The difference in molecular abundance can be the result of stellar evolution, metallicities, initial masses, mass-loss processes, dust properties, shock processes, morphological structures, and interactions with the surrounding interstellar medium, just to name a few. In order to understand the roles of these various factors in circumstellar chemistry, it would be necessary to perform high-sensitivity spectral line survey of a large sample of evolved stars over wide frequency ranges. High angular resolution mapping of a large variety of lines would also be useful. We hope that this paper will provide the impetus of future work using larger facilities such as ALMA.

We thank the anonymous referee for helpful comments. The 12 m telescope and SMT are operated by the Arizona Radio Observatory (ARO), Steward Observatory, University of Arizona. We are grateful to the ARO staff for their help during the observing run. Financial support for this work was provided by the Research Grants Council of the Hong Kong under grants HKU7073/11P and HKU7027/11P. D.-V.-T. acknowledges the financial support from Vietnam National Foundation for Science and Technology (NAFOSTED) under contract 103.08-2010.26.