CHEMICAL COMPLEXITY IN THE HELIX NEBULA: MULTI-LINE OBSERVATIONS OF H₂CO, HCO⁺, AND CO

The final phase of stellar evolution for most intermediate-mass stars (0.5–8 M_☉) is the planetary nebula (PN) stage (e.g., Kwok 2000). PNe are formed after the star leaves the main sequence and passes through the red giant (RG) and asymptotic giant branch (AGB) phases. During the RG, and particularly on the AGB, significant mass loss occurs, creating a large, dusty envelope around the central star (e.g., Huggins et al. 2005). By the PN stage, the star has shed most of its original mass, becoming a white dwarf, an intense emitter of ultraviolet radiation (Kwok 2008). Consequently, the material of the remnant AGB shell becomes highly ionized. PNe are thus usually characterized by bright atomic emission lines, arising from [O iii], [O ii], C ii, Ne ii, He ii, and [N ii] (e.g., Kwok 2000; Meaburn et al. 2008). More recently, it has become clear that there are significant quantities of neutral gas, as traced by the 2.12 μm lines of vibrationally excited H₂ (Speck et al. 2002; Kwok 2008). This neutral gas appears to exist in a clumpy medium, often exhibiting cometary-like structures (Gonçalves et al. 2001; Meixner et al. 2005; O'Dell et al. 2007).

One of the best-studied PNe is NGC 7293, the Helix. It is thought to be the oldest known PNe, with an estimated age of ∼11,000–12,000 years (Meaburn et al. 2008). At a distance of ∼213 pc (Harris et al. 2007), it has an angular extent of over 1000'' in optical emission lines, H₂, and CO (Meaburn et al. 2008; Matsuura et al. 2009; Young et al. 1999). From the numerous studies at optical and infrared wavelengths (see Matsuura et al. 2009), the geometry of the Helix is thought to consist of two rings, one tilting about 23° with respect to the plane of the sky, and a second oriented about 90° with respect to the first (O'Dell et al. 2004).

Much of the previous work on the Helix Nebula has focused on its structure and composition, as deduced from optical atomic and infrared H₂ transitions (e.g., see O'Dell et al. 2005, 2007). These observations have demonstrated that the inner region of the nebula (r ⩽ 125''), which appears as a hole on the classic optical image, is characterized by emission lines from highly ionized gas, such as from Hα, He ii, [Ne iii], [O iv], and [O iii] (Cox et al. 1998; Speck et al. 2002; O'Dell et al. 2004). The classic optical "ring" region is rich in neutral and ionized atomic material, as traced by H i, [S ii], [N ii], C i, and [O i] (e.g., Rodríguez et al. 2002; O'Dell et al. 2004, 2005; Young et al. 1997), and molecular gas in the form of H₂ and CO (e.g., Meixner et al. 2005; Hora et al. 2006; Young et al. 1999; Healy & Huggins 1990). Large-scale maps of the Helix show that both the J = 2 → 1 transition of CO and the 2.12 μm line of vibrationally excited H₂ extend out to a radius r ∼ 500'' from the central star (Young et al. 1999; Speck et al. 2002). As gleaned from IR molecular hydrogen observations, dense globules are present throughout the ring regions, often appearing as striking "cometary knots" (e.g., O'Dell et al. 2007; Hora et al. 2006; Matsuura et al. 2009). It is estimated that over 20,000 such globules exist in the Helix nebula, with sizes on the order of ∼01–1'' (O'Dell et al. 2007). Densities in the clumps are estimated to be in the range 10⁴–10⁶ cm⁻³ (Matsuura et al. 2007). Modeling of molecular hydrogen emission indicates gas temperatures between 900 K and 1800 K, suggesting that the globules are quite warm (O'Dell et al. 2007; Matsuura et al. 2007).

The Helix Nebula is thus characterized by thousands of very dense, possibly self-shielding clumps of gas where molecular material is present, albeit chiefly diatomic species. O'Dell et al. (2007) postulate that CO is simply an abundant tracer of more complex molecules, which have yet to be found. This idea has been supported by the detection of polyatomic species in the Helix at one position near the western part of the rings. Here, Bachiller et al. (1997) observed CN, HCN, HNC, and HCO⁺. More recently, Tenenbaum et al. (2009) detected multiple transitions of H₂CO, C₂H, and c-C₃H₂ toward this position. It could be argued, however, that this particular region is unique, and not representative of the nebula as a whole. It would be enlightening to investigate the presence of polyatomic molecules in other regions of the Helix Nebula.

Results from chemical models of the Helix, conducted in a clumpy medium (Redman et al. 2003; Ali et al. 2001), suggest that molecular content in this object and other PNe should be severely limited due to the destructive effect of the central star's radiation field. For example, Redman et al. (2003) predict at least a 10⁴ decrease in abundance for common triatomic species such as HCN and CCH as the nebular age increases from 2000 to 10,500 years. It has certainly been a common perception that PNe are shells of only photoionized gas (Kwok 2010), especially for highly evolved objects like the Helix.

In order to further elucidate its chemical content, we have conducted observations of HCO⁺ and H₂CO toward eight new positions across the Helix nebula via multiple transitions at 1, 2, and 3 mm. Measurements of the J = 1 → 0, 2 → 1, and 3 → 2 lines of CO were made at these positions, as well. Additional data were also obtained at the location studied by Bachiller et al. (1997) and Tenenbaum et al. (2009). HCO⁺ and H₂CO have been detected at all eight positions, as well as the three lines of CO. With these new data, the gas kinetic temperature and density were established across the nebula, as well as molecular abundances. In this paper, we present our observations and data analysis, and discuss their implications for the chemistry in evolved PNe. We also speculate on the relationship of this molecular material in the overall life cycle of interstellar matter.

The measurements were carried out between 2008 April and 2011 December using the telescopes of the Arizona Radio Observatory (ARO). Observations at 2 and 3 mm were taken with the ARO 12 m telescope on Kitt Peak, AZ, which utilized three different receiver systems over the course of the observations. Receivers with dual-polarization, single-sideband SIS mixers were used for the majority of the observations, one at 2 mm (130–175 GHz) and another at 3 mm (65–115 GHz). Measurements made after 2008 May at 89 GHz (HCO⁺, J = 1→0) employed a new receiver with ALMA-type Band 3 sideband-separating (SBS) mixers. Image rejection was typically ⩾15 dB for all of the receivers. The backends used were 256 channel filter banks operated in the parallel mode (2 × 128 channels) with 250, 500, or 1000 kHz resolution, depending on the frequency. The temperature scale was determined by the chopper-wheel method, correcting for forward spillover losses, and is given as T_R*, which is defined as T_R = T_R*/η_c, where η_c is the corrected beam efficiency.

The ARO 10 m Submillimeter Telescope (SMT) on Mt. Graham, AZ was used for the 1 and 0.8 mm observations. The 1 mm receiver at the SMT employs dual-polarization ALMA-type Band 6 SBS SIS mixers, with image rejection typically >15 dB. The dual-polarization 0.8 mm receiver is double-sideband (DSB), with SIS mixers based on an SMA design. The backends used were 250 and 1000 kHz resolution filter banks configured in parallel mode (2 × 256 channels and 2 × 1024 channels, respectively). The temperature is given as T_A*, where T_R = T_A*/η_b, as determined by the chopper-wheel method, and η_b is the beam efficiency. It was assumed that the DSB receiver has equal gains in the signal and image sidebands. Estimated calibration uncertainty at both telescopes is 15%.

The observations were conducted at nine separate positions in the Helix Nebula, offset from that of the central star at α = 22^h29^m386, δ = −20°50'180 (J2000); coordinates are listed in Table 1. The observations were done in position-switching mode with a reference offset of 30' west in azimuth for 1, 2, and 3 mm measurements and an offset of 15' in elevation at 0.8 mm. For the HCO⁺ and H₂CO data, local oscillator shifts were done to test for image contamination. Pointing and focusing were checked every ∼1.5–2 hr on planets or strong continuum sources. Telescope parameters are given in Table 2, along with rest frequencies of observed lines.

Table 1. Positions Observed in the Helix Nebula

Offset from Central Stara	α(J2000.0)	δ(J2000.0)
(R.A, decl)	(h m s)	(° ' '')
(130, −180)	22 29 47.9	−20 53 18
(390, −30)	22 30 06.3	−20 50 47
(−15, 270)	22 29 37.5	−20 45 49
(−372, 0)b	22 29 12.1	−20 50 20
(125, 185)	22 29 47.4	−20 47 13
(−120, 240)	22 29 29.9	−20 46 18
(−435, 75)	22 29 07.6	−20 49 04
(−300, −200)	22 29 17.2	−20 53 38
(−240, −100)	22 29 21.5	−20 51 58

Notes. ^aCentral position (J2000.0): α = 22^h29^m386, δ = −20°50'18''. ^bPosition previously studied (Bachiller et al. 1997; Tenenbaum et al. 2009).

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CO and HCO⁺ have simple rotational manifolds, but that of H₂CO is more complicated, as it is an asymmetric top. In this case, each energy level splits into 2J + 1 components, labeled by the quantum numbers J, K_a, and K_c. The presence of two identical protons in H₂CO also gives rise to ortho (K_a = 1, 3, 5, ...) and para (K_a = 0, 2, 4, ...) spin states. Note that the highest energy levels probed in this work are for CO (E(J = 3) ∼ 33 K). For HCO⁺ and H₂CO, the highest levels probed lie ⩽25 K.

Three transitions of CO (J = 1 → 0, 2 → 1, and 3 → 2) and one of HCO⁺ (J = 1 → 0) were detected at all nine positions. The J = 3 →2 line of HCO⁺ was detected at only five out of nine positions—perhaps not unexpected, given the high dipole moment (μ = 3.9 D) for this molecular ion. For H₂CO, the five transitions of interest (J_Ka,Kc = 1_0,1 → 0_0,0, 2_1,2 → 1_1,1, 2_0,2 → 1_0,1, 2_1,1 → 1_1,0, and 3_0,3 →2_0,2) were initially searched for and detected at four positions. As it became apparent that this molecule was present across the nebula, only one transition (J_Ka,Kc = 2_1,2 → 1_1,1) was studied at the remaining five positions, where it was clearly visible.

Figure 1 shows spectra of the J = 1 → 0 transition of HCO⁺ (upper) and the J_Ka,Kc = 2_1,2 → 1_1,1 line of H₂CO (lower) measured at the eight new positions across the Helix Nebula. The velocity resolutions are typically 0.84 km s⁻¹ and 1.1 km s⁻¹ for HCO⁺ and H₂CO, respectively. The location of the eight positions within the nebula is indicated on an optical R-band image taken from Young et al. (1999). Overlying the image is the lowest contour of HCO⁺ emission in the Helix, extracted from a fully sampled map made across the entire nebula (N. Zeigler et al. 2013, in preparation). The typical beam size used for the measurements is shown on the lower left-hand corner of the image. HCO⁺ and H₂CO are clearly present at each position, and the spectra of the two molecules closely resemble each other. Multiple velocity components are also visible in the data at several of the positions. More detailed spectra at four of these positions are shown in Figures 2–5, and the CO data at the remaining positions are presented in Figure 6.

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A summary of the observations is given in Table 3. Here, line intensities (in uncorrected antenna temperatures T_A* or T_R*, as well as T_R), linewidths at full width at half-maximum (ΔV_1/2), and LSR velocities are given for each feature observed. Note that multiple components typically exist at almost every position, as also observed by Young et al. (1999). Line parameters are listed individually for each resolved component. The CO spectra (J = 2→1) measured here and those of Young et al. (1999) are in very good agreement.

Figures 2–5 consist of multiple panels. The left panels display the three observed transitions of CO and the two of HCO⁺; the five H₂CO transitions are shown in the right panels. The spectra are centered at the LSR velocity of −24 km s⁻¹ (velocity of the central star), and the temperature scale is in mK, T_R* for the 12 m data or T_A* for the SMT data. Integration times for each spectra range from 2 to 50 hr.

The spectra in Figure 2, observed toward offset (130, −180), clearly display two distinct velocity components near −10 km s⁻¹ and −47 km s⁻¹, as also found in the CO J = 2 → 1 line by Young et al. (1999). In the three CO transitions, the velocity component near −47 km s⁻¹ is typically twice the intensity of that at −10 km s⁻¹. In contrast, the intensities of the two components are roughly equivalent in the HCO⁺ and H₂CO data.

Figure 3 shows spectra taken toward offset (390, −30). At this position, there is only one apparent velocity component, centered at V_LSR = −33 km s⁻¹, but it typically has a broader linewidth than those at other positions (6–8 km s⁻¹ versus 3–4 km s⁻¹: see Table 3). Young et al. (1999) observed a second narrow feature at −17 km s⁻¹ in CO near this position; in our data, it appears as a "shoulder" on the CO spectra, contributing to the overall linewidth. Note that the J = 3 → 2 line of HCO⁺ is quite narrow relative to the other features and may trace only one velocity component.

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Two closely spaced velocity components at −27 and −35 km s⁻¹ are apparent toward the offset position (−15, 270), as shown in Figure 4. Both components have similarly narrow linewidths near 3–4 km s⁻¹ (see Table 3). However, the relative intensities of the two features in the three CO transitions vary, with the −35 km s⁻¹ component steadily decreasing in antenna temperature with respect to that at −27 km s⁻¹. In comparison, the two features in HCO⁺ and H₂CO generally have similar intensities.

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The data for offset (−372, 0) are displayed in Figure 5. This position has been the focus of previous Helix observations at millimeter wavelengths (Bachiller et al. 1997; Tenenbaum et al. 2009). The p-H₂CO spectra shown are taken from Tenenbaum et al. (2009). At this position, there appears to be a single prominent velocity component at V_LSR ≈ −15 km s⁻¹, with a linewidth of 3.3 km s⁻¹. This feature may consist of multiple blended velocity components.

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The CO spectra (J = 1 → 0, 2 → 1, and 3 → 2) for the other five positions are displayed in Figure 6. The data for the (125, 185), (−120, 240), and (−435, 75) positions show multiple velocity components in all three transitions (also see Table 3). At (−300, −200), a second component is visible in the J = 3 → 2 spectrum near −27 km s⁻¹, which on closer inspection, is present in the other two transitions but at a lower signal level, likely a result of beam dilution. At the (−240, −100) position, a second component is apparent in the J = 1 → 0 spectrum at −17 km s⁻¹, which is very weak in the other two transitions. It likely traces lower densities where the other two lines are not readily excited.

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The data were analyzed by two methods. First, rotational diagrams were constructed for each molecule for the positions where at least two transitions were detected. This criterion was met by CO at all of the positions and about half of the positions for HCO⁺ and H₂CO. A separate diagram was constructed for each velocity component, when possible. The ortho and para data were combined for the analysis, adopting an ortho:para ratio of three. A uniform filling factor was assumed. This assumption is justified based on a complete map of the Helix in HCO⁺, which showed extended molecular emission across the entire optical image of the nebula (see Figure 1 and N. Zeigler et al. 2013, in preparation). The rotational partition function used for the asymmetric top H₂CO was Q_rot ∼ 1/2[π T_rot³/ABC]^1/2, where A, B, and C are the rotational constants, in K (see Turner 1991; Gordy & Cook 1984). The rotational temperatures T_rot and column densities N_tot derived from this analysis are presented in Table 4. The rotational diagrams indicate optically thin emission in all three species.

The measured line intensities of the three molecules at a given position were also modeled with the non-LTE radiative transfer program RADEX (van der Tak et al. 2007). In this code, collisional excitation is assumed and balanced with radiative decay to solve for statistical equilibrium, with an escape velocity formalism that assumes an isothermal homogenous medium. Gas kinetic temperatures T_K, densities n(H₂), and molecular column densities N_tot are derived by matching the model predictions to the observed spectral intensities. Each velocity component specified in Table 3 was modeled separately. A uniform filling factor was assumed in all of the cases, and the only collision partner considered was para-H₂. Modeling results for CO, H₂CO, and HCO⁺ are summarized in Table 5.

CO was analyzed first, as it was observed in three transitions at all nine positions. The modeling was conducted over temperature and density ranges of 10–70 K and 10³–10⁷ cm⁻³. Using values of these parameters outside these ranges resulted in line intensities vastly different from those observed.

For H₂CO, ortho and para lines were modeled separately. The temperature, gas density, and column density were determined independently from the modeling for p-H₂CO, where three transitions were observed. In general, the kinetic temperatures and gas densities determined from H₂CO were in excellent agreement with those from the CO analysis, within the uncertainties. For the o-H₂CO species, T_K and n(H₂) were held fixed to the values of the para species, and N_tot was modeled. The ortho:para ratios for H₂CO that resulted from the analysis were found in the range 2.0 ± 0.7 to 3.4 ± 1.1, for an average value of 2.9 ± 0.7—close to the equilibrium value of 3 (see Table 6).

RADEX was also used to determine the column density for HCO⁺. Because only two transitions were measured, the H₂ density was modeled but the kinetic temperature was held fixed to values established for CO. Again, gas densities determined from HCO⁺ were consistent with those derived from CO and H₂CO, within the uncertainties.

The RADEX modeling results were found to be consistent with the rotational diagram analysis (see Tables 4 and 5). The column densities agree to within the uncertainties for all three species. Furthermore, the rotational temperatures T_rot derived from the diagrams are typically less than the gas kinetic temperatures (T_rot ⩽ T_K), as expected for optically thin emission.

At the positions where only one transition each of HCO⁺ and H₂CO were measured, column densities were also derived using RADEX, but fixing the kinetic temperature and hydrogen density to that determined from the CO analysis. For HCO⁺, values were derived on the basis of the J = 1 → 0 transition; the J_Ka,Kc = 2_1,2 → 1_1,1 ortho line was used for formaldehyde, and then scaled by an ortho:para ratio of three. The resulting total column densities are also listed in Table 5.

5.1. Physical Conditions in the Molecular Gas

5.2. Column Densities and Molecular Abundances

5.3. Comparison with Chemical Models

5.4. The Link between AGB Envelopes and Diffuse Clouds?

The polyatomic molecules HCO⁺ and H₂CO have been found to have a widespread distribution in the Helix Nebula. The gas in which they are present is dense and warm, with n(H₂) ∼ 10⁴–10⁵ cm⁻³ and T_K ∼ 15–40 K. The complex spectra exhibited by these species, with multiple and physically distinct velocity components, suggest that the polyatomic molecules exist across the intricate ring structures observed in CO and H₂. Abundances for both HCO⁺ and H₂CO are surprisingly high—many orders of magnitude greater than models predict at this stage of PN evolution. The abundance of HCO⁺ in the Helix may have been enhanced by photochemistry during the PPNe and early PNe phases. The presence and abundance of formaldehyde is more difficult to explain, and could be representative of remnant material from the AGB phase, as is postulated for H₂. The molecular content in the Helix suggests that evolved PNe may be seeding the diffuse ISM with polyatomic species that have been observed toward many lines of sight. Additional studies of the chemical content of evolved PNe are necessary to establish the actual connection between their molecular ejecta and diffuse interstellar gas.

This research was supported by NSF grants AST-0906534, AST-1140030, and AST-1211502. The SMT and Kitt Peak 12 m are operated by the Arizona Radio Observatory (ARO), Steward Observatory, University of Arizona, with support through the NSF University Radio Observatories program (URO: AST-1140030). We thank the ARO telescope operators, engineers, and staff for their assistance with the observations and N. Zeigler and T. Folkers for assistance with modeling the data.