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Feb 25, 2013 - ABSTRACT. Observations of CO, HCO+ , and H2CO have been carried out at nine positions across the Helix Nebula (NGC 7293) using the ...
The Astrophysical Journal, 765:112 (14pp), 2013 March 10  C 2013.

doi:10.1088/0004-637X/765/2/112

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

CHEMICAL COMPLEXITY IN THE HELIX NEBULA: MULTI-LINE OBSERVATIONS OF H2 CO, HCO + , AND CO L. N. Zack1,2,3 and L. M. Ziurys1,2

1

Department of Chemistry, University of Arizona, P.O. Box 210041, Tucson, AZ 85721, USA; [email protected] 2 Department of Astronomy and Steward Observatory, Arizona Radio Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA Received 2012 July 17; accepted 2013 January 28; published 2013 February 25

ABSTRACT +

Observations of CO, HCO , and H2 CO have been carried out at nine positions across the Helix Nebula (NGC 7293) using the Submillimeter Telescope and the 12 m antenna of the Arizona Radio Observatory. Measurements of the J = 1 → 0, 2 → 1, and 3 →2 transitions of CO, two transitions of HCO + (J = 1 → 0 and 3 →2), and five lines of H2 CO (JKa, Kc = 10, 1 → 00, 0 , 21, 2 → 11, 1 , 20, 2 → 10, 1 , 21, 1 → 11, 0 , and 30, 3 →20, 2 ) were conducted in the 0.8, 1, 2, and 3 mm bands toward this highly evolved planetary nebula. HCO + and H2 CO were detected at all positions, along with three transitions of CO. From a radiative transfer analysis, the kinetic temperature was found to be TK ∼ 15–40 K across the Helix with a gas density of n(H2 ) ∼ 0.1–5 × 105 cm−3 . The warmer gas appears to be closer to the central star, but high density material is distributed throughout the nebula. For CO, the column density was found to be Ntot ∼ 0.25–4.5 × 1015 cm−2 , with a fractional abundance of f (CO/H2 ) ∼ 0.3–6 × 10−4 . Column densities for HCO + and H2 CO were determined to be Ntot ∼ 0.2–5.5 × 1011 cm−2 and 0.2–1.6 × 1012 cm−2 , respectively, with fractional abundances of f (HCO + /H2 ) ∼ 0.3–7.3 × 10−8 and f (H2 CO/H2 ) ∼ 0.3–2.1 × 10−7 —several orders of magnitude higher than predicted by chemical models. Polyatomic molecules in the Helix appear to be well-protected from photodissociation and may actually seed the diffuse interstellar medium. Key words: astrochemistry – ISM: molecules – planetary nebulae: individual (NGC 7293) – radio lines: ISM

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., Rodr´ıguez 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 ∼0. 1–1 (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

1. INTRODUCTION The final phase of stellar evolution for most intermediatemass 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 (Gon¸calves 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). 3 Current address: Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.

1

The Astrophysical Journal, 765:112 (14pp), 2013 March 10

Zack & Ziurys Table 2 Frequencies and Telescope Parameters of Observed Transitions

Table 1 Positions Observed in the Helix Nebula Offset from Central Stara (R.A. , decl. )

α(J2000.0) (h m s )

δ(J2000.0) (◦   )

Molecule

(130, −180) (390, −30) (−15, 270) (−372, 0)b (125, 185) (−120, 240) (−435, 75) (−300, −200) (−240, −100)

22 29 47.9 22 30 06.3 22 29 37.5 22 29 12.1 22 29 47.4 22 29 29.9 22 29 07.6 22 29 17.2 22 29 21.5

−20 53 18 −20 50 47 −20 45 49 −20 50 20 −20 47 13 −20 46 18 −20 49 04 −20 53 38 −20 51 58

CO

HCO + H2 CO

Notes. a Central position (J2000.0): α = 22h 29m 38s.6, δ = −20◦ 5018 . b Position previously studied (Bachiller et al. 1997; Tenenbaum et al. 2009).

Transition

ν (MHz)

Telescope

θb ( )

ηc or ηb

J=1→0 J=2→1 J=3→2 J=1→0 J=3→2 JKa, Kc = 10, 1 → 00, 0 JKa, Kc = 21, 2 → 11, 1 JKa, Kc = 20, 2 → 10, 1 JKa, Kc = 21, 1 → 11, 0 JKa, Kc = 30, 3 → 20, 2

115271.2 230538.0 345796.0 89188.5 267557.6 72837.9 140839.5 145602.9 150498.3 218222.2

ARO 12 m ARO SMT ARO SMT ARO 12 m ARO SMT ARO 12 m ARO 12 m ARO 12 m ARO 12 m ARO SMT

55 33 22 70 28 86 45 43 42 35

0.84 0.77 0.70 0.89 0.76 0.94 0.76 0.75 0.74 0.78

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 TR ∗ , which is defined as TR = TR ∗ /ηc , where ηc 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 ALMAtype Band 6 SBS SIS mixers, with image rejection typically >15 dB. The dual-polarization 0.8 mm receiver is doublesideband (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 TA ∗ , where TR = TA ∗ /ηb , as determined by the chopper-wheel method, and ηb 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 = s 22h 29m 38.6, δ = −20◦ 5018. 0 (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 H2 CO 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.

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 H2 CO, C2 H, and c-C3 H2 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 H2 CO 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 H2 CO 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.

3. RESULTS CO and HCO + have simple rotational manifolds, but that of H2 CO 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, Ka , and Kc . The presence of two identical protons in H2 CO also gives rise to ortho (Ka = 1, 3, 5, . . .) and para (Ka = 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 H2 CO, 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

2. OBSERVATIONS 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 sideband2

The Astrophysical Journal, 765:112 (14pp), 2013 March 10

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Figure 1. Spectra of the J = 1 → 0 transitions of HCO + (top panel) at 89 GHz and the JKa,Kc = 21,2 →11,1 line of H2 CO (lower panel) near 140 GHz measured with the ARO 12 m telescope at eight positions in the Helix. The positions are indicated on the upper panel by the offset in R.A. and decl. (in arcseconds) from that of the central star (J2000.0: α = 22h 29m 38s.6, δ = −20◦ 5018 ), and are marked on an R-band optical image of the Helix (Young et al. 1999). An asterisk marks the position (−372, 0), previously studied by Bachiller et al. (1997) and Tenenbaum et al. (2009). Overlaid on the optical image is the lowest contour of the peak brightness temperature of the J = 1 → 0 transition of HCO + (N. Zeigler et al. 2013, in preparation). The beam size at 89 GHz is shown below the image. Spectral resolution is 250 kHz (0.84 km s−1 ) for the HCO + data, except at position (−120, 240), where it is 500 kHz (1.7 km s−1 ). For H2 CO, the resolution is 500 kHz (1.1 km s−1 ), except at (−300, −200), where a 1 MHz (2.2 km s−1 ) resolution spectrum is shown. Both H2 CO and HCO + are clearly present at all eight positions.

H2 CO, the five transitions of interest (JKa,Kc = 10,1 → 00,0 , 21,2 → 11,1 , 20,2 → 10,1 , 21,1 → 11,0 , and 30,3 →20,2 ) were initially searched for and detected at four positions. As it became apparent that this molecule was present across the nebula, only one transition (JKa,Kc = 21,2 → 11,1 ) 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 JKa,Kc = 21,2 → 11,1 line of H2 CO (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 H2 CO, 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 H2 CO 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. A summary of the observations is given in Table 3. Here, line intensities (in uncorrected antenna temperatures TA ∗ or TR ∗ , as well as TR ), linewidths at full width at half-maximum (ΔV1/2 ), 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 H2 CO 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, TR ∗ for the 12 m data or TA ∗ 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 H2 CO data. Figure 3 shows spectra taken toward offset (390, −30). At this position, there is only one apparent velocity component, centered at VLSR = −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. 3

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Figure 2. Spectra of the J = 1 → 0, 2 → 1, and 3 →2 transitions of CO, the J = 1 → 0 and 3 →2 lines of HCO + (left panels), and the JKa,Kc = 10,1 → 00,0 , 21,2 → 11,1 , 20,2 → 10,1 , 21,1 → 11,0 , and 30,3 →20,2 transitions of H2 CO (right panels), measured toward the Helix Nebula at offset position (130, −180). The data at 1 and 0.8 mm were measured with the ARO SMT (spectral resolution 1 MHz, or 0.9–1.4 km s−1 ) and the other spectra with the ARO 12 m telescope (resolution 500 kHz or 1.0–2.1 km s−1 ). Two velocity components, located at VLSR = −10 and −47 km s−1 , are clearly present in every transition for all three molecules.

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 H2 CO generally have similar intensities. 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-H2 CO spectra shown are taken from Tenenbaum et al. (2009). At this position, there appears to be a single prominent velocity component at VLSR ≈ −15 km s−1 , with a linewidth of 3.3 km s−1 . This feature may consist of multiple blended velocity components. 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. 4. ANALYSIS 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 H2 CO. 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 H2 CO was Qrot ∼ 1/2[π Trot 3 /ABC]1/2 , where A, B, and C are the rotational constants, in K (see Turner 1991; Gordy & Cook 1984). The rotational temperatures Trot and column densities Ntot 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 4

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Figure 3. Same as Figure 2, but measured toward the offset position (390, −30). Only one velocity component is evident in these data, located at VLSR ∼ −33 km s−1 . This component is slightly broader than the features at other positions, with an average ΔV1/2 ∼ 7 km s−1 (see Table 3), likely indicating blended velocity features.

from HCO + were consistent with those derived from CO and H2 CO, 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 Trot derived from the diagrams are typically less than the gas kinetic temperatures (Trot  TK ), as expected for optically thin emission. At the positions where only one transition each of HCO + and H2 CO 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 JKa,Kc = 21,2 → 11,1 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.

decay to solve for statistical equilibrium, with an escape velocity formalism that assumes an isothermal homogenous medium. Gas kinetic temperatures TK , densities n(H2 ), and molecular column densities Ntot 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, H2 CO, 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 H2 CO, ortho and para lines were modeled separately. The temperature, gas density, and column density were determined independently from the modeling for p-H2 CO, where three transitions were observed. In general, the kinetic temperatures and gas densities determined from H2 CO were in excellent agreement with those from the CO analysis, within the uncertainties. For the o-H2 CO species, TK and n(H2 ) were held fixed to the values of the para species, and Ntot was modeled. The ortho:para ratios for H2 CO 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

5. DISCUSSION 5.1. Physical Conditions in the Molecular Gas Previous estimates of the physical properties of the molecular gas in the Helix have been obtained primarily from modeling observed transitions of H2 in the infrared (e.g., O’Dell et al. 2007). Based on such studies, the gas densities in this nebula were estimated to be n(H2 ) ∼ 104 –105 cm−3 (e.g., Meixner et al. 2005; Matsuura et al. 2007). However, densities up to 106 cm−3 have been derived for the dense cores of the cometary globules (O’Dell et al. 2005). Based on CO, CN, HCO + , and HCN observations, Bachiller et al. (1997) estimated densities in 5

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Figure 4. Same as Figure 2, but measured toward offset (−15, 270). The JKa,Kc = 30,3 → 20,2 spectra of H2 CO has been smoothed to a resolution of 500 kHz from 250 kHz. Two closely spaced velocity components at VLSR = −27 and −35 km s−1 are present in the spectra, but exhibit different relative intensities depending on the molecule.

several PNe as high as 1–4 × 105 cm−3 , including one position in the Helix. Huggins et al. (2002) conducted interferometer observations of CO in one globule in the Helix and found n(H2 )  2 × 104 cm−3 . There have been fewer measurements of the gas kinetic temperature. Modeling of the vibrationally excited lines of molecular hydrogen indicates an excitation temperature between 900 and 1800 K (O’Dell et al. 2007; Matsuura et al. 2007). Bachiller et al. (1997) suggest a general kinetic temperature of 25–60 K for evolved PNe, including the Helix, based on rotational lines of CO, HCN, HCO + , and CN, while Huggins et al. (2002) estimated Tex ∼ 18–40 K for CO in the one Helix globule. A cursory look at the temperatures within the Helix can be obtained from the rotational diagram analysis, summarized in Table 4. For CO, the range of rotational temperatures was Trot ∼ 10–31 K across all of the positions. For HCO + , the analysis yielded Trot ∼ 5–6 K, while in the case of H2 CO, Trot ∼ 8–11 K—consistent with the higher dipole moments of both molecules (μ = 3.9 D and 2.33 D, respectively). From the radiative transfer modeling of CO and H2 CO, the gas kinetic temperature was found to be TK ≈ 15–40 K, varying as a function of position. The molecular gas is thus warm, but not nearly as hot as that traced by vibrationally excited H2 (T ∼ 900–1800 K; Matsuura et al. 2007). The variation of TK for different velocity components at a given position can be accounted for by projection effects. There may be a radial dependence of the temperature as well, with positions closer to the star having a somewhat higher TK than those further away.

For example, at position (125, 185), the velocity component near 1 km s−1 is on the inner ring (see Young et al. 1999), and has TK ∼ 40 K. At (−300, −200), the 18 km s−1 component appears to lie on the outer ring, and has TK ∼ 20 K. A more detailed study is required to quantify the gradient, however. The gas densities n(H2 ) could only be established from the radiative transfer analysis. The values derived from CO fall in the range 0.1–5 × 105 cm−3 , and those obtained from HCO + and H2 CO at a given position are similar, with n(H2 ) ∼ 0.7–1.6 × 105 cm−3 and 0.9–2.0 × 105 cm−3 , respectively. There is no apparent radial gradient for the gas density. Certain positions in the outer nebula have substantial densities (n(H2 ) ∼ 105 cm−3 ), comparable to inner ones. For example, one can compare the −29 km s−1 component at (−435, 75) or the −33 km s−1 feature at (390, −30) to the 1 km s−1 feature at (125, 185). This clumpiness may reflect the structure of the remnant AGB shell. These results indicate that the polyatomic molecules trace dense molecular gas in both the inner and outer regions of the nebula. The velocity components found in this study lie in the range VLSR = + 4 km s−1 to −47 km s−1 , centered on the systemic velocity of the nebula near −23 km s−1 (Huggins et al. 2002). This velocity spread and its variation as a function of position closely matches that found in the J = 2 → 1 line of CO by Young et al. (1999). At most positions, multiple velocity components were observed in all three molecules, H2 CO, HCO + , and CO, indicating that the denser gas is well-mixed. These data and the wide extent of the molecular emission suggest that that HCO + 6

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Figure 5. Same as Figure 2, but measured toward the offset position (−372, 0). One velocity component, located at VLSR = −15 km s−1 , is present in all spectra. At this position, previous studies by Bachiller et al. (1997) and Tenenbaum et al. (2009) showed the presence of HCN, HNC, HCO + , CN, CCH, C3 H2 , and H2 CO. The p-H2 CO spectra were taken from Tenenbaum et al. (2009); see Table 3.

Figure 6. Spectra of the J = 1 → 0, 2 → 1, and 3 →2 transitions of CO, observed toward the other five positions. The J = 2 → 1 and 3 →2 data were measured with the ARO SMT (spectral resolution 1 MHz or 1.3 km s−1 at 230 GHz and 0.9 km s−1 at 345 GHz). The J = 1 → 0 data were obtained with the ARO 12 m dish (resolution 500 kHz or 1.3 km s−1 ). All of the positions show evidence of multiple velocity components.

a molecular hydrogen column density of 7.5 × 1018 cm−2 was assumed, based on infrared observations of vibrationally excited H2. These data are typically modeled to estimate a total column density for molecular hydrogen, averaged over several globules (e.g., O’Dell et al. 2007). Estimates of Ntot (H2 ) in the Helix from infrared measurements vary from ∼1 × 1017 cm−2 to 6 × 1019 cm−2 (Matsuura et al. 2007; O’Dell et al. 2005, 2007; Cox et al. 1998). One of the most recent estimates is

and H2 CO may be located in the cometary knots that contain H2 (Speck et al. 2002; Matsuura et al. 2007, 2009; Meixner et al. 2005; O’Dell et al. 2007). 5.2. Column Densities and Molecular Abundances Total column densities Ntot for the three molecules were derived from a radiative transfer analysis, as described above (see Section 4 and Table 5). To determine the fractional abundances, 7

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Table 3 Observed Line Parameters for CO, HCO + , and H2 CO in the Helixa Offset (Δα, Δδ) (130, −180)

Molecule

Transition

TR ∗ or TA ∗ (mK)

TR (mK)

ΔV1/2 (km s−1 )

VLSR (km s−1 )

CO

J=1→0

250 ± 39 560 ± 25 540 ± 13 900 ± 13 660 ± 88 1480 ± 88 60 ± 16 70 ± 16 15 ± 4 9±4 10 ± 2 10 ± 2 21 ± 5 26 ± 5 13 ± 4 14 ± 4 14 ± 3 13 ± 3 4±2 4±2 450 ± 29 830 ± 31 620 ± 86 75 ± 10 12 ± 5 12 ± 4 10 ± 3 6±3 6±3 5±2 320 ± 30 160 ± 25 800 ± 59 320 ± 20 1130 ± 74 280 ± 74 55 ± 10 40 ± 10 13 ± 5 10 ± 5 5±2 5±3 14 ± 5 8±5 8±4 6±4 10 ± 3 8±3 3±2 5±2 850 ± 50 1500 ± 50 1460 ± 80 110 ± 20 25 ± 5 25 ± 6 60 ± 5 35 ± 7 33 ± 10 10 ± 5 85 ± 23 180 ± 23 110 ± 23 75 ± 23

298 ± 45 667 ± 30 702 ± 17 1169 ± 17 943 ± 126 2114 ±126 67 ± 18 79 ± 18 20 ± 5 12 ± 5 11 ± 2 11 ± 2 28 ± 7 34 ± 7 17 ± 5 19 ± 5 19 ± 4 18 ± 4 5±3 5±3 536 ± 35 1078 ± 40 886 ± 123 84 ± 11 16 ± 7 13 ± 5 13 ± 4 8±4 8±4 6±3 381 ± 36 190 ± 30 1039 ± 76 416 ± 26 1614 ± 106 400 ± 106 62 ± 11 45 ± 11 17 ± 6 13 ± 6 5±2 5±3 18 ± 6 11 ± 6 11 ± 5 8±5 14 ± 4 11 ± 4 4±3 6±3 1011 ± 60 1948 ± 65 2086 ± 114 124 ± 22 33 ± 7 27 ± 6 79 ± 6 47 ± 9 45 ± 14 13 ± 6 101 ± 27 214 ± 27 131 ± 27 89 ± 27

3.3 ± 1.3 3.3 ± 1.3 2.6 ± 1.3 3.3 ± 1.3 2.7 ± 0.9 2.3 ± 0.9 3.4 ± 1.7 5.0 ± 1.7 3.3 ± 1.1 2.8 ± 1.1 4.1 ± 2.1 6.2 ± 2.1 4.2 ± 1.1 3.2 ± 1.1 2.1 ± 1.0 4.1 ± 1.0 3.0 ± 1.0 4.5 ± 1.0 4.2 ± 1.4 2.8 ± 1.4 6.5 ± 1.3 6.5 ± 1.3 7.2 ± 0.9 8.4 ± 1.7 3.3 ± 2.2 8.2 ± 2.1 6.4 ± 1.1 7.2 ± 2.1 8.0 ± 2.0 8.4 ± 1.4 3.9 ± 1.3 3.9 ± 1.3 2.6 ± 1.3 3.9 ± 1.3 2.7 ± 0.9 3.6 ± 0.9 5.0 ± 1.7 5.0 ± 1.7 3.3 ± 1.1 3.3 ± 1.1 6.2 ± 2.1 4.1 ± 2.1 4.2 ± 1.1 3.2 ± 1.1 4.2 ± 1.0 4.2 ± 1.0 3.5 ± 1.0 4.0 ± 1.0 2.0 ± 0.6 2.0 ± 0.6 3.3 ± 1.3 3.3 ± 1.3 4.5 ± 0.9 5.0 ± 1.7 3.3 ± 1.1 4.1 ± 2.1 3.2 ± 1.1 3.1 ± 1.0 3.0 ± 1.0 4.1 ± 1.4 3.9 ± 1.3 2.6 ± 1.3 3.9 ± 1.3 5.2 ± 1.3

−10.1 ± 1.3 −47.0 ± 1.3 −9.6 ± 1.3 −47.6 ± 1.3 −9.5 ± 0.9 −47.0 ± 0.9 −9.1 ± 1.7 −46.6 ± 1.7 −9.8 ± 1.1 −47.6 ± 1.1 −9.8 ± 2.1 −47.8 ± 2.1 −9.4 ± 1.1 −47.2 ± 1.1 −9.7 ± 1.0 −46.7 ± 1.0 −10.2 ± 1.0 −47.9 ± 1.0 −7.9 ± 1.4 −47.4 ± 1.4 −33.7 ± 1.3 −33.9 ± 1.3 −34.2 ± 0.9 −32.8 ± 1.7 −33.7 ± 1.1 −33.8 ± 2.1 −33.4 ± 1.1 −32.6 ± 2.1 −34.7 ± 2.0 −33.6 ± 1.4 −28.2 ± 1.3 −35.1 ± 1.3 −27.9 ± 1.3 −35.3 ± 1.3 −27.9 ± 0.9 −35.3 ± 0.9 −28.0 ± 1.7 −34.9 ± 1.7 −27.9 ± 1.1 −35.1 ± 1.1 −27.3 ± 2.1 −35.7 ± 2.1 −27.5 ± 1.1 −35.4 ± 1.1 −28.0 ± 1.0 −35.8 ± 1.0 −28.8 ± 1.0 −35.4 ± 1.0 −27.2± 0.6 −36.0 ± 0.6 −15.0 ± 1.3 −15.1 ± 1.3 −15.9 ± 0.9 −14.4 ± 1.7 −14.8 ± 1.1 −14.1 ± 2.1 −15.2 ± 1.1 −15.0 ± 1.0 −14.4 ± 1.0 −14.3 ± 1.4 1.0 ± 1.3 −12.4 ± 1.3 −20.9 ± 1.3 −25.6 ± 1.3

J=2→1 J=3→2 HCO +

J=1→0 J=3→2

H2 CO

JKa,Kc = 10,1 → 00,0 JKa,Kc = 21,2 → 11,1 JKa,Kc = 20,2 → 10,1 JKa,Kc = 21,1 → 11,0 JKa,Kc = 30,3 → 20,2

(390, −30)

CO

HCO + H2 CO

(−15, 270)

CO

J=1→0 J=2→1 J=3→2 J=1→0 J=3→2 JKa,Kc = 10,1 → 00,0 JKa,Kc = 21,2 → 11,1 JKa,Kc = 20,2 → 10,1 JKa,Kc = 21,1 → 11,0 JKa,Kc = 30,3 → 20,2 J=1→0 J=2→1 J=3→2

HCO +

J=1→0 J = 3 → 2b

H2 CO

JKa,Kc = 10,1 → 00,0 JKa,Kc = 21,2 → 11,1 JKa,Kc = 20,2 → 10,1 JKa,Kc = 21,1 → 11,0 JKa,Kc = 30,3 → 20,2 b

(−372, 0)

CO

HCO + H2 CO

(125, 185)

CO

J=1→0 J=2→1 J=3→2 J=1→0 J=3→2 JKa,Kc = 10,1 → 00,0 c JKa,Kc = 21,2 → 11,1 JKa,Kc = 20,2 → 10,1 c JKa,Kc = 21,1 → 11,0 JKa,Kc = 30,3 → 20,2 c J=1→0

8

The Astrophysical Journal, 765:112 (14pp), 2013 March 10

Zack & Ziurys Table 3 (Continued)

Offset (Δα, Δδ)

Molecule

Transition

TR ∗ or TA ∗ (mK)

TR (mK)

ΔV1/2 (km s−1 )

VLSR (km s−1 )

J=2→1

200 ± 23 400 ± 40 95 ± 15 55 ± 15 300 ± 34 240 ± 34 70 ± 34 70 ± 34 ∼ 10 46 ± 7 ∼ 10 ∼ 10 6±4 16 ± 4 250 ± 30 160 ± 21 460 ± 15 340 ± 15 530 ± 52 460 ± 70 24 ± 5 26 ± 5