11institutetext:  Green Bank Observatory, 155 Observatory Road, P.O. Box 2,
Green Bank, WV 24944, USA 22institutetext: School of Physics and Astronomy,
Rochester Institute of Technology, Rochester NY 14623, USA 33institutetext:
Laboratory for Multiwavelength Astrophysics, Rochester Institute of
Technology, USA 44institutetext: Center for Imaging Science, Rochester
Institute of Technology, USA 55institutetext: Institut de Planétologie et
d’Astrophysique de Grenoble (IPAG) UMR 5274, F-38041, Grenoble, France
66institutetext: Observatorio Astronómico Nacional, Alfonso XII, 3, 28014,
Madrid, Spain

# Sampling Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN
with UV Flux

J. Bublitz Sampling Molecular Gas in the Helix Planetary Nebula: Variation in
HNC/HCN with UV FluxSampling Molecular Gas in the Helix Planetary Nebula:
Variation in HNC/HCN with UV FluxSampling Molecular Gas in the Helix Planetary
Nebula: Variation in HNC/HCN with UV FluxSampling Molecular Gas in the Helix
Planetary Nebula: Variation in HNC/HCN with UV FluxSampling Molecular Gas in
the Helix Planetary Nebula: Variation in HNC/HCN with UV FluxSampling
Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN with UV
FluxSampling Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN
with UV FluxSampling Molecular Gas in the Helix Planetary Nebula: Variation in
HNC/HCN with UV Flux J.H. Kastner Sampling Molecular Gas in the Helix
Planetary Nebula: Variation in HNC/HCN with UV FluxSampling Molecular Gas in
the Helix Planetary Nebula: Variation in HNC/HCN with UV FluxSampling
Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN with UV
FluxSampling Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN
with UV FluxSampling Molecular Gas in the Helix Planetary Nebula: Variation in
HNC/HCN with UV FluxSampling Molecular Gas in the Helix Planetary Nebula:
Variation in HNC/HCN with UV Flux P. Hily-Blant Sampling Molecular Gas in the
Helix Planetary Nebula: Variation in HNC/HCN with UV FluxSampling Molecular
Gas in the Helix Planetary Nebula: Variation in HNC/HCN with UV Flux T.
Forveille Sampling Molecular Gas in the Helix Planetary Nebula: Variation in
HNC/HCN with UV FluxSampling Molecular Gas in the Helix Planetary Nebula:
Variation in HNC/HCN with UV Flux M. Santander-García Sampling Molecular Gas
in the Helix Planetary Nebula: Variation in HNC/HCN with UV FluxSampling
Molecular Gas in the Helix Planetary Nebula: Variation in HNC/HCN with UV Flux
J. Alcolea Sampling Molecular Gas in the Helix Planetary Nebula: Variation in
HNC/HCN with UV FluxSampling Molecular Gas in the Helix Planetary Nebula:
Variation in HNC/HCN with UV Flux V. Bujarrabal Sampling Molecular Gas in the
Helix Planetary Nebula: Variation in HNC/HCN with UV FluxSampling Molecular
Gas in the Helix Planetary Nebula: Variation in HNC/HCN with UV Flux

###### Abstract

Context. Observations of molecular clouds, prestellar cores, and
protoplanetary disks have established that the HNC/HCN ratio may be a potent
diagnostic of molecular gas physical conditions. The processes that govern the
relative abundances of these molecules nevertheless remain poorly understood.

Aims. We seek to exploit the wide range of UV irradiation strengths within the
$\sim$1 pc diameter Helix planetary nebula to explore the potential role of UV
radiation in driving HNC/HCN.

Methods. We performed IRAM 30 m and APEX 12 m radio line observations across
six positions within the Helix Nebula, making use of radiative transfer and
photodissociation modeling codes to interpret the results for line intensities
and line ratios in terms of the molecular gas properties.

Results. We have obtained the first detections of the plasma-embedded Helix
molecular knots (globules) in HCN, HNC, HCO+, and other trace molecules.
Analysis of the HNC/HCN integrated line intensity ratio reveals an increase
with radial distance from the Helix central star. In the context of molecular
line ratios of other planetary nebulae from the literature, the HNC/HCN ratio
appears to be anticorrelated with UV emission over four orders of magnitude in
incident flux. Models of the photodissociation regions within the Helix using
the RADEX and Meudon codes reveal strong constraints on column density
(1.5–2.5$\times$1012 cm-2) of the molecular gas, as well as pressure and
temperature. Analysis of the molecular ion HCO+ across the Helix indicates
that X-ray irradiation is likely driving HCO+ production in the outer regions
of planetary nebulae, where photodissociation is limited, yet cold gas and
ionized molecules are abundant.

Conclusions. Although the observational results clearly indicate that UV
irradiation is important in determining the HNC/HCN ratio, our PDR modeling
indicates that the UV flux gradient alone cannot reproduce the observed
variation of HNC/HCN across the Helix Nebula. Instead, HNC/HCN appears to be
dependent on both UV irradiation and gas pressure and density.

##  1 Introduction

Planetary nebulae (PNe) form through rapid mass loss during the asymptotic
giant branch (AGB) stages of low-to-intermediate mass stars (0.8-8 M⊙). As the
newly revealed, inert stellar core reaches sufficiently hot temperatures to
produce far UV photons ($\geq 13.6$ eV), the ensuing photodissociation and
ionization of material ejected during the AGB phase establishes the PN. Most
of the central stars of PNe (CSPNe) have large UV fluxes as a consequence of
their high Teff (often exceeding 100 kK) and large Lbol (100–1000 L⊙) (e.g.,
Frew, 2008). Many PNe are also luminous X-ray sources, where X-ray photons
originate with hot CSPN photospheres, X-ray-bright CSPN companions, and/or
energetic wind shocks (Leahy et al., 1996; Kastner et al., 2012; Freeman et
al., 2014; Montez Jr. et al., 2015).

Despite harboring these intense internal sources of high-energy radiation,
some PNe retain sizable masses of cold ($\sim$102 K) molecular gas (e.g.,
Huggins & Healy, 1989; Huggins et al., 2005; Schmidt & Ziurys, 2016, 2017).
This UV- and X-irradiated molecular gas and dust emits in the millimeter
regime (Bublitz et al., 2019, and references therein), providing rich radio
sources well-suited to improving our understanding of the chemistry within
photo-dissociation regions (PDRs).

In this study, we focus on what PNe can teach us about the molecules HCN and
HNC, which form primarily through dissociative recombination of HCNH+ with
electrons. The ongoing investigations of HNC/HCN in OMC-1 make clear the
ratio’s potential as a temperature probe for cold molecular gas (Schilke et
al., 1992; Graninger et al., 2014; Hacar et al., 2019). Studies of dark cloud
cores (Hirota et al., 1998; Nickerson et al., 2021), prestellar cores
(Padovani et al., 2011), star-forming Hii regions (Jin et al., 2015) and
galaxies (Cañameras et al., 2021), the protoplanetary disk orbiting TW Hya
(Graninger et al., 2015; Long et al., 2021), and even low-mass protostars and
young brown dwarfs (Riaz et al., 2018) reveal the utility of HNC/HCN ratio
measurements across environments ranging from molecular clouds through early
stages of stellar evolution. The interplay between the two molecules appears
to be governed primarily by the reaction HNC + H $\rightarrow$ HCN + H. At
temperatures above $\sim$100 K, this process favors conversion of HNC to HCN,
thus decreasing the HNC/HCN ratio as protostellar evolution proceeds (Jin et
al., 2015). Modeling by Graninger et al. (2014) suggests that a temperature
range of 25–40 K is sufficient to prompt conversion of HNC to HCN, suggesting
kinetic-driven reactions, despite the higher barrier temperature predicted by
theory.

Selective photodissociation of HNC may also produce a gradient in the HNC/HCN
ratio within molecular clouds. Aguado et al. (2017) predicted that the
photodissociation rate of HNC can reach 2–10 times that of HCN in the presence
of strong high-energy radiation fields. In the case of PNe, photodissociation
should be most important in the exposed layers of molecular gas, but may be
less effective in the densest gas or outer reaches of a PN. We would then
expect to see pre-PN levels of HNC and HCN where the gas is shielded from UV,
while HCN abundance rises with respect to HNC at the surface layers of the
molecular gas due to selective photodissociation.

A recent survey of molecule-rich PNe (Bublitz et al., 2019) established that
the HNC/HCN ratio is anticorrelated with PN CSPN UV luminosity, indicating
that UV irradiation could be driving the conversion of HNC into HCN. However,
these results suggest that HNC/HCN should also vary within an individual PN
due to the gradient of incident UV photons across the molecular gas regions.
This provides motivation for followup studies focused on variation in the
irradiation of a geometrically well-characterized distribution of molecular
gas. The Helix Nebula provides such a powerful testbed for HNC/HCN evolution
due to its highly extended molecular envelope, which presents gas parcels
exposed to a wide range of UV flux across the nebula.

NGC 7293 is one of the nearest known ($199.6\pm 0.6$ pc; Brown et al., 2021)
and most extended (0.46 pc radius) PNe. Its massive molecular envelope has
been mapped in mm-wave CO (Young et al., 1999), HCO+ (Zeigler et al., 2013),
and near-IR H2 emission (Kastner et al., 1996; Hora et al., 2006). The inner
ionized cavity of the nebula also contains many embedded, compact regions of
molecular gas and dust that have been identified by a variety of names such as
knots, globules, and filaments (e.g., Huggins et al., 1992; O’Dell et al.,
2005, 2007). Throughout this paper, such features will be referred to as
‘globules’. Estimates of the number of globules range from $\sim$3500 to tens
of thousands (O’Dell et al., 2007; Hora et al., 2006). They reside primarily
within the outer edges of the ionized core, though are also present along the
inner ring of molecular gas (O’Dell et al., 2004). A characteristic mass of
$\sim$10-5 M⊙ has been attributed to individuals in the globule population
(Meaburn et al., 1996; O’Dell et al., 2007), with a typical density of 106
cm-3 (Huggins et al., 1992; Meaburn et al., 1996). A recent analysis of one
such globule (identified as C1, Huggins et al., 1992) uses ALMA maps of CO
isotopologues to refine these estimates, finding a molecular mass of
$\sim$2$\times 10^{-4}$ M⊙ (Andriantsaralaza et al., 2019). The internal
structures of globules, such as their temperature and density gradients, have
yet to be established.

Due to the immense span of the the Helix’s molecular regions, from the dense
globules scattered within 1.5–2.5′ (2.7–4.5$\times$1017 cm) of the CSPN to the
outer molecular plumes at distances of $\sim$7.5′ (1.3$\times$1018 cm), there
exists a significant (factor $\sim$20) gradient in the CSPN radiation incident
on the molecular gas within this PN. The Helix central star emits strongly in
the UV, with CSPN $T_{eff}=$ 104 kK and a luminosity $L_{bol}$ = 89
$L_{\odot}$ (Napiwotzki, 1999; Montez Jr. et al., 2015), as well as a point-
like source of X-ray emission (Guerrero et al., 2001). These properties make
the Helix a prime testbed to study the effects of central star irradiation on
PN molecular gas chemistry. Schmidt & Ziurys (2017) performed multi-position
molecular line studies, probing eight regions of the extended Helix envelope
with 3 mm observations that yielded detections of HCN and HNC. The eight
positions they targeted provided good coverage of the Helix’s primary
molecular ring. However, both studies focus on points within the molecular
shell at offsets of 3.7–7.4′ from the central star, given the $\sim$1.2′ beam
size of these measurements, this coverage is insufficient to establish whether
HNC/HCN varies systematically across the PN.

In this work, we present a targeted molecular line study of the Helix Nebula
using the Institut de Radioastronomie Millimétrique (IRAM) 30 m telescope and
Atacama Large Pathfinder Experiment (APEX) 12 m telescope. The primary goal is
to further investigate the apparent anticorrelation between the HNC/HCN line
ratio and UV radiation in PNe by measuring the ratio with respect to distance
from the Helix central star. In Section 2, we describe the single-dish
molecular line observations. In Section 3, we describe the line detection and
mapping results. In Section 4 we present our analysis of these results, while
in Section 5, radiative transfer and photodissociation region modeling are
discussed. Conclusions from this work are presented in Section 6.

Figure 1: Spectra for transitions of molecules detected in the six Helix
positions using IRAM 30m. Individual spectra have been scaled by a multiplier
indicated for each line to facilitate comparison. The x-axis indicates
velocity with respect to the local standard of rest (VLSR) and the y-axis is
the antenna main-beam temperature (K). Vertical dotted lines mark the systemic
velocity of individual emission features with respect to the entire nebula.
Hyperfine structure lines are indicated in red. The two separate velocity
features identified towards the Globule A, Helix Rim, and West positions
represent emission from nearer and more distant clumps of gas. Positions are
indicated on an HST optical image of the Helix (NASA, NOAO, ESA, the Hubble
Helix Nebula Team, M. Meixner (STScI), and T.A. Rector (NRAO)), with the HCN
($J=1\rightarrow 0$) beamsize (27.6′′) and positions of our line survey
observations as circles (globules A, B, C – from Huggins et al. 1992 (Huggins
et al., 1992) – molecular Rim, East, and West positions). Table 1: Observed
Positions

Position |  $\alpha$ (J2000.0) |  $\delta$ (J2000.0) | N, E Offset (′′)
---|---|---|---
Globule A | 22h29m35.0s | -20°52′30.0′′ | (-136.4, -49.6)
Globule B | 22h29m43.0s | -20°49′02.6′′ | (+71.0, +62.5)
Globule C | 22h29m37.8s | -20°47′58.0′′ | (+135.6, -10.4)
Helix Rim | 22h29m47.9s | -20°53′18.0′′ | (-184.4, +131.2)
Helix East | 22h30m09.6s | -20°51′29.0′′ | (-75.4, +435.4)
Helix West | 22h29m07.5s | -20°48′59.0′′ | (+74.6, -435.2)

111RA and dec of the observed regions in the Helix, as well as their offsets
from the Helix CSPN in arcseconds. For reference, the central star is located
at 22h29m38.5s, -20°50′13.6′′.

##  2 Observations

###  2.1 IRAM 30m

Six positions in the Helix Nebula were observed in 2018 February and May with
the IRAM 30m telescope on Pico Veleta. The targeted positions were selected to
reflect a range in distances from the CSPN (Figure 1 and Table 1). Three
globule structures (hereafter Globules A, B, and C), previously the focus of
IRAM 30 m CO observations (Huggins et al., 1992), were targeted to exploit
their proximity to the CSPN. The position labeled “Helix West” was the subject
of the previously mentioned PN molecular line survey (Bublitz et al., 2019). A
position directly opposite the CSPN, labeled “Helix East”, was chosen as a
comparison for molecular and UV properties in the extended molecular envelope.
The final “Helix Rim” position was selected from among the positions observed
by Schmidt & Ziurys (2017), so as to sample an intermediate distance from the
CSPN.

Data were obtained with the Eight MIxer Receiver (EMIR) and Fast Fourier
Transform Spectrometer (FTS) backend, which allowed for observing in both the
3 mm and 1 mm regimes simultaneously, with 8 GHz bandwidth per sideband and
velocity resolutions of 0.66 and 0.22 km s-1, respectively. Two frequency
setups were devised, with central frequencies of 89 and 267 GHz for
simultaneous acquisition of the $J=1\rightarrow 0$ and $J=3\rightarrow 2$
lines of HCN, HCO+, and HNC, as well as the central frequencies of 111 and 227
GHz for lines of CO and neighboring molecular transitions.

Weather was typically clear with calm winds. Strong winds resulted in loss of
observing time for two of the nine observing days allocated. Another day was
lost to excessive snow and wind, while a fourth was lost to an electrical
fault.

Globules A, B, and C were also targeted with 5-point maps, using observational
offsets of 10$"$ in $J=1\rightarrow 0$ 13CO, 12CO, and $J=2\rightarrow 1$ 12CO
lines (Figures 10–12). The intent was to roughly ascertain the spatial
extension of the globules with respect to the 30 m beam (Section 3.2).
Calibration of data used the chopper wheel method with scaling in units of
main-beam temperature (Tmb). Worst-case flux calibration uncertainties from
ripples in the receiver (by coupling to hot and cold calibration loads) are
given at 2.5% (Carter et al., 2012), however local fluctuation around
individual molecular transitions contain stable baselines.

The beam sizes (half power beam widths) are 27.8′′ and 9.25′′, with beam
efficiencies of 0.77 and 0.45, respectively, at the 88.6 GHz and 265.9 GHz
frequencies of HCN $J=1\rightarrow 0$ and $J=3\rightarrow 2$. Venus and Mars
were used to check telescope pointing and focus every hour. Pointing errors
were corrected to an accuracy of $\sim$1.5′′. Observations were made in
position-switching mode. Offset positions that display no detected CO emission
were chosen from Young et al. (1999): (+28.6′′, +35.0′′) from the CSPN for
Globules B and C, ($-24.81^{\prime\prime}$, $-67.41^{\prime\prime}$) from the
CSPN for Globule A and Rim position, and two positions well outside the
molecular envelope (400′′ east and 250′′ west of positions East and West,
respectively).

Integration times varied by globule and by molecular transition, as
integrations for the receiver setting covering the $J=1\rightarrow 0$
transitions of HCN, HCO+, and HNC ranged from 2.8 hours (Rim) to 10.4 hours
(Globule C), for a total of 38 hours across the six positions. HCN and HNC
(3-2) transitions were observed for $\sim$1 hour at all positions. Select
observations of the CO isotopologues were made during the followup observing
run of the globules with integration times of $\sim$20 minutes to yield
similar noise constraints.

###  2.2 APEX

The six Table 1 positions in the Helix Nebula were also targeted with APEX in
2019 August using the SEPIA180 receiver in Band 5 (Figure 2). A baseband setup
at 177.8 GHz was used, with resolution of 10 MHz and a velocity resolution of
$\delta$v = 0.3 km s-1. The backend consisted of the eXtended Fast Fourier
Transform Spectrometer (XFFTS), whose bandwidth of 4 GHz allowed simultaneous
observation of the $J=2\rightarrow 1$ lines of HCN (177.26 GHz) and HCO+
(178.38 GHz). Due to its close proximity to a 183 GHz telluric water line, the
HNC $J=2\rightarrow 1$ line at 181.33 GHz was not measurable. Data collection
was performed in total power/position switching mode.

Beam width for this frequency range is 35′′, with a main beam efficiency of
0.86. The brightness temperature and pointing calibrators were EP Aqr, RAqr,
SGru, and $\pi^{1}$Gru. Focusing was performed on Jupiter before observations
of each position. Integration time on-source ranged from 30-60 minutes per
position, for a total observing time of 15.6 hours.

Figure 2: Spectra for $J=2\rightarrow 1$ transitions of HCN and HCO+ detected
in the six Table 1 positions with the APEX 12m Telescope. X- and Y-axes are
same as Figure 1. Hyperfine lines of HCN — where identified — have been
indicated in red.

###  2.3 Data Reduction

Reduction of the IRAM 30 m and APEX 12 m spectra was performed using the
Continuum and Line Analysis Single-dish Software
(CLASS)222https://www.iram.fr/IRAMFR/GILDAS/. A more detailed account of
methods for data reduction used in this work are described in Bublitz et al.
(2019). In brief, data reduction consisted of scan averaging, rescaling the
spectra to main beam brightness temperature ($T_{mb}$), and baseline
subtraction of a low-order polynomial.

##  3 Results

###  3.1 Line Detections and Properties

In total, seven molecular species across multiple transitions were identified
throughout the six positions targeted. We have obtained detections of HCN,
HCO+, and HNC for the first time in the Helix globules, as well as detections
of these molecules in the three PN envelope positions, with the IRAM 30 m
telescope. The $J=2\rightarrow 1$ transitions of HCN and HCO+ were also
detected with APEX across all six positions. The $J=3\rightarrow 2$
transitions of HCN and HNC were only detected by the 30 m telescope toward
Globule B, with upper limits obtained in the other regions. The
$J=3\rightarrow 2$ line of HCO+ was also detected from Globules B and C, in
addition to the Helix East and West positions.

Spectral maps in the $J=1\rightarrow 0$ transitions have identified multiple
emission line features in the Globule A, Rim, and West positions, indicative
of parcels of emitting gas spanning a range of velocities. In Globule A, a
secondary feature is observed at -30.2 km s-1, while two features are
identified at -29.5 and -11 km s-1 towards the extended West envelope region,
in addition to the dominant emission lines detailed in Table
LABEL:table_longtable. These positions feature overlapping hyperfine structure
lines in the molecule HCN. With insufficient information regarding the opacity
and local thermodynamic equilibrium status of the regions, the hyperfine lines
are not trivially disentangled and, as such, the analysis and discussion
presented here is restricted to the brightest components. Towards the Helix
Rim position, however, two velocity components are fully resolved, providing
us with an additional data point, which translates into two different
displacements from the CSPN (discussed further in Section 4.1). At -47.3 and
-9.9 km s-1, these features are hereafter referred to as ‘Outer Rim’ and
‘Inner Rim’, respectively, in order to differentiate their displacements from
the CSPN.

Measured line intensities range from 20 mK in weak HCN hyperfine structure
components to 2.09 K in CO towards Globule C. The corresponding FWHM line
widths varied from 0.6-3.3 km s-1 for well-resolved lines, to upwards of 5.7
km s-1 for blended lines that required multi-gaussian fitting. For the 30 m
observations, the average S/N for HCN $J=1\rightarrow 0$ integrated line
intensities in the globules is 23.0, while a S/N ratio of 5.6 is obtained for
the molecular envelope positions. The resulting S/N ratios across the
positions observed with the APEX Telescope are 6.8–10.9.

Properties of detected lines were measured with the Gaussian curve fitting
tool available in CLASS, with individual fitting of all hyperfine lines when
resolved (see Figure 2). Results of the spectral line analysis can be found in
Tables LABEL:table_longtable and LABEL:table_bonuslines, with the individual
spectra presented in Figures 1 and 2 for lines discussed in this work, and 13
for additional lines by source.

Our observations detected the hyperfine splitting of the rotational energy
levels for several molecules. The hyperfine complex of HCN $J=1\rightarrow 0$
was fully resolved, except in the case of the East and West positions where
emission from multiple regions along the molecular envelope line-of-sight has
blended and obscured any individual line components. This is consistent with
observations of the Helix West position in Bublitz et al. (2019). The observed
$J=1\rightarrow 0$ hyperfine complex of HCN is consistent with the expected
relative intensity levels of 3:5:1 for the $F=0\rightarrow 1,2\rightarrow
1,1\rightarrow 1$ transitions between quantum levels. For ratios of the
integrated intensities of HCN hyperfine components I($F=0\rightarrow
1/2\rightarrow 1$)=R02 and I($F=1\rightarrow 1/2\rightarrow 1$)=R12, LTE gas
will follow the theoretical intensity ratios of 0.2$<R_{02}<$1.0 and
0.6$<R_{12}<$1.0 for the case of optically thin gas (e.g., Gottlieb et al.,
1975; Loughnane et al., 2012). Across the observed positions in the Helix
Nebula with resolved hyperfine lines, we measured the ratios in the ranges
R02=0.25–0.40 and R12=0.53–0.75. The similarity of hyperfine ratios in the
Helix globules and Rim positions, within uncertainties of 4%, indicate that
the Helix is optically thin in HCN. While HNC $J=1\rightarrow 0$ also exhibits
hyperfine splitting, the line frequencies vary only by $\sim$0.1 MHz or $<$0.5
km s-1. Thus, the individual emission lines of HNC could not be resolved in
these observations. Hyperfine lines of C2H and CN were detected in the
globules for the first time, with C2H detected in the Rim position (also
previously detected by Schmidt et al., 2018) and marginal detections in Helix
East (Table LABEL:table_bonuslines, Figure 13).

Due to the complex nature of the line profiles, the results for the Helix East
and West positions listed in Table LABEL:table_longtable only include those
for the central peak gaussian fit. The integrated line intensity used for the
analysis described in Section 4.1 and Section 5, however, includes the
summation of all resolved velocity components.

Table 2: Molecular Transitions Detected

Molecule | Resolved Quantum Numbers |  $\nu$ (GHz) | Rel. Intensity
---|---|---|---
CCH | N=1$\rightarrow$0 | J=$\frac{3}{2}$$\rightarrow$$\frac{1}{2}$ | F=2$\rightarrow$1 | 87.317 |
|  | J=$\frac{1}{2}$$\rightarrow$$\frac{1}{2}$ | F=1$\rightarrow$1 | 87.402 |
HCN |  | J=1$\rightarrow$0 | F=0$\rightarrow$1 | 88.630 | 0.3333
|  |  | F=2$\rightarrow$1 | 88.632 | 0.5555
|  |  | F=1$\rightarrow$1 | 88.634 | 0.1111
HCO+ |  | J=1$\rightarrow$0 |  | 89.189 |
HNCa |  | J=1$\rightarrow$0 |  | 90.664 |
13CO |  | J=1$\rightarrow$0 |  | 110.201 |
CN | N=1$\rightarrow$0 | J=$\frac{1}{2}$$\rightarrow$$\frac{1}{2}$ | F=$\frac{3}{2}$$\rightarrow$$\frac{1}{2}$ | 113.170 |
|  | J=$\frac{1}{2}$$\rightarrow$$\frac{1}{2}$ | F=$\frac{3}{2}$$\rightarrow$$\frac{3}{2}$ | 113.191 |
|  | J=$\frac{3}{2}$$\rightarrow$$\frac{1}{2}$ | F=$\frac{5}{2}$$\rightarrow$$\frac{3}{2}$ | 113.491 |
12CO |  | J=1$\rightarrow$0 |  | 115.271 |
HCN |  | J=2$\rightarrow$1 | F=2$\rightarrow$2 | 177.260 | 0.0833
|  |  | F=1$\rightarrow$0 | 177.260 | 0.1111
|  |  | F=2$\rightarrow$1 | 177.261 | 0.2500
|  |  | F=3$\rightarrow$2 | 177.261 | 0.4667
|  |  | F=1$\rightarrow$2 | 177.262 | 0.0056
|  |  | F=1$\rightarrow$1 | 177.263 | 0.0833
HCO+ |  | J=2$\rightarrow$1 |  | 178.375 |
HNC |  | J=2$\rightarrow$1 |  | 181.325 |
12CO |  | J=2$\rightarrow$1 |  | 230.538 |
HCN |  | J=3$\rightarrow$2 |  | 265.886 |
HCO+ |  | J=3$\rightarrow$2 |  | 267.558 |
HNC |  | J=3$\rightarrow$2 |  | 271.981 |
333 Line frequencies and relative intensities were measured in the laboratory
and published in Müller et al. (2001) and Müller et al. (2005). Frequencies of
HCN transitions (and their hyperfine components) were established by Mullins
et al. (2016).
$a$$a$footnotetext: The hyperfine structure of HNC (J=1$\rightarrow$0) is
unresolved in these observations.

###  3.2 Mapping the Globules in CO

Spectra obtained for the 5-point maps targeting the globules are presented in
the Appendix for the $J=1\rightarrow 0$ lines of 13CO and 12CO, as well as
$J=2\rightarrow 1$ for 12CO (Figures 10–12). For Globule A, the western
position ($-$10, 0) presents a weaker emission intensity at 29–47% of its
globule core value, which suggests a lack of centering on the emission source,
or that there is a decrease in molecular gas along that side of the globule.
Globules B and C display a similar drop-off in CO isotopologue intensities
along their Southern sides (0, $-$10). Moreover, minimal emission is found at
the western position of Globule B. When compared with the alignment of each
globule observed in the optical, the decrease is consistent with gas facing
the central star. The mapping might then be identifying the lack of molecular
CO in the ionized shell that protects the cold molecule-rich gas from the
CSPN’s radiation.

Newly published ALMA maps ($J=2\rightarrow 1$ transitions of 12CO, C18O, and
13CO) have revealed that Helix Globule C consists of a N-S-oriented
filamentary structure with a length of 11–16′′ and average thickness of 2′′
(Andriantsaralaza et al., 2019). The ALMA data yield a velocity- and
spatially-integrated line flux of 14.4 Jy km s-1. Within the two 30 m
positions whose beams span the Globule’s 12CO-emitting region detected in the
ALMA data, we measure integrated line intensities of 1.70 and 1.54 K km s-1,
in the 10′′ $J=2\rightarrow 1$ beams, for a total beam intensity of 3.24 K km
s-1. Given the conversion factor of S/Tmb=4.95 J/K for the 30m telescope at
230
GHz)444https://www.iram.es/IRAMES/telescope/telescopeSummary/telescope_summary.html,
we compute an integrated flux of 16.04$\pm$0.71 Jy km s-1, in reasonable
agreement with the total line flux measured by ALMA.

##  4 Analysis

In this section, we consider the variations of three key line ratios across
the Helix Nebula, to identify whether and how these variations may be related
to the local intensity of high-energy radiation from the CSPN.

###  4.1 HNC/HCN in the Helix and Other PNe

To calculate the UV flux incident on the targeted regions of molecular gas in
the Helix, we have inferred their linear distances from the CSPN. We used the
intrinsic Helix geometrical model presented in Meaburn et al. (1998) to infer
the 3D structure of the globules and envelope emission-line components from
their velocities and projected positions. The resulting deprojected distances
from the CSPN, along with the inferred incident CSPN UV fluxes, are listed in
Table 3. Note that these incident UV flux estimates only account for
geometrical dilution; we do not attempt to correct for potential extinction
along the line of sight between gas parcel and CSPN.

In Figure 3, we plot the integrated HNC and HCN line intensities and their
line ratio as functions of distance from CSPN and incident CSPN UV flux. Both
molecular lines increase monotonically in intensity with increasing distance
from the CSPN (Figure 3, top panel). Such an increase in intensity may be
indicative of decreasing beam dilution with the more distant positions, i.e.,
increasing emitting region solid angle as one goes from the compact inner
globules to the more diffuse molecular rim. The lower panel of Figure 3
reveals that the HNC/HCN ratio increases as CSPN displacement increases and,
hence, FUV declines.

Figure 3: Top: Integrated line intensities of HCN and HNC for seven regions
throughout the Helix Nebula at varying deprojected distance from the CSPN.
Computed UV flux units are shown along the upper axis. Bottom: Line ratio of
HNC/HCN against distance. The blue dashed line indicates a linear regression
fit, with the shaded region representing 1$\sigma$ uncertainty. Table 3: PNe
used to compute HNC/HCN ratio

Object | HCN $\int{Idv}$ | HNC $\int{Idv}$ | HNC/HCN | Distance from | UV Fluxc
---|---|---|---|---|---
Name | (K km s-1) | (K km s-1) | Ratio | CSPN (pc) | (ergs cm-2 s-1)
Helix Globule A | 0.25 (0.01) | 0.11 (0.01) | 0.46 (0.01) | 0.14 (0.02) | 0.15 (0.01)
Helix Globule B | 0.25 (0.02) | 0.16 (0.01) | 0.64 (0.06) | 0.11 (0.01) | 0.25 (0.01)
Helix Globule C | 0.18 (0.01) | 0.09 (0.00) | 0.48 (0.04) | 0.14 (0.02) | 0.15 (0.01)
Helix Rim (Outer) | 0.47 (0.10) | 0.30 (0.03) | 0.64 (0.14) | 0.35 (0.08) | 0.02 (0.00)
Helix Rim (Inner) | 0.39 (0.09) | 0.23 (0.02) | 0.59 (0.14) | 0.24 (0.04) | 0.05 (0.00)
Helix East | 0.30 (0.14) | 0.33 (0.07) | 1.11 (0.58) | 0.44 (0.08) | 0.02 (0.00)
Helix West | 0.76 (0.06) | 0.49 (0.16) | 0.66 (0.22) | 0.44 (0.08) | 0.02 (0.00)
NGC 7027 | 11.6 (0.03) | 0.31 (0.02) | 0.03 (0.001) | 0.03a | 240.82
Hb 5 | 0.63 (0.22) | 0.24 (0.06) | 0.38 (0.17) | 0.09a | 18.33
NGC 6720 | 1.83 (0.02) | 0.67 (0.02) | 0.37 (0.01) | 0.17a | 0.44
NGC 6445 | 4.54 (0.02) | 1.12 (0.02) | 0.25 (0.01) | 0.19a | 0.85
NGC 2346 | 1.0 (0.2) | 1.0 (0.2) | 1.0 (0.28) | 0.32a | 0.01
NGC 6720 Rim | 2.08 (0.03) | 0.60 (0.03) | 0.29 (0.01) | 0.16 (0.07) | 0.52 (0.03)
NGC 6853 | 0.64 (0.01) | 0.20 (0.07) | 0.32 (0.01) | 0.16b | 0.42
NGC 2440 | 0.37 (0.12) | 0.05 (0.0) | 0.14 (0.05) | 0.12a | 4.83
NGC 6772 | 0.42 (0.02) | 0.15 (0.01) | 0.37 (0.03) | 0.20 (0.01) | 0.21 (0.02)
NGC 6781 | 3.83 (0.02) | 1.73 (0.02) | 0.45 (0.01) | 0.32 (0.09) | 0.12 (0.04)
Helix-SZ 1 | 0.13 (0.07) | 0.08 (0.03) | 0.63 (0.09) | 0.22-0.29 | 0.047 (0.018)
Helix-SZ 2 | 0.17 (0.09) | 0.16 (0.06) | 1.00 (0.26) | 0.34-0.36 | 0.024 (0.007)
Helix-SZ 3 | 0.18 (0.07) | 0.12 (0.04) | 0.59 (0.10) | 0.40-0.48 | 0.015 (0.004)

555 NGC 2346 line intensities from Bachiller et al. (1989), while NGC 2440 and
Hb 5 integrated intensities computed from Schmidt & Ziurys (2016, 2017).
Helix-SZ values from Schmidt & Ziurys (2017). Other PN line intensities from
Bublitz et al. (2019).
$a$$a$footnotetext: Distance estimated using H$\alpha$ radius (Frew, 2008),
assumed 50% error in computed fluxes $b$$b$footnotetext: Distance estimated
from H2 map (Kastner et al., 1996). $c$$c$footnotetext: Incident UV flux
assuming CSPN LUV = 3.55$\times$1035 erg s-1 (Montez Jr. et al., 2015).
All other distances computed from observed angular displacement and expansion
velocities. UV Flux intensities calculated using deprojected distances of
targeted positions from CSPN and CSPN UV luminosities (Bachiller et al., 1989;
Frew, 2008; Montez Jr. et al., 2015; Bublitz et al., 2019). Error estimated
from 12 m beam.

To place these results for the apparent dependence of Helix HNC/HCN on UV flux
in context, we identified PNe with previous HNC and HCN observations and for
which we could estimate the UV irradiation (Table 3). The Helix Nebula
molecular envelope was previously observed in HNC and HCN by Schmidt & Ziurys
(2017) across eight regions, including two locations close to those targeted
in this work. Line intensities from these positions were divided into three
distance bins (see Helix-SZ 1–3 in Table 3) and averaged into line ratios
representative of the inner, middle, and outer Helix envelope. Other PNe
studied in HNC and HCN (Bublitz et al., 2019, and references therein) with
molecular gas velocities distinct from their CSPN systemic velocity, such as
NGC 6720 (rim position), NGC 6772, and NGC 6781, were also included in the
sample, using the same method as used for the Helix to calculate the UV flux
incident on the molecular gas. The remaining objects listed in Table 3 were
either unresolved or observed directly along the line-of-sight to their CSPN,
thus sampling gas across a significant range of UV illumination. For these
cases, displacement from CSPN to irradiated gas cannot be determined, so we
adopt the H$\alpha$ radii of these PNe, with assumed 50% uncertainties (Frew
et al., 2016). Due to its highly filamentary nature (Huggins et al., 1996;
Salama et al., 2000), the extent of NGC 6853’s molecular envelope is poorly
represented by the H$\alpha$ radius. We instead estimate the extent of
molecular gas by selecting the midpoint to the outer edge of the nebula’s H2
region (Kastner et al., 1996). The only Table 3 PN not included in Figure 4 is
the pinched-waist bipolar nebula Hb 5. Far infrared studies of Hb 5 and
subsequent modeling have found dust mass levels higher than most PNe (Pottasch
& Surendiranath, 2007), with significant quantities of molecular hydrogen in
the core likely due to a high progenitor mass star. A nebular radius estimate
from H$\alpha$ flux does not adequately represent the region where the
molecular gas resides, as this PN has been shown to have highly filamentary
lobes that stem from a dense core of material that is shaped by fast outflows
(López et al., 2012).

Figure 4: HNC/HCN line ratio versus UV flux for the averaged representative
Helix Nebula positions (blue symbols) and similar molecule-rich PNe (red
symbols with associated NGC numbers). A linear regression fit to all data
points is indicated as a red dashed line, with the range of 1$\sigma$
uncertainty shown as red shading.

The inclusion of these additional data points from PN literature sources
extends the anticorrelation found between HNC/HCN and UV flux from the CSPN
(Figure 4). A linear regression fit over all PNe yields a power-law slope of
$-0.32$. We thus broadly conclude that the relationship of HNC/HCN with UV
flux takes the form

$\frac{HNC}{HCN}\sim F_{UV}^{-1/3}.$

That the power law slope of all PNe in this study is similar albeit steeper
than $-0.29$ for the Helix alone may reflect the fact that most of these
objects represent CSPNe with levels of UV irradiation 3–1600 times that of the
UV incident on the Helix Nebula. When the seven regions of the Helix Nebula
observed in this study are separated into three averaged bins, representing
the globules of the ionized region, the inner rim positions, and the East and
West positions of the outer envelope (dark blue, Figure 4), the points are
highly compatible with the general trend across all PNe. Despite the scatter
in individual measurements, and the fact that the PNe in this study span a
wide range of ages and morphologies, it is apparent that the anticorrelation
of HNC/HCN with UV irradiation extends over 4 orders of magnitude in UV flux.
We further explore the potential dependence of HNC/HCN on UV irradiation in
Section 5.2.

###  4.2 Variation of HCO+ with Radius

In Figures 5 and 6, we plot the integrated intensities of HCO+, and their
ratio to HCN and HNC, as functions of projected distance from the CSPN and UV
flux. These results demonstrate that HCO+ increases in intensity with distance
from the CSPN more rapidly and steadily than either HCN or HNC. HCO+ has been
well discussed as a likely diagnostic of X-ray emission incident on high-
density gas, wherein the HCO+ is enhanced via the production of H${}_{3}^{+}$
and is shielded from UV-induced dissociative recombination (e.g., Kimura et
al., 2012). Cosmic rays may also play a role in HCO+ production, though one
might anticipate that CSPN-produced X-rays are more important within the
Helix. HCO+/HCN and HCO+/HNC are found to rise with increased distance from
the source of PN UV emission at slopes of 1.8 and 0.9 compared to the near
unity increase of HNC/HCN with radius, respectively, with a correlation
coefficient of $\sim$0.9 for both HCO+ line ratios.

Figure 5: Top: Integrated line intensities of HCO+ and HCN plotted against the
deprojected distances from the CSPN. Computed UV flux emission at a given
distance from the CSPN is included along the upper axis. Bottom: HCO+/HCN line
ratio against distance. Linear regression fit with 1$\sigma$ uncertainty is
included in blue. Figure 6: Top: Integrated line intensities of HCO+ and HNC
plotted against the deprojected distances from the CSPN. Computed UV flux
emission at a given distance from the CSPN is included along the upper axis.
Bottom: HCO+/HNC line ratios against distance. Linear regression fit with
1$\sigma$ uncertainty is included in blue.

HCO+ has previously been found to exhibit unusually high abundances in the
molecular envelope of the Helix (Zack & Ziurys, 2013). Figures 5 and 6 hint at
an explanation for this enhanced HCO+ production. As X-rays penetrate gas
beyond the PDR, where dissociative UV photons are blocked, the extended
molecular cloud can more readily produce and maintain heightened HCO+ emission
compared to regions that are highly UV-irradiated, such as the inner globules.

This correlation becomes apparent in the steep incline of the HCO+/HCN ratio
(Figure 5), wherein the outer envelope positions display $\sim$4 times the
line ratio value of those positions closest to the CSPN. The HCO+/HNC ratio is
a factor $\sim$2 larger in the outer envelope than in the globules. The
implication is that the molecular gas forms and maintains HCO+ more readily
where UV-irradiation is low and the molecule is not heavily dissociated, yet
X-irradiation persists.

##  5 Modeling

###  5.1 HCN and HNC Column Densities

To interpret our molecular line data in terms of Helix globule properties such
as density and kinetic temperature, we used RADEX, a publicly available, non-
LTE radiative transfer code (van der Tak et al., 2007). RADEX takes in a set
of initial conditions for a one-dimensional slab model of gas and uses an
escape probability formulation to calculate the emergent line intensities
within the modeled medium. The RADEX outputs are further refined through
comparison with multiple transitions of the target molecular species. By
varying parameters such as gas temperature and density and then comparing the
outputs with the observed transition strengths sampled with the 30m and APEX,
we have attempted to constrain the abundances of HCN and HNC.

As the only position with resolved $J=1\rightarrow 0$ and $J=3\rightarrow 2$
transitions for HCN and HNC, as well as HCN $J=2\rightarrow 1$, Globule B
provides good constraints on the molecular excitation. We hence use Globule B
as the subject of the modeling discussed here. A range of kinetic temperatures
consistent with PDR gas (10–100 K) were explored, along with a range of H2
number densities and HCN and HNC column densities typical of molecular cloud
environments (104–107 cm-3 and 1010–1014 cm-2, respectively; Meaburn et al.,
1998; Huggins et al., 1992). Background radiation temperature was set to 2.73
K, while the linewidths were fixed to 1.0 km s-1 based on our measurements of
emission lines from Globule B (Table LABEL:table_longtable).

Preliminary analysis of ALMA interferometric mapping of Globule B (Bublitz et
al. 2021, in prep.) indicates that its structure is similar to that of Globule
C observed with ALMA (Andriantsaralaza et al., 2019). Thus, the structure of
Globule B is represented by an elongated rectangle of dimensions 12′′ by 2′′
pointing away from the CSPN, for the purposes of beam dilution correction.
Given the beamsizes of the IRAM and APEX telescopes (27.8′′ and 35.2′′,
respectively), the beam dilution factors are hence 25 and 40.

In Figure 7, we compare the observed line intensities for $J=1\rightarrow
0,2\rightarrow 1,$ and $3\rightarrow 2$ molecular transitions in Globule B,
corrected for beam dilution effects, with those predicted by the model through
contour maps in log-density and log-column density space. Contours correspond
to the ranges of predicted intensities that agree with the observations to
within 1$\sigma$. The confluence of these curves mark the acceptable solution
space for the range of density and column density explored at each value of
$T_{kin}$.

The results of incrementally varying gas kinetic temperature in the model
indicate that, up to $T_{kin}$ = 60 K, tight constraints exist on the column
densities of HCN and HNC. The measurement of three low-lying J transitions of
HCN provide the narrow constraints on N(HCN) and n(H2), as demonstrated in
Figure 7 for $T_{kin}$ = 20 and 40 K (black star). These comparisons of the
RADEX models to the data yield estimated column densities of $\sim$2.5$\times
10^{12}$ cm-2 and $\sim$1.5$\times 10^{12}$ cm-2 for HCN and HNC,
respectively. The models indicate densities of 106.5–105.4 cm-3 across the
temperature range of 10–40 K. For HNC, however, the H2 density remains
degenerate with kinetic temperature. We find no clear trend in the HNC/HCN
column density ratio with temperature from the RADEX modeling, suggesting that
the line ratio indeed serves as a proxy for the abundance ratio in the Tkin
regime of interest.

---
Figure 7: Loci of density and kinetic temperatures compatible with the
$J=1\rightarrow 0,2\rightarrow 1$, and $3\rightarrow 2$ HCN and HNC line
intensities towards Globule B. The shaded regions indicate 1$\sigma$
uncertainties. A black star indicates highly constrained regions of overlap
across all three transitions of HCN.

###  5.2 PDR Modeling

To interpret the RADEX results for HCN and HNC column densities in terms of a
physical model of the globules, we employed the publicly available Meudon PDR
code (Le Petit et al., 2006, http://ism.obspm.fr). As a first approximation,
we modeled the globule as a plane-parallel slab of gas and dust, irradiated by
a fixed UV radiation field, and computed the radiative transfer equation for
each point through an iterative process. Heating and cooling processes (such
as the photoelectric effect and cosmic rays, and infrared and millimeter
emission, respectively) are incorporated into the model, which utilizes a
large chemical network for the purposes of predicting abundances. The model
code then computes the abundances of relevant species for an assumed set of
physical conditions. A model spectrum representing a 100,000 K white dwarf
star (Levenhagen et al., 2017), scaled to the flux of the Helix CSPN (Oke,
1990), provided the ionization source to one side of the slab, while the
standard interstellar radiation field was assumed to irradiate the other side.
The ionized region of the Helix that surrounds a globule is assumed to result
in constant pressure across the ionized-neutral zones.

The density of the slab of gas was initially set to 103 cm-3, with a gas
temperature of 100 K. Using the analysis of O’Dell et al. (2005) and neutral
gas properties in PNe (Natta & Hollenbach, 1998), we can constrain the
expected pressure outside the globules. Assuming a constant pressure boundary
is necessary to maintain the globules for the age of the nebula, we estimate a
representative pressure of $\sim$107 K cm-3 for the Meudon models. This is
consistent with an extinction (due to dust) within the globule of
A${}_{V}\geq$0.5 (O’Dell et al., 2005). Given a typical globule diameter of
$\sim$2′′ (O’Dell et al., 2005; Meaburn et al., 1998) or a thickness of 400
AU, we then varied the pressure in our computed models until they achieved
consistent depth for extinctions of AV=0.5–1.0.

The resulting chemical abundances of several key molecular and atomic species
are displayed in Figure 8. In these models, we find the HNC/HCN ratio is below
unity across the slab. A fixed initial pressure results in heightened density
of the gas inside the model globule and a gradient in temperatures across
$\sim$40–60 K, consistent with the range predicted by Graninger et al. (2014).
Curiously, the models show that the HNC/HCN ratio declines with decreasing
temperature inside an individual globule, contrary to what is observed for
samples of cloud cores (Schilke et al., 1992; Graninger et al., 2014; Riaz et
al., 2018).

We used the same fundamental PDR model to simulate molecular gas parcels at
three positions of the Helix Nebula as observed with the 30m telescope: a
globule (A or C), the outer Rim, and the plume positions (East and West). In
one set of models (hereafter Model Set 1), we fixed gas pressure and density
across the three positions, with values of 107 K cm-3 and 105 cm-3,
respectively, and varied UV flux according to the relative distances of three
positions from the CSPN. This set of models is illustrated in the left panel
of Figure 9. The right panel of Figure 9 represents a set of models in which
density is progressively decreased across the three modeled positions (Model
Set 2). In addition to the detailed results of the modeling of HNC/HCN as a
function of AV, we have calculated an AV-weighted mean ratio for each model,
for comparison with the observed HNC/HCN ratios (bottom panels of Figure 9 and
Table 4).

The model curves demonstrate that, in each case, the HNC/HCN ratio declines
toward the center of the modeled region, reaching a minimum near
A${}_{V}\sim$0.7. However, in Model Set 1, an increase in distance from the UV
source leads to a decrease in the weighted mean HNC/HCN, counter to
observations (Figure 9, bottom left). In contrast, we find Model Set 2 — in
which pressure, density, and UV irradiation are all simultaneously decreased,
to mimic increasing distance from an irradiated central star — appears to
yield good agreement with the observed variation in HNC/HCN line ratios
(Figure 9, bottom right).

The preceding comparison between the models and observations suggests that the
combination of changing pressure (density) and UV irradiation, as opposed to
one or the other “ingredient”, may best explain the anticorrelation of HNC/HCN
with distance from CSPN that is observed in the Helix. Model Set 2 should not
be considered a ‘best fit’ given that we have not explored the full parameter
space, but rather an indication that the combination of well-constrained
variation in UV flux and variation in pressure can reproduce the observed
trend in HNC/HCN.

Figure 8:  Molecular and atomic densities and gas parameters across a gas slab
of extinction AV=0.5 (top) and AV=1.0 (bottom), with fixed pressure P=$10^{7}$
K cm-3 and density $\rho$=$10^{5}$ cm-3, irradiated by a WD model spectrum of
T=100,000 K (Levenhagen et al., 2017). Left: Density of selected species
across the visual extinction of the slab. The abundance ratio of HNC/HCN is
plotted as a solid purple line, with scale indicated on the right-hand y-axis.
Right: Temperature and density across the model slab.

Figure 9:  Top row. Curves of the [HNC]/[HCN] abundance ratio output by the
Meudon PDR modeling code are plotted against extinction, for a representative
slab of gas with integrated AV=1.0 of a representative slab of gas. Points are
colored based on kinetic gas temperature, which peaks toward the edges of the
slab. Bottom row. The average abundance ratio for each model curve is marked
with the corresponding symbol (light blue), outlining the predicted trend with
respect to displacement from the UV flux source. Additional points (red,
green, blue) mark the IRAM 30m observed line ratios for the three modeled
positions (Globules, Rim, Plumes), respectively. Left: Model Set 1. HNC/HCN of
three model slabs with increasing distances from the UV source, thus
decreasing incident UV flux. Pressure and density remain fixed. Right: Model
Set 2. UV flux, pressure, and density are all decreased with increasing
distance from the CSPN. See Section 5.2.  Table 4: Average Line Ratios from
PDR Meudon Code

| Model Set 1 | Model Set 2 | Observed Ratio
---|---|---|---
Pressure (K cm-3) | 107 | 5$\times$107 | 106 | 105 |
UV Field: 0.14 pc | 0.64 | 0.48 |  |  | 0.46-0.48
UV Field: 0.35 pc | 0.48 |  | 0.55 |  | 0.64
UV Field: 0.44 pc | 0.46 |  |  | 0.73 | 0.66-1.11

666Average value of the HNC/HCN line ratio from Meudon PDR models (Figure 9).
The observed ratios for Helix positions with similar UV field strengths (see
Table 3) are presented in the right-most column.

###  5.3 Comparison of RADEX and PDR Model Results

Contours of HCN and HNC column density in Figure 7 indicate that HCN
preferentially resides somewhat deeper within the globules. If the conversion
of HNC into HCN does scale with local gas temperature (Schilke et al., 1992;
Graninger et al., 2014; Hacar et al., 2019), we would expect to find a shell
of low ratio HNC/HCN surrounding an increasing ratio in the densest regions,
where the gas is coldest and HNC is better shielded from UV that could drive
chemical reprocessing. However, the RADEX models suggest that HNC/HCN
decreases towards the core of the globule.

Modeling of photodissociation with a gas slab using the Meudon code produced
similar results. A notable increase in HCN can be seen at the core of the PDR
model slab, even with respect to the rise in HNC density (Figure 8, left and
right). HNC/HCN drops to 0.43-0.52 at the core compared to the globule surface
value of 0.93 (Figure 9, left). By decreasing the pressure, and thus the
density, of the model slabs, we achieve good agreement with the observed
HNC/HCN line ratios across the Helix (Figure 9, right). The fact that this
model well reproduces the observational results suggests that both UV
irradiation and the local gas physical conditions – in particular, gas
pressure (or density) – play a role in determining the HNC/HCN ratio.

Nevertheless, the process that connects UV irradiation to the relative
production and destruction rates of HCN and HNC remains poorly constrained.
The HNC/HCN ratio has been found to be well correlated with gas heating in PDR
environments (e.g., Graninger et al., 2014; Hacar et al., 2019), while
selective photodissociation directly relates UV irradiation with the
conversion of HNC into HCN (Aguado et al., 2017). The results presented here
suggest that UV irradiation likely plays a key role via one or both of these
mechanisms. That is, UV photons may be heating the gas via photoionization and
the photoelectric effect on dust grains, or may be preferentially suppressing
the HNC abundance via selective photodissociation; either or both processes
would enhance the abundance of HCN relative to HNC as UV flux increases.

The molecule C2H is a strong tracer of UV ionization in PDR environments and
comparisons with HNC/HCN would establish the significance ionization plays on
the ratio. As a byproduct of isocyanide dissociation, the presence of CN in
regions of suppressed HNC/HCN would alternatively suggest the effect of
selective photodissociation on the ratio abundance. Thus, additional
observations of such photodissociation-generated species could help
disentangle the effects of UV-driven heating vs. photodissociation in driving
HNC/HCN.

##  6 Conclusions

In this study, we present the results of a 1–3 mm line survey of the Helix
Nebula using the IRAM 30 m and APEX 12 m telescopes. The targeted regions
consist of three prominent dense molecular knots within the ionized zone, a
position that has been kinematically resolved into two locations along the
molecular rim of the nebula, and two diametrically opposite positions at the
edges of the extended molecular envelope. Transitions from five molecules were
targeted and detected across the regions: the $J=1\rightarrow 0$ and
$J=3\rightarrow 2$ lines of HCN, HCO+, and HNC, the $J=2\rightarrow 1$ lines
of HCN and HCO+, as well as 12CO and 13CO in all globules. These observations
have yielded the first detections of HCN, HNC, HCO+, C2H, and CN in the
globules of NGC 7293.

The results support previous indications that HNC is more readily destroyed
than its isomer HCN in regions of higher UV irradiation in PNe. Targeting
positions of variable distance to the Helix Nebula central star as a means to
test the anticorrelation between the HNC/HCN line ratio and CSPN UV luminosity
in PNe (Bublitz et al., 2019), we have determined that the HNC/HCN ratio is
indeed anticorrelated with distance from the CSPN, as expected if the HNC/HCN
ratio decreases as irradiating CSPN UV flux increases. This suggests that
significant UV-driven modification of the HNC/HCN ratio likely occurs during
the PN stage, wherein the ratio may not be fixed during earlier (late AGB and
pre-PN) evolutionary stages (as asserted by Schmidt & Ziurys, 2017). These
Helix Nebula HNC/HCN line ratio data, combined with data from previous PN
studies, demonstrate that this anticorrelation between HNC/HCN and the
strength of UV irradiation spans 0.03–1.11 in HNC/HCN integrated line
intensity ratio and a factor 104 in UV flux.

Radiative transfer (RADEX) models fit to the Globule B observed line
intensities indicate column densities of $\sim$2.5$\times$1012 cm-2 and
$\sim$1.5$\times$1012 cm-2 for HCN and HNC, respectively. Although the
observational results within the Helix Nebula and across a larger sample of
PNe clearly indicate that UV irradiation is important in determining the
HNC/HCN ratio in PN molecular gas, our PDR modeling indicates that the UV flux
gradient alone cannot reproduce the observed variation of HNC/HCN across the
Helix. Instead, HNC/HCN appears to be dependent on both UV irradiation and gas
pressure and density.

Additionally, the HCO+/HCN and HCO+/HNC ratios are both found to increase with
distance from the CSPN. The increase in relative abundance of HCO+ suggests
that X-rays, with their superior penetrating power relative to UV, may be
increasingly important in driving PN molecular chemistry as distance from the
CSPN increases.

###### Acknowledgements.

J.B. wishes to acknowledge useful discussion with E. van Dischoeck. This
publication is based on observations carried out under project number 109-17
with the IRAM 30m telescope. IRAM is supported by INSU/CNRS (France), MPG
(Germany) and IGN (Spain). This work is also based on data acquired with the
Atacama Pathfinder Experiment (APEX) under program ID 0103.D-0682. APEX is a
collaboration between the Max-Planck-Institut fur Radioastronomie, the
European Southern Observatory, and the Onsala Space Observatory. The work of
T.F. is supported in part by the French National Research Agency in the
framework of the Investissements d’Avenir program (ANR-15-IDEX-02), through
the funding of the “Origin of Life” project of the Université Grenoble-Alpes.
M.S.G., J.A., and V.B. acknowledge support of the AxiN and EVENTs / NEBULAE
WEB research programs supported by the Spanish MICINN (grants AYA2016-78994-P
and PID2019-105203GB-C21). The authors also acknowledge IPAG and the support
of the Chateaubriand Fellowship of the Office for Science & Technology of the
Embassy of France in the United States, by which much of this work was funded.

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## Appendix A

The following tables comprise a detailed list of the properties of all
emission line features obtained from this study, as well as spectral line
figures that are not substantially addressed in this work.

Figure 10: Spectra of Globule A in the $J=1\rightarrow 0$ lines of 13CO (left)
and 12CO (center), as well as the $J=2\rightarrow 1$ line of 12CO (right).
Offset positions from the central pointing are indicated within each spectral
window by their R.A. and dec. The spacing of 10′′ between pointings is roughly
half the 30m beam at half-power at 110 GHz, and 1 beamwidth at 230 GHz. The
CSPN is to the NE.

Figure 11: Spectra of Globule B in the $J=1\rightarrow 0$ lines of 13CO (left)
and 12CO (center), as well as the $J=2\rightarrow 1$ line of 12CO (right).
Offset positions are indicated as in Figure 10. The CSPN is to the SW,
coinciding with the pointings that display decreased CO emission.

Figure 12: Spectra of Globule C in the $J=1\rightarrow 0$ lines of 13CO (left)
and 12CO (center), as well as the $J=2\rightarrow 1$ line of 12CO (right).
Offset positions are indicated as in Figure 10. The CSPN is to the south,
coinciding with decreased CO emission at (0, –10).

Figure 13: Additional spectral lines observed in each of the six targeted
positions of the Helix Nebula.