# The role of C/O in nitrile astrochemistry in PDRs and planet-forming disks

Romane Le Gal Harvard-Smithsonian Center for Astrophysics, 60 Garden St.,
Cambridge, MA 02138, USA  Madison T. Brady  Noland Internship at Harvard-
Smithsonian Center for Astrophysics (summer 2018)  California Institute of
Technology, Pasadena, CA 91125, USA  Karin I. Öberg Harvard-Smithsonian Center
for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA  Evelyne Roueff
Franck Le Petit  Sorbonne Université, Observatoire de Paris, Université PSL,
CNRS, LERMA, F-92190, Meudon, France

(Received July 30th, 2019; Revised October 1st, 2019; Accepted October 2nd,
2019)

###### Abstract

Complex nitriles, such as HC3N, and CH3CN, are observed in a wide variety of
astrophysical environments, including at relatively high abundances in photon-
dominated regions (PDR) and the UV exposed atmospheres of planet-forming
disks. The latter have been inferred to be oxygen-poor, suggesting that these
observations may be explained by organic chemistry in C-rich environments. In
this study we first explore if the PDR complex nitrile observations can be
explained by gas-phase PDR chemistry alone if the elemental C/O ratio is
elevated. In the case of the Horsehead PDR, we find that gas-phase chemistry
with C/O $\gtrsim$ 0.9 can indeed explain the observed nitrile abundances,
increasing predicted abundances by several orders of magnitude compared to
standard C/O assumptions. We also find that the nitrile abundances are
sensitive to the cosmic ray ionization treatment, and provide constraints on
the branching ratios between CH3CN and CH3NC productions. In a fiducial disk
model, an elevated C/O ratio increases the CH3CN and HC3N productions by more
than an order of magnitude, bringing abundance predictions within an order of
magnitude to what has been inferred from observations. The C/O ratio appears
to be a key variable in predicting and interpreting complex organic molecule
abundances in photon-dominated regions across a range of scales.

astrochemistry – ISM: molecules – methods: numerical – photon-dominated region
(PDR) – protoplanetary disks

††software: Pandas (McKinney, 2010), Matplotlib (Hunter, 2007), NumPy (van der
Walt et al., 2011), SciPy (Jones et al., 2001–), Meudon PDR Code (Le Bourlot
et al., 1993; Le Petit et al., 2006; Le Bourlot et al., 2012), Nautilus-v1.1
(Hersant et al., 2009; Ruaud et al., 2016; Wakelam et al., 2016).

=20

##  1 Introduction

Origins of life on Earth must have been closely linked to the emergence of
information-rich polymers such as DNA (deoxyribonucleic acid) or RNA
(ribonucleic acid). While their initial formation on the early Earth remains
mysterious, there are plausible chemical pathways to their building blocks on
the early Earth through a nitrile-centered UV-driven chemistry (Powner et al.,
2009; Patel et al., 2015; Sutherland, 2016). Simple and complex nitriles are
abundantly found at all stages of star and planet formation, including in
planet-forming disks, suggesting that the organic chemistry that preceded life
on Earth is not unique to the Solar System (Chapillon et al., 2012; Öberg et
al., 2015; Bergner et al., 2018; Loomis et al., 2018). Perhaps surprisingly
CH3CN and HC3N are two of the most commonly detected larger organic molecules
in disks, and the origins of these high abundances are uncertain. Öberg et al.
(2015) and Loomis et al. (2018) both invoke grain-surface chemical pathways to
predict sufficient amounts of CH3CN, but these predictions are extremely
uncertain due to lack of experimental data on ice nitrile chemistry and
desorption.

One important observational constraint is that observed HC3N and CH3CN
emissions appear to come from the upper most layer of disks or disk
atmospheres (Öberg et al., 2015; Bergner et al., 2018; Loomis et al., 2018).
Disk atmospheres are proposed analogs to the more well-studied photon-
dominated regions (PDR). Interestingly, complex nitriles have also been
detected at unexpectedly high abundances in the deeply characterized PDR, the
Horsehead nebula (Gratier et al., 2013). Located in the Orion constellation
and seen almost edge-on (Abergel et al., 2003), the Horsehead nebula
constitutes a perfect template source to study in detail the physics and
chemistry occurring in PDRs. With the WHISPER survey111http://www.iram-
institute.org/$\sim$horsehead/
Horsehead_Nebula/WHISPER.html (Wideband High-resolution Iram-30m Survey at two
Positions with Emir Receivers, PI: J. Pety), the chemistry of this PDR has
been surveyed at unprecedented detail, both at the edge of the PDR (defined by
the HCO peak emission, Gerin et al., 2009), and toward an interior ‘core’
position (defined by the DCO+ peak, Pety et al., 2007). Of interest to this
study, Gratier et al. (2013) found that the CH3CN emission is $\sim 40$ times
brighter at the PDR position than in the ‘Core’. Similar to protoplanetary
disks, this excess in CH3CN could not be explained by gas-phase chemistry
alone, and Gratier et al. (2013) instead suggested that a combination of UV-
mediated surface chemistry with surface desorption processes were responsible.
However, models developed by Le Gal et al. (2017), coupling the Meudon PDR (Le
Bourlot et al., 1993; Le Petit et al., 2006; Le Bourlot et al., 2012) and the
Nautilus (Hersant et al., 2009; Ruaud et al., 2016) astrochemical codes, could
not reproduce the abundance of CH3CN at the PDR position by about two orders
of magnitude when taking these processes into account and advanced alternative
explanations that (i) either CH3CN originates from deeper inside of the cloud
than previously assumed; or, (ii) the photo-desorption rate is higher and ice
photolysis rate lower than those currently implemented in models; or, (iii)
critical chemical formation pathways are missing in current astrochemical
networks.

Another possible explanation for these high nitrile abundances could be the
elemental gas-phase C/O ratio. Indeed, the relative elemental gas-phase
abundances of oxygen and carbon are known to strongly impact the chemistry of
star-forming regions (van Dishoeck & Blake, 1998). For instance, small
hydrocarbons, such as C2H, C3H, C3H2 and C4H, observed in a wide variety of
astrophysical objects including PDRs (Fuente et al., 2003; Pety et al., 2005,
2012; Cuadrado et al., 2015; Guzmán et al., 2015) and protoplanetary disks
(Dutrey et al., 1997; Fuente et al., 2010; Henning et al., 2010; Qi et al.,
2013; Kastner et al., 2015; Guilloteau et al., 2016; Bergin et al., 2016;
Kastner et al., 2018; Cleeves et al., 2018; Bergner et al., 2019; Loomis et
al., 2019), are believed to be mainly formed from atomic carbon (i.e. C+
and/or C). However, atomic carbon is readily converted into CO. Therefore,
depending upon the UV-shielding and C/O ratio, more or less carbon can be
locked into CO, hampering the production of hydrocarbons and more complex
carbon-containing molecules such as CH3CN and HC3N. In planet-forming disks, a
super-solar C/O ratio ($\gtrsim 0.8$) explains the hydrocarbon observations
well and is reasonably justified by oxygen removal through water formation and
other non-volatile O-bearing species (e.g. Hogerheijde et al., 2011; Cleeves
et al., 2018).

Here, we explore whether the observed CH3CN and other complex nitriles in the
Horsehead PDR can be explained by pure gas-phase chemistry when taking into
account a revised understanding of the cosmic-ray (CR) ionization rate, a more
complex gas-phase chemistry network, and most importantly, a C-rich
environment. We then carry out a smaller study of complex nitrile production
in planet-forming disks with elevated C/O ratios. In § 2, we describe the
physical and chemical properties we used and developed within the Meudon PDR
Code as well as our fiducial protoplanetary disk model. The resulting
molecular abundances and their dependence upon the CR ionization rate, C/O
ratio, and complex nitrile formation pathways are presented in § 3. In § 4, we
discuss the dominant reaction pathways for the four nitrile molecules detected
toward the Horsehead nebula - C3N, HC3N, CH3CN and CH3NC - as well as which
parameters affect these nitrile abundances. Our conclusions are summarized in
§ 5.

##  2 Modeling

For the PDR chemical investigations we use the Meudon PDR Code, tuned to the
physical conditions of the Horsehead nebula, and extended to incorporate a
more complete gas-phase chemical network for nitriles up to CH3CN and CH3NC in
complexity. In the second, smaller part of this paper we use a fiducial
protoplanetary disk model previously described in Le Gal et al. (2019) to test
whether our nitrile-optimized PDR chemistry can also explain high abundance of
complex nitriles in disks.

###  2.1 PDR Physical structure

The Meudon PDR Code is a 1D astrochemical modeling code which considers a
stationary plane-parallel slab of gas and dust illuminated by a radiation
field (Le Petit et al., 2006), which can be introduced at will. Assuming a
cloud at steady-state, it solves the physical and chemical conditions at
different visual extinction throughout the cloud, taking into account
radiative transfer from UV absorption, cooling emissions, and heating
processes.

Figure 1 displays the typical physical structure we computed for the present
study, assuming that the cloud has a fixed pressure of $4\times 10^{6}$ K cm-3
in the PDR region, and a constant density of $2\times 10^{5}$ n the core
(Habart et al., 2005), i.e. in our model for $A_{\rm{V}}$ $\gtrsim 2$ mag. The
incident radiation upon this cloud is that of $\sigma$ Ori, an O 9.5 V star
system, which results in an incident FUV intensity upon the cloud of about
$\chi=60$ (i.e $60~{}\times$ the ISRF in Draine’s units $\approx 60\times
2.7\times 10^{-3}$ erg s-1 cm-2, Draine, 1978; Habart et al., 2005). The
physical structure shown here was built considering standard initial gas-phase
elemental abundances, see Table 1, i.e. a C/O ratio of $\approx 0.46$ (Pety et
al., 2005; Goicoechea et al., 2006).

Figure 1: Horsehead nebula profiles of the temperature (top panel), the
density (middle panel) and the UV flux (bottom panel) as function of the
visual extinction, $A_{\rm{V}}$.

Another parameter to consider is the CR ionization rate $\zeta$. Low energy
cosmic rays (10-100 MeV, e.g Grenier et al., 2015) can penetrate deep into
dense clouds, producing ions that drive the gas-phase chemistry via fast ion-
neutral reactions. Diffuse clouds usually present higher values of $\zeta$
than denser clouds (e.g. Indriolo et al., 2015; Le Petit et al., 2016), with
$\zeta~{}\approx~{}(1-5)\times 10^{-17}$ s-1 per H2 being a typical dense
cloud value (e.g. Goicoechea et al., 2009). We highlight here that what we
labeled as $\zeta$ in the present study is the CR ionization rate per H2,
which corresponds to approximately twice the value of the CR ionization rate
per H atom (Glassgold & Langer, 1974). In a previous modeling study of the
Horsehead nebula, Rimmer et al. (2012) found that chemical predictions are in
better agreement with observations when $\zeta$ is allowed to vary across the
cloud, considering the following equation adapted from Nath & Biermann (1994)
by Rimmer et al. (2012):

$\zeta=3.05\times 10^{-16}(A_{\rm{V}})^{-0.6}+10^{-17}{\,\rm
s^{-1}}\mathrm{per}\,\ce{H2}.$ (1)

For the PDR position, where $A_{\rm{V}}$ $\approx 2$ mag, Eq. (1) gives
$\zeta\approx 2\times 10^{-16}{\,\rm s^{-1}}$ per H2. In § 3, we test the
impact of this higher value of $\zeta$ on the nitrile chemistry, by comparison
to the canonical value of $\zeta=5\times 10^{-17}{\,\rm s^{-1}}$ per H2 used
in Pety et al. (2005) and Goicoechea et al. (2006).

Lastly, while the public version of the Meudon PDR Code (v.1.5.2) does not
include grain chemistry, it does model the formation of H2 on grains and
computes the charge and temperature distribution of grains. In this study, we
kept the default grain size distribution, i.e with grain radius from $1\times
10^{-3}$ to 0.3 $\mu$m and their relative abundances described by the MRN
distribution (Mathis et al., 1977).

###  2.2 PDR model Chemistry

Table 1: Initial gas-phase elemental abundances Species |  $n_{i}/n_{\text{H}}$ (a)
---|---
He | 0.1
O(b) | $3.02\times 10^{-4}$
C | $1.38\times 10^{-4}$
N | $7.95\times 10^{-5}$
S | $3.50\times 10^{-6}$
Si | $1.73\times 10^{-8}$
Fe | $1.70\times 10^{-9}$

Each model was performed using the same initial abundance set as in Pety et
al. (2005) and Goicoechea et al. (2006), except for the oxygen abundance that
we varied in some models to explore the impact of the C/O ratio on the
chemistry (Table 1). We updated and extended the PDR Meudon Code (v.1.5.2)
chemical network with 39 species and 913 reactions relevant to the chemistry
of C3N, HC3N, and CH3CN, that we extracted from the KIDA
database222http://kida.obs.u-bordeaux1.fr/ for most of them. We also extended
the chemical network to the chemistry of CH3NC, based on theoretical studies
(e.g. Defrees et al., 1985) and the chemistry of its isomer CH3CN (see § 3.3).
In total, our network is composed of 191 species and 3616 chemical reactions,
including gas-phase bi-molecular reactions (i.e. radiative associations, ion-
neutral and neutral-neutral reactions), recombinations with electrons,
ionization and dissociation reactions by direct cosmic rays and secondary
photons (i.e. photons induced by cosmic rays), and by UV-photons (see Le Petit
et al., 2006, for rate formulae details). The critical reactions discussed in
this paper are summarized in Table 2, with rates and references.

UV-photo-reactions are expected to play a crucial role in PDR chemistry. The
Meudon PDR Code allows the choice between two different methods to compute the
photo-reaction rates: 1) if the photo-ionization and/or photo-dissociation
cross-sections of the molecule is known, the most accurate approach consists
in integrating this cross-section over the radiation field at each given
position in the cloud; 2) if the photo-cross-section of the molecule is
unknown, an analytical expression as function of the visual extinction is
estimated, i.e. considering fixed fitted parameters for each molecules and
computing their photo-rates as function of the visual extinction (see for an
example Eq. (14) of Heays et al., 2017). We updated the cross-sections of all
the molecules available in the Leiden
database333https://home.strw.leidenuniv.nl/$\sim$ewine/photo/ that are
included in our chemical network in the Meudon PDR Code (Heays et al., 2017).

###  2.3 Protoplanetary disk physical structure

Figure 2: Disk physical structure fed in our fiducial protoplanetary disk
astrochemical model. The 2D temperature (first panel), density (second panel),
visual extinction (third panel) and UV flux (fourth panel) profiles are
represented as functions of disk radius versus height, both in au. The dashed
black line, on the densities panels, delineates 1 scale height.

Our fiducial protoplanetary disk astrochemical model is based on the MWC 480
disk model of Le Gal et al. (2019), which consists in a 2D parametric physical
structure onto which the chemistry is post-processed (see §2.4). The disk
physical structure assumes a disk that is symmetric azimuthally and with
respect to the midplane. Thus, it can be described in cylindrical coordinates
centered on the inner star along two perpendicular axes characterizing the
radius and height in the disk. Figure 2 represents the profiles of the gas
temperature, density, visual extinction and UV flux throughout the disk, for
which the parameterization is briefly summarized below and further described
in Le Gal et al. (2019).

For a given radius $r$ from the central star, the vertical temperature profile
is computed following the formalism of Rosenfeld et al. (2013) and Williams &
Best (2014), originally developed by Dartois et al. (2003):

$\small
T(z)=\left\\{\begin{array}[]{ll}T_{\rm{mid}}+(T_{\rm{atm}}-T_{\rm{mid}})\left[\sin\left(\frac{\pi
z}{2z_{q}}\right)\right]^{2\delta}&\mbox{if}\,z<z_{q}\\\
T_{\rm{atm}}&\mbox{if}\,z\geq z_{q},\end{array}\right.$ (2)

where $T_{\mathrm{mid}}$ and $T_{\mathrm{atm}}$ are respectively the midplane
and atmosphere temperatures that vary as power law of the radii (Beckwith et
al., 1990; Piétu et al., 2007; Le Gal et al., 2019). $z_{q}=4H$ with $H$ the
pressure scale height that, assuming vertical static equilibrium, can be
expressed as follows:

$H=\sqrt{\frac{k_{\rm{B}}\,T_{\rm{mid}}\,r^{3}}{\mu\,m_{\rm{H}}\,G\,M_{\star}}},$
(3)

with $k_{\rm{B}}$ the Boltzmann constant, $\mu=2.4$ the reduced mass of the
gas, $m_{\rm{H}}$ the proton mass, $G$ the gravitational constant, and
$M_{\star}$ the mass of the central star. The midplane temperature
$T_{\mathrm{mid}}$ is estimated following a simple irradiated passive flared
disk approximation (e.g. Chiang & Goldreich, 1997; Dullemond et al., 2001;
Huang et al., 2018):

$T_{\rm{mid}}(r)\approx\left(\frac{\varphi L_{\star}}{8\pi
r^{2}\sigma_{\rm{SB}}}\right)^{1/4},$ (4)

with $L_{\star}=24~{}L_{\odot}$ the stellar luminosity (Andrews et al., 2013),
$\sigma_{\rm{SB}}$ the Stefan-Boltzman constant and $\varphi=0.05$ a typical
flaring angle. The atmosphere temperature, $T_{\mathrm{atm}}$, is based on
observational constraints. So here we consider
$T_{\mathrm{atm}}=T_{\mathrm{atm},100\,\rm{au}}(\frac{r}{100\,\rm{au}})$, with
$T_{\mathrm{atm},100\,\rm{au}}$=48 K from Guilloteau et al. (2011).

The disk is assumed to be in hydrostatic equilibrium. Thus, for a given
vertical temperature profile, the vertical density structure is determined by
solving the equation of hydrostatic equilibrium, as described from Eq. (17) to
(20) in Le Gal et al. (2019). The surface density of the disk is assumed to
follow a simple power law varying as $r^{-3/2}$ (Shakura & Sunyaev, 1973;
Hersant et al., 2009):

$\Sigma(r)=\Sigma_{R_{c}}\left(\frac{r}{R_{c}}\right)^{-3/2},$ (5)

where $\Sigma_{R_{c}}$ is the surface density at the characteristic radius
that can be expressed as function of the mass of the disk, $M_{\rm{disk}}$,
and its outer radius, $R_{\rm{out}}$:

$\Sigma_{R_{c}}=\frac{M_{\rm{disk}}R_{c}^{-3/2}}{4\pi\sqrt{R_{\rm{out}}}},$
(6)

with here $M_{\rm{disk}}=0.18~{}M_{\odot}$ (Guilloteau et al., 2011).

The visual extinction profile is derived from the hydrostatic density profile
using the gas-to-extinction ratio of $N_{\ce{H}}/A_{\rm{V}}=1.6\times 10^{21}$
(Wagenblast & Hartquist, 1989), with $N_{\ce{H}}=N(\ce{H})+2N(\ce{H2})$ the
vertical hydrogen column density of hydrogen nuclei. This gas-to-extinction
ratio assumes a typical mean grain radius size of 0.1 $\mu$m and dust-to-mass
ratio of 0.01, consistent with model assumptions.

Finally, the UV flux profile is computed considering the UV flux impinging the
disk convolved with the visual extinction profile. The unattenuated UV flux
factor, $f_{\rm{UV}}$, at a given radius $r$ depends on both the photons
coming directly from the central embedded star and on the photons that are
downward-scattered by small grains in the upper atmosphere of the disk. Thus,
following Wakelam et al. (2016), we consider:

$f_{\rm{UV}}=\frac{f_{\rm{UV},R_{c}}/2}{\left(\frac{r}{R_{c}}\right)^{2}+\left(\frac{4\rm{H}}{R_{c}}\right)^{2}}.$
(7)

###  2.4 Protoplanetary disk chemical model

The disk chemistry is computed time-dependently in 1+1D using the gas-grain
astrochemical model Nautilus (v.1.1) (Hersant et al., 2009; Wakelam et al.,
2016) in three phase mode (Ruaud et al., 2016), i.e. including gas-phase,
grain-surface and grain-bulk chemistry (see Le Gal et al., 2019, for more
details). First, the chemical evolution of a representative starless dense
molecular cloud is modeled up to a characteristic age of $1\times 10^{6}$
years (e.g. Elmegreen, 2000; Hartmann et al., 2001). For this 0D model we use
typical constant physical conditions: grain and gas temperatures of 10 K, a
gas density of $2\times 10^{4}and$ζ=5×10^-17${\,\rm s^{-1}}$
$per\ce{H2};thisparentmolecularcloudisalsoconsideredtobeshieldedfromexternalUVphotonsbyavisualextinctionof30mag.Forconsistency,weusethesameinitialabundancesasforourPDRmodel(seeTable~{}\ref{tab:abun})forthisfirstsimulationstep.Theoutcomingchemicalgasandicecompositionsofthisparentmolecularcloudarethenusedasinitialchemistryforour1+1Ddiskmodel.Second,weranthechemistryofour1+1Ddiskmodeluptoonemillionyears,typicalchemicalageofadiskwhengraingrowthisnotconsidered\cite[citep]{(e.g.
\@@bibref{AuthorsPhrase1Year}{cleeves2015}{\@@citephrase{,
}}{})}.Whilethediskchemistryhasnotreachedsteadystateatthattime,itsevolutionisslowenoughthattheresultspresentedhereholdforadisktwiceyoungerorolder.NotethatincontrasttothePDRmodel,thediskchemicalcodedoesincludegrainsurfacereactions.Howeverthegrain-
surfacereactionspathwaystoCH$_3$CNandHC$_3$N,thetwomoleculesorparticularinterestforthisstudy,remainpoorlyconstrained.\par\par$

##  3 Results

###  3.1 Impact of cosmic-ray treatment

Figure 3 presents the abundances of C3N, HC3N and CH3CN computed with the
Meudon PDR Code as function of the visual extinction $A_{\rm{V}}$, for two
models. Both models consider our new chemical network and the initial gas-
phase elemental abundances prescribed in Pety et al. (2005) and Goicoechea et
al. (2006) (see Table 1) but each model uses a different CR ionization rate.
The standard model uses the CR ionization rate canonical value of
$\zeta=5\times 10^{-17}{\,\rm s^{-1}}$ per H2 (Pety et al., 2005; Goicoechea
et al., 2006), and the high-$\zeta$ model uses a higher CR ionization rate of
$\zeta=2\times 10^{-16}{\,\rm s^{-1}}$ per H2, as calculated from (Eq. 1). By
impacting the ion abundances in molecular clouds, the CR ionization rate
indirectly drives the abundances of their daughter neutral molecules (see §
2.1). The nitrile abundances are indeed higher with the high-$\zeta$ model
than with the standard model, but both models under-predict by several orders
of magnitude the abundances observed toward the Horsehead nebula.

Rimmer et al. (2012) showed that a varying $\zeta$ across the cloud tends to
produce more accurate results. However, for the visual extinctions associated
with the PDR region and for molecules of interest studied here, varying
$\zeta$ across the cloud does not significantly impact the results compared to
a constant-$\zeta$ model. In the Core region, the varying-versus-constant
$\zeta$ model abundances are about half an order of magnitude different.

Changing the CR ionization rate also impacts the gas temperature, as shown in
the bottom panels of Fig. 4. Typically, increasing $\zeta$ shifts the
temperature gradient closer to the PDR’s edge. As a result, a higher $\zeta$
leading to higher temperatures and thus higher reaction rates, the absolute
abundances of nitriles are slightly increased in the PDR with a high-$\zeta$
model. In addition, likely due to the shift in temperature, the abundance
patterns are shifted outwards (i.e. closer to the illuminated edge of the PDR)
in the case of a higher $\zeta$. In summary, while the CR treatment has an
impact on the complex nitrile chemistry, increasing nitrile abundances by
almost an order of magnitude in the PDR region, the effect is small compared
to the mismatch between models and observations (see Fig. 3).

Figure 3: Computed C3N (dark blue) HC3N (purple) and CH3CN (orange) abundances
with respect to H nuclei, as function of the visual extinction $A_{\rm{V}}$
obtained with the standard model (solid lines) and with the high-$\zeta$ model
(dashed lines), see § 3.1. These model results are compared to the
observations from Gratier et al. (2013) (dashed boxes and arrow). 50% error
bars are included on the observations. The PDR (1 mag $<$ $A_{\rm{V}}$ $<$ 2
mag) and Core ($A_{\rm{V}}$ $\gtrsim$ 8 mag) regions are shaded.

###  3.2 Impact of the C/O ratio

Major carriers of O and C are expected to freeze out under different
conditions. In particular a substantial amount of O can become incorporated
into water ice which is one of the least volatile common interstellar
molecules, resulting in an elevated C/O ratio in the gas-phase. In order to
mimic the differential freeze-out of volatiles on grains, we varied the oxygen
gas-phase elemental abundance from $3.45\times 10^{-4}$ to $9.2\times 10^{-5}$
while keeping the carbon abundance fixed. This led to a variation of the C/O
ratio from 0.4 to 1.5. The lowest considered O abundance is a factor of two
higher than the CO abundance derived in the Horsehead PDR ($5.6\times
10^{-5}$, Pety et al., 2005), while the highest considered O abundances is
below the cosmic O abundance of $4.9\times 10^{-4}$ (Asplund et al., 2009) to
$5.75\times 10^{-4}$ (Przybilla et al., 2008). The choice of fixing the carbon
elemental abundance and varying the oxygen one, is also justified by the fact
that, between these two elements, the elemental gas-phase abundance of oxygen
is the less constrained (Jenkins, 2009; Whittet, 2010; Jones & Ysrad, 2019),
as discussed in Le Gal et al. (2014).

Figure 4: C3N, HC3N and CH3CN abundances with respect to H nuclei, as well as
the gas temperature, computed with our model of the Horsehead nebula as
function of the visual extinction, $A_{\rm{V}}$, for varying C/O and the
standard- (left column) and high- (right column) CR ionization rates
considered in this study. The observations from Gratier et al. (2013) are
represented by the black hatched boxes, which consider 50% error bars, and the
downward arrow. The core ($A_{\rm{V}}$ $>$ 8 mag) and PDR (1 mag $<$
$A_{\rm{V}}$ $<$ 2 mag) regions are shaded.

Figure 4 shows the impact of the gas-phase C/O ratio on the abundances of C3N,
HC3N and CH3CN and on the gas temperature as function of the visual extinction
$A_{\rm{V}}$ in our model of the Horsehead nebula. An O-poor chemistry (i.e. a
high C/O ratio) results in higher abundances of the three nitriles. For a CR
ionization rate of $\zeta=2\times 10^{-16}{\,\rm s^{-1}}$ per H2 and a gas-
phase C/O ratio in the range $0.9-1.5$, our new gas-phase chemistry model can
reproduce the three nitrile observations at the PDR position within an order
of magnitude. As for the Core position, our best fit models are found for
lower C/O ratios, in the range $0.6-0.9$. This lowering of C/O with increasing
visual extinction could be explained by photon-mediated release of refractory
carbon into gas phase in the PDR region, and/or the onset of freeze out of
carbon species in the core region. Whatever the mechanism, the decrease of C/O
with increasing visual extinction suggests that the gas-phase C/O ratio vary
across astrophysical objects.

It is also important to mention that the chemical rates used in astrochemical
models sometimes present large uncertainties. We ran two additional models to
test the impact of such uncertainties on the major reaction rates listed in
Table 2 which are driving the complex nitrile chemistry. These additional
simulations compute the chemistry with (i) the maximum allowed rates, and (ii)
the minimum allowed rates. The results are that the nitrile abundances of
interest for this study vary by less than a factor of three in the PDR and
Core regions, which is small compared to the more than two orders of magnitude
mismatch between observations and models using the standard C/O value. Though
this does not constitute a rigorous detailed sensitivity analysis such as
those developed for instance by Vasyunin et al. (2004, 2008) and Wakelam et
al. (2005, 2006, 2010), our simple analysis suggests that our results are
robust.

Since we are mainly interested in the PDR nitrile chemistry, we consider our
best-fit model the model with the lowest C/O ratio that reproduces at the PDR
position the three complex nitrile abundances shown Fig. 4. The model with
$\zeta=2\times 10^{-16}{\,\rm s^{-1}}$ per H2 and C/O $=1.0$ fulfills these
criteria.

Figure 5 shows the modeled abundances, obtained with our best-fit model, of
other typical oxygenated and carbonated molecules that were also observed
toward the Horsehead nebula, i.e CO (Pety et al., 2005), HCO+ (Goicoechea et
al., 2009), H2CO (Guzmán et al., 2011), and the hydrocarbons C2H, c-C3H, and
C4H (Pety et al., 2005; Guzmán et al., 2015). For comparison, the standard
model results are also presented in the same figure. The C/O variation does
not significantly impact the CO abundance throughout the cloud, which is
consistent with the fact that CO is the main reservoir of carbon and the
carbon elemental abundance is fixed in our models. Our best fit model displays
better agreement between model and observations in the PDR for the other
O-bearing molecules we consider, H2CO and HCO+.

With regards to the hydrocarbons, our best model better matches the
observations at the PDR position, generally by orders of magnitude, compared
to the standard model. This is an expected results because atomic O is a main
destroyer for small hydrocarbons such as C2H, c-C3H and C4H (Millar et al.,
1987; Millar & Herbst, 1990). Thus, while C is kept constant, diminishing O
increases the hydrocarbon abundances. However, even our best fit model does
not fully reproduce the observed abundances (see for instance C4H in Fig. 5),
indicative of that the C/O ratio does not provide a complete explanation for
the abundant hydrocarbon chemistry in the Horsehead PDR.

Regarding the Core position, our best fit model generally over-predicts the
observations, but this might simply be explained by the fact that freeze-out
on grains is not included in our model. It could also be that the gas-phase
C/O ratio decreases within the nebula, as suggested by the C/O grid results
shown in Fig. 4 when compared to the observations in each observed positions.

Figure 5: CO, HCO+, H2CO, C2H, c-C3H and C4H abundances with respect to H
nuclei, as function of the visual extinction $A_{\rm{V}}$ computed with our
best-fit model (solid lines) and standard model (dashed lines) of the
Horsehead nebula, compared to published observations (Pety et al., 2005;
Goicoechea et al., 2009; Guzmán et al., 2011, 2015) represented by the filled
and hatched boxes and the downward arrows. 50% error bars are included on the
observations. The core ($A_{\rm{V}}$ $>$ 8 mag) and PDR (1 mag $<$
$A_{\rm{V}}$ $<$ 2 mag) regions are shaded.

###  3.3 CH3NC vs CH3CN chemical pathways

Figure 6: CH3CN (dark blue) and CH3NC (orange) abundances with respect to H
nuclei, as function of the visual extinction, $A_{\rm{V}}$, in the modeled
Horsehead nebula. Three different models, based on our best-fit model (see §
3.2), are depicted here, testing the izomerization branching ratio of the
reaction pathway (9): (i) 100% (dotted lines); (iii) 80% (solid lines - best
model); (iii) 0% (dashed lines). The model results are also compared to
published observations from Gratier et al. (2013), where 50% error bars are
included (dashed boxes and downward arrow). The core ($A_{\rm{V}}$ $>$ 8 mag)
and PDR (1 mag $<$ $A_{\rm{V}}$ $<$ 2 mag) regions are shaded.

Another interesting nitrile molecule to study is the methyl isocyanide
(CH3NC), the isomer of methyl cyanide (CH3CN). First detected toward Sgr B2
(Cernicharo et al., 1988; Remijan et al., 2005), CH3NC was also detected
toward the Horsehead nebula (Gratier et al., 2013), Orion KL (López et al.,
2014), and more recently toward the solar-type binary protostar IRAS
16293-2422 (Calcutt et al., 2018). A few theoretical and experimental studies
have investigated the isomers’ chemistry and their abundance ratio (Huntress &
Mitchell, 1979; Defrees et al., 1985; Anicich et al., 1995), and converged on
the same major gas-phase production pathways for both via the reaction:

$\displaystyle\mhchemoptions{arrow-min-
length=1em}\ce{CH3++HCN->(CH3NCH+)$^{*}$->[$k_{2}$]CH3NCH++$h\nu$},$ (8)
$\displaystyle\mhchemoptions{arrow-min-
length=1em}\ce{->[$k_{3}$]CH3CNH++$h\nu$},$ (9)

with $k_{2}$ and $k_{3}$ given in Table 2, followed by the dissociative
recombinations of both protonated ions CH3NCH+ and its isomer CH3CNH+ to form
CH3NC and CH3CN, respectively (see reaction rates in Table 2). However, the
branching ratio is poorly constrained and depends on the stabilization
processes of the intermediate complex (CH3NCH+)∗ (e.g. Anicich et al., 1995).
Due to its lower energy state, CH3CNH+ is found to be the major product of the
reaction CH3+ + HCN (9). However, its formation requires the isomerization of
the intermediate complex (CH3NCH+)∗, which likely happens due to collisions
with a third body. Thus, the ratio between the two isomeric ions depends on
the competition between the relaxation and isomerization rates of the
intermediary complex. The resulting CH3NCH+/CH3CNH+ ratio was estimated to lie
in the range 0.1–0.4 by one theoretical study and assumed to propagate to a
CH3NC/CH3CN ratio of 0.1–0.4 via the respective subsequent dissociative
recombinations (Defrees et al., 1985).

Here, we investigated the impact of the branching ratios in between the
pathways (8) and (9) on the resulting CH3NC/CH3CN ratio in our PDR model.
Figure 6 presents the results obtained using our best fit model and three
different branching ratios leading to: 100%, 80% and 0% of isomerization. The
best fit results are obtained for a branching ratio of 80% (i.e. CH3NC/CH3CN
$\sim 0.2$), in agreement with the theoretical calculation of Defrees et al.
(1985). However, to our knowledge the CH3NCH+ dissociative recombination has
not been studied yet and even though the rate of the CH3CND+ dissociative
recombination was measured (Vigren et al., 2008) its branching ratio remains
uncertain (e.g. Plessis et al., 2010, 2012; Loison et al., 2014). It would
thus be interesting to study whether the dissociative recombination of CH3CNH+
and CH3NCH+ could lead to disproportionate prevalence of each initial isomer.
Further theoretical and experimental studies are therefore needed to assess
the validity of our astrochemically motivated branching ratios.

###  3.4 Complex nitrile production in a protoplanetary disk with a high C/O
ratio

Figure 7: Radial profile of the column density of CH3CN and HC3N computed with
our fiducial protoplanetary disk astrochemical model for four different
models, differing in (i) their C/O ratio, with (a) C/O$=0.46$ (in purple) as
in our PDR standard model and (b) C/O$=1.0$ (in orange) as in our PDR best fit
model; (ii) their grain chemical network that includes (solid lines) or not
(dashes lines) the formation of CH3CN and HC3N on grains. The horizontal gray
lines represent the column density derived from the MWC 480 disk observations
of (Bergner et al., 2018).

To test if our new understanding of the complex nitrile PDR chemistry can be
generalized to disks, we used a fiducial protoplanetary disk astrochemical
model, loosely based on the disk around MWC 480, from Le Gal et al. (2019)
described § 2.3 and § 2.4. We ran the chemical post-processing for two
different C/O ratios: (i) C/O$=0.46$, as in our PDR standard model, and (ii)
C/O$=1.0$ as in our PDR best fit model. For each of these C/O ratios we ran
two disk models, a full gas-grain model and a gas-grain model where CH3CN and
HC3N are only formed in the gas phase. The results of this total of four disk
models on the abundances of HC3N and CH3CN are shown in Fig. 7. A huge gap is
observed from $\sim~{}25$ to $\sim 200$ au in the computed nitrile column
densities for the standard C/O ratio disk models, and disappears for higher
C/O. The prevalence of grains’ pathway formation increases with C/O, and even
becomes negligible in the formation of HC3N for standard C/O. Even though our
disk model also includes grain chemistry, the main result from our PDR study
holds for disk astrochemistry, i.e. that an elevated C/O ratio better
reproduce the nitrile observations. Without any tuning of our disk model, our
best-fit model predictions are within an order of magnitude for the CH3CN
case. For the HC3N, the results are in agreement, at the order of magnitude
level, for the inner 100 au of the disk, where likely most of the emission
originates (Bergner et al., 2018).

##  4 Discussion

###  4.1 Nitrile formation pathways

In our PDR models, the C3N formation is dominated by the reaction:

$\ce{c-C3H+N->[k_{4}]H+C3N},$ (10)

with $k_{4}$ given in Table 2. c-C3H being itself mainly produced by the
electronic recombination of c-C3H2+. Thus, the under-prediction of C3N by our
model in the PDR region could be explained by the under-prediction of c-C3H
(see Fig. 5). Therefore, for a fixed abundance of N, a carbon-enriched medium
would enhance the production of C3N. As for its destruction, photo-
dissociation dominates in the PDR (see the corresponding reaction rate Table
2), but depending on the C/O ratio two other reactions also participate in the
C3N destruction, i.e.:

$\displaystyle\ce{O+C3N->[$k_{5}$]CO+CCN},$ (11)
$\displaystyle\ce{C+C3N->[$k_{6}$]C3+CN},$ (12)

with $k_{5}$ and $k_{6}$ given in Table 2. Reaction (11) even becomes the
primary destruction pathway of C3N in O-rich (C/O $\approx 0.4$) PDR. While, a
priori, it may seem odd for a photo-dissociation process to not be the primary
destruction mechanism in PDR, in our model this is explained by the high
concentration of atomic oxygen in this region for low C/O ratios. In O-poor
(C/O $\gtrsim 1$) PDR, C3N is primarily destroyed through a combination of
photo-dissociation and by atomic carbon (12).

HC3N is formed from a variety of different reactions involving carbon- and
nitrogen-containing molecules:

$\displaystyle\ce{HC3NH++e-->[$k_{7}$]H+HC3N},$ (13)
$\displaystyle\ce{C4H+N->[$k_{8}$]C+HC3N},$ (14)
$\displaystyle\ce{C+H2CCN->[$k_{9}$]H+HC3N},$ (15)
$\displaystyle\ce{c-C3H2+N->[$k_{10}$]H+HC3N},$ (16)
$\displaystyle\ce{C2H2+CN->[$k_{11}$]H+HC3N},$ (17)

with $k_{7}$ to $k_{11}$ given in Table 2. Thus, with a lower amount of one of
the main hydrocarbon destroyer, atomic O, and a higher amount of ‘free’ carbon
in the gas phase, more reaction pathways meaningfully contribute to the
formation of HC3N, via these diverse carbon-rich intermediates. HC3N is mainly
destroyed by UV-photons up to an $A_{\rm{V}}$ $\approx 4$ mag, via the
reaction:

$\ce{HC3N+h\nu->[k_{12}]C2H+CN},$ (18)

with $k_{12}$ given in Table 2. For $A_{\rm{V}}$ $\gtrsim 4$ mag, the impact
of destruction by dominant ions (e.g. H+, H3+, H3O+, C+, HCO+) gradually
increases with the optical depth, since UV-photon penetration diminishes and
most of the ion abundances increase. Other destruction pathways involving
atomic carbon forming bigger carbon chain molecules appear with increasing
optical depth, but these are typically far less common in our grid models and
are only relevant in dense clouds with higher carbon abundances.

The formation of CH3CN is dominated by the dissociative recombination of
CH3CNH+ with electrons, where CH3CNH+ itself is primarily formed by the
radiative association (9) and the following:

$\ce{HNC+CH3+->[k_{13}]CH3CNH++h\nu,}$ (19)

with $k_{13}$ given in Table 2. Similarly, and as already presented in § 3.3,
the formation of CH3NC is dominated by the dissociative recombination of
CH3NCH+ with electrons, with CH3NCH+ primarily formed by the radiative
association (8). CH3+ is formed via successive hydrogenation from C+. HCN and
HNC also descend from atomic carbon (Le Gal et al., 2014; Loison et al.,
2014). As a consequence, the formations of CH3CN and its isomer CH3NC seem to
be guided mostly by the carbon abundance, explaining that the abundance of
CH3CN increases with C/O (see Fig. 4). The destruction of the isomers are
dominated by photo-dissociation:

$\ce{CH3CN/CH3NC+h\nu->[k_{14}]CH3+CN},$ (20)

with $k_{14}$ given in Table 2.

To summarize, the enhancement in nitrile abundances appear to be tightly
correlated with the C/O ratio. More interestingly however, our study
highlights the importance of the relative elemental gas-phase abundances with
respect to one another, and emphasizes the indirect role of oxygen in nitrile
chemistry. The latter has a dramatic impact on the carbon chemistry in O-rich
molecular environments, where most of the carbon is rapidly locked in CO and
atomic O is a main destroyer for hydrocarbons, hampering the development of
more complex carbon chemistry. In addition, we have shown in § 3.2 that the
nitrile abundances increase with $\zeta$ (Fig. 4). Indeed, the ionization
fraction is directly linked to $\zeta$, which governs the production of ions,
such as CH3+, HC3NH+ and c-C3H2+, parent molecules of the complex nitriles
here under study. CH3+ react with HCN and HNC to produce CH3CNH+, that readily
recombines with electrons to form CH3CN; HC3NH+ recombines with electrons to
form HC3N (13); and c-C3H2+ recombines with electrons to form c-C3H which
reacts with N to produce C3N (10).

###  4.2 The role of C/O in PDR and disk atmosphere nitrile chemistry

The strong impact of the C/O ratio on the nitrile chemistry can likely be
explained by the fact that in the gas phase, for a fixed amount of C element,
O-removal decreases one of the main destruction pathways of hydrocarbons,
which are the parent molecules of nitriles. To this effect adds the reactions
of small carbon and oxygen species to form CO. Typically, in molecular clouds,
most of the carbon hastily reacts with all available oxygen to form CO,
effectively removing it from the reaction pathways that build up more complex
molecules, such as complex nitriles. O-removal thus leaves more ‘free’ carbon
available in the gas phase to form carbon-containing molecules such as
hydrocarbons, carbon chains and nitriles. As a comparison, the standard model
results in a CO abundance of almost $1.38\times 10^{-4}$, i.e. quasi all the
carbon available in our models (see Table 1), whereas our best-fit model
produces a CO abundance of $\sim 1.34\times 10^{-4}$. This leaves $\sim
6.0\times 10^{-6}$ ‘free’ carbon to build more complex carbon-containing
molecules.

Varying the C/O ratio also impacts the gas temperature for $A_{\rm{V}}$
$\lesssim 1.5$ mag, as shown in the last panel row of Fig. 4. An increase in
C/O ratio increases the gas temperature. This is due to the fact that, in the
present work, we varied the abundance of atomic O to change the C/O ratio,
thus reducing one of the main gas coolant in this region of the PDR. To test
the impact of varying the C/O ratio via the carbon elemental abundance instead
of the oxygen, we ran additional models. The main difference is in the
resulting CO abundance. For a fixed C/O ratio, it increases with the amount of
carbon. As a consequence, the gas temperature decreases at the edge of the
PDR, since CO is another important gas coolant. However, these differences
diminish with the increase of the visual extinction and are minor at the PDR
position and in particular on the nitrile abundances. Thus, the main results
found in the present work on the C/O impact on the Horsehead nebula chemistry
is agnostic to whether C or O is varied to achieve a C/O ratio of $\sim$1.

In disks, the C/O ratio is also strongly impacting the nitrile chemistry with
the additional effect of changing the morphology of the nitrile abundance
throughout the disk, as shown in Fig. 7. Whether or not CH3CN forms in gas or
through gas-grain chemistry in disks, an elevated C/O in disks also helps in
better reproducing the observations. However, grain chemistry seems to be
needed to better reproduce the observations, in agreement with Öberg et al.
(2015) and Loomis et al. (2018). Our finding of a C/O$\gtrsim 1$ needed to
reproduce the complex nitriles chemistry observed in disk atmospheres is in
good agreement with the results of Bergin et al. (2016) that also find that a
C/O ratio exceeding unity is required to reproduce the observations of C2H in
disks. These authors therefore proposed C2H as probe of C/O-enriched disk
layers. Here we propose that complex nitriles could also serve as such probe
in both PDR and disks, with the vantage of also probing the internal parts of
the latter ($\lesssim 100$ au) as predicted by our models (see Fig. 7).
Moreover, the fact that complex nitriles, such as HC3N and CH3CN, are much
more commonly observed in disks than O-containing complex molecules, such as
CH3OH, highly suggests that organic chemistry is regulated by the C/O ratio
and that disk atmosphere chemistry seems to be more generally C-rich than
O-rich.

##  5 Conclusions

We tackled the chemistry of nitriles in PDR, in order to, first, understand
the observations found for the nitriles C3N, HC3N, CH3CN and CH3NC toward the
Horsehead PDR (Gratier et al., 2013), and second, test if our improved PDR
chemistry could help to explain the recent observations of HC3N and CH3CN in
disk atmospheres (Öberg et al., 2015; Bergner et al., 2018). To this aim, we
extended the chemistry of the Meudon PDR code (v.1.5.2) up to these four
nitriles and explored the impact of some key parameters, such as the cosmic-
ray ionization rate $\zeta$ and the gas-phase elemental C/O ratio, on our
modeled nitrile results. Our main conclusions are summarized below:

  1. 1.

Varying the C/O ratio between 0.4 and 1.5 in a model of the Horsehead PDR
results in orders of magnitude changes in nitrile abundances.

  2. 2.

A gas-phase C/O ratio of $\gtrsim 0.9$ can reproduce the C3N, HC3N, CH3CN and
CH3NC abundances within an order of magnitude in the Horsehead PDR, without
any grain-surface chemistry.

  3. 3.

The cosmic-ray ionization rate moderately affects the nitrile chemistry
through its impact on electrons and hydrocarbon ions (e.g. CH3+, C3H2+). A
$\zeta=2\times 10^{-16}{\,\rm s^{-1}}$ per H2 better fits the observations
than the standard value of $\zeta=5\times 10^{-17}{\,\rm s^{-1}}$ per H2.

  4. 4.

Our best fit PDR model (i.e. with $\zeta=2\times 10^{-16}{\,\rm s^{-1}}$ per
H2 and C/O$=1$) can reproduce both the relative abundances of CH3NC and CH3CN
when adopting a branching ratio of 0.8 isomerization for the reaction CH3+ +
HCN (9).

  5. 5.

An elevated C/O ratio ($\sim 1.0$) could also be the key for understanding
complex nitrile disk chemistry. Using a fiducial protoplanetary disk
astrochemical model, we find that disk observations of CH3CN and HC3N are
reproduced within an order of magnitude, while our standard model under-
predicts the same molecules by 2-3 orders of magnitude.

While the good agreement between observations and models in both a classic PDR
and a planet-forming disk, it is important to note that the nitrile grain
chemistry is still poorly constrained, and it may contribute to both kinds of
regions (e.g. Bertin et al., 2017a, b; Calcutt et al., 2018; Nguyen et al.,
2019). Further experiments and theory on nitrile grain surface chemistry and
desorption are needed to make progress here. Thus, it would be interesting to
add grain chemistry, and in particular grain nitrile chemistry, in the Meudon
PDR code to test how the results presented here would be affected.
Furthermore, other parameters would be worth testing in future model
developments, such as the impact of stellar X-ray irradiation on disk
chemistry which could affect its ionization (e.g. Glassgold et al., 1997; Rab
et al., 2018; Waggoner & Cleeves, 2019), and the sensitivity of disk chemistry
to grain sizes (e.g. Wakelam et al., 2019) as smaller grains provide a higher
surface area relative to their volume and thus more reaction sites and also
tend to have temperatures closer to that of the gas. In the meantime we note
that the strong impact of C/O on nitrile chemistry may enable us to use
nitriles to constrain this important parameter in disks and PDR analogs.

The authors would like to thank the anonymous referee for constructive
suggestions and comments. R. LG. also thanks Tom J. Millar for useful
discussion. This work was supported by an award from the Simons Foundation
(SCOL # 321183, KO). M. T. B. acknowledges support from the Noland Internship
at Caltech.

##  Appendix A Critical chemical reactions added to the Meudon PDR Code
network

Table 2: Rates of the critical chemical reactions discussed in this study.  Chemical reactions | $\alpha$ | $\beta$ | $\gamma$ |  $k$ rate |  $T$ range |  Ref.(b) | Rate
---|---|---|---|---|---|---|---
|  |  |  |  |  |  ($\rm{cm}^{3}{\,\rm s^{-1}}$) |  |  |  type(a) | (K) |  |  uncertainties(c)
Main formation and destruction pathways for CH3CNH+ & CH3CN |
CH3+ |  HCN | $\rightarrow$ |  CH3CNH+ | $h\nu$ |  | 7.20(-9) | -0.50 | 0.00 | (1) | $10-299$ | [1], [2] | $F_{0}=10,\,g=0$
CH3+ |  HCN | $\rightarrow$ |  CH3CNH+ | $h\nu$ |  | 8.00(-11) | -3.00 | 0.00 | (1) | $300-800$ | [2], [3] | $F_{0}=2,\,g=0$
CH3+ |  HNC | $\rightarrow$ |  CH3CNH+ | $h\nu$ |  | 9.00(-9) | -0.50 | 0.00 | (1) | $10-300$ | [4] | $F_{0}=10,\,g=0$
CH3CNH+ |  e- | $\rightarrow$ |  H |  H |  H2CCN | 8.00(-8) | -0.50 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
CH3CNH+ |  e- | $\rightarrow$ |  H |  CH3CN |  | 1.30(-7) | -0.50 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
CH3CNH+ |  e- | $\rightarrow$ |  HNC |  CH3 |  | 6.00(-8) | -0.50 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
CH3CNH+ |  e- | $\rightarrow$ |  HCN |  CH3 |  | 6.00(-8) | -0.50 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
CH3CN | $h\nu$ | $\rightarrow$ |  CN |  CH3 |  | 2.95(-9) | 0.00 | 3.07 | (3) | – | [5] | $F_{0}=1.3,\,g=0$
Main formation and destruction pathways for CH3NCH+ & CH3NC |
CH3+ |  HCN | $\rightarrow$ |  CH3NCH+ | $h\nu$ |  | 1.80(-9) | -0.50 | 0.00 | (1) | $10-299$ | [1], [2] | $F_{0}=10,\,g=0$
CH3+ |  HCN | $\rightarrow$ |  CH3NCH+ | $h\nu$ |  | 2.00(-11) | -3.00 | 0.00 | (1) | $300-800$ | [2], [3] | $F_{0}=2,\,g=0$
CH3NCH+ |  e- | $\rightarrow$ |  H |  CH3NC |  | 1.30(-7) | -0.50 | 0.00 | (2) | $10-300$ |  [4](⋆) | $F_{0}=3,\,g=0$
CH3NCH+ |  e- | $\rightarrow$ |  HCN |  CH3 |  | 6.00(-8) | -0.50 | 0.00 | (2) | $10-300$ |  [4](⋆) | $F_{0}=3,\,g=0$
CH3NC | $h\nu$ | $\rightarrow$ |  CN |  CH3 |  | 2.95(-9) | 0.00 | 3.07 | (3) | – |  [5](⋆) | $F_{0}=1.3,\,g=0$
Main formation and destruction pathways for C3N |
N |  c-C3H | $\rightarrow$ |  H |  C3N |  | 1.10(-10) | 0.17 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
C3N | $h\nu$ | $\rightarrow$ |  C2 |  CN |  | 5.00(-10) | 0.00 | 1.80 | (3) | – | [6] | $F_{0}=2,\,g=0$
C3N |  O | $\rightarrow$ |  CO |  CCN |  | 1.00(-10) | 0.00 | 0.00 | (2) | $10-298$ | [7] | $F_{0}=3,\,g=2.97$
C3N |  C | $\rightarrow$ |  CN |  C3 |  | 2.40(-10) | 0.00 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
Main formation and destruction pathways for HC3N |
HC3NH+ |  e- | $\rightarrow$ |  H |  HC3N |  | 6.00(-7) | -0.58 | 0.00 | (2) | $10-800$ | [8] | $F_{0}=1.4,\,g=0$
C4H |  N | $\rightarrow$ |  C |  HC3N |  | 7.00(-11) | 0.17 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
C |  H2CCN | $\rightarrow$ |  H |  HC3N |  | 1.00(-10) | 0.00 | 0.00 | (2) | $10-300$ | [4] | $F_{0}=3,\,g=0$
N |  c-C3H2 | $\rightarrow$ |  H |  HC3N |  | 1.00(-11) | 0.00 | 2000.00 | (2) | $10-800$ | [8] | $F_{0}=3,\,g=500$
C2H2 |  CN | $\rightarrow$ |  H |  HC3N |  | 2.72(-10) | -0.52 | 19.00 | (2) | $10-280$ | [6] | $F_{0}=1.25,\,g=0$
HC3N | $h\nu$ | $\rightarrow$ |  CN |  C2H |  | 7.13(-9) | 0.00 | 2.59 | (3) | – | [5] | $F_{0}=1.3,\,g=0$

## References

  * Abergel et al. (2003) Abergel, A., Teyssier, D., Bernard, J. P., et al. 2003, A&A, 410, 577
  * Andrews et al. (2013) Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129
  * Anicich (2003) Anicich, V. G. 2003, JPL Publication 03-19, 1
  * Anicich et al. (1995) Anicich, V. G., Sen, A. D., Huntress, Wesley T., J., & McEwan, M. J. 1995, J. Chem. Phys., 102, 3256
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
  * Beckwith et al. (1990) Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. 1990, AJ, 99, 924
  * Bergin et al. (2016) Bergin, E. A., Du, F., Cleeves, L. I., et al. 2016, ApJ, 831, 101
  * Bergner et al. (2018) Bergner, J. B., Guzmán, V. G., Öberg, K. I., Loomis, R. A., & Pegues, J. 2018, ApJ, 857, 69
  * Bergner et al. (2019) Bergner, J. B., Öberg, K. I., Bergin, E. A., et al. 2019, ApJ, 876, 25
  * Bertin et al. (2017a) Bertin, M., Doronin, M., Fillion, J. H., et al. 2017a, A&A, 598, A18
  * Bertin et al. (2017b) Bertin, M., Doronin, M., Michaut, X., et al. 2017b, A&A, 608, A50
  * Calcutt et al. (2018) Calcutt, H., Fiechter, M. R., Willis, E. R., et al. 2018, A&A, 617, A95
  * Cernicharo et al. (1988) Cernicharo, J., Kahane, C., Guelin, M., & Gomez-Gonzalez, J. 1988, A&A, 189, L1
  * Chapillon et al. (2012) Chapillon, E., Dutrey, A., Guilloteau, S., et al. 2012, ApJ, 756, 58
  * Chiang & Goldreich (1997) Chiang, E. I., & Goldreich, P. 1997, ApJ, 490, 368
  * Cleeves et al. (2015) Cleeves, L. I., Bergin, E. A., Qi, C., Adams, F. C., & Öberg, K. I. 2015, ApJ, 799, 204
  * Cleeves et al. (2018) Cleeves, L. I., Öberg, K. I., Wilner, D. J., et al. 2018, ApJ, 865, 155
  * Cuadrado et al. (2015) Cuadrado, S., Goicoechea, J. R., Pilleri, P., et al. 2015, A&A, 575, A82
  * Dartois et al. (2003) Dartois, E., Dutrey, A., & Guilloteau, S. 2003, A&A, 399, 773
  * Defrees et al. (1985) Defrees, D. J., McLean, A. D., & Herbst, E. 1985, ApJ, 293, 236
  * Draine (1978) Draine, B. T. 1978, ApJS, 36, 595
  * Dullemond et al. (2001) Dullemond, C. P., Dominik, C., & Natta, A. 2001, ApJ, 560, 957
  * Dutrey et al. (1997) Dutrey, A., Guilloteau, S., & Guelin, M. 1997, A&A, 317, L55
  * Elmegreen (2000) Elmegreen, B. G. 2000, ApJ, 530, 277
  * Fuente et al. (2010) Fuente, A., Cernicharo, J., Agúndez, M., et al. 2010, A&A, 524, A19
  * Fuente et al. (2003) Fuente, A., Rodrıguez-Franco, A., Garcıa-Burillo, S., Martın-Pintado, J., & Black, J. H. 2003, A&A, 406, 899
  * Gerin et al. (2009) Gerin, M., Goicoechea, J. R., Pety, J., & Hily-Blant, P. 2009, A&A, 494, 977
  * Glassgold & Langer (1974) Glassgold, A. E., & Langer, W. D. 1974, ApJ, 193, 73
  * Glassgold et al. (1997) Glassgold, A. E., Najita, J., & Igea, J. 1997, ApJ, 480, 344
  * Goicoechea et al. (2009) Goicoechea, J. R., Pety, J., Gerin, M., Hily-Blant, P., & Le Bourlot, J. 2009, A&A, 498, 771
  * Goicoechea et al. (2006) Goicoechea, J. R., Pety, J., Gerin, M., et al. 2006, A&A, 456, 565
  * Gratier et al. (2013) Gratier, P., Pety, J., Guzmán, V., et al. 2013, A&A, 557, A101
  * Grenier et al. (2015) Grenier, I. A., Black, J. H., & Strong, A. W. 2015, ARA&A, 53, 199
  * Guilloteau et al. (2011) Guilloteau, S., Dutrey, A., Piétu, V., & Boehler, Y. 2011, A&A, 529, A105
  * Guilloteau et al. (2016) Guilloteau, S., Reboussin, L., Dutrey, A., et al. 2016, A&A, 592, A124
  * Guzmán et al. (2011) Guzmán, V., Pety, J., Goicoechea, J. R., Gerin, M., & Roueff, E. 2011, A&A, 534, A49
  * Guzmán et al. (2015) Guzmán, V. V., Pety, J., Goicoechea, J. R., et al. 2015, ApJ, 800, L33
  * Habart et al. (2005) Habart, E., Abergel, A., Walmsley, C. M., Teyssier, D., & Pety, J. 2005, A&A, 437, 177
  * Harada et al. (2010) Harada, N., Herbst, E., & Wakelam, V. 2010, Astrophysical Journal, 721, 1570
  * Hartmann et al. (2001) Hartmann, L., Ballesteros-Paredes, J., & Bergin, E. A. 2001, ApJ, 562, 852
  * Heays et al. (2017) Heays, A. N., Bosman, A. D., & van Dishoeck, E. F. 2017, A&A, 602, A105
  * Henning et al. (2010) Henning, T., Semenov, D., Guilloteau, S., et al. 2010, ApJ, 714, 1511
  * Herbst (1985) Herbst, E. 1985, Astrophysical Journal, 291, 226
  * Hersant et al. (2009) Hersant, F., Wakelam, V., Dutrey, A., Guilloteau, S., & Herbst, E. 2009, A&A, 493, L49
  * Hogerheijde et al. (2011) Hogerheijde, M. R., Bergin, E. A., Brinch, C., et al. 2011, Science, 334, 338
  * Huang et al. (2018) Huang, J., Andrews, S. M., Dullemond, C. P., et al. 2018, arXiv e-prints, arXiv:1812.04041
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science Engineering, 9, 90
  * Huntress & Mitchell (1979) Huntress, W. T., J., & Mitchell, G. F. 1979, ApJ, 231, 456
  * Indriolo et al. (2015) Indriolo, N., Neufeld, D. A., Gerin, M., et al. 2015, ApJ, 800, 40
  * Jenkins (2009) Jenkins, E. B. 2009, ApJ, 700, 1299
  * Jones & Ysrad (2019) Jones, A. P., & Ysrad, N. 2019, arXiv e-prints, arXiv:1906.01382
  * Jones et al. (2001–) Jones, E., Oliphant, T., Peterson, P., et al. 2001–, SciPy: Open source scientific tools for Python, , .  http://www.scipy.org/
  * Kastner et al. (2015) Kastner, J. H., Qi, C., Gorti, U., et al. 2015, ApJ, 806, 75
  * Kastner et al. (2018) Kastner, J. H., Qi, C., Dickson-Vandervelde, D. A., et al. 2018, ApJ, 863, 106
  * Le Bourlot et al. (2012) Le Bourlot, J., Le Petit, F., Pinto, C., Roueff, E., & Roy, F. 2012, A&A, 541, A76
  * Le Bourlot et al. (1993) Le Bourlot, J., Pineau Des Forets, G., Roueff, E., & Flower, D. R. 1993, A&A, 267, 233
  * Le Gal et al. (2017) Le Gal, R., Herbst, E., Dufour, G., et al. 2017, A&A, 605, A88
  * Le Gal et al. (2014) Le Gal, R., Hily-Blant, P., Faure, A., et al. 2014, A&A, 562, A83
  * Le Gal et al. (2019) Le Gal, R., Öberg, K. I., Loomis, R. A., Pegues, J., & Bergner, J. B. 2019, ApJ, 876, 72
  * Le Petit et al. (2006) Le Petit, F., Nehmé, C., Le Bourlot, J., & Roueff, E. 2006, ApJS, 164, 506
  * Le Petit et al. (2016) Le Petit, F., Ruaud, M., Bron, E., et al. 2016, A&A, 585, A105
  * Loison et al. (2014) Loison, J.-C., Wakelam, V., & Hickson, K. M. 2014, MNRAS, 443, 398
  * Loison et al. (2017) Loison, J.-C., Agúndez, M., Wakelam, V., et al. 2017, MNRAS, 470, 4075
  * Loomis et al. (2019) Loomis, R., Oberg, K. I., Andrews, S., & et al. 2019, submitted to ApJ
  * Loomis et al. (2018) Loomis, R. A., Cleeves, L. I., Öberg, K. I., et al. 2018, ApJ, 859, 131
  * López et al. (2014) López, A., Tercero, B., Kisiel, Z., et al. 2014, A&A, 572, A44
  * Mathis et al. (1977) Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425
  * McKinney (2010) McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, ed. S. van der Walt & J. Millman, 51 – 56
  * Millar & Herbst (1990) Millar, T. J., & Herbst, E. 1990, MNRAS, 242, 92
  * Millar et al. (1987) Millar, T. J., Leung, C. M., & Herbst, E. 1987, A&A, 183, 109
  * Nath & Biermann (1994) Nath, B. B., & Biermann, P. L. 1994, MNRAS, 270, L33
  * Nguyen et al. (2019) Nguyen, T., Fourré, I., Favre, C., et al. 2019, A&A, 628, A15
  * Öberg et al. (2015) Öberg, K. I., Guzmán, V. V., Furuya, K., et al. 2015, Nature, 520, 198
  * Patel et al. (2015) Patel, B. H., Percivalle, C., Ritson, D. J., Duffy, C. D., & Sutherland, J. D. 2015, Nature Chemistry, 7, 301 EP .  https://doi.org/10.1038/nchem.2202
  * Pety et al. (2007) Pety, J., Goicoechea, J. R., Hily-Blant, P., Gerin, M., & Teyssier, D. 2007, A&A, 464, L41
  * Pety et al. (2005) Pety, J., Teyssier, D., Fossé, D., et al. 2005, A&A, 435, 885
  * Pety et al. (2012) Pety, J., Gratier, P., Guzmán, V., et al. 2012, A&A, 548, A68
  * Piétu et al. (2007) Piétu, V., Dutrey, A., & Guilloteau, S. 2007, A&A, 467, 163
  * Plessis et al. (2012) Plessis, S., Carrasco, N., Dobrijevic, M., & Pernot, P. 2012, Icarus, 219, 254
  * Plessis et al. (2010) Plessis, S., Carrasco, N., & Pernot, P. 2010, J. Chem. Phys., 133, 134110
  * Powner et al. (2009) Powner, M. W., Gerland, B., & Sutherland, J. D. 2009, Nature, 459, 239 EP .  http://dx.doi.org/10.1038/nature08013
  * Przybilla et al. (2008) Przybilla, N., Nieva, M.-F., & Butler, K. 2008, ApJ, 688, L103
  * Qi et al. (2013) Qi, C., Öberg, K. I., Wilner, D. J., & Rosenfeld, K. A. 2013, ApJ, 765, L14
  * Rab et al. (2018) Rab, C., Güdel, M., Woitke, P., et al. 2018, A&A, 609, A91
  * Remijan et al. (2005) Remijan, A. J., Hollis, J. M., Lovas, F. J., Plusquellic, D. F., & Jewell, P. R. 2005, ApJ, 632, 333
  * Rimmer et al. (2012) Rimmer, P. B., Herbst, E., Morata, O., & Roueff, E. 2012, A&A, 537, A7
  * Rosenfeld et al. (2013) Rosenfeld, K. A., Andrews, S. M., Wilner, D. J., Kastner, J. H., & McClure, M. K. 2013, ApJ, 775, 136
  * Ruaud et al. (2016) Ruaud, M., Wakelam, V., & Hersant, F. 2016, MNRAS, 459, 3756
  * Shakura & Sunyaev (1973) Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337
  * Sutherland (2016) Sutherland, J. D. 2016, Angewandte Chemie International Edition, 55, 104.  https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201506585
  * van der Walt et al. (2011) van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science and Engineering, 13, 22
  * van Dishoeck & Blake (1998) van Dishoeck, E. F., & Blake, G. A. 1998, ARA&A, 36, 317
  * Vasyunin et al. (2008) Vasyunin, A. I., Semenov, D., Henning, T., et al. 2008, ApJ, 672, 629
  * Vasyunin et al. (2004) Vasyunin, A. I., Sobolev, A. M., Wiebe, D. S., & Semenov, D. A. 2004, Astronomy Letters, 30, 566
  * Vigren et al. (2008) Vigren, E., Kamińska, M., Hamberg, M., et al. 2008, Physical Chemistry Chemical Physics (Incorporating Faraday Transactions), 10, 4014
  * Wagenblast & Hartquist (1989) Wagenblast, R., & Hartquist, T. W. 1989, MNRAS, 237, 1019
  * Waggoner & Cleeves (2019) Waggoner, A. R., & Cleeves, L. I. 2019, arXiv e-prints, arXiv:1908.08048
  * Wakelam et al. (2019) Wakelam, V., Chaietillon, E., Dutrey, A., et al. 2019, MNRAS, 484, 1563
  * Wakelam et al. (2010) Wakelam, V., Herbst, E., Le Bourlot, J., et al. 2010, A&A, 517, A21
  * Wakelam et al. (2006) Wakelam, V., Herbst, E., & Selsis, F. 2006, A&A, 451, 551
  * Wakelam et al. (2016) Wakelam, V., Ruaud, M., Hersant, F., et al. 2016, A&A, 594, A35
  * Wakelam et al. (2005) Wakelam, V., Selsis, F., Herbst, E., & Caselli, P. 2005, A&A, 444, 883
  * Wakelam et al. (2012) Wakelam, V., Herbst, E., Loison, J. C., et al. 2012, ApJS, 199, 21
  * Whittet (2010) Whittet, D. C. B. 2010, ApJ, 710, 1009
  * Williams & Best (2014) Williams, J. P., & Best, W. M. J. 2014, ApJ, 788, 59