Neutral–neutral synthesis of organic molecules in cometary comae

ABSTRACT

Remote and in situ observations of cometary gases have revealed the presence of a wealth of complex organic molecules, including carbon chains, alcohols, imines, and the amino acid glycine. Such chemical complexity in cometary material implies that impacts by comets could have supplied reagents for prebiotic chemistry to young planetary surfaces. However, the assumption that some of the molecules observed in cometary comae at millimetre wavelengths originate from ices stored inside the nucleus has not yet been proven. In fact, the comae of moderately-active comets reach sufficient densities within a few thousand kilometres of the nucleus for an active (solar radiation-driven) photochemistry to ensue. Here, we present results from our latest chemical-hydrodynamic models incorporating an updated reaction network, and show that the commonly-observed HC₃N (cyanoacetylene) and NH₂CHO (formamide) molecules can be efficiently produced in cometary comae as a result of two-body, neutral–neutral, gas-phase reactions involving well-known coma species. In the presence of a near-nucleus distributed source of CN (similar to that observed by the Rosetta spacecraft at comet 67P), we find that sufficient HC₃N and NH₂CHO can be synthesized to match the abundances of these molecules observed previously in Oort cloud comets. The precise coma origins of these (and other) complex organic molecules can be verified through radio interferometric mapping observations, for example using the Atacama Large Millimeter/submillimeter Array.

astrochemistry, methods: numerical, comets: general

1 INTRODUCTION

Cometary ices are some of the most pristine, ancient materials in our Solar System. They have remained largely unaltered since they accreted during the birth of the planets (or earlier, in the interstellar medium), so their study provides unique information on the chemical conditions prevalent during the earliest history of our Solar System (Mumma & Charnley 2011; Altwegg et al. 2017). Comets are also believed to have delivered volatiles and organics during impacts with planets, so understanding their compositions provides insight into the chemical regents that may have been present to drive prebiotic chemistry on the surfaces of Solar System bodies (Ehrenfreund & Charnley 2000; Martins & Sephton 2010).

Cometary ice abundances are derived primarily through multiwavelength remote observations of their atmospheres/comae (Cochran et al. 2015), while in situ spacecraft missions provide further details on select comets (e.g. Wyckoff et al. 1988; Rubin et al. 2019). Coma mapping observations reveal that several well-known cometary molecules (including C₂, CN, HNC, H₂CO, and others) have ‘distributed’ sources, identified through their extended, relatively flat spatial profiles (A’Hearn et al. 1995; Cottin & Fray 2008; Cordiner et al. 2014), compared with the strongly centrally peaked spatial profiles of species released directly from the nucleus (`parents'). Interpreted within the Haser (1957) paradigm of an isotropically expanding, constant-velocity outflow, it is clear that some ubiquitously observed cometary molecules do not originate primarily from the nucleus, but instead arise in the coma, at distances of thousands to tens-of-thousands of kilometres from the nucleus. Coma ‘daughter’ species, for example, are believed to be produced from the breakdown of larger parent molecules (sublimated directly from the nucleus), as a result of photodissociation. A plausible source for some of the observed distributed coma molecules is from the destruction of dust grains or large organic molecules in the coma (Cottin & Fray 2008). Recently, the amino acid glycine was detected by the Rosetta spacecraft during its mission to comet 67P Churyumov-Gerasimenko, with a radial density profile consistent with a distributed source, from the sublimation of ice-coated dust grains (Altwegg et al. 2016; Hadraoui et al. 2019).

Millimetre-wave spectroscopy has emerged as the leading ground-based method for identifying new coma molecules (e.g. Bockelée-Morvan et al. 2000; Biver et al. 2014), including the first detections of cyanoacetylene (HC₃N), formamide (NH₂CHO), formic acid (HCOOH), ethylene glycol (C₂H₆O₂), and most recently: glycolaldehyde (C₂H₄O₂) and ethanol (C₂H₅OH; Biver et al. 2015). It is commonly assumed that they originate from the sublimation of ices stored inside the nucleus, but the presence of these species inside cometary nuclei is largely unproven. The majority of ground-based observations of organic molecules are made using single-pointing observations with a single-dish millimetre-wave telescope (such as the IRAM 30 m, with its ∼10 arcsec-diameter angular resolution; corresponding to ∼7000 km at 1 au Geocentric distance), and are therefore lacking in spatial information required to constrain the nucleus versus coma origins of these gases.

Rodgers & Charnley (2001a) used a chemical/hydrodynamic model (upon which our present study is based) to investigate the possible coma synthesis of four organic molecules (HCOOH, HCOOCH₃, HC₃N, and CH₃CN), which were detected in comet C/1995 O1 (Hale-Bopp) using radio spectroscopy. They determined that coma chemistry was insufficient to reproduce the observed abundances of these species. However, our latest models – which now include distributed sources of CN and H₂CO in the coma – show that some molecules can, in fact, be produced rapidly as a result of gas-phase chemical reactions. Here, we present chemical model calculations for HC₃N and NH₂CHO, demonstrating the synthesis of these species in detectable quantities.

2 MODEL

The details of our coma model were described by Rodgers & Charnley (2002), and the chemical network has been updated for carbon, nitrogen, and oxygen-bearing species, as well as including negative ion chemistry (see Cordiner & Charnley 2014). The number densities (n_i) of 283 gas-phase species (i), and the temperatures (T_x) of four fluids (neutrals, electrons, and positive and negative ions) are calculated as a function distance (r) from the nucleus, using the dvode package (Hindmarsh 2019) to solve the following set of differential equations:

$$\begin{eqnarray*} \frac{\mathrm{ d}n_i}{\mathrm{ d}r}=\frac{K_i}{v}-\frac{n_i}{v}\frac{\mathrm{ d}v}{\mathrm{ d}r}-\frac{2n_i}{r} \end{eqnarray*}$$

(1)

$$\begin{eqnarray*} \frac{\mathrm{ d}T_x}{\mathrm{ d}r}=\frac{(\gamma _x-1)T_x}{v}\left(\frac{G_x}{n_xk_BT_x}-\frac{2v}{r}-\frac{\mathrm{ d}v}{\mathrm{ d}r}-\frac{N_x}{(\gamma _x-1)n_x}\right) \end{eqnarray*}$$

(2)

$$\begin{eqnarray*} \frac{\mathrm{ d}v}{\mathrm{ d}r} &=& \frac{1}{\rho _s{v}^2-(\gamma {n}k_BT)_s}\nonumber\\ &&\times \,\left(F_sv-((\gamma -1)G)_s-M_sv^2+\frac{2v}{r}(\gamma {n}k_BT)_s\right) \end{eqnarray*}$$

(3)

The chemical source terms (K_i) are equal to the sum over all production and loss rates for each species, v is the coma outflow velocity, T_x and N_x are the respective temperature and density source terms for each fluid (x), and γ_x are the ratios of specific heat (Laplace’s coefficient) of the fluids. G_x are the thermal energy source terms, which include contributions due to the the chemical reaction enthalpies, collisions between ions, neutrals and electrons, radiative energy loss from H₂O, and loss of fast H and H₂ from the coma. M and F are the mass and momentum source terms, respectively, and ρ is the mass density; subscript s implies summation over all four fluids in the model.

Parent gases are released from the nucleus and undergo isotropic expansion into the vacuum, reaching v = 0.7 km s⁻¹ by r = 1000 km. The initial gas kinetic temperature was set to 100 K, with a nucleus radius of 2.5 km. The computed coma temperature and outflow velocity evolve in a very similar way to Fig. 1 of Rodgers & Charnley (2002). Photodissociation of outflowing gases occurs due to solar radiation (using a nominal heliocentric distance R_h = 1 au), and the ensuing photochemistry is calculated following a network of 3842 reactions. Abundances of parent molecules are chosen for a typical ‘organic rich’ comet (see Table 1); based on observations at infrared (Dello Russo et al. 2016) and radio (Bockelée-Morvan & Biver 2017) wavelengths, and supplemented by in situ measurements of O₂ and N₂ in comet 67P by Bieler et al. (2015) and Rubin et al. (2019), respectively. We adopt an H₂O production rate of 5 × 10²⁹ s⁻¹ (released directly from the nucleus), which is representative of a moderately active comet at R_h = 1 au.

Figure 1.

Coma model output showing molecular number densities as a function of radius. Parent species are shown with solid, colored curves, and photolysis products are shown with dot–dashed line styles. Thick black curves show HC₃N (left column) and NH₂CHO (right column), formed as a result of equations (4 and 5), respectively. Results from Model A (panels (a) and (b); top row) include a distributed source of H₂CO (P1) and two distributed sources of CN (P2 and P3). Model B (panels (c) and (d); middle row) have single distributed sources of CN (P2) and H₂CO (P1). Panels ((e) and (f); bottom row) are for Model C, which is the base model, with no additional sources of CN or H₂CO.

Our model has the ability to include distributed sources of molecules from the photolysis of (unidentified) parent species. In particular, we include distributed sources of H₂CO and CN (named P1 and P2, respectively), with photolysis rates of Γ_P1 = 1.3 × 10⁻⁴ s⁻¹ and Γ_P2 = 3.23 × 10⁻⁵ s⁻¹. These rates were chosen to be consistent with previous observations showing spatially extended distributions for these gases, with Haser parent scale lengths (at R_h = 1 au) of L_p = 5000 km for H₂CO (Biver et al. 2021) and L_p = 3.1 × 10⁴ km for CN (Fray et al. 2005). An additional, inner-coma CN source (P3) is also included in some of our models (see Section 3.1), based on a recent analysis of CN data from comet 67P (Hänni et al. 2020).

The synthesis of cyanoacetylene (HC₃N) occurs in the coma via the following neutral–neutral, gas-phase reaction, measured in the laboratory by Lichtin & Lin (1986) and Sims et al. (1993):

$$\begin{eqnarray*} {\rm CN} + {\rm C_2H_2} \longrightarrow {\rm HC_3N} + {\rm H} \end{eqnarray*}$$

(4)

Formamide (NH₂CHO) is produced by the neutral–neutral reaction:

$$\begin{eqnarray*} {\rm NH_2} + {\rm H_2CO} \longrightarrow {\rm NH_2CHO} + {\rm H} \end{eqnarray*}$$

(5)

This reaction was studied theoretically by Barone et al. 2015 and Skouteris et al. 2017, who calculated it to be efficient at the low (10–100 K) temperatures found in interstellar clouds and cometary comae; we adopt the lower estimate for the rate coefficient (k = 7.79 × 10⁻¹⁵(T/300)^−2.56e^−4.9/T cm³ s⁻¹), from the latter study.

3 RESULTS

3.1 HC₃N and NH₂CHO

Fig. 1 shows the number densities (n_i(r)) of the molecules most relevant to this study, including parent species, photochemical daughters, and products of coma chemistry. Three modelling scenarios are shown – Model A (panels (a) and (b)) includes a distributed source of H₂CO from the breakdown of a large (unidentified) organic precursor molecule P1 at distances r ∼ 5000 km from the nucleus (see Section 2), as well as two distributed sources of CN (P2 and P3), which give rise to peak gas-phase CN production at distances around r ∼ 10⁴ km and r ∼ 100 km, respectively. Model B (panels (c) and (d)) has a single distributed source of H₂CO (P1) and a single, outer-coma distributed source of CN (P2). Model C (panels (e) and (f)) has no additional distributed sources of H₂CO or CN. In model C, H₂CO is a parent species (Table 1) with a relatively short photolysis scale-length of ∼10⁴ km (due to its large photolysis rate |$\Gamma _{\rm H_2CO}=2.3\times 10^{-4}$| s⁻¹); however, there is still a significant contribution to the coma H₂CO abundance at distances r ∼ 10⁵ km due to the photodissociation of methanol (CH₃OH + |$h\nu \, \longrightarrow$| H₂CO + H₂), which occurs at a slower rate (Huebner & Mukherjee 2015).

Table 1.

Parent abundances with respect to H₂O.

Species	Abundance	Species	Abundance
H2O	1.00	CH4	0.01
CO2	0.10	NH3	0.01
CO	0.05	H2CO	5.0 × 10−3
O2	0.04	C2H2	3.0 × 10−3
CH3OH	0.04	HCN	2.0 × 10−3
C2H6	0.01	N2	9.0 × 10−4

A significant source of the CN radical in all models is via the photodissociation reaction HCN + |$h\nu \, \longrightarrow$| CN + H. Indeed, this is the dominant source of CN in Model C, but it was shown by Bockelee-Morvan & Crovisier (1985), A’Hearn et al. (1995), Fray et al. (2005), and Dello Russo et al. (2016) that the observed abundances of CN in comets are often inconsistent with a dominant origin from HCN photolysis. Furthermore, Fray et al. (2005) showed that the mean production scale length of CN in comets at R_h < 3 au is not consistent with HCN photolysis, so an additional coma source of CN is indicated. Models A and B are therefore considered to better represent the chemistry of real comets. Using an initial abundance for the CN parent (P2) of 0.32  per cent with respect to H₂O (A’Hearn et al. 1995), Model B reaches a peak CN density of n_CN = 4.7 × 10³ cm⁻³ around 800 km from the nucleus, whereas Model C (with no additional CN parent) reaches only n_CN = 1.0 × 10³ cm⁻³. The elevated CN density translates almost linearly to a larger HC₃N abundance via equation (4). The distributed H₂CO source (from the breakdown of parent species P1) has a less noticeable impact on the overall coma H₂CO number density, which reaches |$n_{\rm H_2CO}=1.3\times 10^3$| cm⁻³ at r = 10⁴ km in Model B and |$n_{\rm H_2CO}=0.8\times 10^3$| cm⁻³ in Model C.

The total yield of HC₃N and NH₂CHO in our models is quantified using an ‘effective production rate’ Q_e. This quantity is closely related to the observationally derived production rate (Q), and is defined as the production rate that would be measured from our model using a telescope beam diameter of 10 arcsec (the beam size of the IRAM 30-m telescope at 250 GHz), at a cometocentric distance of Δ = 1 au, under the assumption that the molecule of interest originates from the nucleus. The latter assumption has been employed in all previously published HC₃N and NH₂CHO production rates derived from ground-based mm-wave observations, so Q_e values allow our model output to be compared directly with observations taken at a similar cometocentric distance (Δ ∼ 1 au). The Q_e values (Table 2) are calculated by comparing our modelled column densities (averaged over a 10 arcsec beam) with a Haser parent model, using an outflow velocity equal to the column density-weighted mean HCN outflow velocity from our model (〈v〉 = 0.74 km s⁻¹), and photolysis rates from Huebner & Mukherjee (2015) and Heays, Bosman & van Dishoeck (2017). The HCN molecule is used for this purpose since HCN is a common probe of the coma outflow velocity at mm/sub-mm wavelengths, but use of other parent molecules such as CH₃OH and H₂O to measure 〈v〉 produces very similar results. The Q_e values are then converted to effective abundances (a_e) by taking the ratio with respect to the model H₂O production rate of 5 × 10²⁹ s⁻¹.

Table 2.

Effective production rates (Q_e) and abundances (⁠|$a_e=Q_e/Q_{\rm H_2O}$|⁠) from our coma models.

	Model A		Model B		Model C
Species	Qe	ae	Qe	ae	Qe	ae
	(1024 s−1)	(%)	(1024 s−1)	(%)	(1024 s−1)	(%)
HC3N	87.3	1.8 × 10−2	6.7	1.4 × 10−3	1.5	2.9 × 10−4
NH2CHO	58.1	1.2 × 10−2	4.9	1.0 × 10−3	4.7	9.4 × 10−4

Upon inclusion of a distributed source of CN (P2), the effective HC₃N production rate increases by a factor of 5 from 1.5 × 10²⁴ s⁻¹ to 6.7 × 10²⁴ s⁻¹, whereas a distributed H₂CO source (P1) only results in a modest, 4 per cent increase to the NH₂CHO production rate. The corresponding effective abundances for model B (see Table 2) of 1.4 × 10⁻³  per cent for HC₃N and 1.0 × 10⁻³  per cent for NH₂CHO are significant – indeed, potentially detectable – but are still less than the lowest values reported in the literature for these molecules in Oort Cloud comets (OCCs; 2 × 10⁻³  per cent and 8 × 10⁻³  per cent, respectively; Bockelée-Morvan & Biver 2017). OCCs have relatively long orbital periods, covering distances up to hundreds of thousands of astronomical units from the Sun. They are observationally distinct from the Jupiter Family Comets (JFCs), which orbit at distances R_h ≲ 10 au and are exposed to more frequent, repeated heating during successive perihelion passages. Statistical studies show that JFCs tend to be depleted relative to OCCs in some volatiles such as CH₄, C₂H₂, and CO (Dello Russo et al. 2016), and before the Rosetta mission to JFC 67P, there were no reported detections of HC₃N or NH₂CHO in any JFC. Both these molecules were detected early in the Rosetta mission by Le Roy et al. (2015) around R_h = 3.1 au, but a more useful comparison is with the values measured by Rubin et al. (2019) closer to perihelion (R_h ∼ 1.5 au) when the comet was more fully activated; these latter observations obtained HC₃N/H₂O = 4 × 10⁻⁴  per cent and NH₂CHO/H₂O = 4 × 10⁻³  per cent, respectively. Direct comparison between our model results and the measurements of comet 67P, however, requires the impact of the lower H₂O production rate of this comet to be considered (see Section 4).

A more prominent increase is seen in our model for both HC₃N and NH₂CHO when including a second distributed source of CN in the inner coma (P3). The properties of this additional source were chosen to match in situ measurements of comet 67P (Churyumov-Gerasimenko) by the Rosetta spacecraft (Hänni et al. 2020). Throughout the mission to 67P, the ROSINA mass spectrometer detected a clear signal due to gas-phase CN at cometocentric distances 20–200 km, with a local abundance ratio of ∼0.01–0.1 with respect to HCN at dates around perihelion. The CN spatial distribution was observed to be relatively flat compared with H₂O and other parent species in the coma, consistent with a distributed source of CN, with an abundance far in excess of what could be explained by photolysis of any known coma nitriles (see also Hänni et al. 2021). The observed excess CN signal was tentatively attributed by Hänni et al. (2020) to the breakdown of CN-bearing refractory particles, such as salts (ammonium cyanide – NH₄CN, for example), nitrogen-rich dust, or organic macromolecules. The production rate (⁠|$Q_{P3}/Q_{\rm H_2O}=6\times 10^{-3}$|⁠) and photolysis rate (Γ_P3 = 3.5 × 10⁻² s⁻¹) of this additional (unidentified) CN parent were chosen in our model to produce a maximum n_CN/n_HCN ratio of ≈0.05 between r = 100 and 200 km from the nucleus, in line with the ROSINA measurements close to perihelion.

As a consequence of the increased CN density in the inner coma, equation (4) proceeds more rapidly and the HC₃N effective abundance in Model A increases to 0.018 per cent. The presence of additional CN has several other knock-on effects for the coma chemistry. In particular, the CN radical quickly reacts with NH₃ (sublimating from the nucleus) to produce HCN + NH₂ (Sims et al. 1994; Talbi & Smith 2009). Some of this additional NH₂ reacts with H₂CO (via equation 5) to produce NH₂CHO, leading to a significant (factor of 12) increase in the NH₂CHO abundance, which then reaches a_e = 0.012 per cent. Consequently, in Model A, both HC₃N and NH₂CHO attain abundances with respect to H₂O that are well within the range of values previously detected in OCCs (0.002–0.068 per cent for HC₃N and 0.008–0.021 per cent for NH₂CHO; Bockelée-Morvan & Biver 2017), with no need for a nucleus (parent) source of either molecule.

3.2 Other molecules

The reaction between CN and O₂ was studied in the laboratory by Sims et al. (1994), and found to proceed rapidly at low temperatures. Feng & Hershberger 2009 determined OCN + O to be the dominant product channel, so large amounts of OCN are produced in our models. The effective OCN abundance inside a 10 arcsec beam is a_e = 0.2 per cent in Model A and a_e = 4 × 10⁻³  per cent in Model B, assuming a generic photolysis rate of Γ_OCS = 10⁻⁵ s⁻¹. Gas-phase OCN was detected by the Rosetta spacecraft in the coma of comet 67P during a dust impact event (Altwegg et al. 2020), but has not yet been detected in any other comets. It has a moderate dipole moment of 0.64 D, with several rotational transitions in the millimetre and submillimetre range. Consequently, if the coma CN and O₂ abundances are similar to those measured in comet 67P close to perihelion, OCN may be bright enough to be detectable in a sufficiently active OCC. Indeed, since CN + O₂ is the main pathway to OCN in our model (other pathways are negligible), a measurement of the OCN production rate could be used to infer the product of CN × O₂ abundances in the inner coma of future comets, thus providing an indirect measurement of the O₂ abundance, which has so-far been impossible to obtain with ground-based observations.

A smaller, but still significant, amount of NO is also produced as a result of the alternative product channel CN + O|$_2\, \longrightarrow$| CO + NO. The resulting NO goes on to react with OCN to produce N₂O and CO.

In addition to the main product channel (leading to NH₂ + HCN), the reaction between CN + NH₃ was suggested by Herbst et al. (1994) as a possible source of NH₂CN (cyanamide) in the interstellar medium. If this reaction proceeds with reasonable efficiency, NH₂CN could reach detectable abundances in the inner coma (0.08 per cent in Model A, assuming an NH₂CN product branching ratio of 1/3). More recent quantum calculations by Talbi & Smith (2009), however, indicate that this product channel may be negligible in comparison to the NH₂ + HCN channel.

3.3 Synthetic coma maps

Our predictions regarding the origins of cometary HC₃N and NH₂CHO (and other molecules) in comets, may be tested through mapping observations of their spatial distributions with respect to the nucleus. Parent molecules (released directly from the nucleus) have compact brightness distributions that fall rapidly as ∼1/ρ, where ρ is the nucleocentric distance projected in the plane of the sky. Daughter species (or products of coma chemistry), on the other hand, have flatter, more extended distributions. These two scenarios can be readily distinguished through interferometric millimetre/submillimetre observations (for example, using the Atacama Large Millimeter/submillimeter Array (ALMA) telescope; Cordiner et al. 2014), or using a single-dish facility, in the case of an unusually close-up apparition (such as 252P/Linear in 2016, which reached a Geocentric distance of only 0.04 au; Coulson et al. 2017). Detailed coma mapping observations can also provide crucial information on production scale-lengths for comparison with numerical models, to help elucidate the specific production pathway for the species in question.

Synthetic mm-wave flux maps are shown for the case of HC₃N as a parent molecule in Fig. 2 (top panel), and for HC₃N produced from the reaction of CN with C₂H₂ according to Model B (bottom panel). These maps were constructed for the J = 26–25 transition by raytracing the 3D projection of our model density output along the observer-comet sightline, using the ratran Sky code (Hogerheijde & van der Tak 2000). An excitation temperature of 50 K and Geocentric distance Δ = 1 au were assumed, and the resulting maps were integrated along the spectral axis, then convolved with a Gaussian beam of FWHM =1 arcsec, similar to ALMA’s lowest resolution at this frequency. Distributed sources with parent scale lengths less than a few thousand kilometres are difficult to map reliably using a single-dish facility such as the IRAM 30 m telescope, as shown by the extent of the scale bars relative to the synthetic brightness distributions in Fig. 2. ALMA observations, on the other hand, are readily able to distinguish between the two scenarios, and can therefore provide proof of a nucleus or coma origin for HC₃N, NH₂CHO, and other species.

Figure 2.

Simulated HC₃N coma images (flux maps) for the J = 26–25 transition at 236.5 GHz, assuming an excitation temperature of 50 K, smoothed to an angular resolution (beam FWHM) of 1 arcsec. The top panel is for HC₃N as a parent (sublimating directly from the nucleus with Q(HC₃N) = 10²⁶ s⁻¹). Bottom panel is for HC₃N produced via equation (4), according to the model density profile in Fig. 1(c). Horizontal scale bars in the top panel indicate the characteristic spatial resolution of the ALMA and IRAM 30 m telescopes (1 and 10 arcsec, respectively).

Previous analyses of observational data obtained using radio interferometry of cometary gases have relied on simple Haser models to interpret the observed spatial profiles for distributed coma species such as H₂CO, HNC, and CS (Boissier et al. 2007; Cordiner et al. 2014, 2017). This approach assumes the detected molecules arise only as a result of photodissociation of a single parent species, and that the parent species (as well as the daughter species in question) does not have any additional sources or sinks as a result of chemical reactions or dust sources in the coma. Coma chemistry results in radial density profiles that can be distinctly different from Haser-model density profiles (see Fig. 1), so sufficiently detailed (high signal to noise) ALMA observations should have the ability to distinguish between different chemical production scenarios, as well as photodissociation, production from icy grains, and sublimation from the nucleus (or a combination these mechanisms).

4 DISCUSSION

Our chemical models show that significant quantities of HC₃N, NH₂CHO and other molecules can be synthesized in the coma through neutral–neutral reactions involving simple chemical precursor species (CN, C₂H₂, NH₂, O₂, and H₂CO), already known to be abundant from previous comet observations. The presence of a distributed source of CN in the inner coma (as observed by Hänni et al. 2020 for comet 67P), strongly enhances the efficiency of both reactions (4) and (5), bringing the effective abundances for Model A (see Table 2) into the range of previously observed values for these molecules. The presence of such an additional CN source is consistent not only with Rosetta measurements of comet 67P, but also with previous studies regarding the (still unidentified) source of the closely related HNC molecule in comets (see Cordiner et al. 2017, and references therein).

When HNC was first detected in comet C/1995 O1 (Hale-Bopp), the large HNC/HCN mixing ratio (similar to the value found in the interstellar medium) was taken as evidence that pristine (unprocessed) interstellar material may be incorporated into cometary nuclei. However, maps of the HNC spatial distribution in comet Hale-Bopp (Blake et al. 1999), as well as strong variability of the HNC/HCN ratio with heliocentric distance in a sample of 14 comets (Lis et al. 2008), pointed towards a distributed (coma) source of HNC, which was hypothesized to originate from the breakdown of macromolecular or dust precursor material (see also Rodgers & Charnley 2001b). Detailed interferometric mapping using ALMA provided definitive evidence for a distributed source of HNC at distances of a few hundred kilometres from the nucleus of comet C/2013 S1 (ISON), leading to the conclusion that this molecule most likely originates from the degradation of nitrogen-rich organic refractory material (Cordiner et al. 2014, 2017).

Low-mass, refractory organic particles (CHON grains) were detected in large abundances in comet 1P/Halley by the Giotto mission (Kissel et al. 1986), and Wyckoff, Tegler & Engel (1991) determined that 90 per cent of this comet’s nitrogen budget was contained within the refractory dust component. More recent in situ work on comet 67P using the Rosetta COSIMA instrument revealed the presence of very large macromolecular compounds in the cometary dust, analogous to the insoluble organic matter present in carbonaceous meteorites (Fray et al. 2016). With a mean N/C ratio of 3.5 per cent (Fray et al. 2017), this material presents a plausible source of additional CN radicals in the coma, among other small N-bearing organics. Macromolecules such as HCN polymer or hexamethylenetetramine (HMT; recently detected in meteorites by Oba et al. 2020) present another possible source of coma CN, but these specific compounds are yet to be found in cometary samples. Polyoxymethylene (POM, or formaldehyde polymer) has been studied extensively as another plausible macromolecular grain component in comets, and detailed models show that POM could explain the distributed H₂CO sources in comets 1P/Halley and C/1995 O1 (Hale-Bopp) (Cottin et al. 2004; Fray et al. 2006).

Hänni et al. (2020) also considered the dissociation of NH₄CN as a plausible source of CN in the inner coma of comet 67P. The NH₄CN salt (also known as NH|$_4\, ^+$|CN⁻) is unstable in the gas phase, but could be carried into the coma as a solid embedded in (or adsorbed on the surface of) dust grains, before sublimating and dissociating. The possibility of ammoniated salts as a reservoir of HCN and NH₃ in comets was first discussed by Mumma et al. (2018). Altwegg et al. (2020) reported the likely presence of five different ammonium salts (NH|$_4\, ^+$|X⁻, where X⁻ is a deprotonated acid, such as Cl⁻, NCO⁻ or HCOO⁻) in the coma of comet 67P, based on ROSINA mass spectrometry during a dust impact event. Evidence for abundant ammonium salts on 67P’s surface (including NH₄CN) was also found with Rosetta infrared spectroscopy (Poch et al. 2020).

While HCN + NH₃ is believed to be the dominant dissociation channel of NH₄CN, other products are possible (Altwegg et al. 2020; Hänni et al. 2020). By analogy with the dissociation of NH₄Cl, which has been studied using ab initio methods, as well as in the laboratory (see Hänni et al. 2019 and references therein), it is suggested that CN and CN⁻ could be products of NH₄CN dissociation. Our models show that the majority of CN⁻ produced in the inner coma from the spontaneous dissociation reaction NH₄CN |$\longrightarrow$| NH|$_4\, ^+$| + CN⁻ would be converted almost immediately to neutral CN (+ H) upon collision with NH|$_4\, ^+$| (see Harada & Herbst 2008). This therefore represents another possible source of CN to drive the neutral–neutral synthesis of HC₃N and NH₂CHO. More laboratory studies of NH₄CN dissociation products are needed to confirm this hypothesis.

In light of the recent detections of salts in comet 67P, the results of Hänni et al. (2019) and Altwegg et al. (2020) imply a possible contribution to the NH₂CHO coma abundance from NH₄COOH (ammonium formate) salt dissociation. Our models show that the presence of additional sources of molecules in the inner coma (such as NH₃ and HCN), from the dissociation of salts including ammonium formate, ammonium cyanide, and ammonium cyanate (see Altwegg et al. 2020), lead to increased abundances of complex organics as a result of subsequent gas-phase reactions. Further investigations of the coma chemistry arising from such reactions are therefore warranted. The injection of ions, radicals, and other reactive neutrals into the inner coma, following the dissociation of ammonium salts, would give rise to further, previously unstudied chemical processes in the outflowing cometary gas. To model this in detail, however, would require improved knowledge of the initial salt abundances and their full range of dissociation products, as well as the inclusion of a population of outflowing, sublimating grains into our model, which is beyond the scope of the present study.

Our findings for HC₃N are in contrast to Rodgers & Charnley (2001a), whose model predicted a low HC₃N/H₂O abundance ratio (averaged inside an 11 arcsec beam) of 7 × 10⁻⁴  per cent for Hale-Bopp, compared with the observed value of 1.7 × 10⁻²  per cent. In their model, HC₃N formation was driven by the CN + C₂H₂ reaction (4), with CN produced photolytically from HCN released directly from the nucleus. Consequently, they concluded that the observed HC₃N could not be synthesized in the coma by equation (4) alone, and is therefore likely to be present in the nuclear ice. The Rodgers & Charnley (2001a) model should have been more efficient than ours at producing HC₃N due to the omission of the (experimentally observed) 20 K activation energy barrier in equation (4), allowing the reaction to proceed more rapidly at low temperatures in their model. The ability of our new model to effectively reproduce the HC₃N observations is attributed primarily to the inclusion of the two distributed sources of CN (P2 and P3) in the coma for Model A, which were not considered by Rodgers & Charnley (2001a).

It is interesting to note that HC₃N/H₂O ratio in comet 67P (4 × 10⁻⁴; Rubin et al. 2019) is significantly lower than in the sample of OCCs observed to-date (2 × 10⁻³–6.8 × 10⁻⁴; Bockelée-Morvan & Biver 2017). Our modelling work provides a natural explanations for this, without requiring peculiar/anomalously low HC₃N abundances in 67P’s nucleus compared with OCCs. To investigate the production of HC₃N (and NH₂CHO) in lower density coma environments such as that of 67P, we ran additional model calculations spanning a range of water production rates |$Q_{\rm H_2O}=3\times 10^{27}$|–5 × 10³⁰ s⁻¹ (covering the range of values observed in typical cometary apparitions). The chemical reaction rates for formation and destruction of the species of interest in our study vary as nonlinear functions of the coma density and temperature, so the changes in their coma abundances in response to |$Q_{\rm H_2O}$| is nontrivial. The results of our tests show that for |$Q_{\rm H_2O}$| above a few times 10²⁹ s⁻¹, the HC₃N and NH₂CHO abundances with respect to water are not strongly dependent on the production rate (they vary by <15 per cent in this |$Q_{\rm H_2O}$| range). For |$Q_{\rm H_2O}\lesssim 10^{29}$| s⁻¹, the size of the region dense enough for rapid neutral–neutral reactions to occur shrinks considerably, leading to significant reductions in the yields of HC₃N and NH₂CHO via reactions (4) and (5).

To simulate comet 67P for comparison with Rosetta mass spectrometry measurements, we ran the |$Q_{\rm H_2O}=3\times 10^{27}$| s⁻¹ model at R_h = 1.5 au, using Rubin et al. (2019)’s measured parent abundances and observational circumstances (C₂H₂ was not measured by Rubin et al. 2019, so we adopt the mean JFC mixing ratio of 0.07 per cent for this species, from Dello Russo et al. 2016). The inner-coma CN production rate was scaled to reproduce the CN/HCN ratio measured by Hänni et al. (2020) around the time of the Rubin et al. (2019) measurements, and our modelled abundances (a(X), with respect to H₂O) were extracted at a distance of 220 km from the nucleus, which is close to the average distance at which the Rubin et al. (2019) measurements were obtained. For Model A, we find a(HC₃N) = 3.0 × 10⁻⁴  per cent and a(NH₂CHO) = 1.5 × 10⁻⁵  per cent; for model B: a(HC₃N) = 5.5 × 10⁻⁶  per cent and a(NH₂CHO) = 1.1 × 10⁻⁵  per cent; and for model C: a(HC₃N) = 8.9 × 10⁻⁷  per cent and a(NH₂CHO) = 1.1 × 10⁻⁵  per cent. These values can be compared with the Rosetta measurements of a(HC₃N) = (4 ± 2) × 10⁻⁴  per cent and a(NH₂CHO) = (4 ± 2) × 10⁻³  per cent. The agreement for HC₃N (within the observational uncertainties) using Model A is surprisingly good considering the uncertain radial density profile of the inner-coma CN source. Our HC₃N/HCN ratio of 2.1 × 10⁻³ is also in agreement with the value of (2.9 ± 1.9) × 10⁻³ from Rubin et al. (2019), but is somewhat less that the mean value of (4.6 ± 0.8) × 10⁻³ measured by Hänni et al. (2021) between R_h = 1.24 and 1.74 au. This discrepancy could be accounted for by variability in the CN, HCN, and C₂H₂ abundances during the extended (5 month) time period covered by the Hänni et al. (2021) study. We note, however, that purely gas-phase chemistry would be expected to give rise to a steeper slope in the HC₃N/HCN ratio as a function of heliocentric distance than observed in 67P, so some contribution from an additional (nucleus) source of HC₃N seems likely. For NH₂CHO, the failure of all our models to reproduce the measured abundance in comet 67P by more than two orders of magnitude implies the presence of an additional source for this molecule – for example, from the dissociation of NH₄COOH salt (Hänni et al. 2019), or from sublimation of NH₂CHO ice directly from the nucleus, albeit with a substantially lower abundance than found previously in OCC comae (Bockelée-Morvan & Biver 2017).

Our modelling work implies that HC₃N and NH₂CHO could be present in cometary nuclei at abundances that are significantly less than implied by previous (ground-based) observations. There is some evidence that the abundances of HC₃N and NH₂CHO are enhanced in typical cometary comae compared with the warm envelope of the solar-type protostar IRAS 16293-2422, which is rich in the sublimated interstellar ices believed to be a major constituent of comets (Kahane et al. 2013; Jaber Al-Edhari et al. 2017; Drozdovskaya et al. 2019). On the other hand, the protostellar HC₃N/HCN ratio (which is easier to measure from the ground than the ratio with respect to H₂O) is only marginally smaller in IRAS 16293-2422 (0.36 per cent; Drozdovskaya et al. 2019) than in 67P (0.44 per cent; Hänni et al. 2021; full Rosetta mission). Gas-phase HC₃N/HCN ratios may be even larger in protoplanetary discs (3–134 per cent, depending on the assumed temperature; Bergner et al. 2018), so it is likely that HC₃N can be incorporated into cometary nuclei during their accretion out of ice in the disc mid-plane. Comparison between cometary and interstellar/protostellar/disc abundances is nontrivial due to the possibility of chemical alteration during the passage of interstellar ices into the protoplanetary disc mid-plane and ultimately, into cometary nuclei. Indeed, HC₃N abundances are subject to significant modification by gas-phase processing in the warm regions surrounding the protostar (Walsh et al. 2014). Nevertheless, our results show that chemical processing in the coma can lead to elevated abundances of some organic molecules, and this possibility should be taken into account when comparing abundances between interstellar ices and cometary comae, as a means for obtaining insights into the origin of cometary matter.

Impacts between comets and planets were common during the early history of the Solar System, and may have allowed the delivery of organic molecules to planetary surfaces (e.g. Pierazzo & Chyba 1999; McCaffrey et al. 2014; Todd & Öberg 2020). Both HC₃N and NH₂CHO have been implicated in the prebiotic synthesis of amino acids and DNA nucleobases on the primordial Earth (Ferris, Sanchez & Orgel 1968; Saladino et al. 2012; Patel et al. 2015). Our finding that these molecules may be less abundant in cometary ices than previously believed could therefore be of importance for theories concerning the chemical inventory of material available for the origin of life.

An important caveat concerning the extent of HC₃N and NH₂CHO synthesis in comets as a result of gas-phase coma chemistry is the uncertainty regarding the additional distributed CN sources (P2 and P3). The survey of Dello Russo et al. (2016) identified variability in the importance of the primary extended source of CN (P2) throughout the comet population, and the inner-coma CN source (P3) has only been detected in a single comet to-date (67P, although we are not aware of any dedicated attempts to detect a distinct, inner-coma CN source in any other comets). In our Model A, P3 was introduced as a photochemical source of CN, with a production rate and scale length tailored to reproduce the CN/HCN ratio measured by Hänni et al. (2020) in comet 67P. However, the detailed radial behaviour of this CN source is not yet well constrained, and it remains to be determined how well the CN abundance in OCCs may be represented by the CN/HCN ratio in 67P. Consequently, although we believe our models represent plausible scenarios for moderately active OCCs, the specific, numerical results remain uncertain until inner-coma CN measurements are made in a larger sample of comets, and the properties of the dominant coma CN sources are fully elucidated.

5 CONCLUSION

Our chemical models for a moderately active comet, with organic-rich parent abundances, demonstrate that gas-phase synthesis of HC₃N and NH₂CHO occurs as a result of neutral–neutral reactions between simple precursor molecules known to be abundant in the coma. The presence of a distributed CN source in the inner coma, similar to that observed by Rosetta in comet 67P, increases the efficiency of these reactions, leading to effective HC₃N and NH₂CHO abundances in our model that can reach levels similar to those observed in moderately high-activity comets using ground-based millimetre-wave observations. Neutral–neutral coma chemistry can also reproduce the lower HC₃N/H₂O ratio measured by Rosetta in the relatively low-activity comet 67P before perihelion at R_h ∼ 1.5 au. As a result of such active gas-phase chemistry, the abundances of complex organics in the coma are therefore not necessarily representative of those stored in the nucleus ice. High-resolution mapping using millimetre/submillimetre facilities such as ALMA will be crucial for determining the importance of nucleus versus coma sources for these, and other complex organic molecules in future cometary apparitions. Additional observations, laboratory work, and modelling will be required to elucidate the distribution and origin of the inner-coma CN sources in comets other than 67P, and to determine the full impact of the dissociation products from ammonium salts and organic macromolecules on coma chemistry.

ACKNOWLEDGEMENTS

This research was supported by the NASA Planetary Science Division Internal Scientist Funding Program through the Fundamental Laboratory Research work package (FLaRe).

DATA AVAILABILITY

All numerical data (model output) produced by this study are available from the authors upon reasonable request.