Abstract

Methyl isocyanate (CH3NCO) is one of the important complex organic molecules detected on the comet 67P/Churyumov–Gerasimenko by Rosetta’s Philae lander. It was also detected in hot cores around high-mass protostars along with a recent detection in the solar-type protostar IRAS 16293−2422. We propose here a gas-grain chemical model to form CH3NCO after reviewing various formation pathways with quantum chemical computations. We have used nautilus three-phase gas-grain chemical model to compare observed abundances in the IRAS 16293−2422. Our chemical model clearly indicates the ice phase origin of CH3NCO.

1 INTRODUCTION

Comets are considered to be the repository of the most pristine material from the origin of the Solar system in the form of ice, dust, silicate and refractory organic material (Mumma & Charnley 2011). It is believed that some of the water and organic material found on Earth may have been delivered by comets (Hartogh et al. 2011). In the Solar system, when a comet passes close to the Sun, it warms and begin to evaporate their surface and evolve gasses. This process, called outgassing, produces a coma of gas and dust that has been extensively observed (Crovisier 2006). More than 20 organic molecules have been identified in the coma of comets via ground- and space-based observations (Biver et al. 2014; Crovisier et al. 2004). The chemical composition of comets clearly indicates that these objects are populated with many organic compounds that are commonly detected in the interstellar medium (ISM). Biver et al. (2015) have found a good correlation between the type of species detected in the coma of comets and those of warm molecular clouds.

Recently, the spacecraft Rosetta has detected many complex organic molecules (COMs) [such as ethanol (CH3CHO), formamide (NH2CHO), methyl isocyanate (CH3NCO), ethylamine (C2H5NH2) and many more] on the material of the comet 67P/Churyumov–Gerasimenko by the COSAC experiment (Goesmann et al. 2015) and even simplest amino acid glycine accompanied by methylamine and ethylamine in the coma measured by the ROSINA (Altwegg et al. 2016). CH3NCO is one of those organics that could play a role in the synthesis of amino acid chains called peptides (Pascal, Boiteau & Commeyras 2005). It was first detected in Sgr B2 by Halfen et al. (2015) and later in Orion KL by Cernicharo et al. (2016). Recently, it was also detected in the solar-type protostar IRAS 16293−2422 by Martín-Doménech et al. (2017) and Ligterink et al. (2017).

However, it is not well understood how CH3NCO is formed in the ISM. Recently, Martín-Doménech et al. (2017) have included the chemistry proposed by Halfen et al. (2015) and suggested that the production of CH3NCO could occur mostly via the gas-phase chemistry after the evaporation of HNCO from grain surface. Belloche et al. (2017) have considered a grain surface production of CH3NCO in their model via the radical-addition reaction between CH3 and OCN. Another study by Ligterink et al. (2017) claimed that CH3NCO can be formed in the solid state by VUV irradiation of CH4:HNCO mixtures through CH3 and NCO recombinations. This motivated us to revisit the chemistry of CH3NCO in the ISM.

This paper reports the first public gas-grain chemical network for CH3NCO followed by astrochemical modelling of low-mass protostar IRAS 16293. The chemistry is presented in Section 2. The chemical model is described in Section 3, while the results are discussed in the last Section.

2 REVIEW OF THE INTERSTELLAR CHEMISTRY OF CH3NCO

Despite an intensive search, we did not find any reaction producing efficiently CH3NCO in the gas phase. Halfen et al. (2015) proposed the following gas-phase formation route:
(1)
(2)
(3)

But we have found that reaction 1 is endothermic by 77 kJ mol−1 and shows a transition state (TS) located 83 kJ mol−1 above the entrance level (see Table 4 in the online supplementary material) and thus cannot play any role in gas phase neither on grain surface at low temperature. Reaction 2 has been studied experimentally by Wight & Beauchamp (1980) and they observed proton transfer process that forms H2NCO+ and CH4, instead of CH3NCOH+ and H2. Reaction 3 has then no impact on the CH3NCO formation. An alternative could have been the CH3NC + OH→ H + CH3NCO reaction, which is exothermic by 107 kJ mol−1, and may not show any barrier. However, CH3NC has a low abundance in molecular clouds (Cernicharo et al. 1988; Gratier et al. 2013). So the reaction CH3NC + OH→ H + CH3NCO will involve very low fluxes and we can thus neglect this reaction.

The detection of CH3NCO being limited to warm sources (hot cores and hot corinos) suggests a formation of this molecule on grains rather than in the gas phase (Cernicharo et al. 2016). We have found four potential grain surface reactions that may produce CH3NCO efficiently. The first one is the s-CH3 + s-OCN→ s-CH3NCO reaction (here ‘s’ is to represent species on the surface). As it is a reaction between two radicals CH3 + OCN, this reaction is barrier-less and leads to CH3NCO, which arises from the pairing up of electrons on the two reactants radicals.

The second one is the CH3 + OCN- → CH3NCO + e- reaction, which is exothermic by 30 kJ mol−1 at M06-2X/AVTZ level in the gas phase. The M06-2X highly non-local functional is developed by Zhao & Truhlar (2008) and is well suited for structures and energetics of the TSs. OCN- is widely observed on interstellar ice (van Broekhuizen et al. 2005) and CH3 is supposed to be relatively abundant on ice and relatively mobile (Wakelam et al. 2017), then this reaction may play a role in the CH3NCO formation. However, the adsorption energy of OCN- on ice is large due to dipole–ion interaction, and even if a free electron is also strongly bound to ice (Kammrath et al. 2006; de Koning et al. 2016), this reaction may be endothermic on ice. By comparison, the H + OCN- → HNCO + e- reaction is more exothermic (by 107 kJ mol−1 in the gas phase), which should prevent OCN- detection on ice if this reaction was also exothermic on ice due to the importance of H reaction on ice. Then free electron should be less bounded on ice than OCN-, as a result CH3 + OCN- → CH3NCO + e- reaction is likely endothermic on ice and is neglected here.

Another reaction is induced through the HCN...CO van der Waals formation on ice. As introduced in Ruaud et al. (2015), the proximity of HCN and CO in the van der Waals complex favors the reaction between excited H2CN* (formed through s-HCN + s-H reaction) and CO (see Table 3 in the online supplementary material and Fig. 1 for the energy profile diagram of the H + HCN⋅⋅⋅CO reaction). Then considering the large amount of CO and HCN, this reaction may be important. We then characterize the H + HCN and H2CN + CO reactions to estimate the importance of these reactions to CH3NCO formation on ice. The H + HCN→ H2CN shows a notable barrier (computed to be equal to 15.4 kJ mol−1 (Jiang & Guo 2013), 28.3 kJ mol−1 at M06-2X/AVTZ level (this work, see Table 2 in the online supplementary material) and 36.4 kJ mol−1 at CCSD(T)/6-311++G level Sumathi & Nguyen 1998). Despite this barrier, this reaction is enhanced on ice due to tunneling (Ruaud, Wakelam & Hersant 2016), leading to the formation of excited H2CN*. As the amount of energy in H2CN* is equal to 105.3 kJ mol−1 (initially with a very narrow distribution), there is a competition between relaxation and reactivity for all the HCN linked to CO as the TS for the H2CN + CO→ H2CNCO is located 44.1 kJ mol−1 above the H2CN + CO level, so 61.2 kJ mol−1 below the energy of the H2CN* formed through the H + HCN reaction. As the energy distribution of the H2CN* is initially very narrow, a notable part of the H2CN* will react with CO. It should be noted that this mechanism of reaction induced through van der Waals complex will also lead to HNCO formation through N⋅⋅⋅CO + H→HNCO reaction, mechanism which should be very efficient in that case.

Potential energy diagram for the H + HCN⋅⋅⋅CO reaction on the doublet surface calculated at the M06-2X/aug-cc-pVTZ level including ZPE.
Figure 1.

Potential energy diagram for the H + HCN⋅⋅⋅CO reaction on the doublet surface calculated at the M06-2X/aug-cc-pVTZ level including ZPE.

The fourth reaction that can produce CH3NCO is the s-N + s-CH3CO reaction. The first step, leading to s-CH3C(N)O in a triplet state, is barrierless characteristic of a radical–radical reaction. The s-CH3C(N)O can evolve towards s-CH3 + s-OCN on the triplet surface, isomerize into s-CH3NCO on the triplet surface or being converted into s-CH3C(N)O in a singlet state (which can also isomerize into s-CH3NCO (or s-CH3OCN) on the singlet surface). Considering the exothermictiy of the various step (see Table 6 in the online supplementary material), the formation of s-CH3NCO is without doubt the most favorable exit channel, either through adduct isomerization or through the recombination of s-CH3 + s-OCN. Very minor CH3OCN may also be produced, and some s-CH3C(N)O may also be stabilized as the TS for dissociation or isomerization are notably above the CH3C(N)O energy. s-CH3C(N)O will react with s-H leading ultimately to CH3C(O)NH2 which are, however, not considered here.

All the introduced and reviewed reactions discussed here are presented in Table 1 in this paper.

Table 1.

List of major gas-phase and grain surface reactions added to the model for CH3NCO formation.

ReactionαβγReference
1HNCO + CH3→ CH3NCO + H1.00 × 10−1008.04 × 103(1)
2CH3NCO + H3+→ CH3NCOH+ + H21.00 × 10−9−0.50(2)
3CH3NCO + HCO+→ CH3NCOH+ + CO1.09 × 10−9−0.50(2)
4CH3NCO + H+→ CH3NCO+ + H1.00 × 10−9−0.50(2)
5CH3NCO + CO+→ CH3NCO+ + CO1.00 × 10−9−0.50(2)
6CH3NCO + He+→ CH3NCO+ + He1.00 × 10−9−0.50(2)
7CH3NCO+ + e-→ CH3 + OCN1.50 × 10−7−0.50(3)
8CH3NCOH+ + e-→ CH3NCO + H3.00 × 10−7−0.50(3)
9CH3NCO + CRP→ CH3 + OCN4.00 × 10300(3)
10CH3NCO + Photon→ CH3 + OCN5.00 × 10−100.00(3)
11HCN + s-CO→ s-HCN⋅⋅⋅CO100(4)
12s-HCN⋅⋅⋅CO + s-H→ s-H2CNCO102.40 × 103(5)
13s-H2CNCO + s-H→ s-CH3NCO100(6)
14s-CH3 + s-HNCO→ s-CH3NCO + s-H108.04 × 103(1)
15s-CH3 + s-OCN→ s-CH3NCO100(7)
15s-CH3 + s-OCN-→ s-CH3NCO + e-000(8)
16s-N + s-CH3CO→ s-CH3NCO100(9)
ReactionαβγReference
1HNCO + CH3→ CH3NCO + H1.00 × 10−1008.04 × 103(1)
2CH3NCO + H3+→ CH3NCOH+ + H21.00 × 10−9−0.50(2)
3CH3NCO + HCO+→ CH3NCOH+ + CO1.09 × 10−9−0.50(2)
4CH3NCO + H+→ CH3NCO+ + H1.00 × 10−9−0.50(2)
5CH3NCO + CO+→ CH3NCO+ + CO1.00 × 10−9−0.50(2)
6CH3NCO + He+→ CH3NCO+ + He1.00 × 10−9−0.50(2)
7CH3NCO+ + e-→ CH3 + OCN1.50 × 10−7−0.50(3)
8CH3NCOH+ + e-→ CH3NCO + H3.00 × 10−7−0.50(3)
9CH3NCO + CRP→ CH3 + OCN4.00 × 10300(3)
10CH3NCO + Photon→ CH3 + OCN5.00 × 10−100.00(3)
11HCN + s-CO→ s-HCN⋅⋅⋅CO100(4)
12s-HCN⋅⋅⋅CO + s-H→ s-H2CNCO102.40 × 103(5)
13s-H2CNCO + s-H→ s-CH3NCO100(6)
14s-CH3 + s-HNCO→ s-CH3NCO + s-H108.04 × 103(1)
15s-CH3 + s-OCN→ s-CH3NCO100(7)
15s-CH3 + s-OCN-→ s-CH3NCO + e-000(8)
16s-N + s-CH3CO→ s-CH3NCO100(9)

References. (1) Current work and see Table 4 in the online supplementary material for detailed calculation; (2) Anicich (1993); (3) Considering the similar reactivity of HNCO; (4) Following van der Waals formation on ice by Ruaud et al. (2015); (5) Current work and see Tables 1 and 2 in the online supplementary material for detail calculation; (6) Current work and see Table 3 in the online supplementary material for detailed calculation; (7) Following Belloche et al. (2017); (8) We neglect this reaction since we do not know exactly the value of the endothermicity; and (9) Current work and see Table 6 in the online supplementary material for detailed calculation.

Table 1.

List of major gas-phase and grain surface reactions added to the model for CH3NCO formation.

ReactionαβγReference
1HNCO + CH3→ CH3NCO + H1.00 × 10−1008.04 × 103(1)
2CH3NCO + H3+→ CH3NCOH+ + H21.00 × 10−9−0.50(2)
3CH3NCO + HCO+→ CH3NCOH+ + CO1.09 × 10−9−0.50(2)
4CH3NCO + H+→ CH3NCO+ + H1.00 × 10−9−0.50(2)
5CH3NCO + CO+→ CH3NCO+ + CO1.00 × 10−9−0.50(2)
6CH3NCO + He+→ CH3NCO+ + He1.00 × 10−9−0.50(2)
7CH3NCO+ + e-→ CH3 + OCN1.50 × 10−7−0.50(3)
8CH3NCOH+ + e-→ CH3NCO + H3.00 × 10−7−0.50(3)
9CH3NCO + CRP→ CH3 + OCN4.00 × 10300(3)
10CH3NCO + Photon→ CH3 + OCN5.00 × 10−100.00(3)
11HCN + s-CO→ s-HCN⋅⋅⋅CO100(4)
12s-HCN⋅⋅⋅CO + s-H→ s-H2CNCO102.40 × 103(5)
13s-H2CNCO + s-H→ s-CH3NCO100(6)
14s-CH3 + s-HNCO→ s-CH3NCO + s-H108.04 × 103(1)
15s-CH3 + s-OCN→ s-CH3NCO100(7)
15s-CH3 + s-OCN-→ s-CH3NCO + e-000(8)
16s-N + s-CH3CO→ s-CH3NCO100(9)
ReactionαβγReference
1HNCO + CH3→ CH3NCO + H1.00 × 10−1008.04 × 103(1)
2CH3NCO + H3+→ CH3NCOH+ + H21.00 × 10−9−0.50(2)
3CH3NCO + HCO+→ CH3NCOH+ + CO1.09 × 10−9−0.50(2)
4CH3NCO + H+→ CH3NCO+ + H1.00 × 10−9−0.50(2)
5CH3NCO + CO+→ CH3NCO+ + CO1.00 × 10−9−0.50(2)
6CH3NCO + He+→ CH3NCO+ + He1.00 × 10−9−0.50(2)
7CH3NCO+ + e-→ CH3 + OCN1.50 × 10−7−0.50(3)
8CH3NCOH+ + e-→ CH3NCO + H3.00 × 10−7−0.50(3)
9CH3NCO + CRP→ CH3 + OCN4.00 × 10300(3)
10CH3NCO + Photon→ CH3 + OCN5.00 × 10−100.00(3)
11HCN + s-CO→ s-HCN⋅⋅⋅CO100(4)
12s-HCN⋅⋅⋅CO + s-H→ s-H2CNCO102.40 × 103(5)
13s-H2CNCO + s-H→ s-CH3NCO100(6)
14s-CH3 + s-HNCO→ s-CH3NCO + s-H108.04 × 103(1)
15s-CH3 + s-OCN→ s-CH3NCO100(7)
15s-CH3 + s-OCN-→ s-CH3NCO + e-000(8)
16s-N + s-CH3CO→ s-CH3NCO100(9)

References. (1) Current work and see Table 4 in the online supplementary material for detailed calculation; (2) Anicich (1993); (3) Considering the similar reactivity of HNCO; (4) Following van der Waals formation on ice by Ruaud et al. (2015); (5) Current work and see Tables 1 and 2 in the online supplementary material for detail calculation; (6) Current work and see Table 3 in the online supplementary material for detailed calculation; (7) Following Belloche et al. (2017); (8) We neglect this reaction since we do not know exactly the value of the endothermicity; and (9) Current work and see Table 6 in the online supplementary material for detailed calculation.

3 ASTROCHEMICAL MODELLING

3.1 The nautilus chemical model

To investigate the chemistry of CH3NCO in ISM, we have used the state-of-the-art chemical code nautilus described in Ruaud et al. (2016). nautilus computes the chemical composition as a function of time in the gas-phase, and at the surface of dust grains. Here, surface chemistry is solved using the rate equation approximation and assuming a different chemical behaviour between the surface of the mantle and the bulk (i.e. a three-phase model). The equations and the chemical processes included in the model are described in Ruaud et al. (2016). nautilus includes physisorption of gas-phase species on grain surfaces, diffusion of species at the surface of the grains resulting in chemical reactions and several desorption mechanisms. Desorption can be due to the temperature (thermal desorption), cosmic-ray heating (cosmic-ray induced desorption, Hasegawa & Herbst 1993), UV photon impact (photodesorption) and chemical (Garrod, Wakelam & Herbst 2007).

3.2 Modification of the network

Our gas-phase chemistry is based on the public chemical network kida.uva.2014 (Wakelam et al. 2015a) with the updates on chemistry of HNCO (and their isomers) from the KIDA data base1 and chemistry of CH3NCO discussed in Section 2 and listed in Table 1 in this work. The surface network is based on the one of Garrod et al. (2007) with several additional processes from Ruaud et al. (2015) and Table 1 in this work. The entire network considered here is available on the KIDA website.

3.3 Physical models

To simulate the chemistry of CH3NCO in the ISM, we have considered two different physical models that are representative of (i) dense core, and (ii) solar-type protostar (representative of IRAS 16293). For dense core, nautilus is used with homogeneous conditions and integrated over 107 yr. The initial elemental abundances are same as in Hincelin et al. (2011) with depleted value of fluorine abundance of 6.68 ×  10−9 from Neufeld, Wolfire & Schilke (2005) and we have used a standard C/O ratio of 0.7 (Wakelam et al. 2015b; Majumdar et al. 2016). The model was run with constant dust and gas temperature of 10 K, a total proton density of 2 × 104 cm−3, a cosmic-ray ionization rate of 1.3 × 10−17 s−1 and a visual extinction of 30.

For low-mass protostar IRAS 16293, we have used the same physical structure as in Wakelam et al. (2014) and Majumdar et al. (2016) and that was computed using the radiation hydrodynamical (RHD) model from Masunaga & Inutsuka (2000). Here, the model initially starts from a dense molecular cloud core with a central density n(H2) ∼3 × 104 cm−3 and the core is extended up to r = 4 × 104 au with a total mass of 3.852 M. The prestellar core evolves to the protostellar core in 2.5 × 105 yr. When the protostar is formed, the model again follows the evolution for 9.3 × 104 yr, during which the protostar grows by mass accretion from the envelope.

4 RESULTS AND DISCUSSIONS

4.1 Chemistry in dark cloud

Fig. 2 shows the time evolution of the abundances of HNCO and CH3NCO under typical dark cloud conditions. Here, we have shown the chemical evolution of CH3NCO together with HNCO since in the past HNCO was assumed to be the main precursor for CH3NCO formation by Martín-Doménech et al. (2017) and Halfen et al. (2015). But this is not the case from our revised chemistry.

HNCO and CH3NCO abundances (with respect to H) predicted by our model for typical dense cloud conditions (see Section 3.3) as a function of time in the gas-phase and at the surface of the grains (represented by ‘s’). Here, abundance of gas-phase CH3NCO is negligible.
Figure 2.

HNCO and CH3NCO abundances (with respect to H) predicted by our model for typical dense cloud conditions (see Section 3.3) as a function of time in the gas-phase and at the surface of the grains (represented by ‘s’). Here, abundance of gas-phase CH3NCO is negligible.

Recently, Ruaud et al. (2016) suggested a best-fitting chemical age for TMC-1 (CP) to be a few 105 yr. At this time, 70 per cent of the observed species in TMC-1 (CP) are reproduced by the model within a factor of 10. At 2 × 105 yr, abundance of gas-phase HNCO predicted by our model is 3 × 10−10 with respect to nH. This is in good agreement with the observed abundance of 2 × 10−10 in TMC-1 (CP) (Agúndez & Wakelam 2013). At this age, HNCO is formed mainly from the barrier-less surface reaction s-N + s-HCO and the gas-phase dissociative recombination reaction of HNCOH+.

In our model, CH3NCO is formed efficiently only in the surface via the reactions of s-H + s-H2CNCO and s-N + s-CH3CO since the main gas-phase formation route CH3 + HNCO has an large activation barrier of 8040 K. s-H2CNCO is formed from the reaction between van der Waals complex s-HCN...CO and highly mobile s-H atoms. Here, s-HCN...CO is considered to be formed when gas-phase HCN land on the proximity of s-CO on the grain surfaces (Ruaud et al. 2015). s-CH3CO forms mainly via the reaction s-H + s-H2CCO. The peak gas-phase abundance of CH3NCO from our model is of the order of ∼10−32 with respect to nH whereas ice phase abundance is 7 × 10−10 around few 105 yr. This shows that CH3NCO is frozen in the ices around TMC-1 (CP) (also have lower rotational dipole moment compared to HNCO) and thus not free to rotate. Hence, CH3NCO is not detectable via its millimeter wavelength rotational spectra around TMC-1 (CP).

4.2 Chemistry in low-mass protostar

In order to validate our chemistry in Fig. 3, we present the computed abundances of CH3NCO, in the gas phase and at the surface of the grains in the protostellar envelope as a function of radius to the central protostar and compare with the observation of CH3NCO in IRAS 16293. The abundance profiles of CH3NCO can be discussed by considering two different regions. The first region is defined by radii larger than 200 au where the temperature is below 50 K. In this region, most of the CH3NCO in the grains is inherited from the cold core phase. The second region is defined by radii smaller than 100 au where the temperature reaches above 100 K and the gas phase abundance of CH3NCO increases sharply. The CH3NCO abundance on grains has an inverse profile showing that at low temperature, the CH3NCO molecules are formed on the grains and are thermally desorbed in the inner part of the envelope.

Abundance with respect to H2 predicted by our low-mass protostar model for CH3NCO and HNCO as a function of distance to the central star. s-CH3NCO and s-HNCO represent CH3NCO and HNCO on the grain surface.
Figure 3.

Abundance with respect to H2 predicted by our low-mass protostar model for CH3NCO and HNCO as a function of distance to the central star. s-CH3NCO and s-HNCO represent CH3NCO and HNCO on the grain surface.

Martín-Doménech et al. (2017) have determined an upper limit of 1.4 × 10−10 (with respect to molecular H2) for CH3NCO in the envelope of IRAS 16293 B at about 60 au from the central protostar. Another study by Ligterink et al. (2017) has also determined an upper limit of 3.3 × 10−10 (with respect to molecular H2) for CH3NCO in the same source IRAS 16293 B. Our model is in agreement with these upper limits at this radius (2 × 10−10). At 60 au, the gas-phase CH3NCO/HNCO abundance ratio from our model is 2 × 10−2, which is also reasonably close to the ratio 8 × 10−2 measured by Martín-Doménech et al. (2017) and Ligterink et al. (2017). The ice phase CH3NCO/HNCO ratio from our model in the outer part of the envelope (>1000 au) where possible comets should be formed is of the order of 3.7. This is very close to the CH3NCO/HNCO ∼ 4.33 ratio initially measured by the Philae lander on the comet 67P/Churyumov–Gerasimenko (Goesmann et al. 2015). This observation is, however, now questioned (can only be considered as an upper limit) by the recent measurement from the Double Focusing Mass Spectrometer (DFMS) of the ROSINA experiment (Altwegg et al. 2017).

5 CONCLUSION AND PERSPECTIVES

In this Letter, we have provided new insights concerning the chemistry of CH3NCO in the ISM. Our computation allowed us to confirm the hypothesis made by Cernicharo et al. (2016) about its grain surface origin. Moreover, we tested the impact of these new kinetic data on the prediction of CH3NCO abundance in the low-mass protostar IRAS 16293−2422 and on the CH3NCO/HNCO abundance ratio observed by the Philae lander on the comet 67P/Churymov–Gerasimenko. However, the study of the CH3NCO/HNCO abundance ratio in high-mass protostars with proper chemo-dynamical model is out of the scope of the current Letter, but could be done in the near future by comparing with the observations in SgrB2 (N) (Halfen et al. 2015; Belloche et al. 2017) and in Orion KL (Cernicharo et al. 2016).

Acknowledgements

LM, PG, VW and AC thanks ERC starting grant (3DICE, grant agreement 336474) for funding during this work. LM also acknowledges partial support from the NASA postdoctoral program. VW, PG and J-CL acknowledge the French programme Physique et Chimie du Milieu Interstellair (PCMI) funded by the Conseil National de la Recherche Scientifique (CNRS) and Centre National d’Etudes Spatiales (CNES). A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

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