The atmospheric chemistry of the warm Neptune GJ 3470b: influence of metallicity and temperature on the CH4/CO ratio
Olivia Venot, Marcelino Agundez, Franck Selsis, Marcell Tessenyi, Nicolas Iro
AAstronomy & Astrophysics manuscript no. gj3470b˙article˙V4 c (cid:13)
ESO 2018November 6, 2018
The atmospheric chemistry of the warm Neptune GJ 3470b:influence of metallicity and temperature on the CH /CO ratio Olivia Venot , Marcelino Ag´undez , , Franck Selsis , , Marcell Tessenyi , Nicolas Iro Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium Univ. Bordeaux, LAB, UMR 5804, F-33270, Floirac, France CNRS, LAB, UMR 5804, F-33270, Floirac, France University College London, Department of Physics and Astronomy, Gower Street, London WC1E 6BT, UK Theoretical Meteorology group, Klimacampus, University of Hamburg, Grindelberg 5, 20144, Hamburg, Germanye-mail: [email protected]
Received; accepted
ABSTRACT
Context.
Current observation techniques are able to probe the atmosphere of some giant exoplanets and get some clues about theiratmospheric composition. However, the chemical compositions derived from observations are not fully understood, as for instancein the case of the CH / CO abundance ratio, which is often inferred di ff erent from what has been predicted by chemical models.Recently, the warm Neptune GJ 3470b has been discovered and because of its close distance from us and high transit depth, it is avery promising candidate for follow up characterisation of its atmosphere. Aims.
We study the atmospheric composition of GJ 3470b in order to compare with the current observations of this planet, to preparethe future ones, but also as a typical case study to understand the chemical composition of warm (sub-)Neptunes. The metallicity ofsuch atmospheres is totally uncertain, and vary probably to values up to 100 × solar. We explore the space of unknown parameters topredict the range of possible atmospheric compositions. Methods.
We use a one-dimensional chemical code to compute a grid of models, with various thermal profiles, metallicities, eddydi ff usion coe ffi cient profiles, and stellar UV incident fluxes. Thanks to a radiative transfer code, we then compute the correspondingemission and transmission spectra of the planet and compare them with the observational data already published. Results.
Within the parameter space explored we find that in most cases methane is the major carbon-bearing species. We howeverfind that in some cases, typically for high metallicities with a su ffi ciently high temperature the CH / CO abundance ratio can becomelower than unity, as suggested by some multiwavelength photometric observations of other warm (sub-)Neptunes, such as GJ 1214band GJ 436b. As for the emission spectrum of GJ 3470b, brightness temperatures at infrared wavelengths may vary between 400 and800 K depending on the thermal profile and metallicity.
Conclusions.
Combined with a hot temperature profile, a substantial enrichment in heavy elements by a factor of ≥
100 with respectto the solar composition can shift the carbon balance in favour of carbon monoxide at the expense of methane. Nevertheless, currentobservations of this planet do not allow yet to determine which model is more accurate.
Key words. astrochemistry – planets and satellites: atmospheres – planets and satellites: composition – planets and satellites: indi-vidual (GJ 3470b)
1. Introduction
In the recent past, multiwavelength observations of transiting ex-oplanets have been used to provide the first constraints on thechemical composition of exoplanet atmospheres. The identifi-cation of atmospheric constituents is currently restricted to gasgiant planets with small orbital distances, because of the largetransit depth variations. Most such e ff orts have concentrated onJupiter size planets that orbit around solar-type stars, the so-called hot Jupiters. These planets are heavily irradiated by thenearby (early K-, G-, or late F-type) star, resulting in planetaryequilibrium temperatures in excess of 1000 K. Transmission anddayside emission spectra of hot Jupiters such as HD 209458band HD 189733b have revealed the presence of moleculessuch as CO, H O, CH , and CO in their atmospheres (Tinettiet al. 2007; Grillmair et al. 2008; Swain et al. 2008, 2009a,b;Madhusudhan & Seager 2009), although contradictory conclu-sions among di ff erent studies are not rare. Chemical models ofhot Jupiter atmospheres which incorporate to a di ff erent degreeprocesses such as thermochemical kinetics, vertical mixing, hor- izontal transport, and photochemistry (Line et al. 2010; Moseset al. 2011; Kopparapu et al. 2012; Venot et al. 2012; Ag´undezet al. 2012) indicate that in such a hot hydrogen-helium domi-nated atmosphere, carbon monoxide and water vapour should bethe major reservoirs of carbon and oxygen, while methane andcarbon dioxide would be somewhat less abundant.Even more challenging, transit spectra have recently al-lowed to characterise the atmosphere of the Neptune size planetGJ 436b and the mini Neptune or super-Earth GJ 1214b, both or-biting around M dwarf stars. Unlike Jupiter size planets, whichhave a very low occurrence rate around M dwarf stars (Johnsonet al. 2007; Bonfils et al. 2013), (sub-)Neptune size planets arefound around both solar-type and M dwarf stars, although theyare more easily observed around the latter type of stars becauseof the higher planet-to-star contrast which favour primary andsecondary transit observations. These planets have at least a cou-ple of interesting di ff erences with respect to hot Jupiters. Thefirst is related to the fact that the host M dwarf star is smallerand significantly cooler than a solar-type star, so that the planet a r X i v : . [ a s t r o - ph . E P ] D ec enot et al.: The atmospheric chemistry of the warm Neptune GJ 3470b is less severely heated (even if the orbital distances, in the range0.01 – 0.04 AU, are as small as for hot Jupiters), resulting inplanetary e ff ective temperatures below 1000 K. Interestingly, itis around this temperature that gaseous mixtures with solar el-emental abundances show, under thermochemical equilibriumand at pressures around 1 bar, a sharp transition concerningthe major carbon reservoir, CO and CH being the dominantcarbon-containing species above and below 1000 K, respectively(Fig. 1). In this regard it is interesting to note that transit spec-tra of GJ 436b indicates that its atmosphere is poor in methane(Stevenson et al. 2010; Madhusudhan & Seager 2011; Knutsonet al. 2011), yet this species is predicted to be the major car-bon reservoir at thermochemical equilibrium. Such interpreta-tion has been however disputed by Beaulieu et al. (2011) basedon a di ff erent analysis of transmission spectra. A detailed chemi-cal model by Line et al. (2011), which considered thermochemi-cal kinetics, vertical mixing, and photochemistry, concluded thatCH should be the major carbon-bearing molecule in GJ 436b’satmosphere under most plausible conditions.A second important di ff erence with respect to hot Jupiters isthat the lower mass of (sub-)Neptune planets allows to expectan elemental atmospheric composition significantly enriched inheavy elements, with respect to the solar composition, becauseof their lower e ffi ciency to retain light elements (Elkins-Tanton& Seager 2008). In the case of GJ 1214b, its flat transmissionspectrum indicates that the planet atmosphere either is hydro-gen dominated but contains clouds or hazes, or has a high meanmolecular weight, for instance an H O-rich atmosphere (Beanet al. 2010, 2011; D´esert et al. 2011; Croll et al. 2011; Crossfieldet al. 2011; de Mooij et al. 2012; Berta et al. 2012). The possibil-ity of a hydrogen dominated atmosphere for GJ 1214b has beenexplored through chemical modelling by Miller-Ricci Kemptonet al. (2012), who found that methane would be the major car-bon reservoir, just as the findings of Line et al. (2011)’s model onthe atmosphere of GJ 436b, and that photolysis of CH , whichcould lead to the formation of hazes, would take place at heightssubstantially higher than required by the observations. Theseprevious photochemical studies dedicated to (sub-)Neptunes ex-plored high metallicities up to 50 × solar metallicity. In the solarsystem, Neptune and Uranus atmospheres have indeed carbonabundances about 50 times higher than in the Sun (oxygen be-ing trapped in the deep and hot layers of the atmospheres whichcannot be probed yet by observations). This carbon abundanceis significantly higher than that of the atmosphere of Jupiter andSaturn, which is about 3 times solar (Hersant et al. 2004). Thebulk metallicity of icy giants is, however, much higher than thatof their atmosphere, as they consist in a large fraction of rocksand ice (e.g. Pollack et al. 1996; Alibert et al. 2005). In a warmNeptune that would have the same bulk composition as Neptuneor Uranus, a larger fraction of the ices would be in the formof gases in the atmosphere, which may no longer be dominatedby H and He. Although the mass and radius of the planet, de-rived from radial velocities and transit measurements, can beused to constrain the bulk metallicity they do not provide a con-straint on the metallicity of the envelope. This was shown byBara ff e et al. (2008) who modelled the evolution of Jupiter- andNeptune-mass planets with all the heavy elements in the core ordistributed uniformly in the whole planet. They also used dif-ferent approximations to model the equation of state of the en-riched envelope. Their conclusion is that although planets witha uniform enrichment tend to have a smaller radius after about1 Gyr compared with those with a core, the uncertainty relatedwith the equation of state exceeds this di ff erence. Therefore, themass and radius of a planet may show that a large fraction of the Table 1: GJ 3470b’s model parameters. Parameter Value a Stellar radius 0.503 R (cid:12) Stellar e ff ective temperature 3600 KPlanetary radius 4.2 R ⊕ Planetary mass 14.0 M ⊕ Planet-star distance 0.0348 AU a Bonfils et al. (2012). planet mass consists in H -He but does not tell whether the en-velope and the atmosphere are dominated by these compounds.The atmospheric abundance of H O, for instance, could reach orexceed that of H giving the atmosphere a high mean molecu-lar weight and small scale height. In this study, we consideredan enrichment in heavy elements between 1 and 100 times so-lar. Using solar abundances from Asplund et al. (2009) and as-suming that all the oxygen is in the form of H O, these enrich-ments correspond to a mean molecular mass between 2.3 and4.1 g / mole. Heavy elements enrichment in the range 50-100 areextremely interesting because they correspond to a change of thecarbon reservoir (either CH or CO) for pressures within 1 and100 bar and temperatures within 1000 and 2000 K (see Fig. 1).The deep atmospheric layers where such conditions are foundcan contaminate most of the atmosphere due to the chemicalquenching associated with vertical mixing (e.g. Prinn & Barshay1977; Lewis & Fegley Jr 1984; Visscher & Moses 2011; Moseset al. 2011; Venot et al. 2012).In this work, we address the e ff ects of the heavy elements en-richment in the transiting warm Neptune GJ 3470b discoveredby Bonfils et al. (2012). This planet is a promising candidatefor follow-up characterisation of its atmosphere and for a betterunderstanding of the atmospheric chemistry of (sub-)Neptunes.GJ 3470b has a mass of 14 M ⊕ , in between those of GJ 436b(23 M ⊕ ; Southworth 2010) and GJ 1214b (6 M ⊕ ; Harpsøe et al.2013). Its radius of 4.2 R ⊕ implies a high amount of hydrogenin the envelope. Indeed, a planet with the same mass but madeonly of water would have half this radius. Some spectroscopicobservations during primary transit have already been held dur-ing the past few months (Demory et al. 2013; Fukui et al. 2013;Crossfield et al. 2013; Nascimbeni et al. 2013), leading some-times to di ff erent and contradictory interpretations: hazy, cloud-free, metal-rich, low mean molecular weight, etc. Thus, moreprecise observations are needed to characterise its atmosphericstructure and composition. While we wait for future observa-tions, we study composition of the atmosphere of GJ 3470b witha model that includes thermochemical and photochemical kinet-ics and vertical mixing. We explore the influence of the ther-mal profile, the vertical mixing e ffi ciency, the poorly constrainedUV irradiation and the metallicity on the chemical composition.We compute the resulting transmission and emission spectra thatwe compare with the observations available so far. While thiswork was being finalised, a similar study has been published onGJ 436b by Moses et al. (2013). We do not compare in detailsour results to theirs, but they are globally in agreement.
2. The model
We aim at studying the atmospheric chemical composition in thedayside of GJ 3470b in the vertical direction. We have adoptedthe planetary and stellar parameters derived by Bonfils et al.(2012), which are given in Table 1. Note that the planetary pa-rameters of GJ 3470b have been recently refined by Demoryet al. (2013) and Fukui et al. (2013), leading to a larger radius metallicity ζ t e m p e r a t u r e ( K ) bar10 bar1 bar10 − bar10 − bar10 − bar 10 − bar10 − bar 10 − bar COCH Fig. 1: Transition temperature for the C-bearing species (e.g.CO / CH ) at the thermochemical equilibrium depending ofmetallicity, at di ff erent pressures. Above the curve, CO is thedominant C-bearing species, while CH dominates below. Thetemperature of the transition decreases when metallicity in-creases, an e ff ect which is more important for high pressures.so to a smaller density than what was predicted first by Bonfilset al. (2012). These new observations imply that GJ 3470b hasa quite low density ( ρ p < − ) compared to Uranus andNeptune. The atmosphere model relies on some key input infor-mation such as the elemental composition, the vertical profile oftemperature, the eddy di ff usion coe ffi cient, and the stellar ultra-violet (UV) flux, which are badly constrained. In order to ex-plore to some extent the sensitivity of the atmospheric chemicalcomposition to these uncertain parameters we have varied themaround some standard choices. Hereafter we describe our choiceof standard parameters and the range over which they have beenvaried. The radiation spectrum of the host star a ff ects in two major waysthe planetary atmosphere. On the one side, the visible-infraredpart of the incoming stellar radiation controls the atmosphericthermal structure of the planet, and on the other, the UV radiationdetermines the photodissociation rates. Longward of 240 nm, weadopt a Phoenix NextGen synthetic spectrum (Hauschildt et al.1999) for a star with T e ff = g = . cm s − , and so-lar metallicity. The flux of UV radiation emitted by M dwarfstars may vary by orders of magnitude depending of the de-gree of chromospheric activity of the star (France et al. 2013).Unfortunately, the UV spectrum of GJ 3470 has not been ob-served to our knowledge, and we have therefore adopted the ob-served spectrum of the active M3.5V star GJ 644 (Segura et al.2005) in the 115-240 nm wavelength range and the mean of Sunspectra at maximum and minimum activity (Gueymard 2004)shortward of 115 nm. The final composite spectrum (shown inFig. 2) is adopted as the standard stellar spectrum. Due to thelarge uncertainties at UV wavelengths, when exploring the spaceof parameters, we allow for a variation in the UV flux between0.1 and 10 times the standard spectrum.
100 200 300 400 500 600 700 800 λ (nm) F λ ( p h o t o n c m − s − n m − ) Fig. 2: Stellar spectrum adopted for GJ 3470, where the flux F λ isnormalised to an orbital distance of 1 AU. Vertical dashed linesat 115 and 240 nm indicate the positions of junction betweenspectra from di ff erent sources (see text). To understand the history of GJ 3470b, it would be importantto constrain its atmospheric metallicity, which is currently veryuncertain. As it has been explained in the Introduction, the atmo-sphere of this planet can be enriched. The host star of GJ 3470bhas a metallicity slightly above the solar value, [Fe / H] = + ζ =
10 with respect to the solar values compiled by Asplundet al. (2009). However, given the large uncertainties in the ele-mental composition, when exploring the e ff ect of metallicity onthe atmospheric chemical composition we choose two extremecases with ζ = ζ =
100 (high metal-licity). In this study, we do not change the C / N / O relative abun-dance ratios compared to their solar values.
The vertical profile of temperature in GJ 3470b’s atmosphere iscomputed with the radiative-convective model described by Iroet al. (2005), with the update of Ag´undez et al. (2012). We adoptthe planetary and stellar parameters given in Table 1 as well asthe input information corresponding to our standard model. Themixing ratios of the main species that provide opacity are es-timated through thermochemical equilibrium, which is expectedto be a good approximation as long as the abundances of CO andH O (the main species that a ff ect the thermal structure) are closeto the chemical equilibrium values. As seen in Section 3.1, thisis likely to be the case for H O although not for CO through-out a good part of the atmosphere, which may add an uncer-tainty to the calculated thermal profile. In the deep atmosphere,the temperature is regulated by convective, rather than radiative,processes, and the internal flux of the planet becomes the mostrelevant parameter. The internal flux of the planet is highly un-certain since it depends on the age of the planet and on processesof dissipation of energy which may be triggered by for instancetidal e ff ects (Ag´undez et al. 2013). We have adopted an internal
500 1000 1500 2000 temperature (K) -8 -7 -6 -5 -4 -3 -2 -1 p r e ss u r e ( b a r ) temperature K zz (cm s − ) K zz Fig. 3: Standard vertical profile of temperature (solid line re-ferred to the lower abscissa axis) and of eddy di ff usion coe ffi -cient (dashed line referred to the upper abscissa axis) adoptedfor the atmosphere of GJ 3470b.flux which corresponds to an internal temperature of 100 K, avalue commonly used in previous studies in the absence of rel-evant constraints. The temperature is calculated vertically as afunction of pressure between 1000 and 10 − bar, and above thislatter pressure level an isothermal atmosphere is assumed. Thecalculated vertical profile of temperature, which is adopted asthe standard one, is shown in Fig. 3. Given the various uncer-tainties that a ff ect the calculated temperature profile, we exploreit in our space of parameters choosing two bounding cases inwhich a value of 100 K is added and subtracted to the standardtemperature profile. Another important parameter for the chemical model is the ver-tical profile of the eddy di ff usion coe ffi cient, which determinesthe e ffi ciency of the vertical mixing as a function of pressure. Inthe case of exoplanet atmospheres, constraints on this parametercome solely from global circulation models (GCMs). For the at-mosphere of GJ 3470b we adopt a parametric profile for the eddydi ff usion coe ffi cient, with a high value of K zz = cm s − inthe convective region of the atmosphere (which is approximatelylocated below the 100 bar pressure level), and values inferredfrom the GCM of GJ 436b developed by Lewis et al. (2010). Bymultiplying a mean vertical wind speed by the local scale height,these authors estimated K zz values of 10 cm s − at 100 bar and10 cm s − at 0.1 mbar. We have therefore adopted these valuesand assumed a linear behaviour in the logarithm of K zz with re-spect to the logarithm of pressure in the 10 − – 100 bar regime,and a constant value for K zz at higher atmospheric layers. Theresulting vertical profile, which we adopt as the standard one, isshown in Fig. 3 referred to the upper abscissa axis. However, be-cause the GCM of Lewis et al. (2010) is constructed for GJ 436band not for GJ 3470b, and also because the method used toestimate the eddy di ff usion coe ffi cient is highly uncertain (e.g.Parmentier et al. 2013). We have explored the sensitivity of thechemical abundances to the eddy di ff usion coe ffi cient and con-sider two limiting cases in which K zz is divided and multiplied Table 2: Model’s parameter space explored. All the parametersare changed with respect to the standard values showed in Figs. 2and 3. The standard metallicity is 10 × solar ( ζ = Parameter Range of values SymbolMetallicity Solar ( ζ = ζ High ( ζ = ζ Temperature Warm atmosphere ( +
100 K) T + Cool atmosphere ( −
100 K) T − Eddy di ff usion coe ffi cient High ( K zz × K × zz Low ( K zz ÷ K ÷ zz Stellar UV flux High irradiation ( F λ × F × λ Low irradiation ( F λ ÷ F ÷ λ by a factor of ten with respect to the standard profile above theconvective region. Once the physical parameters and elemental composition are es-tablished, the atmospheric chemical composition is computedby solving the equation of continuity in the vertical directionfor 105 species composed of H, He, C, N, and O. The reactionnetwork and photodissociation cross sections used are describedin Venot et al. (2012). This chemical network, which includes ∼ ∼ ∼
700 reactions and 51 and 61 species for respectively Lineet al. 2011 and Miller-Ricci Kempton et al. 2012) and reverseall reaction rates using the principle of microscopic reversibility(Visscher & Moses 2011; Venot et al. 2012). However, contraryto our network, none of them have been validated as a wholethrough experiments. Line et al. (2011) use the chemical networkconceived for Jovian planets (Liang et al. 2003, 2004, and ref-erence therein) updated for high temperature (Line et al. 2010),enhanced with nitrogen reactions and a small set of H S reac-tions. Miller-Ricci Kempton et al. (2012) use chemical networkof Zahnle et al. (2009b), so also originally made for Jovian planet(Zahnle et al. 1995) and upgraded for high temperature atmo-spheres with an arbitrary selection of new reaction rates fromavailable data (Zahnle et al. 2009a). As it has been shown inVenot et al. (2012), di ff erent chemical schemes can lead to dif-ferent quenching levels and thus to di ff erences in computed at-mospheric composition. Thus, some di ff erences found between,on one hand, this study and, on the other hand, Line et al. (2011)and Miller-Ricci Kempton et al. (2012), may be due to the useof di ff erent chemical schemes.
3. Results and discussion
Our standard set of parameters to build up the chemical modelof GJ 3470b’s atmosphere consists of an elemental compositiongiven by ζ =
10, the vertical profiles of temperature and eddydi ff usion coe ffi cient shown in Fig. 3, and the stellar UV spec- -8 -7 -6 -5 -4 -3 -2 -1 mole fraction -8 -7 -6 -5 -4 -3 -2 -1 p r e ss u r e ( b a r ) CO H ON CH NH CO HCN
Fig. 4: Vertical distribution of molecular abundances in the stan-dard model of GJ 3470b’s atmosphere as computed through ther-mochemical equilibrium (dashed lines) and with the model thatincludes thermochemical kinetics, vertical mixing, and photo-chemistry (solid lines).trum shown in Fig. 2. Apart from this standard model we haveconstructed a grid of 16 models in which we have explored thesensitivity of the chemical composition to the metallicity, tem-perature, eddy di ff usion coe ffi cient, and stellar UV flux, accord-ing to the choices detailed in Table 2. For all of the seventeenmodels, the initial conditions are the thermochemical equilib-rium. At both upper and lower boundaries, we impose a zero fluxfor each species. The steady-state is reached after an integrationtime of t = s ( K × zz ) or t = s ( K ÷ zz ). In this section, we present the results of our standard modeland compare them with previous publications dealing with(sub-)Neptunes: Line et al. (2011) on GJ 436b and Miller-Ricci Kempton et al. (2012) on GJ 1214b. Because these modelsdo not use the same thermal profiles as us, nor the same eddy dif-fusion profiles and elemental abundances, it is di ffi cult to com-pare quantitatively our results. Nevertheless, di ff erent cases havebeen studied in these publications so we can compare qualita-tively the results that we obtained. Figure 4 shows the atmospheric composition of GJ 3470b atthe chemical equilibrium (dashed lines) and at the steady-state,computed with the model taking into account thermochemicalkinetics, vertical mixing, and photochemistry (solid lines). Theabundances of all species remain at chemical equilibrium forpressures higher than about 40 bar, while at lower pressures wecan see the e ff ect of vertical mixing. Around 40 bar the abun-dances of HCN and NH depart from chemical equilibrium, andat somewhat lower pressure, around 2 bar, the abundances ofCO , CO, CH , and H O get quenched, i.e. they are frozen at thechemical equilibrium value of the quench level. This quenchinge ff ect makes CH , H O, and N to be slightly less abundant thanwhat thermochemical equilibrium predicts, so that CO, NH ,CO , and HCN can be more abundant than the equilibrium pre- diction. In the upper atmosphere (above the 10 − bar level), wesee the e ff ect of photodissociations: some species (for exampleH O and CH ) are destroyed by photolysis, whereas other (asCO and CO) see their abundance increased. Globally, between10 and 10 − bar, the most abundant species of the atmosphereof GJ 3470b (after H and He) are, by decreasing order, H O,CH , and CO.First, we compare our results with those of Line et al. (2011).We focus on their cases where elemental abundances are solarand 50 × solar. Our T − P profile is not very di ff erent from theirso we expect to have results quite similar. Even if our eddy dif-fusion coe ffi cient is not identical, the abundances we find for allspecies are in between these two cases. In the region where verti-cal quenching dominates (in between the thermochemical equi-librium and photochemical regions) the behaviour of abundancesis rather similar since the eddy di ff usion coe ffi cient adopted forthe quenching level is not very di ff erent (10 cm s − by Lineet al. (2011) and somewhat higher in our case). However, in theupper layers our adopted K zz value is substantially higher thanthe value of 10 cm s − adopted by Line et al. (2011), so thatin their model the region where photochemistry takes place isshifted to lower heights.Then, we compare our results with those obtained by Miller-Ricci Kempton et al. (2012) using 5 × and 30 × solar ele-mental abundances and an eddy di ff usion coe ffi cient of K zz = cm s − . We expect our results to be in between these two re-sults. That is what we find for most species, except CO and CO .For these two species, at the steady-state, our model gives abun-dances about 100 times higher than in their case ζ =
30. Thisis due to the fact that the abundances of these species departfrom chemical equilibrium at a higher pressure in the study ofMiller-Ricci Kempton et al. (2012) than in ours ( ∼ bar and ∼ T − P profile the temperatureincreases with pressure, in theirs, the temperature remains con-stant between 1 and 100 bar. Consequently, the temperature inthe deeper part of the atmosphere, where quenching happens, iscolder than in our T − P profile. This di ff erence has consequenceson the abundances of some species at the chemical equilibrium(for a given pressure level, CO and CO have equilibrium abun-dances smaller than in our model) and also at the steady-statebecause quenching happens at di ff erent levels. /CO abundance ratio The CH / CO abundance ratio is an important parameter to dis-cuss, since some observational and modelling studies seem toindicate a poor methane content in the atmosphere of warm (sub-)Neptunes while thermochemical equilibrium predicts that CH should be the major carbon reservoir in such atmospheres (e.gStevenson et al. 2010; Madhusudhan & Seager 2011; Knutsonet al. 2011 for GJ 436b and Miller-Ricci Kempton et al. 2012for GJ 1214b). Of course chemical equilibrium depends on the T − P profile and the assumed elemental composition, but thisfindings have suggested the need to invoke non-equilibrium pro-cesses such as mixing and photodissociations to help explainingthese non expected chemical compositions. Nevertheless, eventaking into account these non-equilibrium processes, 1D chemi-cal models have not been able to find the set of parameters thatmay lead to a CH / CO abundance ratio lower than 1. In the caseof the warm Neptune GJ 436b, observations of the dayside emis-sion seem to indicate that this planet has an atmosphere domi- nated by CO and poor in CH (CH / CO abundance ratio equalsto 10 − – 10 − for Stevenson et al. 2010 and Madhusudhan &Seager 2011), although a di ff erent interpretation has been pro-vided by Beaulieu et al. (2011) based on a re-analysis of thesame secondary eclipse data and on primary transit observations,which indicates a high methane content in the atmosphere, witheventually traces of CO or CO . Whatever the right interpreta-tion, the chemical modelling done by Line et al. (2011) showsthat CH is more abundant than CO (between 10 − and 1 barthe CH / CO abundance ratio is ∼ × and ∼ ζ = should be themajor carbon reservoir in the atmosphere, with CH / CO abun-dance ratios of ∼ × and ∼ between 10 − and 1 bar formetallicities of ζ = model that best fits the observations of this planet.With the standard value of the parameters of GJ 3470b, wefind a CH / CO abundance ratio of 2 at 1 bar, i.e. with CH be-ing slightly more abundant than CO. We then explore how theCH / CO abundance ratio varies within the space of parameters. ζ , T , K zz , and F λ We study the di ff erent possible atmospheric compositions ofGJ 3470b by exploring the space of unknown parameters: metal-licity ( ζ ), temperature ( T ), eddy di ff usion coe ffi cient ( K zz ), andincident UV flux ( F λ ). The computed abundances of CO, CO ,CH , NH , H O and HCN are plotted on Fig. 5. We choose thesespecies because they are the ones that most influence the plane-tary spectra.
An increase in the metallicity obviously produces an abundanceenhancement of all molecules containing heavy atoms (comparered and magenta lines, or green and blue lines, in Fig. 5). Apartfrom this, depending of the molecule, the reaction to a changein the metallicity can be quite di ff erent, with the most sensitiveone being carbon dioxide. When the metallicity changes from ζ = increases by a 4–6 ordersof magnitude, while that of CO increases by 2–4 orders of mag-nitude, and the rest molecules experience less dramatic varia-tions. A large abundance of CO would probably be the best ev-idence of an enhanced metallicity in the planet’s atmosphere, asalready found by Zahnle et al. (2009b) in the case of hot Jupiters.Nitrogen species are also sensitive to metallicity. N and HCNincrease their abundance by ∼ At the typical temperatures expected in the atmosphere of awarm Neptune such as GJ 3470b, a variation of temperature of200 K can produce important changes in the resulting chemicalabundances. These abundance variations depend to a large ex-tent on the adopted metallicity. If we focus on the most abundantmolecules, concretely on the six shown in Fig. 5, there are twoclear behaviours. On the one hand, we have CO, CO , and HCN,which experience an abundance enhancement when the tempera-ture is increased, especially at low metallicities ( ζ = ζ = ff ect, the molar fraction of CO and HCN varying only by a factor ∼ exhibits negligible change. On the other hand, CH , H O,and NH respond to an increase of temperature in the oppositedirection, i.e. decreasing their abundances. In this case the e ff ectis more apparent at high metallicities, with abundance variationsup to one order of magnitude.The chemical composition in the atmosphere of warm (sub-)Neptunes can be quite sensitive to the temperature, especiallyif the temperatures in the quench region, usually located in the0.1–10 bar pressure range, are around 1000 K, since at thesetemperatures and pressures there are important transitions suchas that concerning CO and CH . Uncertainties in the thermalprofile are therefore a major source of error in some of the cal-culated abundance ratios. The stronger vertical mixing is, the deeper quenching happensand the more the upper atmosphere will be contaminated by thechemical composition of the deep atmosphere. This has a cru-cial importance to interpret the observations and thus the com-position of such atmospheres. Globally, a higher eddy di ff usioncoe ffi cient results in a stronger vertical mixing, so in abundanceprofiles more flat in the vertical direction. For CO, CO , andHCN, at pressures above the quenching level, a high K zz leadsto smaller abundances than with a low K zz , whereas for all theother species, a high K zz creates globally higher abundances. For some species (HCN, CO and CO), thanks to vertical mix-ing, the e ff ect of photochemistry propagates quite deep in theatmosphere, down to few bars. For these species (if CH is reser-voir of carbon), the e ff ect of photochemistry is to enhance theirabundance, especially at low metallicity. A more intense UV fluxresults in an increase of their abundance. For the other speciesrepresented on Fig. 5, the e ff ect of the UV flux remains onlyat low pressures ( < − bar). These species are destroyed byphotolysis, so a higher photochemistry shifts photodestructionof molecules to lower heights. /COabundance ratio The main finding of this paper is that there exists a combinede ff ect of the temperature, the vertical mixing, and the metal-licity that can explain the CH / CO abundance ratio lower thanunity found by observations in some atmospheres. To clearly seethe dependence of the CH / CO ratio with the parameters of ourstudy, we plot for each ζ − T choice, the two more extreme cases, K × zz F ÷ λ and K ÷ zz F × λ (Fig. 6). The two other cases are in be-tween.In the cases of our low and standard metallicity, the CH / COabundance ratio is always above 1 (for pressures higher than10 − mbar), whatever the choice of the parameters T , K zz and F λ (4 top panels on Fig. 6). The maximum value reached is ∼
200 be-tween 10 − and 1 bar (with the case ζ T − ). When the metal-licity is increased up to ζ = / CO abun-dance ratio may become lower than unity if the warm choiceof temperature profile is adopted. In the cases ζ T + (ma-genta curves on Fig. 5), whatever the choice of K zz and F λ ,CO is clearly more abundant than CH (in the area 10 − –1 bar,CH / CO ranges between 0.04 and 0.06). We can see on Fig. 6 -9 -8 -7 -6 -5 -4 -3 -2 -1 -8 -7 -6 -5 -4 -3 -2 -1 p r e ss u r e ( b a r ) CO -9 -8 -7 -6 -5 -4 -3 -2 -1 -8 -7 -6 -5 -4 -3 -2 -1 p r e ss u r e ( b a r ) CH -9 -8 -7 -6 -5 -4 -3 -2 -1 mole fraction -8 -7 -6 -5 -4 -3 -2 -1 p r e ss u r e ( b a r ) ζ T +100 ζ T − ζ T +100 ζ T − K × zz F × λ K × zz F ÷ λ K ÷ zz F × λ K ÷ zz F ÷ λ H O -9 -8 -7 -6 -5 -4 -3 -2 -1 -8 -7 -6 -5 -4 -3 -2 -1 CO -9 -8 -7 -6 -5 -4 -3 -2 -1 -8 -7 -6 -5 -4 -3 -2 -1 NH -9 -8 -7 -6 -5 -4 -3 -2 -1 mole fraction -8 -7 -6 -5 -4 -3 -2 -1 HCN
Fig. 5: Vertical distribution of the abundances of selected molecules as calculated through each of the 16 models in which the spaceof parameters of metallicity, temperature, eddy di ff usion coe ffi cient, and stellar UV flux are explored. Each colour corresponds toa set of metallicity and temperature, and each line style to a set of eddy di ff usion coe ffi cient and stellar UV flux (see legend in theH O panel and meaning of each symbol in Table 2).(bottom panels) that this result is determined by the thermo-dynamic equilibrium: because the temperature is high in thedeep atmosphere, CO is thermochemically favoured over CH .Vertical mixing then makes the abundances of CO and CH toquench in the vertical direction, so that CO remains more abun-dant than methane in all the upper atmosphere, despite thermo-chemical equilibrium predicts an inversion of C-bearing species between ∼ / CO ra-tio higher than 1 for the cases ζ T − (blue curves on Fig. 5).This indicates that not only a high metallicity is necessary to aCH / CO ratio under unity, but also a su ffi ciently high internaltemperature.These results show that it is possible for GJ 3470b, but alsofor the observed GJ 436b and, in a less extent because of its P r e ss u r e ( b a r ) Molar fraction
CO CH4 P r e ss u r e ( b a r ) Molar fraction
CO CH4 P r e ss u r e ( b a r ) Molar fraction
COCH4 P r e ss u r e ( b a r ) Molar fraction equilibrium
CO CH4
Fig. 6: Vertical abundances of CO and CH in eight selected models (left) and the corresponding value of the CH / CO ratio (right).Each line style correspond to a set of eddy di ff usion coe ffi cient and stellar UV flux (see legend in the left bottom panel and meaningof each symbol in Table 2). The CH / CO = / CO ratio underunity. A very high metallicity, compared to the Sun, combinedwith a high temperature, may be the key to explain the obser-vations of warm exoplanets, similar to GJ 3470b, which indi- cate that CO is more abundant than methane. Moreover, plan-ets with a bulk composition similar to Neptune or Uranus areexpecting to have such enrichment. The study shows also thatgetting back to the elementary abundances from observations is very di ffi cult, and requires to know the temperature profile, themetallicity and the vertical mixing. The solution might be to usea self-consistent model taking into account and calculating si-multaneously all these parameters. To determine if future observations of GJ 3470b could be used toconstrain the values of the parameters that we varied in the pre-vious section, we compute synthetic spectra for our 17 models(Fig. 7). Emission spectra are calculated using the line-by-lineradiative transfer codes described in Tinetti et al. (2005, 2006).Transmission spectra are calculated using the line-by-line radia-tive transfer codes described in Hollis et al. (2013). For bothtype of spectra, we used line lists from HITRAN (Rothman et al.2009, 2010), except for CO, CO , and CH for which we usedHITEMP (Rothman et al. 2010). For H O we used the BT2 list(Barber et al. 2006). We use the same NextGen stellar model asin Sect. 2.1.We end up with five groups of spectra influenced by the ther-mal profile and the metallicity. The vertical mixing, as well asthe UV flux used in the di ff erent models, have very little ef-fect on spectra, which are dominated by the temperature and themetallicity of the atmosphere. Both for primary and secondaryspectra, we notice that the reddish and greenish spectra exhibitbroader variations than the two others, because they correspondto the low metallicity cases, so to atmospheres with smaller op-tical depth. This result has also been found by Ag´undez et al.(2013) and Moses et al. (2013) for GJ 436b.Thereby, for emission spectra, we see five levels of bright-ness temperature. The highest temperature corresponds to thecase ζ T + (reddish curves), and the lowest to the case ζ T − (blueish curves). The standard model is logically in be-tween the four other groups of spectra. With an identical thermalprofile, the enhancement of metallicity (by a factor 100) leads toa lowering of the brightness temperature by ∼ ff erences of brightness temperature. Ofcourse, in case of temperature inversion, one could have the op-posite e ff ect, and see higher brightness temperature with highermetallicities. Constraining the metallicity from the brightnesstemperature is made di ffi cult by the strong dependency of thislatter on the temperature, and therefore there is a degeneracy.Apart from the level of brightness temperature, the spectra areglobally similar and exhibit the same features. Nevertheless, wecan notice slight di ff erences between the ζ and ζ spectra attwo locations. First, around 4.5 µ m, the absorption by CO andCO are more defined in the ζ cases compared to the very closepeaks characteristic of water absorption that we see around 4.5 µ m in the ζ cases. Then, around 10 µ m, the high peaks dueto NH and H O are very strong features in the ζ spectra butare attenuated on the ζ spectra. This is due to the high abun-dance of CO , that absorb a lot from 9 µ m (as much or evenmore than water), and thus contribute importantly to spectra.The variation of the other parameters (eddy di ff usion coe ffi cientand UV flux) has almost no impact on the emission spectra, ex-cept for the case ζ T + (reddish curves). Between 10 and 11 µ m there are di ff erences in the brightness temperature of about10 K due to the change of ammonia abundance. Between 13.5and 14 µ m, the small variations of brightness temperature areattributed to HCN and NH , that both contribute strongly to thespectra in this wavelength region. Nevertheless, the di ff erences from one spectra to another, due only to the change of eddy dif-fusion coe ffi cient and UV flux, are very small, and probably notdetectable with our current technologies (e.g. Stevenson et al.2010) do not obtained uncertainties lower than 20 K for GJ 436bwith the Spitzer Space Telescope ).The transmission spectra are also separated depending onthe temperature and the metallicity. Nevertheless, we notice thatthe greenish and yellowish spectra (respectively ζ T − and ζ T + ) are quite close and intersect between 4 and 5 µ m al-though the chemical composition corresponding to these 8 casesare quite di ff erent. The apparent planetary radius found with oursynthetic spectra goes from 4.25 to 4.75 R ⊕ . It is important tokeep in mind that these numerical values depend on the choiceof the radius of the planet at the 1 bar pressure level. Indeed, theobservations give only the apparent radius of the planet and wecannot know to which pressure level it corresponds. Changingthe radius at the 1 bar pressure level will translate the spectravertically. What is important to study is the relative variation ofspectra from one model to another. The radius at 1 bar is a pa-rameter than can be adjusted to fit the observations. We decidedto put the 1 bar pressure level at 4.28 R ⊕ , which correspondsto the minimum apparent radius observed (Demory et al. 2013),slightly adjusted in order to fit the maximum of observationaldata points (Demory et al. 2013; Fukui et al. 2013; Crossfieldet al. 2013) with the ζ T + and standard models. With a higherradius at 1 bar, the ζ T − and ζ T + (greenish and yellow-ish curves respectively) can also fit most of the observations. Onthe contrary, we see that the last case ( ζ T − ) is too flat to bein the error bars. None of the models can perfectly match all thedata points of Crossfield et al. (2013).The higher radius is found with the model ζ T + (reddishcurves), because the mean molecular weight is low (as opposedto the high metallicity cases), resulting in a higher atmosphericscale height, and thus in a higher radius. Compared to the yel-lowish curves, we see an increase up to 0.2 R ⊕ . On the opposite,the smaller radius is found with the model ζ T − (blueishcurves), because of the low atmospheric scale height due to thehigh mean molecular weight (4.1 g / mole). We see that the 17transmission spectra exhibit globally the same features, what-ever the apparent planetary radius. Transmission spectra probean upper part of the atmosphere (with a lower temperature), com-pared with emission spectra, and are thus more sensitive to UVphotolysis, and vertical mixing. For one given ζ − T case, wecan observe several variation on the spectral features. Around3.3 µ m and between 7 and 9 µ m, we clearly see that the CH features change from one model to an other. Between 4 and 5 µ m we see that the contribution of CO and CO evolve for thelow metallicity cases only. It is consistent with the fact that theabundances of these two species almost don’t change for the highmetallicity cases (see Fig. 5). Finally, the NH feature around 10 µ m changes in the ζ T + case because the abundance of ammo-nia changes importantly with di ff erent K zz and F λ for this cases(see Fig. 5). These variation are quite small (less than 0.1 R ⊕ )but could be detectable with current observational technologies.The Okayama Astrophysical Observatory (Fukui et al. 2013) andthe
Hubble Space Telescope (Pont et al. 2009, for the planetGJ 436b) for instance, are able to give error bars of only 0.1 R ⊕ .A detailed study like Tessenyi et al. (2013) applied to EChO andShabram et al. (2011) with JWST about the capacities of thesefuture telescopes to di ff erentiate our models is beyond the scopeof this paper, but will be the subject of a follow-up study.Although it is the only case with [CO] > [CH ], the ζ T + spectra do not show strong features due to this di ff erent CH / COratio, except maybe the fact that the 3.3-to-4.7 µ m radius ratio standard Fig. 7: Synthetic emission spectra of GJ 3470b corresponding to the grid of 16 models as well as the standard model. Each colourcorrespond to a set of metallicity and thermal profile. A colour gradient is then used to di ff erentiate the eddy di ff usion coe ffi cientsand stellar UV fluxes (see legend in the top panel and meaning of each symbol in Table 2). The standard values are shown in Figs. 2and 3. The standard metallicity is 10 × solar ( ζ =
4. Summary and discussion
We studied the atmospheric composition of GJ 3470b, a warmNeptune that is a promising target for spectral characterisation.In order to prepare and to predict these future observations, weexplored the space of parameters that are uncertain (metallicity,vertical mixing, temperature of the atmosphere, and UV flux ofthe parent star) and computed 17 models. They allowed us toframe the di ff erent compositions that are possible for this planet.In most cases, the CH / CO ratio is above 1, although we foundthat under plausible conditions carbon monoxide becomes moreabundant than methane. This can happen for the highest metal-licity tested (100 × solar), which can be expected for planets witha similar bulk composition as Uranus and Neptune; we foundthat in this case, some models (with a high atmospheric temper- ature) lead to a CH / CO ratio under unity, down to a value of0.04 in the 10 − –1 bar pressure range. We did not explore hottertemperature profiles because without increasing significantly theinternal heat source (like what has been done by Ag´undez et al.2013 for GJ 436b) there is no reason to get such higher temper-ature for a given irradiation. It has already been shown with hotJupiters that a higher temperature leads to a CH / CO ratio lowerthan 1 (e.g. Moses et al. 2011; Venot et al. 2012). Moreover, ourgoal is not to map all the possible ranges of temperature, verticalmixing and metallicity that can produce a CH / CO ratio lowerthan unity, but to address how to get it. Because of quite similarphysical properties, this result can be extrapolated to other warm(sub-)Neptunes such as GJ 436b or GJ 1214b. Recently, a similarstudy has been carried out by Moses et al. (2013), who find alsothat a high metallicity could lead to a CH / CO ratio lower than1 in GJ 436b. While the identification of the C-bearing speciesfrom observations is still under debate for these kind of planets(Stevenson et al. 2010; Madhusudhan & Seager 2011; Beaulieuet al. 2011, with GJ 436b), these results show that even from standard
Fig. 8: Synthetic transmission spectra of GJ 3470b, in terms of apparent planetary radius, computed for all the 16 models of our gridas well as the standard model. Each colour corresponds to a set of metallicity and thermal profile. A colour gradient is then usedto di ff erentiate the eddy di ff usion coe ffi cients and stellar UV fluxes (see legend in the top panel and meaning of each symbol inTable 2). The standard values are shown in Figs. 2 and 3. The standard metallicity is 10 × solar ( ζ = may or may not be the major carbon reservoir, depending on boththe metallicity, the temperature, and the vertical mixing. Indeed,we show in this paper that there is a combined e ff ect of these pa-rameters on the chemical composition of atmospheres. Becauseof quenching, the composition of the middle atmosphere can bea ff ected by temperatures found much deeper than the observa-tions. This carbon anomaly depends on the temperature contrastbetween the probed layers and the quenching level and on the ef-ficiency of the vertical mixing. At metallicity higher than 100 × solar, the vertical vertical mixing can propagate a CO / CH ratioabove unity to the upper layers of the atmospheres. To retrievethe elemental abundances of such atmospheres, self-consistentmodels that couple all these influences are needed. Nevertheless,a very high metallicity ( ≥
100 times solar metallicity) seems tobe a solution to explore to interpret future observations, as it isvery likely for these atmospheres. The synthetic spectra we com- puted indicate that the brightness temperature as well as the tran-sit depth vary significantly with the metallicity and the thermalprofile, so future observations of GJ 3470b may be able to deter-mine the metallicity and the temperature of this planet. Indeed,spectra corresponding to high metallicity models (100 × solar),because of the strong opacities, produce smaller features thanlow metallicity models (1 × solar). On primary transit, we foundthat the 3.3-to-4.7 µ m ratio changes together with the CO / CH ratio. Observations at these wavelengths are a possible way toconstrain this ratio. Acknowledgements.
O.V. acknowledges support from the KU Leuven IDOproject IDO / / ARTHs). Computer time for this study was provided by thecomputing facilities MCIA (M´esocentre de Calcul Intensif Aquitain) of theUniversit´e de Bordeaux and of the Universit´e de Pau et des Pays de l’Adour.
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