Connecting planet formation and astrochemistry: C/O and N/O of warm giant planets and Jupiter-analogs
Alex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, Ralph E. Pudritz
AAstronomy & Astrophysics manuscript no. main c (cid:13)
ESO 2020September 8, 2020
Connecting planet formation and astrochemistry
C/O and N/O of warm giant planets and Jupiter-analogs
Alex J. Cridland (cid:63) , Ewine F. van Dishoeck , , Matthew Alessi , & Ralph E. Pudritz , Leiden Observatory, Leiden University, 2300 RA Leiden, the Netherlands Max-Planck-Institut für Extraterrestrishe Physik, Gießenbachstrasse 1, 85748 Garching, Germany Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada, L8S 4E8 Origins Institute, McMaster University, Hamilton, Ontario, Canada, L8S 4E8Received September 8, 2020
ABSTRACT
The chemical composition of planetary atmospheres has long been thought to store information regarding where and when a planetaccretes its material. Predicting this chemical composition theoretically is a crucial step in linking observational studies to the under-lying physics that govern planet formation. As a follow-up to a study of hot Jupiters in our previous work, we present a populationof warm Jupiters (semi-major axis between 0.5-4 AU) extracted from the same planetesimal formation population synthesis model asused in our previous work. We compute the astrochemical evolution of the protoplanetary disks included in this population to predictthe carbon-to-oxygen (C / O) and nitrogen-to-oxygen (N / O) ratio evolution of the disk gas, ice, and refractory sources, the accretionof which greatly impacts the resulting C / O and N / O in the atmosphere of giant planets. We confirm that the main sequence (betweenaccreted solid mass and atmospheric C / O) we found previously is largely reproduced by the presented population of synthetic warmJupiters. And as a result, the majority of the population fall along the empirically derived mass-metallicity relation when the nataldisk has solar or lower metallicity. Planets forming from disks with high metallicity ([Fe / H] > / O and N / O ratiosshows that Jupiter does not fall among our population of synthetic planets, suggesting that it likely did not form in the inner 5 AUof the solar system before proceeding into a Grand Tack. This result is consistent with recent analysis of the chemical compositionof Jupiter’s atmosphere which suggests that it accreted most of its heavy element abundance farther than tens of AU away from theSun. Finally we explore the impact of di ff erent carbon refractory erosion models, including the location of the carbon erosion front.Shifting the erosion front has a major impact on the resulting C / O ratio of Jupiter and Neptune-like planets, but warm Saturns see asmaller shift in C / O, since their carbon and oxygen abundances are equally impacted by gas and refractory accretion.
Key words. giant planet formation, astrochemistry
1. Introduction
It is now well established that the study of an exoplanetary at-mospheric carbon-to-oxygen ratio (C / O) represents an importantstep in understanding the physical processes that govern planetformation (Öberg et al. 2011; Helling et al. 2014; Madhusud-han et al. 2014; Cridland et al. 2016, 2019a). To date, measure-ments of atmospheric C / O have largely been carried out for hotJupiters and hot Neptunes because their proximity to their hoststar make high signal to noise transmission and emission spectramore easily attainable (Madhusudhan 2012; Moses et al. 2013;Brogi et al. 2014; Line et al. 2014; Brewer & Fischer 2016;Gandhi & Madhusudhan 2018; Pinhas et al. 2019; MacDonald& Madhusudhan 2019).Farther away from their host star are cold Jupiters (a.k.adirectly imaged planets), with orbital radii ≥ ff orts of direct spec-troscopy and interferometry. The GRAVITY consortium withtheir recent e ff ort for β Pic b (at 9.2 AU, Gravity Collaborationet al. 2020), have provided a precise measurement of C / O forthat planet and shown that such a measurement is feasible withthe interferometric mode of the Very Large Telescope (VLTI,alsosee Gravity Collaboration et al. 2019). This method of chemical (cid:63) [email protected] characterization will compliment the e ff orts of the directly imag-ing community which have planned both Early Release Science and Guaranteed Time Observations with the James Webb SpaceTelescope (JWST) for planets at larger distances.At orbital radii between the hot and cold Jupiters are a popu-lation of exoplanets that have not been well studied chemically.These ‘warm’ Jupiters are defined as having orbital radii be-tween 0.5 - 10 AU. They orbit too close to their host star to bedetectable by direct imaging, but far enough away that their de-tection via the transit method would be limited due to their longorbital period. With this definition Jupiter and Saturn, with e ff ec-tive temperatures of 134 K and 97 K respectively (Aumann et al.1969), are classified as ‘warm’ Jupiters. We note that this clas-sification is not based on the e ff ective temperature of the planet(which can depend strongly on internal processes), but insteadonly depends on the planet’s orbital radius.In Figure 1 we show the population of known exoplanetscoloured by their primary discovery method . Additionally we see: see: Extracted from exoplanet.eu Article number, page 1 of 18 a r X i v : . [ a s t r o - ph . E P ] S e p & A proofs: manuscript no. main W a r m J u p it e r s Fig. 1: The current population of confirmed exoplanets extractedfrom http: // exoplanet.eu / on 07 / / ffi cult, and as such there are few examples wheresuch a measurement has been attempted. Regardless, occurrencerate studies of giant planets have shown that Jupiter-analogs (gi-ant planets orbiting between 3-6 AU) should be more abundant( ∼ ∼ ff erentiate between these di ff erent for-mation pathways. Another popular planet formation scenario isgravitational instability, which is thought to lead to planets onwider orbits than our giant planets (see for example Dodson-Robinson et al. 2009).If Jupiter and Saturn formed through planetesimal accretionnear the water ice line, then they would have to undergo a GrandTack (Walsh et al. 2011) to migrate out to their current orbital ra-dius (from 1-3 AU to 5.5 and 9.5 AU respectively). This process,however, is very sensitive to the mass ratio of the two planets andrequires particular orbital radii arrangement to function (Ray-mond & Morbidelli 2014; Chametla et al. 2020). In this way,there could be many solar systems in the galaxy that have plan-ets that underwent similar formation histories to Jupiter, but didnot undergo a Grand Tack. Our simulated population of warm Jupiters orbit at radii inward of 4 AU (see below), and hence canbe thought of as Jupiter- and Saturn- analogs that did not undergoa Grand Tack.This work is a follow up to our previous work that studied thechemistry of a population of hot Jupiters (Cridland et al. 2019c,Paper 1). The population we study here is extracted from thesame population synthesis model as was our hot Jupiter modelin Paper 1 (taken from Alessi et al. 2020). In Paper 1 we founda relation between the atmospheric C / O in these hot Jupitersto the fraction of their total mass that was accreted as solids.We dubbed this relation a ‘main sequence’ of atmospheric C / Oand highlighted the fact that solid accretion - as planetesimalsin our model - are important for determining the bulk chemicalproperties of hot Jupiter atmospheres. The well known (empir-ically derived) mass-metallicity relation (Kreidberg et al. 2014)directly follows from this main sequence. Its prediction - thathigher mass planets have lower bulk metallicity - is explained byour main sequence as being caused by the fact that high massplanets tend to be more dominated by gas accretion than solidaccretion.Does this main sequence - and hence the mass-metallicityrelation - continue to work for warm Jupiters? And can thechemical structure of Jupiter’s atmospheres (and by extensionits formation history) be explained by our planetesimal accretionmodel? Unlike hot Jupiters, the orbital radii of warm Jupitersranges across large chemical gradients in the disk, including thewater ice line (between 2-4 AU) and the carbon erosion front( ∼ ff erence between the two types of planets.In what follows we run a similar method as was reported inPaper 1. We compute the astrochemical evolution in the proto-planetary disks that produce each of the warm Jupiters in ourmodel. We then track the abundance of carbon, oxygen, and ni-trogen that are available to be accreted into the planetary atmo-sphere from the disk gas, ice, and refractory sources. We de-rive the resulting elemental ratios and analyze the connection be-tween these ratios and the physical properties that govern planetformation. We briefly outline our method in §2, report our re-sults in §3, 4 and 5 and discuss the implication on understandingJupiter-analogs in §6. We conclude on this study in §7.
2. Method: combining astrochemistry and planetformation
As discussed in Paper 1, the main feature of our work is thecombination of evolving astrochemical models of protoplanetarydisks with a planetesimal accretion model. In this way, we canprescribe the chemical properties (abundances of carbon, oxy-gen, and nitrogen) in the gas, ice, and refractory components ofthe protoplanetary disk at the same time and place as the grow-ing proto-planet. The population synthesis model that producedour population of planets is described in Alessi et al. (2020).The chemical kinetic code that predicts the gas and ice compo-sition of the disk is based on the work of Fogel et al. (2011) andCleeves et al. (2014), but has been modified for our purposesand described in Paper 1. The chemical model that describesthe chemical composition of the refractory component (dust and
Article number, page 2 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry planetesimals) was introduced in Cridland et al. (2019a) and in-cludes the possibility of carbon erosion in the inner disk. Weoutline some of the important concepts here, for more detailssee Cridland et al. (2019c) and Alessi et al. (2020).
As a planet grows it evolves through the mass-semi-major axisdiagram in Figure 1 through a combination of solid accretionfollowed by gas accretion (increasing vertically in Figure 1) andthrough planetary migration (decreasing horizontally in Figure1). Alessi et al. (2020) uses the planetesimal accretion paradigm(Pollack et al. 1996; Ikoma et al. 2000; Kokubo & Ida 2002;Ida & Lin 2004; Alibert et al. 2005) to build the initial plane-tary core.The rate of growth is dictated by the surface densityof planetesimals which we take as being equal to the dust sur-face density at any given time. Our dust surface density evolvesaccording to the semi-analytic model of Birnstiel et al. (2012),primarily through radial drift that quickly empties the outer diskof dust Planetesimal formation dictates that the core growth rate is(Pollack et al. 1996): dM plnt dt = dM c dt = M c τ c , acc (cid:39) M c . × (cid:32) Σ dust − (cid:33) (cid:18) a (cid:19) − / (cid:32) M c M ⊕ (cid:33) − / (cid:32) M s M (cid:12) (cid:33) / × (cid:32) Σ gas . × gcm − (cid:33) − / (cid:18) a (cid:19) / (cid:32) m g (cid:33) / − g yr − , (1)for a planet core of mass M c currently orbiting at a around a starof mass M s accreting planetesimals of (assumed constant) mass m . The solid surface density Σ dust is determined from the Birn-stiel et al. (2012) model, while the gas surface density Σ gas is de-termined by a semi-analytic model based on Chambers (2009) .Once the planet is su ffi ciently large, it clears the majority ofits ‘feeding zone’ of planetesimals and core growth is drasticallyslowed (Ida & Lin 2004) . Particularly since the planet migratesthrough the disk it can continue to accrete planetesimals into itsproto-atmosphere, delivering any carbon and oxygen containedwithin the planetesimal (see below). Due to the reduced plan-etesimal accretion rate the core begins to cool - which enables astage of gas accretion to begin (Ikoma et al. 2000). Gas accre-tion begins at a very slow rate, limited by the Kelvin-Helmholtztimescale (Ida & Lin 2004) such that the mass of the planetevolves as: dM plnt dt = dM gas dt + dM c dt , (2)where dM gas / dt = M plnt / t KH , and dM c / dt proceeds at the afore-mentioned reduced rate. The Kelvin-Helmholtz time scales with In principle the dust surface density also evolves due to the produc-tion of planetesimals (for example see Voelkel et al. 2020), however ourcurrent implementation is limited as it does not allow such a connec-tion. In practice such a connection will lead to less e ffi cient planetesi-mal formation and slower initial core growth. Overall this change willnot drastically change the main conclusions of the paper. But see Alessi & Pudritz (2018) for the full details of the disk model Practically speaking, we increase τ c , acc by two orders of magnitudein this stage. the total mass of the planet (Ikoma et al. 2000; Alessi & Pudritz2018): t KH = yr (cid:32) M plnt M ⊕ (cid:33) − . (3)In the population synthesis model of Alessi et al. (2020) gasaccretion is assumed to halt when the planet reaches some fi-nal mass. This final mass is proportional to the gap openingmass with a proportional constant that is generated from a log-normal distribution as part of the population synthesis model.While the general problem of late stage gas accretion remainsunsolved, our approach captures the essential points of morecomplex physical models of the end state of gas accretion (seefor example D’Angelo et al. 2010; Cridland 2018).The population synthesis model of Alessi et al. (2020) sto-castically selects a set of the initial disk mass, disk lifetime, andmetallicity to initialize the radial distribution of the gas and dustsurface densities, the gas temperature, and control the evolutionof the disk’s mass accretion rate. The initial disk (gas) mass anddisk lifetime are selected from a log-normal distribution withan average of 0.1 M (cid:12) and 3 Myr respectively. Their distributionhave a 1 σ range of 0.073-0.137 M (cid:12) and 1.8-5 Myr respectively.The disk metallicity ([Fe / H]) is selected from a normal distri-bution with an average of -0.02 (marginally sub-solar) and a 1 σ range of -0.22-0.18. The disk metallicity sets the initial gas-to-dust ratio, using the expression: f gtd = f gtd , [Fe / H] , (4)where f gtd , = .
01 is the typical interstellar medium (ISM) gas-to-dust ratio, such that the radial distribution of dust mass is: Σ dust ( r , t = = f gtd Σ gas ( r , t = , (5)where Σ gas is derived from the disk model of Chambers (2009).Changes in the initial dust surface density impact the rate of theinitial core growth through the availability of core-building ma-terial at a given ratios.In Paper 1 we derived the total mass evolution for the setof generated disks and compared them to recent observationalsurveys of young stellar systems. We found that the populationof disks used by Alessi et al. (2020) reproduced the high-massend of the observed population of protoplanetary disks, and gen-erally agreed better with the population of Class 0 / I objects ofTychoniec et al. (2018). In this way our generated disks can bethought of as beginning as marginally Class I objects (similar toHL Tau, ALMA Partnership et al. 2015) when we start planetformation, although we ignore the impact of any remaining en-velope.As previously mentioned, growing planets migrate to smallerorbital radii through interactions with the protoplanetary diskgas (Lin & Papaloizou 1986; Ward 1991). Planet migration isan ever growing topic since it was first pointed out that the typi-cal timescale for Type-I migration (for low mass planets that donot open gaps) is too short compared to the typical planetesimalaccretion timescale to explain the known population of exoplan-ets (Ward 1997). A way to remedy this discrepancy is to eitherslow planetary migration, or speed up planetary accretion. Theformer solution, typically called ‘planet trapping’ posits that dis-continuities in the gas density, temperature, or dust opacity canlead to a change in the strength of the torques responsible for We are using the typical notation where [Fe / H] ≡ log (Fe / H) − log (Fe / H) (cid:12) , such that [Fe / H] (cid:12) = & A proofs: manuscript no. main migration (Masset et al. 2006). This change can slow the migra-tion rate, stop it completely, or even reverse its direction (Mas-set et al. 2006; Hasegawa & Pudritz 2010, 2011; McNally et al.2018, 2020).In our planet formation model we use the three planet trapsoutlined in Hasegawa & Pudritz (2011) - the water ice line, thedead zone edge, and the heat transition - to dictate where thegrowing planet must be, up until the point where it opens a gapin the disk (discussed below). The particular trap which housesa given planet dictates where that planets begins its core forma-tion. The typical hierarchy is the water ice line being the mostinward trap, the dead zone next, and the heat transition begin-ning the farthest from the host star. The farther from the host stara planets begins the less material is available for core growth,slowing this initial phase of accretion.Each of the aforementioned planet traps rely on a di ff erenttransition in the properties of the disk. The water ice line is atransition in the dust opacity located at the sublimation tempera-ture (typically ∼
170 K) of water ice. At lower temperatures, wa-ter is frozen out onto the dust grains, and their resulting opacity islarger than at larger temperatures where the water is in its vapourphase. Cridland et al. (2019b) investigated this process in detailand confirmed that such a transition does indeed create a planettrap for the water ice line. Also in Cridland et al. (2019b), thedead zone edge (which represents a transition in the disk turbu-lent α ) and the heat transition (where the primary heating mech-anism changes from viscous to direct irradiation, Hasegawa &Pudritz 2010; Lyra et al. 2010) are tested and similarly found toproduce planet traps. All three of these traps evolve to smallerradii as the disk loses mass due to its own accretion onto thehost star and cools as a result. Hence proto-planets continue tomove inward as they grow, but on a much longer timescale (theviscous timescale) than they do in the standard picture of Type Imigration.Once the planet is su ffi ciently large it opens a gap in its disk(Crida 2009). At which point Type I migration is suppressed andis replaced by Type II migration (Lin & Papaloizou 1986). Dur-ing this stage of planetary migration, the planet acts as an inter-mediary for the angular momentum transport through the disk,and generally migrations inward on the viscous timescale. As weoutlined in Paper 1, when the mass of the planet exceeds the gapopening mass then we assume that its radial evolution proceedson the viscous timescale.Apart from adjusting the rate of migration, other methods ofsaving planets from this ‘Type-I problem’ have been proposed.These include pebble accretion, which posits that the core ini-tial grows through the accretion of cm-sized pebble - a processthat can increase the rate of initial core growth by a factor of ∼ ffi cient time for the growing planet to migrate intothe host star.A final method could simply be that planet formation startsearlier than previously assumed. Recent surveys of protoplane-tary disks (also known as Class II objects) have shown that thereis insu ffi cient dust currently (by 1-3 Myr) available to producethe core of a Juptier-like planet, let alone multiple planets (Ans-dell et al. 2016; Manara et al. 2018; Tychoniec et al. 2018, 2020).Younger Class 0 / I objects, however, have been found to containat least 20 × the dust in Class II objects (Tychoniec et al. 2020).This finding suggests that (at the very least) there is significant planetesimal formation on going in young stellar systems. Plan-ets forming in these systems would likely undergo planet mi-gration, however due to the complex nature of these embeddedsystems the relevant torques have not yet been characterized.Here we continue to use our planetesimal accretion and mi-gration prescriptions developed in our past work (Hasegawa &Pudritz 2013; Alessi et al. 2017; Cridland et al. 2016) and leavethe implications of the aforementioned models to future work. We include an astrochemical model for the evolution of boththe volatile and refractory components of the disk carbon, oxy-gen, and nitrogen. The volatile component of the disk is pri-mary made up of H O, CO , and CO gas and ice - frozen ontodust grains. The disk volatile evolution is computed using theMichigan chemical kinetic code featured in Fogel et al. (2011)and Cleeves et al. (2014), and previously used in Cridland et al.(2016, 2017b). It computes the disk chemistry in a 1 +
1D fash-ion, assuming vertically isothermal gas and dust, and hydrostaticequilibrium. The chemical evolution is initialized with elemen-tal ratios O / H vol = . × − , C / H vol = . × − , and N / H vol = . × − assuming an inheritance scenario. Under thisscenario the carbon and oxygen begin in their molecular form(largely CO, frozen H O) while nitrogen is initialized primarilyin atomic N with ∼
10% molecular N . Under these conditions,the volatile C / O = . / O = . × − / s.The chemical interaction between the dust grain surface andthe gas represents a crucial driver for chemical change. Thechemical network underlying the Michigan chemical code in-cludes a limited set of grain surface reactions, primarily focusedon the production of molecular hydrogen and water. More com-plex grain-surface reactions involving carbon-bearing species (asseen in Walsh et al. 2015; Eistrup et al. 2018; Bosman et al.2018; Krijt et al. 2020), is left out of the chemical model as theytypically become relevant at lower temperatures, outside the CO ice line ( ∼
10 AU). None of our forming warm Jupiters buildtheir atmospheres that far out in the disk. We compute an averagedust grain size for our chemical calculation based on the outputfrom the a semi-analytic model of dust evolution (Birnstiel et al.2012), weighted by the number density of dust grains. For animplementation of this method see Cridland et al. (2017b), thetypical average grain size is ∼ . µ m.The version of the Michigan code that was used in the afore-mentioned works assumed a passive disk model that remains un-changed over the whole evolution of the chemical system. In Pa-per 1 we introduced a new version of the code that allowed thedisk gas density and temperature to evolve in tandem with thechemistry. This new method introduced new chemical featuresthat did not appear in the passive version of the code (see Paper1). A large reservoir of carbon and oxygen also exists in refractorysources - planetesimals and pebbles - in protoplanetary disks(Pontoppidan et al. 2014). These refractory sources are e ff ec-tively chemically neutral, and do not contribute to the bulk el-emental abundances inferred by (sub)millimeter studies of pro-toplanetary disks. A possible exception to this trend is carbon,which has shown evidence in our own solar system for an in- Article number, page 4 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry
AB CD E F
Fig. 2: Evolution and radial distribution of midplane C / O in the gas and solids in one of the disk models used for this work.Specifically we show the chemistry of the disk in the Reset scenario of refractory erosion which governs the high C / O early on indisk life ( A ). We similarly note the region of the disk with high and low water vapour abundances ( B and D respectively), the carbonpoor region due to refractory erosion ( E ), and a region where gaseous CO is converted to frozen CO ( C ). The carbon-richer region( F ) exists outward of the carbon erosion front. With this colour scheme, orange denotes carbon-rich regions (C / O >
1) while bluedenotes carbon-poor regions (C / O < / O = . / O = / Si)of the ISM is approximately 6, and assuming that the majorityof the silicates have the SiO group, then the refractory C / O = / O (as discussedin Cridland et al. 2019a). We assume that there is no refractorycomponent for nitrogen.The Earth is depleted in carbon (relative to silicon) by threeorders of magnitude when compared to the carbon-to-silicon ra-tio of the ISM. Moreover, main-belt asteroids show between oneand two orders of magnitude depletion in their C / Si relative tothe ISM. This depletion prompted Bergin et al. (2015) to pro-pose that some chemical process was eroding the carbon o ff ofthe dust early in the life of our natal disk - consequently enhanc-ing the gas phase carbon. The chemical processes responsiblewere investigated by Lee et al. (2010), Anderson et al. (2017)and Klarmann et al. (2018) but no concrete answer was found.The chemical implication of such a process was investigated by Wei et al. (2019). They found that the majority of the excess car-bon stayed in the gas phase as HCN and hydrocarbons, with only ∼
1% of the carbon condensing back onto the grains in the formof icy long-chain hydrocarbons.We include an analytic prescription that describes the distri-bution and evolution of carbon from the refractory sources intothe gas phase. The distribution of the excess gaseous carbon wasderived in Cridland et al. (2019a) and was based on an empiricalfit to solar system data by Mordasini et al. (2016). There are twomodels which describe the distribution of excess carbon: the ‘re-set’ and ‘ongoing’ models. As outlined in Cridland et al. (2019a)these models represent simple but opposing methods for erod-ing the carbon o ff the dust grains into the gas. The reset modelassumes that during the initial collapse of the molecular clouda thermal event - similar to a FU Ori outburst - sublimates thedust in the young protoplanetary disk, releasing their contentsinto the gas phase. As the disk returns to its natural temperaturethe silicates and iron would recondense into dust, but the carbonwould not. This model assumes that all of the erosion necessary Article number, page 5 of 18 & A proofs: manuscript no. main to explain today’s depleted C / Si of Earth and main-belt asteroidshappens at (e ff ectively) t =
0. The carbon that would be releaseddue to this process would then advect along with the rest of thegas and dust in the disk into the host star.The opposing model, the ongoing model, assumes that thereis some ongoing chemical process that is continually erodingcarbon o ff of dust grains in the protoplanetary disk. This process- while not concretely identified - would continually maintainthe excess carbon in the disk, as carbon-rich dust grains radiallydrift into the region of the disk where the erosion can happen(a few AU, Anderson et al. 2017). The main di ff erence betweenthese two models is that the excess carbon vanishes in the resetmodel after less than 1 Myr (Cridland et al. 2019a, but also seeFigure 2) while the excess carbon survives the full lifetime of thedisk in the ongoing model. In Figure 2 we show the radial distribution and evolution of themidplane C / O for both the gas and the solids (ice and refrac-tories) for a single disk model over a span of just over 1 Myr.We note a few points of interest: first we have included the re-set model of Cridland et al. (2019a) which greatly enhances thegaseous carbon content at the expense of carbon from the refrac-tory component. By approximately 0.8 Myr the extra carbon hasmoved completely into the host star and is no longer available toaccrete into any forming proto-planets. Had the ongoing modelbeen included in Figure 2, the carbon rich region A would haveextended over all time in much the same was as the carbon poorregion E does on the right panel. Note that both the reset andongoing models result in the carbon poor region E because theyboth lead to the required depletion in refractory carbon seen cur-rently in the inner solar system. The radius where the transitionbetween carbon-richer and carbon poor solids - the carbon ero-sion front - begins at 5 AU in the fiducial carbon erosion model.The location of the front remains fixed in the ongoing model sothat the excess carbon in the gas phase perfectly reflects the de-pletion of carbon in the solid phase (transition radius betweenregions E and F). In the reset model, since the excess carbonadvects with the bulk gas in the protoplanetary disk the erosionfront representing the excess gaseous carbon moves inward. Thisevolution can be seen in Figure 2 as the curved white contour be-tween regions A and B. Later in this work we explore the impactof varying the location of this erosion front.When the extra carbon due to the reset refractory erosionmodel advects away from a given disk radius the gas is returnedto a lower C / O which is indicative of the initial C / O used in ourchemical model (0.4). In region B, inward of the water ice line,the same final C / O can be found as was used as initial condi-tions. This region slowly shrinks as the disk cools, and the waterice lines moves inward. Outward of the water ice line, in re-gion D, water is primarily in the ice phase, which brings the gasC / O up to a value closer to unity. The carbon and oxygen carriermolecules are dominated by CO in this region, since we only in-clude CO production in the gas phase - which is generally muchless e ffi cient than it is in the ice phase (as discussed in Paper 1).We do see a short period of CO production in region C whichis produced in the gas before quickly freezing out onto the dustgrains at the cost of frozen H O and gaseous CO. As such there isa local decrease in C / O with a subsequent increase of C / O in thesolids. This process has already been explored by Eistrup et al.(2016) and was similarly observed in Cridland et al. (2019c).However the process lasts only for a few 10 years before the disk becomes too cold in that region for it to occur e ffi ciently.The slightly more carbon rich region just below C is caused by asmall quantity of HCN and long-chain hydrocarbons being pro-duced in the gas phase. We show all of the most abundant gas andice species in the Appendix figures A.1 and A.2 respectively.While the left panel of Figure 2 shows C / O for the gaseousdisk, the right panel shows C / O for the solids. This panel in-cludes C / O for both the ice and refractory sources (dust and plan-etesimals) but it is dominated by the refractory sources (apartfrom the small feature mentioned above). This is why it showsmuch less structure than in left panel - including the decrease inC / O that would accompany the increases seen between regionsB and D in the left panel. Instead it mainly shows the transitionregion inward of the carbon erosion front - the radius where weassume the erosion begin. The carbon refractory erosion modelassumes ISM values of carbon (C / H ref = . × C / H vol ) outwardof the carbon erosion front (assumed to be 5 AU in our fiducialmodel, more below), while rapidly and smoothly depleting thecarbon by a factor of 1000 inside of 5 AU. The functional formof this erosion model was derived empirically by Mordasini et al.(2016) and is shown in Cridland et al. (2019a). As already discussed, the protoplanetary disk has two sources ofcarbon, oxygen, and nitrogen for the growing proto-planet. If thegas accretes onto the planet at a rate of dM gas / dt then the totalrate of change of any element is simply: dXdt = µ m H dM gas dt × ( X / H ) gas , (6)where X / H is the abundance of element X relative to hydrogenas computed by our chemical model (volatiles and carbon ero-sion combined), and µ m H is the average weight of a gas particle.In principle micron-sized dust grains will be accreted into the at-mosphere along with the gas, since they are well coupled. How-ever along the midplane of the disk (from where we assume thematerial is accreted) these grains make up a very small fractionof the total mass of the dust (less than 0.1%).Recently, Cridland et al. (2020) explored the impact of verti-cal accretion on the chemical composition of exoplanetary atmo-spheres and found that the micron-sized grains can play a role,but only if material is accreted from between one and three gasscale heights. In that case the grains typically brought oxygen-rich ices to the growing planet, generally lowering the atmo-spheric C / O. For simplicity we ignore the impact of vertical ac-cretion, and hence assume that the micron-sized grains to notcontribute to the total mass of the planet nor the chemical struc-ture of its atmosphere.Conversely we do account for the mass of carbon and oxygenfrozen or locked in refractories of the planetesimals that accreteinto the proto-atmosphere. For this, we follow the work of Crid-land et al. (2019a) with a simple prescription based on the moredetailed calculations of planetesimal survival in planetary atmo-spheres of Mordasini et al. (2015). We choose an atmosphericmass cuto ff of 3 M ⊕ below which an incoming planetesimal sur-vives its trip through the atmosphere, delivering its refractorymaterial directly to the core . The planetesimal should, however,heat up su ffi ciently to release any volatiles incorporated in theform of ice. We assume that all volatile (ice) species are releasedas the planetesimal passes through the atmosphere. We assume that the core does not contribute to the observed chemicalcomposition of the atmosphere.Article number, page 6 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry
Fig. 3: Typical evolution of atmospheric C / O as a proto-planetgrows (top panel). We show the results for each of the exampleplanets for each of the ongoing (solid line) and reset (dashedline) carbon erosion models. In addition we show the mass andorbital radius evolution of the same planets (bottom panel).When the atmospheric mass exceeds 3 M ⊕ Mordasini et al.(2015) show that planetesimals (regardless of initial size) willcompletely evaporate in the atmosphere. For planets that exceedthis atmospheric mass we assume that all refractory mass is re-leased and e ffi ciently mixed throughout the atmosphere - therebyimpacting the bulk C / O of the planet. We follow Mordasini et al.(2016) in assuming that the relative mass fractions of 2:4:3 forcarbon (in regions with no carbon erosion), silicates, and ironsrespectively. As such silicates make up 4 / /
3. Results: Individual formation and chemicalinheritance
To get a sense for the typical evolution of C / O in our growingplanets we show, in Figure 3, the temporal evolution of C / O (toppanel) and the orbital radius, and planet mass (bottom panel).The planets begin their evolution as large planetary embryoswith M = ⊕ . They slowly build up solid mass by accretingplanetesimals and a small amount of a gas envelope, building theinitial core of M ∼
10 M ⊕ in ∼ . ∼ ffi ciently largethat they can begin to quickly accrete gas, eventually doing so inan unstable manner. Once the planet has reached its prescribedmaximum mass (choosen from a distribution prior to each cal-culation) its evolution is stopped.During the initial build up of the core the ‘atmospheric’ C / O is dominated by the release of volatiles frozen onto incomingplanetesimals as they pass through the early proto-atmosphere.Planets forming near or inward of the water ice line are under-abundant in volatiles, but can contain small amounts of hydro-carbons. These, when combined with the small amount of gas(which is rich in water vapour) that is accreted at this stage leadsto the low atmospheric C / O for the first ∼ Myr. Planets formingoutward of the water ice line accrete planetesimals rich in frozenwater which drives very low initial C / O. All four of these planetsgrow in the transition region of the carbon erosion model, mean-ing that planets forming closer to the host star accrete planetes-imals with less carbon than planets forming farther away. Oncetheir proto-atmosphere is su ffi ciently large, refractories begin tocontribute to the atmospheric C / O and hence planets forming far-ther away (green line) see a steeper increase in C / O than planetscloser in (red and blue lines) after ∼ . / O slightly reduced prior to the beginning of morerapid gas accretion.Once gas accretion starts to dominate the mass evolution,the atmospheric C / O begins to evolve towards the local C / O ofthe protoplanetary disk, this includes the impact of the carbonerosion model. In the case of the reset model (dashed line) theatmospheric C / O evolves towards ∼ . ∼ . / O because their gas accretion is haltedby the photoevaporating disk. In the case of the ongoing modelthere is extra carbon in the gas that is accreted by the growingplanets, enhancing their atmospheric C / O.Because of the unstable gas accretion in our formationmodel, most of the C / O evolution happens over a short periodof time - as the bulk of the atmosphere is accreted. As such,giant planets freeze in the chemical composition of the gas attheir location in the protoplanetary disk where their unstable gasaccretion occurred. Lower mass planets (orange line) do not un-dergo unstable gas accretion and as such the history of their solidaccretion can be more important to their final atmospheric C / O.
4. Results: warm Jupiters compared to hot Jupiters
To follow up our study of hot Jupiters in Paper 1, a natural ques-tion to ask was whether these synthetic warm Jupiters share anychemical similarities to the hot Jupiters. To that end we follow That is, the C / O of the envelope that has collected around the proto-planet Article number, page 7 of 18 & A proofs: manuscript no. main a similar trajectory as in Paper 1 here and outline some generalproperties of our population of planets.
In Figure 4 we show the distribution of the final orbital radius(assuming circular orbits) and mass of the population of warmJupiters from Alessi et al. (2020). These planets orbit between0.5 - 5 AU, with the vast majority orbiting between 1 - 4 AU. Themasses range from a third of Saturn’s mass ( ∼ . Jupiter ) up to ∼
30 M
Jupiter . As such, this population of planets extends into themass range that is typically associated with brown dwarfs stars.In what follows we will not di ff erentiate between brown dwarfsand planets in our analysis, since this distinction is irrelevant forour analysis of bulk elemental abundance ratios.We colour code each planet by the planetary trap from whichit originates. The majority of these planets arise from the waterice line trap (blue). This trap is an optimal location for the gen-eration of planetesimals (Dra¸ ˙zkowska & Alibert 2017), whichis depicted in our model by an enhancement in the dust surfacedensity at the water ice line caused by a ‘tra ffi c jam’ e ff ect (seePinilla et al. 2016; Cridland et al. 2017a, for a discussion of thise ff ect). The dead zone edge (orange) generally begins fartheroutward than the water ice line, and generally leads to planetswhich end their formation farther from their host star than thosefrom the water ice line. A few exceptions to this trend exist, andthese planets generally emerge in disks with longer lifetimes.In our model, longer lived disks also evolve slower, hence thesurface density and temperature reduce slower which keeps thedead zone edge at larger radii for longer. Planets trapped at thedead zone edge see lower densities than planets that begin closerto the host star and they can migrate further inward before theybegin to accrete large amounts of gas which ends their formationcloser to the host star than the average dead zone planet.For a similar reason, planets originating from the heat tran-sition (heat tran, green) trap tend to be larger and closer-in thanthe majority of the water ice line planets. Generally speaking,planets forming in the heat transition trap produce super-Earthplanets (Alessi et al. 2020). The planets formed here grew fromprotoplanetary disks at the low-mass end of our disk mass distri-bution which caused the initial location of the heat transition tobe closer to the host star than would be usual. In our model, theheat transition evolves on the viscous timescale, while the deadzone edge evolves slightly faster (Alessi et al. 2017). Because ofits slower radial evolution, more time passes before the growingplanet reaches a higher density environment where its growthcan proceed more quickly. As such its final radii are generallyfarther inward of the bulk of the water ice line planets. As already mentioned, our population of warm Jupiters does notinclude Jupiter and Saturn in their current orbital states. Howeverour population does include a fair number of planets in a rangeof orbital radii indicative of Jupiter just prior to undergoing apossible Grand Tack (Walsh et al. 2011). As such we considerJupiter-analogs to be planets with a similar mass as Jupiter, but atan orbital radius closer to their host star - having missed a GrandTack. Either because its planetary system lacks a companion, orbecause the mass and / or orbital radii ratios were not tuned tocomplete a successful Grand Tack. Fig. 4: Final mass and orbital range of synthetic planets fromthe (Alessi et al. 2020, APC) population of planets. The colourcoding here (and throughout) denotes the planet trap in which theplanet initially grew. Generally ice line planets (blue) start closerthan the dead zone (orange) and heat transition (green) planets.The population of warm Jupiters exist predominately between1-4 AU. In Figure 5 we show the resulting C / O for our population ofwarm Jupiters, the Jupiter-analogs are highlighted with orangepoints. The main di ff erence in the resulting atmospheric C / O be-tween the reset and ongoing carbon erosion models is a horizon-tal shift in C / O for the majority of planets (although not all, ex-plored below). The ongoing model, with its constant productionof excess carbon, results in more carbon-rich planets comparedto the reset model. There is a small discrepancy in this observa-tion for a few planets that do not migrate inward of the erosionfront (at 5 AU) until after they have accreted the majority of theiratmosphere. These planets are di ffi cult to see here, but are high-lighted and discussed in the following section.We include an estimated C / O for Jupiter based on the mea-surements outlined in Asplund et al. (2009) and the recent oxy-gen measurement of Li et al. (2020). The error bars on this mea-surement are computed with the maximum and minimum C / Hand O / H provided by the 1 σ uncertainty in the above papers.Clearly there is a wide range of possible C / O based on these un-certain measurements. Including these uncertainties, Jupiter ismost consistent with the Jupiter-analogs in the ongoing carbonerosion model. This suggests both that Jupiter accretes the ma-jority of its gas inward of the carbon erosion front (inward ofits current orbit), and that there was an ongoing chemical pro-cess responsible for the processing of carbon o ff of dust grainsthroughout the life of the solar nebula. This conclusion wouldhold if only carbon and oxygen are considered. Nitrogen and thenoble gasses, however, have recently suggested that Jupiter’s ini-tial growth (and at least a fraction of its gas accretion) occurredoutward of the N ice line - at tens of AU (Bosman et al. 2019;Öberg & Wordsworth 2019). As is discussed in more detail be-low, there is a clear discrepancy between Jupiter’s C, N, and Oelemental abundances when they are combined in comparisonwith the presented population of warm Jupiters.In addition to Jupiter we have included the recent measure-ment of β Pic b made by Gravity Collaboration et al. (2020). β Article number, page 8 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry
Fig. 5: The resulting C / O for our population of planets as a func-tion of mass (black points). We note the Jupiter-analogs from ourpopulation in red and observational data in grey. The data pointfor β Pic comes from Gravity Collaboration et al. (2020), and thedata for Jupiter from Asplund et al. (2009) and Li et al. (2020).The gray line accompanying Jupiter’s C / O (noted with J ) showsthe range of possible values based on the 1 σ uncertainty of C / H(Asplund et al. 2009) and O / H (Li et al. 2020).Pic b is a ∼
12 M
Jupiter planet orbiting near 10 AU around itshost star. Its C / O was determined from a pair of retrieval modelsbased on interferometric observations of its atmosphere by Grav-ity Collaboration et al. (2020). Given its orbital radius, it lieson the outer edge of what we defined as warm Jupiters. Indeed,planetesimal accretion in general, and our formation models inparticular struggle to make large planets at these larger radii - anda formation scheme like pebble accretion (Ormel & Klahr 2010;Johansen et al. 2007; Bitsch et al. 2015) may be better suitedto explain their existence. Regardless we find that its measuredC / O is consistent with planets that formed in the reset carbon re-fractory erosion model. This fact argues for its formation to haveoccurred in a region of the disk outward of both the water ice line and the refractory carbon erosion front. For more discussionregarding the carbon erosion front see Section 6.2. Outward ofthe carbon erosion front the gas is less carbon rich than it couldbe inward of the front, but the solids are more carbon rich (recallFigure 2, right panel).
As in Paper 1, we wish to understand the cause of the structurewe see in Figure 5. One major conclusion from Paper 1 was theC / O main sequence, which shows a tight inverse correlation be-tween the fraction of the total mass made up of solids with theatmospheric C / O.In Figure 6 we show the same main sequence as presented inPaper 1, with the data from Paper 1 included as faded points. Aswas done in Paper 1, we di ff erentiate between di ff erent planetmasses; the mass bins are: low mass (M <
10 M ⊕ ), Neptune-like (10 M ⊕ < M <
40 M ⊕ ), Saturn-like (40 M ⊕ < M <
200 M ⊕ ),Jupiter-like (200 M ⊕ < M <
790 M ⊕ ), and super-Jupiter (790 M ⊕ < M). We find that the population of warm Jupiters tend to fol-low the main sequence up to high C / O where it then falls awayfrom the trend. The high C / O end is dominated by the most mas-sive planets (super-Jupiters) with masses even higher than wereobtained in Paper 1. For these most massive planets, their atmo-spheric chemistry is determined almost entirely by gas accretion(with solid accretion contributing less than 1%). As such, in thereset model (bottom panel) one group of the massive planets tendtowards C / O of the disk volatiles used in the chemistry calcula-tion (vertical dashed line) while the other tends to higher C / O.This trend is linked to where the planets accreted their gas - in-ward of the water ice line the C / O tends to the disk C / O whileoutward of the water ice line the C / O tends to unity. These group-ings are not discrete, however, and there are planets which seemto exist between the two extremes. We explore these groupingsin more detail in section 6.1. The same structure can be seenfor the ongoing model (top panel) but it is shifted to higher C / Ocaused by the excess carbon that remains in the gas for the wholelifetime of the disk.In Figure 7 we present the mass-metallicity relation for thepopulation of warm Jupiters and compare them directly to thepopulation of hot Jupiters from Paper 1. We find that (as in Paper1), the mass-metallicity relation directly follows from the mainsequence - that is, the atmosphere metallicity falls with increas-ing planet mass. There is, in addition, a similar turn o ff of themain trend at the higher mass end, with massive planets (of atleast a few Jupiter masses) tending towards a metallicity of be-tween 0.4-0.5 × solar. The low mass end of the population alignvery closely to a region of O / H - mass parameter space that weattribute to planets having accreted their gas outward of the wa-ter ice line (in an oxygen-poor region of the gas disk). In generalmost of the lower mass warm Jupiters sit lower than planets ofsimilar mass in the hot Jupiter population suggesting that this isa general trend. This is a reflection of the fact that warm Saturnand Neptune planets largely accreted their gas outside of the wa-ter ice line. We explore further causes of scatter seen here in afollowing section.
5. Results: exploring different elemental ratios
While the C / O ratio gives an important view of planet formation,it is not the only elemental ratio that can shed light on the prob-lem. After carbon and oxygen, nitrogen is the next most abun-dant in the solar system. As discussed in Bosman et al. (2019),nitrogen chemistry is generally very simple - since the majority
Article number, page 9 of 18 & A proofs: manuscript no. main
Fig. 6: The C / O main sequence for both the ongoing and re-set carbon erosion models. The vertical dashed lines show C / O = . / O end the population appears to drop away fromthe trend found at lower C / O. The planets in this part of the fig-ure are very large mass and are dominated by gas accretion. Thecolour of each point denotes the trap from which the planet orig-inated: ice line (blue), dead zone (orange), and heat transition(green).of the element remains in its molecular form N at gas temper-atures lower than ∼
500 K while at higher temperatures NH becomes dominant (see Figure A.1). Apart from this transition,there is the small build up of HCN that was previously men-tioned, which can hold on the order of 1% of the total nitrogen.Recall that we attribute this HCN enhancement to the carbon richregion just below region C in Figure 2.In Figure 8 we explore the role that nitrogen can play in un-derstanding the physics of planet formation. Here we plot the Fig. 7: The mass-metallicity relation for the (Alessi et al. 2020,APC) population of warm Jupiters, compared to the hot Jupiterpopulation from Paper 1 (faded points). The solar system gi-ants (inferred by methane abundance and taken from Kreidberget al. 2014), and for WASP-43 b (Kreidberg et al. 2014), GJ 436b (Morley et al. 2017), and HAT-P-26 b (MacDonald & Mad-husudhan 2019) (inferred from their water abundance) are alsoshown. In addition we include the recent O / H measurement forJupiter by Li et al. (2020) to show that, within uncertainty, therelation is independent of using C / H or O / H to determine themetallicity. We include O / H for our synthetic population and findthat they follow the relation up to a mass of a few Jupiter masseswhere they appear to flatten out. The colour of each point denotesthe trap from which the planet originated: ice line (blue), deadzone (orange), and heat transition (green). This is a recreation ofFigure 12a. from Paper 1.nitrogen-to-oxygen ratio (N / O) against the C / O ratio for our pop-ulation of warm Jupiters and for both the reset (square) and on-going (circle) models. Note that since we separately run the resetand ongoing models for each planet formed in our model, eachplanet has two points on this figure - one for each carbon erosionmodel. We immediately see that the majority of planets fall ontwo straight lines - one for each of the carbon erosion models.Given that the slope of these lines is the nitrogen-to-carbon ratio(N / C) we can say that for the planets in our model, the N / C ratiois e ff ectively constant. There are a number of planets, however,that do not conform to this rule and they can be grouped intocarbon-rich planets in the reset model and carbon-poor planetsin the ongoing model.We additionally place Jupiter on Figure 8 using the elemen-tal abundances reported in Asplund et al. (2009) and the newoxygen abundance from Li et al. (2020). While it seemed to beconsistent with our population of Jupiter-analogs accreting fromthe ongoing model in Figure 5, Jupiter does not fit well into theirC / O vs. N / O parameter space. Within uncertainty, Jupiter’s C / Oand N / O ratios are consistent with the set of planets forming un-der the reset carbon erosion model. The inconsistency betweenits fit in the mass-C / O parameter space (more consistent with theongoing model) and its fit here (with the reset model) suggeststhat its formation is inconsistent with the formation of warm-Jupiters through planeteimsal formation presented here.This inconsistency provides further evidence that Jupiterformed farther outward in the disk than is achieved by our
Article number, page 10 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry
Fig. 8: The cross reference of the C / O with N / O for the popula-tion of warm Jupiters. We show here both the reset (squares) andongoing (circles) models which generally lie on a pair of straightlines. The slope of these lines represent the elemental ratio N / Cwhich must be generally constant for most planets. The blackpoint and error bars denote Jupiter’s C / O and N / O ratios alongwith estimates for possible ranges. Due to the uncertainty in ob-served elemental abundances Jupiter is consistent with planetsfrom the reset model but not with the ongoing model. The colourof each point denotes the trap from which the planet originated:ice line (blue), dead zone (orange), and heat transition (green).model, furthering a growing belief that was proposed in Öberg& Wordsworth (2019) and Bosman et al. (2019). They placeJupiter’s initial formation location outward of the N ice line attens of AU away from the Sun, likely formed through the ac-cretion of icy pebbles. Here we note that while the planets inour population typically most of their carbon from gas sources,Bosman et al. (2019) propose that Jupiter’s carbon content islargely accreted from frozen CO accompanying the accretingpebbles.Returning to our population of planets, to quantify the dis-tance o ff the general trend in Figure 8 of a constant N / C, wecompute the deviation away from the general trend for all plan-ets in both erosion models relative to N / O. To do this we firstcompute a median N / C (N / C median ) for each of the ongoing andreset model results. We then assume that the connection betweenN / O and C / O can be explained simply by a linear function withslope equal N / C median . Deviation from this general trend wouldhave the form: ∆ N / C = N / O − N / C median · C / O , (7)where N / O and C / O are the elemental ratios computed by ourmodel. The absolute value of ∆ N / C and its sign shows how farfrom the line with slope N / C median and in what direction.We show the result of this calculation in Figure 9. The ma-jority of the points lie within 0.01 of ∆ N / C =
0, meaning thattheir computed elemental abundances are consistent with the av-erage planet in our population. There are a few planets whichshow larger deviations in Figures 8 and 9, and we select threeof these planets to further investigate. Planet A lies to the leftof the average planet in the ongoing model. Its elemental abun-dances do not appear to depend on the erosion model in which itforms (its points overlap in Figure 8). Planet B similarly sits far Fig. 9: The deviation of N / O from the straight lines shown inFigure 8 which represents a constant N / C across all planets inthe population. For further analysis we label three planets thatshow the wide deviation from the median N / C of the population.to the left of the average planet forming in the ongoing model.Finally Planet C is a planet that lies far to the right of an averageplanet from the reset model. Similar to the previous two planets,it shows similar C / O and N / O ratios when it is formed in boththe reset and ongoing carbon erosion models.In Figures 10a - 10c we compare the radial evolution for eachof these planets with the underlying gas C / O. To reflect the timeframe that is most important for setting the chemical composi-tion of each of their atmospheres we only show contours up tothe time where the planet’s growth is truncated in our planet for-mation model. Figure 10a and 10b show very similar pictures forPlanets A and B. They each began growing farther out than thecarbon erosion front (at 5 AU) and never crossed the front untilafter gas accretion has been terminated. As such they both havefed on predominately oxygen-poorer (0.8 < C / O <
1) gas andslightly oxygen-richer (0.6 < C / O < .
8) solids.While the two planets accrete nearly the same amount ofsolids in total ( ∼ ⊕ ) the main di ff erence between them is thatPlanet B ends up accreting roughly an order of magnitude moregas than Planet A. This di ff erence comes from the randomly gen-erated maximum mass parameter from the population synthe-sis model, with Planet B being aloud to accrete for longer thanPlanet A. As such the planet accreted more gas which lead tothe chemistry in the atmosphere of Planet B being more depen-dent on gas accretion than Planet A. A combined measurementof C / O and N / O can help to understand the formation historyof a planet and / or whether its natal disk underwent a refractorycarbon erosion-like process.In Figure 10c we compare the gas chemistry and orbital mi-gration history for Planet C. We can see two important featuresin both the chemical composition of Planet C’s disk as well asthe migration of the planet. The marginally carbon-rich regionof the disk (below region C in Figure 2) extends for much longerin time in this disk than in the disk shown in Figure 2. The wa-ter ice line is also closer to the host star than in Figure 2 whichis a property of colder, less massive disks. Planet C begins itsformation inward of the carbon erosion front, and coincidentalevolves inward at the same rate (and at the same disk radius) asthe erosion front in the reset model between ∼ . .
65 Myr.
Article number, page 11 of 18 & A proofs: manuscript no. main(a) Planet A from Figure 9. (b) Planet B from Figure 9. (c) Planet C from Figure 9.
Fig. 10: Comparison between the planets A, B, and C’s location (black line) and the underlying chemical properties of the gas(coloured contours). Note we only show C / O up to the point where gas accretion is shut o ff in our formation model, since the diskno longer impacts the atmosphere once accretion is stopped. The contours are the same as in Figure 2. Note the change in time axisin the third panel.Because of Planet C’s orbital coincidence with the carbonerosion front, it spends a large portion of its formation accret-ing carbon-rich gas - even in the reset model - as such it endsit formation with a very large C / O for its N / O. In addition, wefind that Planet C’s C / O is nearly independent of the carbon ero-sion model, because it spends a su ffi ciently long time accretingcarbon-rich gas in the reset model. The di ff erence in C / O be-tween the two carbon erosion models for Planet C is only about20% - much smaller than for a typical planet in our population.
6. Discussion: What sets C/O in warm-Jupiteratmospheres?
So far, we have reported on our findings for the C / O and N / Ofor either the entire population of warm Jupiters, or on an indi-vidual level. Generally we have found (as was the case in Paper1) that the fraction of mass that is accreted as solids into the at-mosphere tends to heavily constrain the chemical properties thatresult. There are some exceptions, however, where the formationhistory - particularly the migration history - also has a noticeableimpact on the resulting chemical properties of the atmosphere.In this section we divide the population of planets by their initialdisk conditions and study the resulting C / O in the context of theenvironment in which they form.
In Figures 11 we split the C / O results of both the ongoing andreset models (respectively) into groups of disk metallicity, initialdisk mass, and occupying planet trap. These groups are denotedby separate panels, marker shape, and colour respectively. Theleft panel of the figure denotes the metal-poor systems ([Fe / H] ≤ -0.1), the middle panel denotes solar-like metallicities ( − . < [Fe / H] ≤ . . < [Fe / H] ≤ . ff erentiate between the atmospheric results for planets formingin the reset and ongoing models.In Figure 11 we bin the ongoing and reset model C / O dataas discussed above. In the metal-poor and solar-like panels theplanets lie tightly correlated over a wide range of mass and C / Oratios. The tight correlation implies that planets forming in diskswith metal-poor and solar-like metallicities are the systems thatmost consistently produce planets that agree with the main se-quence of mass-C / O ratio introduced in Paper 1.Generally speaking, planets trapped at the dead zone edgeand heat transition traps require the largest and lightest diskmasses respectively to form warm Jupiters in our formationmodel. This is due to the timescale related to the initial corebuild up, which needs to be su ffi ciently fast to build giant plan-ets within the lifetime of the disk. The low mass disks tend to becooler which moves the heat transition inward to smaller radiiand relatively higher densities than would be present in highermass disks. Conversely the dead zone trap best builds planets indisks with initially higher masses. The dead zone edge is com-puted semi-analytically in Alessi et al. (2020) and is less sensi-tive to the initial disk mass as is the heat transition, hence higherdisk masses lead to higher densities at the trap and faster coregrowth. For lower mass disks at these metallicities, dead zonetrapped planets lead more often to hot Jupiters.The metal-rich panel of planets is the first to show signifi-cant deviations from the general trends of the two other panels.As already discussed in relation to Figure 6, a second group ofwarm Jupiters have higher C / O than would be predicted fromtheir planet mass or fraction of mass accreted as solids. Thisgroup is more evenly spread when binning by metallicity thanwas suggested in Figure 6, showing that the metal-rich systemslead to higher chemical diversity than the lower metallicity sys-tems. Given their high C / O the most likely scenario for theseplanets are that they accreted the majority of their gas outwardof the water ice line. This is most easily done in the metal-richdisks because there is a higher density of solids (by construc-tion) when the metallicity is higher, which reduces the timescale
Article number, page 12 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry
Fig. 11: C / O for synthetic planets in both of the ongoing and reset carbon erosion models. The data for each erosion model areseparated on each panel by a dashed line. Each panels separates the planets by the protoplanetary disk metallicity. The left panelrepresents low metallicity, the middle panel is solar-like metallicity ( − . < [Fe / H] ≤ . . < [Fe / H] ≤ . ff erent point shapes represent di ff erent initial disk masses. The colour of each point denotesthe trap from which the planet originated: ice line (blue), dead zone (orange), and heat transition (green). Generally there is a shiftin C / O between planets growing in the reset and ongoing carbon erosion models. However there are some exceptions: for examplethe heat transition planet (green point) in the first panel which has nearly the same C / O in both the reset and ongoing model (this isPlanet C from above).related to the initial core growth. In these systems core forma-tion can occur e ffi ciently farther away from the host star than inthe lower metallicity systems. This generates a wider variety ofchemical properties as the planets sample chemically di ff erentregions of the disk. This variety causes some of the scatter seenin Figure 7 because their O / H metallicity is constrained by theaccretion of generally oxygen-poorer gas outward of the waterice line.In Figure 11 we also show the reset model. Generally thedi ff erence between the two figures is a shift of all points to lesscarbon-rich atmospheres in the reset model, apart from a fewparticular planets (three of which were discussed above). In par-ticular the heat transition planet in the top panel stands out ashaving the highest C / O in that group (this was Planet C fromabove), and the dead zone planet in the bottom panel that liesthe lowest along the right dashed line (this was Planet A fromabove). Otherwise the structure of the metal-poor and solar-likegroups of planets are grouped by planet mass and C / O in a simi-lar way as in the ongoing model.In the metal-rich panel we see a slight change in the struc-ture of the distribution of planets. The dead zone trapped planetstend to be more carbon-rich than the planets coming from thewater ice line trap in the reset model than was seen in the on-going model. As previously argued, the planets forming at thedead zone edge tend to start their evolution farther from the hoststar than the water ice line planets. As such they accrete carbon-richer gas than is found inward of the water ice line. In the resetmodel the excess carbon is lost to the host star after less than 0.8Myr and planets forming farther outward in the disk are moresensitive to the volatile chemistry than in the ongoing model.Overall we find that for solar-like and metal-poor disks, thereis a reasonably tight correlation between the planet mass andthe C / O. This implies that the main-sequence derived from thepopulation of hot Jupiters extends easily to the warm-Jupiters with much of the scatter at the high planet mass end being pro-duced by metal-rich systems. These metal-rich systems were notfound in Paper 1 because high-metallicity disks tend to buildwarm Jupiters over hot Jupiters in our formation model. At thelow planet mass end of the distribution, there appears to be asmall deviation in C / O caused by di ff erences in initial disk mass.This is particularly apparent in the solar-like metallicity systems,where we see that planets generated in low mass disks tended tobe less carbon-rich than planets of the same planet mass formingfrom high mass disks. For the majority of the paper, and the entirety of Paper 1, wehave assumed that the process of carbon erosion began at 5 AU,with the excess carbon smoothly increasing to 1 AU, inward ofwhich we maintained a constant carbon excess. This assump-tion, however, is largely based on current observations of therefractory component of carbon in the Earth mantle, asteroids,comets, and Jupiter’s current orbital radius (Bergin et al. 2015;Mordasini et al. 2016). Jupiter very likely migrated to its currentlocation, either from smaller radii during a Grand Tack, or fromlarger radii. Indeed Jupiter’s migration is required to explain thecurrent population of Trojan asteroids (Pirani et al. 2019).Since the chemical process that drives refractory erosion isstill an open question, and Jupiter very likely (must have) mi-grated during its formation then it is completely reasonable tovary the radial location of the carbon erosion front. For simplic-ity, we anchor the inner region of the function that describes thecarbon erosion, such that the excess carbon is always constantinward of 1 AU. We then vary the carbon erosion front frombetween 3 - 7 AU. This radius range ensures that the shiftingerosion front remains relevant for the presented population ofplanets.
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Fig. 12: A few selected planetary tracks compared to the loca-tion of the erosion front and the resulting distribution of excesscarbon (in contours).The location of the erosion front impacts the chemical prop-erties of the disk in two ways. First it changes the partitioningof the excess carbon between the gas and refractories throughthe location where carbon is removed from the grains. Movingthe front inward implies that there is generally less carbon avail-able in the gas for accretion, and a wider range of radii wherethe refractories remain carbon-rich. In the reset model, the sec-ond e ff ect is the timing at which the excess carbon is lost to thehost star. We keep the advection speed the same throughout thiswork, so moving the front inward shortens the time it takes theexcess carbon to accrete into the host star. The opposite is true ifwe move the erosion radius farther away from the host star.For illustrative purposes, in Figure 12 we show a compar-ison between a few of our planet tracks (which describe theplanet’s evolution through the mass-semi-major axis diagram),the carbon erosion front, and the resulting excess carbon gener-ated from the refractories (contours). We show the distributionof the excess carbon in the ongoing model for an erosion frontof 5 AU (fiducial model). Clearly, if the front was shifted inwardthen the excess carbon available to some planets will be reduced,while if it is moved outward then a higher carbon excess is avail-able to some of the growing planets earlier in their formation.In Figure 13 we show the impact of shifting the carbon ero-sion front between 3 - 7 AU for both the ongoing (top panel) andreset (bottom panel) models. The planets forming in the ongo-ing model show two distinct shifts in relation to the change inthe carbon erosion front. Lower mass planets (M (cid:46) . Jupiter )shift to higher C / O when the carbon erosion front is shifted tosmaller radii, while the opposite is true for higher mass plan-ets. This di ff erence highlights how higher mass planets dependmore on gas accretion for setting their chemical compositionwhile lower mass planets are more dependent on solid accre-tion. In a sense, a better classification of ‘ice giants’ are planetswith M (cid:46) . Jupiter ∼ ⊕ and gas giants as planet withM > ⊕ . Although we admit that such a classification wouldbe confusing as it would change our solar system to contain onegas giant and three ice giants, nevertheless such a classificationwould better capture the physics of and chemistry of planet for-mation. Fig. 13: Same as Figure 5, but including the e ff ect of shifting theerosion to between 3 AU and 7 AU.In the bottom panel of Figure 13 we see that the majorityof the planets are shifted to more carbon-rich atmospheres whenthe carbon erosion front is moved inward. This is because thereis more carbon in total available for planetary accretion in the re-set model, since fewer solids are chemically processed and lesscarbon is lost to the host star. The lower mass planets see thehighest shift since their chemical composition is most dependenton the refractory source of carbon. There are a few planets wherethe opposite trend is observed, with higher C / O for a carbon ero-sion front farther away from the host star. Like Planet C fromearlier, this is caused by a coincidence between the excess car-bon in the gas and the period of rapid gas accretion during theplanets’ formation.
7. Conclusion
Here we have presented a population of warm Jupiters, derivedfrom a full planet population synthesis model starting from plan-etesimal accretion. We computed the chemical evolution of the
Article number, page 14 of 18lex J. Cridland, Ewine F. van Dishoeck, Matthew Alessi, & Ralph E. Pudritz: Connecting planet formation and astrochemistry disk volatiles in each of the disks used for the population synthe-sis calculation to predict the carbon, oxygen, and nitrogen abun-dances in the gas and ice. When combined with a model for therefractory chemistry - particularly the carbon - we compute theevolution of the total carbon, oxygen, and nitrogen content ofeach protoplanetary disk. These calculations are combined withthe planet tracks derived from the formation model to predict theresulting C / O and N / O in the planetary atmospheres.We generally find that: – Like the hot Jupiters in Paper 1 (Cridland et al. 2019c) thereis a reasonably tight correlation between the C / O in the at-mosphere and the planetary mass. – The spread in the aforementioned correlation is linked toplanets forming in metal-rich disks, which are capable ofproducing more chemically varied atmospheres due to amore rapid initial core build up. – The main sequence of the C / O ratio vs. fraction of solid massaccreted into the atmosphere reported in Paper 1 is upheldfor the warm Jupiters. High mass planets tend to curve awayfrom the general trend, moving asymptotically towards thedisk volatile C / O in the case of the reset model, and to C / O ∼ – There is an arm of higher C / O caused by the metal-rich disksseen in the main sequence that asymptote to a higher C / O inboth carbon erosion models. – Including N / O into our analysis weakens the viability ofplanetesimal formation in the inner disk as the formationmechanism of Jupiter. This result agrees with the purelychemical analysis of Öberg & Wordsworth (2019) andBosman et al. (2019) which places Jupiter’s formation ori-gin outward of tens of AU. – Combining C / O and N / O additionally allows us to identifyplanets that exclusively accrete their atmosphere outside ofthe refractory carbon erosion front - a rare situation for thispopulation of planets. – Shifting the carbon erosion front shows the importance ofsolid accretion in determining the chemical structure of plan-etary atmospheres particularly for planets with mass (cid:46) ⊕ .The observability of these types of planets will continue to bea challenge as they lie in a range of orbital period that make theirchemical characterization di ffi cult by both transit spectroscopyas well as direct imaging. There is a single exoplanet, WASP-167e, that has had its orbital period (of 1071 days) characterizedby both Kepler and Spitzer with enough accuracy to justify anattempt for transit spectroscopy with JWST (Dalba & Tamburo2019). As we enter into the next generation of Extremely LargeTelescopes, and with improvements to coronography that are on-going, it is possible that a direct emission spectrum of warmJupiters could be taken. This could unlock a whole new rangeof planets to study chemically.Along with the observational challenges, there is more to bedone on the modelling side of planet formation and astrochem-istry. This work has made strides to include a simple model thatdescribes the chemical properties of the refractories in the pro-toplanetary disks. The physics that describe how this materialfinds its way into the atmosphere of the planet, and where thecarbon and oxygen are deposited in the atmosphere still remaincomplicated problems that are beyond the scope of this paper.The strict atmospheric mass cuto ff that governs the delivery ofrefractory material into the atmosphere is simply implemented inour model (as described in Paper 1). Self-consistently computingthe arrival and destruction of planetesimals into the atmosphere of a giant planet could deliver refractory material deep enoughinto the atmosphere that it is unable to impact the observableC / O ratios. Such a complication is currently beyond the scope ofthis work.Furthermore the protoplanetary disk models that are used inour planet formation models are smooth - representing a muchsimpler picture than is being seen in current high resolution sur-veys of young star forming regions. These surveys are also push-ing the start time for planet formation - or at least the formationof the first planetesimals - farther back into the Class 0 or ClassI young stellar systems (Tychoniec et al. 2018). It is perfectlypossible that by the time a Class II disk (classically called a pro-toplanetary disk, as it was believed to be the natal system forplanets) emerges from the envelope of the proto-star that planetshave already almost fully formed. Indeed the marginally ClassI / II system HL Tau already shows wide shallow gaps that are of-ten attributed to the presence of at least one large planet (ALMAPartnership et al. 2015; Tamayo et al. 2015). If it is indeed truethat the majority of the initial core growth and atmosphere accre-tion (important for determining the chemistry of the atmosphere)occurs in the Class 0 / I phase, then we will need adjust our diskmodels to incorporate the properties of these systems.With all that being said, it is safe to say that there is stillmuch that can be learned about the physical processes governingplanet formation from models like the ones presented here. Andover the next few decades, as we begin to chemically character-ize the atmospheres of planets as easy as it is now to find them;we should see another surge in our understanding of planet for-mation. A surge that could rival the one we witnessed in the earlyyears of the
Kepler mission, possibly driven by JWST or throughthe upcoming European Space Agency’s ARIEL mission.
Acknowledgements. / Calcul Canada. A.J.C acknowledges additional support by the Euro-pean Union ERC grant H2020 ExoplanetBio supervised by Ignas Snellen. R.E.P.is supported by an NSERC Discovery Grant. M.A. acknowledges funding fromNSERC through the PGS-D Alexander Graham Bell scholarship.
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Appendix A: Breakdown of most abundant species
Here we show the most abundant species found in one particularchemical model in our population of disks. The carbon and oxy-gen carrying species are predominately H O, OH, and CO. thereare periods of time (and ranges of radii) where CO becomesabundant on the icy grains, while molecular oxygen and atomicoxygen become abundant in the gas. Frozen OH is mainly madefrom the dissociation of frozen water by UV photons inducedby collisions of cosmic rays with molecular hydrogen. A verysmall amount of carbon and nitrogen bearing species like CH ,HCN, and C H can be found in the gas phase, however thesespecies do not survive throughout the chemical evolution of thedisk. Unlike some chemical models, we do not produce largeamounts of gaseous CO - which is generally produced throughgrain surface reactions that are not included in our model. Article number, page 17 of 18 & A proofs: manuscript no. main