A Library of Self-Consistent Simulated Exoplanet Atmospheres
Jayesh M. Goyal, Nathan Mayne, Benjamin Drummond, David K. Sing, Eric Hébrard, Nikole Lewis, Pascal Tremblin, Mark W. Phillips, Thomas Mikal-Evans, Hannah R. Wakeford
MMNRAS , 1–26 (2019) Preprint August 6, 2020 Compiled using MNRAS L A TEX style file v3.0
A Library of Self-Consistent Simulated ExoplanetAtmospheres
Jayesh M. Goyal , ? , Nathan Mayne , Benjamin Drummond , , David K. Sing , , ,Eric H´ebrard , Nikole Lewis , Pascal Tremblin , Mark W. Phillips , Thomas Mikal-Evans ,Hannah R. Wakeford Department of Astronomy and Carl Sagan Institute, Cornell University, 122 Sciences Drive, Ithaca, NY, 14853, USA Astrophysics Group, School of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, UK Met Office, Fitzroy Road, Exeter, EX1 3PB, UK Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USA Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD, USA Malson de la Simulation, CEA-CNRS-INRIA-UPS-UVSQ, USR 3441, Centre detude de Saclay, France Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA School of Physics, University of Bristol, HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
Accepted 2020 July 29. Received 2020 July 29; in original form 2020 April 7
ABSTRACT
We present a publicly available library of model atmospheres with radiative-convective equilibrium Pressure-Temperature ( P - T ) profiles fully consistent with equi-librium chemical abundances, and the corresponding emission and transmission spec-trum with R ∼ µ m decreasing to R ∼
35 at 30 µ m, for 89 hot Jupiter exo-planets, for four re-circulation factors, six metallicities and six C/O ratios. We findthe choice of condensation process (local/rainout) alters the P - T profile and therebythe spectrum substantially, potentially detectable by JWST. We find H − opacity cancontribute to form a strong temperature inversion in ultra-hot Jupiters for C/O ratios ≥ P - T structure and the spectrum. We show the role of Fe opac-ity to form primary/secondary inversion in the atmosphere. We use WASP-17b andWASP-121b as test cases to demonstrate the effect of grid parameters across their fullrange, while highlighting some important findings, concerning the overall atmosphericstructure, chemical transition regimes and their observables. Finally, we apply thislibrary to the current transmission and emission spectra observations of WASP-121b,which shows H O and tentative evidence for VO at the limb, and H O emission fea-ture indicative of inversion on the dayside, with very low energy redistribution, therebydemonstrating the applicability of library for planning and interpreting observationsof transmission and emission spectrum.
Key words: planets and satellites: atmospheres – planets and satellites: composition– planets and satellites: gaseous planets – techniques: spectroscopic
The thermal or the pressure-temperature ( P - T ) structure ofa planetary atmosphere is a result of constant feedback be-tween radiative, advective, and chemical processes. Deter- ? E-mail: [email protected] mining the P - T structure of a planet is important for un-derstanding underlying thermochemical and dynamical pro-cesses. The P - T structure of the planetary atmosphere alsogoverns its spectral signatures, when remotely observed us-ing telescopes, spacecrafts or satellites. Therefore, it is nec-essary to constrain the P - T structure of a planet’s atmo-sphere, to understand the various physical processes occur- © a r X i v : . [ a s t r o - ph . E P ] A ug Goyal et al. ring within them as shown in Figure 1. Constraining thethree dimensional P - T structure of the planetary atmosphereis ideally required, but the complexity and the computa-tional resources required for such a model, especially whenconstructing a library of forward model simulations, moti-vates one dimensional (1D) P - T profiles.In Goyal et al. (2018), Goyal et al. (2019a) and Goyalet al. (2019b) we used isothermal P - T profiles and corre-sponding equilibrium chemical abundances for computingtransmission spectra for a wide range of exoplanet atmo-spheres. This extensive library of more than a million modelsimulations is publicly available and has proved to be veryuseful in interpreting observations of various exoplanets us-ing the Hubble Space Telescope (HST), Spitzer and VeryLarge Telescope (VLT) (see for e.g Wakeford et al. 2018;Alam et al. 2018; Zhang et al. 2019; Carter et al. 2020) andfor planning future observations using various telescope fa-cilities, including the James Webb Space Telescope (JWST).However, the assumption of an isothermal P - T profiles isonly accurate for a small region of the atmosphere, specifi-cally the high-altitude, low-pressure regions probed by trans-mission spectra. In fact, the atmosphere even in this regionmay rarely be exactly isothermal, but current transmissionspectra observations cannot differentiate between such smalltemperature changes in P - T profiles (Fortney 2005; Heng &Kitzmann 2017; Goyal et al. 2018), which may be revealedby higher precision, higher resolution, and broader wave-length coverage observations. Furthermore, truly isothermal P - T profiles would give rise to a simple black body emis-sion spectrum, devoid of spectral features. The emissionspectrum is much more strongly and directly dependent onthe temperature than the transmission spectrum (EmissionFlux ∝ T ). Moreover, emission spectrum reveals the day-side/nightside of the exoplanet atmosphere, providing alto-gether different information than the transmission spectrum,which measures the limb. Emission spectrum also probesdeeper (higher pressure) regions of the planetary atmospherein comparison to transmission spectrum. Therefore, to iden-tify features in the emission spectrum as well as to constrainthe P - T profile using these features, we require computationof a more accurate non-isothermal P - T profile.1D P - T profiles of irradiated H /He dominated plan-etary atmospheres with sufficiently high equilibrium tem-peratures are expected to reach a radiative-convective equi-librium condition (see for e.g Marley et al. 1996; Burrowset al. 1997; Seager & Sasselov 1998; Sudarsky et al. 2003;Marley & Robinson 2015; Molli`ere et al. 2015; Gandhi &Madhusudhan 2017; Malik et al. 2019). This is basically aresult of two factors, first the exposure to strong irradia-tion from the host star, rapidly forcing perturbations in the P - T structure back to a radiative equilibrium in the lowerpressure regions ( < ∼
100 bar), and second the dominance ofconvection in the deep atmosphere forcing perturbations inthe P - T structure to convective equilibrium in the higherpressure regions ( > ∼
100 bar). Therefore, combining thelower pressure regions, and higher pressure regions, these at-mospheres are likely to exist close to a radiative-convectiveequilibrium, termed RCE hereafter. Additionally, assumingchemical equilibrium to model hot Jupiter atmospheres is https://exoctk.stsci.edu/generic likely a reasonable assumption, due to the high tempera-ture of these planets, especially where chemical timescalesare likely to be short, particularly for temperatures above ∼ P - T profiles for different planets can vary depend-ing on their gravity, host star distance and spectral type, cir-culation in the planet’s atmosphere and the chemical com-position of the atmosphere. This can then lead to a widerange of possible spectra for a given planet, governed by its P - T profile. Therefore, a library of RCE P - T profiles and thecorresponding chemical abundances and simulated spectrais required to interpret the observations of exoplanet atmo-spheres and constrain the important physical processes oc-curring within them. In this work we compute P - T profilesin radiative - convective equilibrium for 89 observationallysignificant exoplanets, along with their corresponding equi-librium chemical abundances, simulated transmission andemission spectra with resolution of R ∼ µ m de-creasing to R ∼
35 at 30 µ m, and contribution functions,which are publicly available here , .We start by describing the 1D-2D atmosphere modelATMO (Amundsen et al. 2014; Tremblin et al. 2015, 2016,2017; Drummond et al. 2016; Goyal et al. 2018) and theprocedure to compute RCE P - T profiles, followed by recentadditions to ATMO in Section 2. We detail the numericalsetup of this grid with RCE P - T profiles in Section 3, in-cluding the chemistry and opacity setup. In Section 4 wedescribe the parameter space of the grid. We discuss the re-sults in Section 5, where we show the sensitivity of modelsimulations to different model choices by comparing RCE P - T profiles, equilibrium chemical abundances and the trans-mission/emission spectra in Section 5.1. In Section 5.2 weshow the effects caused by high levels of irradiation by us-ing extremely irradiated hot Jupiter WASP-121b as the testcase. Sensitivity to grid parameters, namely; recirculationfactor, metallicity and C/O ratio is discussed is Section 5.3using WASP-17b and WASP-121b as test cases. In Section 6,transmission and emission spectrum observations of WASP-121b are interpreted using the grid of models presented inthis work. Finally, we summarize and conclude in Section7. The implementation and validation of thermal ionization,H − and Fe opacity used in ATMO is detailed in AppendixA. As in Goyal et al. (2018) and Goyal et al. (2019b), in thiswork we use
ATMO , a 1D-2D radiative-convective equilibriummodel for planetary atmospheres. A nice comparison be-tween ATMO and other models, before some of the additionsdescribed in this paper, is shown in Baudino et al. (2017)and Malik et al. (2019). In this section we describe some https://drive.google.com/drive/folders/1zCCe6HICuK2nLgnYJFal7W4lyunjU4JE https://noctis.erc-atmo.eu:5001/fsdownload/hq0z4udQJ/goyal2020 MNRAS000
ATMO , a 1D-2D radiative-convective equilibriummodel for planetary atmospheres. A nice comparison be-tween ATMO and other models, before some of the additionsdescribed in this paper, is shown in Baudino et al. (2017)and Malik et al. (2019). In this section we describe some https://drive.google.com/drive/folders/1zCCe6HICuK2nLgnYJFal7W4lyunjU4JE https://noctis.erc-atmo.eu:5001/fsdownload/hq0z4udQJ/goyal2020 MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres Figure 1.
Illustrative figure to show dominant processes in dif-ferent parts of a hot Jupiter atmosphere with radiative-convectiveequilibrium P - T profiles, with (black) and without inversion(blue). of the details of ATMO along with recent additions to themodel. P - T profiles inRadiative-Convective equilibrium We here discuss the basic methodology used in ATMO tocompute P - T profiles in radiative-convective equilibrium,consistently with equilibrium chemistry. Radiative transferand absorption cross-section calculations along with equilib-rium chemistry computations performed iteratively, all con-tribute to the computation of consistent RCE P - T profiles,discussed in detail in Drummond et al. (2016) and Goyal(2019). We initialise the model with an estimated (initialguess) P - T profile (the starting profile can also be isother-mal although this will likely take longer computation timeto reach convergence). We note that the final RCE P - T in independent of the initial starting P - T profile. Chemi-cal equilibrium abundances are then calculated for this P - T profile. Using these abundances along with the absorptioncross-sections of different chemical species, in the form of k -coefficients (Amundsen et al. 2014), the total opacity iscalculated for each layer of the atmosphere. Following this,the radiative transfer equation is solved to compute incom-ing and outgoing radiative fluxes for each layer of the atmo-sphere. The same approach is followed for convective flux.This is then checked for energy flux balance in each layer ofthe atmosphere as well as the atmosphere as a whole, usingthe energy conservation equation given by F rad + F conv − σ T int = , (1)where F rad the radiative flux and F conv is the convec-tive flux, respectively, as derived in Drummond et al. (2016)and Goyal (2019). T int represents the internal temperatureof planet or the temperature at which the planet is cool-ing. Isotropic scattering is also included in the radiative fluxcomputation. The P - T profile is also constrained by hydro-static equilibrium, which defines the pressure structure as afunction of altitude, implemented using ddz ( P gas + P turb ) − ρ g = , (2) where P gas is pressure due to gaseous species, P turb isturbulent pressure, z is altitude, ρ is density and g is grav-ity. If the conditions for energy conservation and hydrostaticequilibrium are not satisfied within the required numericalaccuracy, corresponding to an error in flux balance (typicalvalue of ∼ − ), the P - T profile is perturbed within mini-mum and maximum step sizes ( ∼ P - T profile that satisfies hydrostatic equi-librium and conservation of energy is obtained, consistentwith equilibrium chemistry and corresponding opacities, fora given set of planetary characteristics.Figure 1 shows radiative-convective equilibrium P - T profiles with and without a temperature inversion. Unlikea static table of chemical abundances used in various mod-els, these P - T profiles (and all models in this grid) are con-sistent with equilibrium chemical abundances, as explainedabove. In this schematic, we also show the dominant physi-cal processes in each region. Convection plays an importantrole only in the deepest parts of the irradiated hot Jupiteratmospheres ( >
100 bar), which current observations can-not probe. Radiation governs the P - T structure across a widerange of pressures. Radiative diffusion leads to an isothermalstructure in the deep atmosphere as shown in Figure 1, pri-marily because the high opacity in this region decreases themean free path for the photons as in stellar atmospheres (Ry-bicki & Lightman 1986). The interplay between absorptionof stellar radiation due to optical opacities and planetaryemission due to infrared opacities, governs the P - T profile inthe radiative region between ∼ ∼ In a planetary atmosphere advection due to winds is oneof the major processes responsible for transporting energy.To incorporate the 3D effect of advection in 1D models asadopted by Fortney & Marley (2007), we simply reduce theincoming flux in the 1D column of the atmosphere by a fac-tor called the “recirculation factor”, hereafter termed f c . Itparameterises the redistribution of input stellar energy inthe planetary atmosphere, by the dynamics, where a valueof equates to no redistribution, while . represents ef-ficient redistribution. The value of 0.5 f c indicates 50% ofthe total incoming stellar energy is advected to the nightside (the side of the planet facing away from the star), while0.25 f c indicates 75% of the total incoming stellar energy isadvected to the night side. It must also be noted that anadditional factor, the incidence angle θ o also contributes tothe reduction in this total incoming stellar energy. θ o = ◦ equating to the dayside (the side of the planet facing towardsthe star) average is the most commonly adopted value of in-cidence angle, contributing to 50% reduction in the totalincoming stellar energy, since cos 60 ◦ = . . MNRAS , 1–26 (2019)
Goyal et al.
The emission spectrum represents the top of the atmosphere(ToA) flux at different wavelengths for a given planet. How-ever, this is a combination of flux from the different layersof the atmosphere. To identify the levels of the atmospherecontributing the most to this ToA emission, the Contribu-tion function (CF) (Chamberlain & Hunten 1987; Knutsonet al. 2009; Drummond et al. 2018) is calculated given by, CF = B ( ν, T ) d ( e − τ ν ) d ( ln ( P )) , (3)where ν is the frequency, T is the temperature, B ( ν, T ) is the Planck emission, τ ν is the optical depth and P is thepressure at each level of the atmosphere. The vertical P - T profile and the wavelength dependent optical depth, arethe primary quantities required to calculate the contribu-tion function. Optical depth is a function of transmittancewhich decreases as we go deeper in the planet’s atmosphere.Therefore, the CF is higher in the region where there is alarger change in the optical depth or transmittance for a unitchange in the pressure (altitude) over the same region. Insimpler terms, the CF peaks in the region where the wave-length dependent optical depth is one, when the planet isbeing probed from the top of the atmosphere. Although wedefine contribution function here, for ease of understand-ing and plotting we compute the Normalised ContributionFunction (NCF), by normalising using the largest value ofthe contribution function along the P - T profile. We include thermal ionization chemistry in ATMO by in-cluding ion species while computing equilibrium chemicalabundances. We also included iron (Fe) and H − opacity. Wedetail their implementation and validation in Appendix A. Computing RCE P - T profiles consistent with equilibriumchemistry is not a trivial task. The P - T profile and the chem-istry are intricately linked as they depend on each other. Thechemical composition is largely dependent on the tempera-ture, and the temperature is largely dependent on composi-tion (via opacities). Moreover, the P - T profile as well as thechemical abundance profile continuously change as the sim-ulation progresses towards the solution. In such a scenario alarge number of temperature and pressure points are encoun-tered. Therefore, it is extremely difficult to obtain converged(satisfying all constraints) RCE P - T profiles for values acrossa large parameter space. There are always the regions of theparameter space where the simulations tend not to reach aconverged solution due to many factors such as the boundaryconditions, numerical instabilities, non-convergence of equi-librium chemistry especially with condensation and manymore. We deal with such problems by incrementally adjust-ing the numerical setup for some of the failed model simu-lations as described in the next section.We use 50 vertical model levels with a maximum opticaldepth of × at 1 µ m. Since ATMO calculates quantities on an optical depth grid, the minimum and maximum opti-cal depths govern the pressure domain (extent of the atmo-sphere). An increase in the maximum optical depth leads toan increase in the pressure domain of the P - T profile, for agiven set of parameters. The model stability when solvingfor radiative-convective equilibrium, consistently with equi-librium chemistry, is very sensitive to the selected top ofthe atmosphere (minimum) optical depth boundary condi-tion, as the atmosphere can become very sparse (less dense)in this region. Therefore, the top of the atmosphere opticaldepth is varied to achieve convergence. The typical valuesused for top of the atmosphere optical depth are 10 − , 10 − ,10 − and 10 − at 1 µ m. Although this is a wide range fortop of the atmosphere optical depth, these extremely lowoptical depth regions are outside the domains of the regionprobed by either transmission or emission spectra. Moreover,we find that a value of 10 − is sufficient for most of the modelsimulations. The top of the atmosphere pressure is restrictedto − bar, which corresponds to the top of the atmosphereminimum optical depth. Even though we vary the minimumoptical depth to achieve convergence, the pressure is alwaysset at − bar for this minimum optical depth, serving as areference for the atmospheric P - T profile.We use 32 band correlated- k cross-sections (Amundsenet al. 2014; Goyal et al. 2018) for generating consistent RCE P - T profiles and 5000 bands to generate transmission spec-tra, emission spectra and contribution functions. The inter-nal temperature of the planet (T int ) defined in Section 2.1is set at 100 K following (Guillot & Showman 2002; Fort-ney et al. 2007). However, we note that following some re-cent studies (Thorngren et al. 2019; Sing et al. 2019), thisassumption might be debatable. We adopt a mixing lengthconstant α = . for calculating convective flux (Baraffe et al.2015), as used in previous ATMO simulations (e.g Drum-mond et al. 2016). To standardise the comparison of trans-mission spectra for a range of variables, we set the pressureat which the radius of the planet is defined at 1 millibar(Lecavelier Des Etangs et al. 2008), only while computingthe transmission spectra. We note that there exists a degen-eracy between reference transit radius and associated refer-ence pressure as highlighted by Lecavelier Des Etangs et al.(2008).The target planet selection technique for this library ofmodels is the same as that adopted in Goyal et al. (2018)with the additional constraint of the planetary equilibriumtemperature. In this library only the planets with equilib-rium temperatures greater than 1200 K, as computed in theTEPCat database (Southworth 2011) are selected, all shownin the Table 3 of the online supplementary material. Thechoice of 1200 K is based on the capability of ATMO toobtain converged solution (RCE P - T profile consistent withequilibrium chemistry) for a range of grid parameter spacevalues. It was found that for planets with equilibrium tem-peratures less than 1200 K a large number of model simula-tions across the grid parameter space fail to converge, mostlikely due to numerical instabilities arising due to inclusionof various condensates in our equilibrium chemistry compu-tation.The input stellar spectra for each planetary model grid MNRAS000
The emission spectrum represents the top of the atmosphere(ToA) flux at different wavelengths for a given planet. How-ever, this is a combination of flux from the different layersof the atmosphere. To identify the levels of the atmospherecontributing the most to this ToA emission, the Contribu-tion function (CF) (Chamberlain & Hunten 1987; Knutsonet al. 2009; Drummond et al. 2018) is calculated given by, CF = B ( ν, T ) d ( e − τ ν ) d ( ln ( P )) , (3)where ν is the frequency, T is the temperature, B ( ν, T ) is the Planck emission, τ ν is the optical depth and P is thepressure at each level of the atmosphere. The vertical P - T profile and the wavelength dependent optical depth, arethe primary quantities required to calculate the contribu-tion function. Optical depth is a function of transmittancewhich decreases as we go deeper in the planet’s atmosphere.Therefore, the CF is higher in the region where there is alarger change in the optical depth or transmittance for a unitchange in the pressure (altitude) over the same region. Insimpler terms, the CF peaks in the region where the wave-length dependent optical depth is one, when the planet isbeing probed from the top of the atmosphere. Although wedefine contribution function here, for ease of understand-ing and plotting we compute the Normalised ContributionFunction (NCF), by normalising using the largest value ofthe contribution function along the P - T profile. We include thermal ionization chemistry in ATMO by in-cluding ion species while computing equilibrium chemicalabundances. We also included iron (Fe) and H − opacity. Wedetail their implementation and validation in Appendix A. Computing RCE P - T profiles consistent with equilibriumchemistry is not a trivial task. The P - T profile and the chem-istry are intricately linked as they depend on each other. Thechemical composition is largely dependent on the tempera-ture, and the temperature is largely dependent on composi-tion (via opacities). Moreover, the P - T profile as well as thechemical abundance profile continuously change as the sim-ulation progresses towards the solution. In such a scenario alarge number of temperature and pressure points are encoun-tered. Therefore, it is extremely difficult to obtain converged(satisfying all constraints) RCE P - T profiles for values acrossa large parameter space. There are always the regions of theparameter space where the simulations tend not to reach aconverged solution due to many factors such as the boundaryconditions, numerical instabilities, non-convergence of equi-librium chemistry especially with condensation and manymore. We deal with such problems by incrementally adjust-ing the numerical setup for some of the failed model simu-lations as described in the next section.We use 50 vertical model levels with a maximum opticaldepth of × at 1 µ m. Since ATMO calculates quantities on an optical depth grid, the minimum and maximum opti-cal depths govern the pressure domain (extent of the atmo-sphere). An increase in the maximum optical depth leads toan increase in the pressure domain of the P - T profile, for agiven set of parameters. The model stability when solvingfor radiative-convective equilibrium, consistently with equi-librium chemistry, is very sensitive to the selected top ofthe atmosphere (minimum) optical depth boundary condi-tion, as the atmosphere can become very sparse (less dense)in this region. Therefore, the top of the atmosphere opticaldepth is varied to achieve convergence. The typical valuesused for top of the atmosphere optical depth are 10 − , 10 − ,10 − and 10 − at 1 µ m. Although this is a wide range fortop of the atmosphere optical depth, these extremely lowoptical depth regions are outside the domains of the regionprobed by either transmission or emission spectra. Moreover,we find that a value of 10 − is sufficient for most of the modelsimulations. The top of the atmosphere pressure is restrictedto − bar, which corresponds to the top of the atmosphereminimum optical depth. Even though we vary the minimumoptical depth to achieve convergence, the pressure is alwaysset at − bar for this minimum optical depth, serving as areference for the atmospheric P - T profile.We use 32 band correlated- k cross-sections (Amundsenet al. 2014; Goyal et al. 2018) for generating consistent RCE P - T profiles and 5000 bands to generate transmission spec-tra, emission spectra and contribution functions. The inter-nal temperature of the planet (T int ) defined in Section 2.1is set at 100 K following (Guillot & Showman 2002; Fort-ney et al. 2007). However, we note that following some re-cent studies (Thorngren et al. 2019; Sing et al. 2019), thisassumption might be debatable. We adopt a mixing lengthconstant α = . for calculating convective flux (Baraffe et al.2015), as used in previous ATMO simulations (e.g Drum-mond et al. 2016). To standardise the comparison of trans-mission spectra for a range of variables, we set the pressureat which the radius of the planet is defined at 1 millibar(Lecavelier Des Etangs et al. 2008), only while computingthe transmission spectra. We note that there exists a degen-eracy between reference transit radius and associated refer-ence pressure as highlighted by Lecavelier Des Etangs et al.(2008).The target planet selection technique for this library ofmodels is the same as that adopted in Goyal et al. (2018)with the additional constraint of the planetary equilibriumtemperature. In this library only the planets with equilib-rium temperatures greater than 1200 K, as computed in theTEPCat database (Southworth 2011) are selected, all shownin the Table 3 of the online supplementary material. Thechoice of 1200 K is based on the capability of ATMO toobtain converged solution (RCE P - T profile consistent withequilibrium chemistry) for a range of grid parameter spacevalues. It was found that for planets with equilibrium tem-peratures less than 1200 K a large number of model simula-tions across the grid parameter space fail to converge, mostlikely due to numerical instabilities arising due to inclusionof various condensates in our equilibrium chemistry compu-tation.The input stellar spectra for each planetary model grid MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b) Figure 2.
Absorption cross-sections (k band ) of all species used in ATMO in each of the 5000 correlated- k bands at 1 bar and 2000 K.These are absolute cross-sections without any dependance on chemical abundances. (a) Cross-sections for H -H (blue), H -He (green),H O (cyan), CO (red), CO (deepskyblue), CH (lawngreen), NH (saddlebrown), Na (purple), K (magenta), Li (orange). (b) Cross-sections for Rb (blue), Cs (khaki), TiO (cyan), VO (red), FeH (deepskyblue), PH (magenta), H S (saddlebrown), HCN (purple), C H (black), SO (orange) and Fe (grey). are taken from the BT-Settl models (Allard et al. 2012; Ra-jpurohit et al. 2013). These stellar spectra are selected ac-cording to the closest obtained host star temperature, grav-ity and metallicity from the TEPCat database (Southworth2011). All the parameters required for model initialisationlike stellar radius, planetary radius, planetary equilibriumtemperature, surface gravity and semi-major axis are alsoadopted from the TEPCat database, shown in the Table 1of the online supplementary material. Similar to Goyal et al. (2018) and Goyal et al. (2019b), we re-strict our calculations to equilibrium chemistry in this work,but with self-consistent RCE P - T profiles. However, in thiswork we also include thermal ionization in the equilibriumchemistry computation, detailed and validated in AppendixA1 . Therefore, in addition to the 258 species as used inGoyal et al. (2018) and Goyal et al. (2019b) which are listedhere , the list of species for equilibrium computation nowalso includes H + , H − , Na + , K + , e − , C + , He + , Ca + and Si + ions along with additional gaseous species NaF, KF, SiO,SiS, CaH, CaOH and condensate species Na AlF in threedifferent forms and LiF in the crystalline form. Thus the to-tal number of species used in the equilibrium chemistry cal-culation adds up to 277 for the simulations presented here. https://phoenix.ens-lyon.fr/Grids/BT-Settl/AGSS2009/SPECTRA/ https://drive.google.com/drive/folders/1g7Bc6pbwvLUDf-QFJOCEOFKX6glKLuqF The potential of a particular species to absorb/emit radia-tion at a particular spectral interval is governed by its ab-sorption cross-sections. Compared to the simulations pre-sented in Goyal et al. (2018) and Goyal et al. (2019b), theopacities due to H − and Fe have been newly included inthis work, in addition to H -H and H -He collision inducedabsorption (CIA) opacities, and opacities due to H O, CO ,CO, CH , NH , Na, K, Li, Rb, Cs, TiO, VO, FeH, CrH, PH ,HCN, C H , H S and SO . The implementation of H − opac-ity is described in Appendix A2 and that of Fe in AppendixA3. The line list sources for all opacities used in this libraryand the type/sources of pressure broadening, are shown inTable 1 and Table 2 of the supplementary material, respec-tively. The effects of these newly added opacities, H − and Feon the P - T profiles and thereby the spectra are discussed inSection 5.2.2 and 5.2.3, respectively.Absorption cross-sections for all the species included inATMO in each of the 5000 correlated- k bands at 1 bar and2000 K are shown in Figure 2. These plots aid identifyingthe major absorbing species in various parts of the spec-trum. However, it must be noted that the final opacities arethe product of absorption cross-sections and chemical abun-dances. Therefore, although species such as TiO,VO, FeHand Fe have strong absorption cross-sections in the opticaltheir contribution to total absorption will be zero if theycondense or don’t form at any given temperature. The library of models with RCE P - T profiles and correspond-ing equilibrium chemical abundances, transmission spectra,emission spectra and contribution functions for various plan-ets are computed at four different recirculation factors (f c =0.25, 0.5, 0.75, 1.0), six metallicities (0.1, 1, 10, 50, 100,200; all in × solar) and six C/O ratios (0.35, 0.55, 0.7, 0.75 MNRAS , 1–26 (2019)
Goyal et al. (a) (b)(c) (d)(e)
Figure 3. (a)
Figure showing RCE P - T profiles for WASP-17b at 0.25 f c and solar metallicity and solar C/O ratio (0.55), with rainout(blue) and local condensation (red). (b) Figure showing equilibrium chemical abundances of important species using P - T profiles shownin Figure 3a, with rainout (solid) and local condensation (dashed). (c) Figure showing transmission spectra using P - T profiles shownin Fig. 3a and chemical abundances shown in Figure 3b, with rainout (blue) and local condensation (red). (d) Figure showing emissionspectra using P - T profiles shown in Fig. 3a and chemical abundances shown in Figure 3b, with rainout (blue) and local condensation(red) . (e) Figure showing contribution function for emission spectra shown in Fig. 3d, with rainout (blue) and local condensation (red)at 1.1 (solid), 1.4 (doted), 2.25 (dashed) and 2.8 (dot-dash) µ m . MNRAS000
Figure showing RCE P - T profiles for WASP-17b at 0.25 f c and solar metallicity and solar C/O ratio (0.55), with rainout(blue) and local condensation (red). (b) Figure showing equilibrium chemical abundances of important species using P - T profiles shownin Figure 3a, with rainout (solid) and local condensation (dashed). (c) Figure showing transmission spectra using P - T profiles shownin Fig. 3a and chemical abundances shown in Figure 3b, with rainout (blue) and local condensation (red). (d) Figure showing emissionspectra using P - T profiles shown in Fig. 3a and chemical abundances shown in Figure 3b, with rainout (blue) and local condensation(red) . (e) Figure showing contribution function for emission spectra shown in Fig. 3d, with rainout (blue) and local condensation (red)at 1.1 (solid), 1.4 (doted), 2.25 (dashed) and 2.8 (dot-dash) µ m . MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b) Figure 4. (a)
Figure showing equilibrium chemical abundances of various species without (solid) and with (dashed) thermal ionic species(ionic species are shown using marked lines) included in the model for WASP-121b at solar metallicity, solar C/O ratio (0.55) and 0.5 f c . (b) Figure showing transmission spectra models, with and without thermal ionic species at solar metallicity, solar C/O ratio and 0.5 f c . P - T profiles andspectra per planet. However, as mentioned earlier, not allmodels in the parameter space achieve convergence, thusleading to absence of some models in the library ( ∼ P - T profiles andcorresponding equilibrium chemical abundances used to gen-erate our transmission and emission spectra are the same, i.ethey span a similar parameter space. Since we are presentinghere a library of model atmospheres and corresponding spec-tra, they are intended to cover a wide range of possibilitiesand all the extremes.The choice of recirculation factor (f c ) covers all possiblescenarios from no recirculation (1.0) to extremely fast winds(0.25). We do not extend the grid to metallicities greaterthan 200 × solar, because above this metallicity the atmo-sphere becomes abundant in species other that H and He,such as CO , H O, CO etc. This would require the inclusionof pressure broadening effects due to these species, and noexisting studies have solved this problem due to lack of lab-based observational data (Fortney et al. 2016). The choiceof C/O ratios in the grid is guided by important transitionregimes as found by previous studies (Madhusudhan 2012;Molli`ere et al. 2015; Goyal et al. 2018; Molaverdikhani et al.2019).As described in Goyal et al. (2018, 2019a,b), there aretwo approaches to treat condensation in our library of mod-els, rainout and local condensation. While computing equi-librium chemical abundances to obtain RCE P - T profileswith rainout condensation, each layer is dependent on otherlayers, specifically only on layers that lie at higher pressures,in contrast to the local condensation approach where eachlayer is independent. This makes the assumption of rainoutwith RCE P - T profiles more realistic for a planetary atmo-sphere as compared to just local condensation. Therefore,we generate RCE P - T profiles with rainout condensation forthe library of models presented in this work. However, weshow the differences in the P - T profiles and the spectra dueto the different approaches in the next section.The structure of the pressure broadened line wings of Na and K can have a substantial effect on the P - T profilesand thereby the emission spectrum of brown dwarfs and hotJupiter exoplanet atmospheres (Burrows et al. 2000; Allardet al. 2003). Even with their high resolution measurements,the shape of the pressure broadened wings are still a matterof debate for Brown dwarfs (Burrows et al. 2002; Burgasseret al. 2003; Allard et al. 2003). For hot Jupiters we havevery recently started to observationally probe the line wingsof Na/K (Nikolov et al. 2018). In Section 2.1 of the onlinesupplementary material of this paper we show the differencesin the P - T profiles and the spectra due to these two linewing profiles for Na and K. The differences are negligibleand unlikely to be detectable by observations. We adopt theNa and K line wing profiles from Allard et al. (2003) forthe library of models presented in this work, which includesdetailed quantum mechanical calculations while computingthese profiles (Amundsen 2015).Although convection plays an important role in deter-mining the P - T profile of brown dwarfs, we see for hot Jupiterexoplanet atmospheres the effect of convection on the P - T structure of the observable atmosphere is negligible. Thisis because of the strong irradiation on these planets fromtheir host stars, which reduces the radiative time scale, thusmaking the atmospheric P - T profile almost entirely depen-dent on the top of the atmosphere irradiation (along withthe atmospheric pressure, temperature and heat capacity),at-least in the region where observations can probe the at-mosphere. Therefore, we conclude that it is not necessaryto include convection while computing RCE P - T profiles forirradiated hot Jupiter exoplanet atmospheres. However, inthis work all the P - T profiles include parameterized convec-tion for completeness, as it is computationally inexpensive.As described in Drummond et al. (2019) there are threedifferent methodologies to vary C/O ratio relative to the so-lar C/O ratio. In the simulations presented in Goyal et al.(2018) and Goyal et al. (2019b), we varied C/O ratio byvarying O/H. However, varying C/O by varying C/H canlead to differences in P - T profiles and equilibrium chemicalabundances as shown by Drummond et al. (2019). Therefore, MNRAS , 1–26 (2019)
Goyal et al. we investigated the effect of varying C/O ratio, by varyingO/H and those by varying C/H using WASP-17b as the testcase, with the results presented in the online supplementarymaterial Section 2.3. Although there are some differences inthe results obtained using these two different methodologies,in the parameter space we consider, they are smaller com-pared to the effects of other parameters in the grid and othermodel choices (for e.g. local or rainout condensation). There-fore, to enable fair comparison between the model spectragenerated in our previous works (Goyal et al. 2018, 2019b)and keep the library of models consistent with them, weagain in this work adopt the methodology of varying C/Oratio by varying O/H. Ideally, we could use O/H and C/H asseparate parameters in the grid, however, that increases thesize of the grid substantially and makes it computationallyexpensive for a large number of exoplanets. Therefore, weselect one methodology over the other.
In this section we initially show the effects of some ofthe important model choices on the RCE P - T profiles andthereby the equilibrium chemical abundances, transmissionand emission spectra, which could effect interpretation of ob-servations. Additional tests showing the sensitivity of someof the other model choices such as the Na and K line-wingprofiles, VO line-list sources and the methodology to varyC/O ratio either by varying O/H or C/H, are all detailedin the online supplementary material of this paper. Decou-pled emission spectrum are also shown and described in theonline supplementary material, to aid identification of differ-ent spectral features in the emission spectra. In the followingsections, we show the sensitivity to the choice of condensa-tion process (rainout/local), high levels of irradiation due tothermal ionization, addition of H − and Fe opacity, and for-mation of temperature inversion in the atmosphere. Finally,we show the sensitivity of the model simulations, i.e P - T profiles, chemical abundances, spectra and the contributionfunctions, to all the grid parameters across their full range,using WASP-121b and WASP-17b as test cases. Goyal et al. (2019b) have demonstrated that the adop-tion of either a rainout or local condensation approach re-sults in differences in the transmission spectra when adopt-ing an isothermal P-T profile. Here, we investigate the ef-fects of these two condensation approaches on the RCE P - T profiles and thereby the equilibrium chemical abun-dances, and transmission/emission spectra. Fig. 3a, 3b, 3c,3d and 3e, show the RCE P - T profiles, equilibrium chemi-cal abundances, transmission spectra, emission spectra andNormalised Contribution Functions (NCF), respectively, forWASP-17b at 0.25 f c , solar metallicity and solar C/O ratio,adopting both rainout and local condensation. A differenceof ∼ P - T profile adopting the local condensation approach having higher temperatures. How-ever, in the deeper atmosphere ( ∼ P - T profile with rainout condensation is hotter by ∼
200 K. Thisdifference in temperature leads to lower abundance of Naand K in the upper atmosphere and a higher abundanceof TiO/VO in the local condensation case, as compared torainout condensation case, shown in Fig. 3b. This higherTiO/VO abundance can also be seen in the transmissionspectra shown in Figure 3c where the spectra with localcondensation show TiO/VO features in the optical, missingin the rainout condensation case. This also strengthens thefindings of Goyal et al. (2019b), that TiO/VO features canreveal dominant physical process (rainout or local conden-sation) in the planet’s atmosphere.The differences in the emission spectra shown in Fig.3d are substantial, primarily due to the differences in the P - T structure. At 1.1 µ m deeper parts of the atmosphere ( ∼ ∼ µ m the wavelength of one of thestrongest water opacity bands, we see the NCF moves to theupper atmosphere and the difference between the pressurelevels being probed using emission spectrum in the case ofthe rainout (0.1 bar) and local condensation (0.01bar) simu-lations are also substantially different. This is mainly due tothe large difference in the temperatures between the rainoutand local condensation simulations between 0.1 and 0.01bar.The difference in the peak pressure level of the NCF as ob-served between 1.1 and 1.4 µ m , the wing and core of waterband, respectively, can be observed more strongly at 2.25and 2.8 µ m , since this is the region of peak emission fora body with temperature similar to the equilibrium tem-perature of WASP-17b. Since the differences in the spectraare substantial, it might be possible to distinguish betweenemission spectra due to rainout and local condensation, andtherefore constrain the P - T profiles and thereby the conden-sation processes using JWST. Thermal ionisation of certain species can have a substantialeffect on the chemistry of the planetary atmospheres, de-pending on the atmospheric temperature. Figure 4a showsthe equilibrium chemical abundances of certain importantspecies for an extremely irradiated hot Jupiter WASP-121b,with (dashed line) and without (solid line) thermal ionicspecies included in the equilibrium chemistry computation.H − opacity has been included in the model simulation withthermal ionic species and Fe opacity in both. The abundanceof Na decreases by about 3 orders of magnitude in the upperatmosphere (transmission spectra probed region) when ther-mal ionic species are included, as Na is ionized to form Na + .Figure 4a shows that the abundance of Na + becomes almostequal to Na without thermal ionic species model simulation,in the upper atmosphere (P < − bar). Similar behaviorcan be observed for K and K + ions. The abundance of H O MNRAS000
200 K. Thisdifference in temperature leads to lower abundance of Naand K in the upper atmosphere and a higher abundanceof TiO/VO in the local condensation case, as compared torainout condensation case, shown in Fig. 3b. This higherTiO/VO abundance can also be seen in the transmissionspectra shown in Figure 3c where the spectra with localcondensation show TiO/VO features in the optical, missingin the rainout condensation case. This also strengthens thefindings of Goyal et al. (2019b), that TiO/VO features canreveal dominant physical process (rainout or local conden-sation) in the planet’s atmosphere.The differences in the emission spectra shown in Fig.3d are substantial, primarily due to the differences in the P - T structure. At 1.1 µ m deeper parts of the atmosphere ( ∼ ∼ µ m the wavelength of one of thestrongest water opacity bands, we see the NCF moves to theupper atmosphere and the difference between the pressurelevels being probed using emission spectrum in the case ofthe rainout (0.1 bar) and local condensation (0.01bar) simu-lations are also substantially different. This is mainly due tothe large difference in the temperatures between the rainoutand local condensation simulations between 0.1 and 0.01bar.The difference in the peak pressure level of the NCF as ob-served between 1.1 and 1.4 µ m , the wing and core of waterband, respectively, can be observed more strongly at 2.25and 2.8 µ m , since this is the region of peak emission fora body with temperature similar to the equilibrium tem-perature of WASP-17b. Since the differences in the spectraare substantial, it might be possible to distinguish betweenemission spectra due to rainout and local condensation, andtherefore constrain the P - T profiles and thereby the conden-sation processes using JWST. Thermal ionisation of certain species can have a substantialeffect on the chemistry of the planetary atmospheres, de-pending on the atmospheric temperature. Figure 4a showsthe equilibrium chemical abundances of certain importantspecies for an extremely irradiated hot Jupiter WASP-121b,with (dashed line) and without (solid line) thermal ionicspecies included in the equilibrium chemistry computation.H − opacity has been included in the model simulation withthermal ionic species and Fe opacity in both. The abundanceof Na decreases by about 3 orders of magnitude in the upperatmosphere (transmission spectra probed region) when ther-mal ionic species are included, as Na is ionized to form Na + .Figure 4a shows that the abundance of Na + becomes almostequal to Na without thermal ionic species model simulation,in the upper atmosphere (P < − bar). Similar behaviorcan be observed for K and K + ions. The abundance of H O MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b)(c) (d) Figure 5. (a)
Figure showing RCE P - T profiles without (blue) and with (red) H − opacity included in the model for WASP-121b at solarmetallicity, solar C/O ratio and 0.5 f c . Fe opacity is not included in both these models (see Section 5.2.2 for details). (b) Same as Figure5a but at C/O ratio of 1.5 and 1.0 f c . (c) Figure showing transmission spectra using P - T profiles shown in Figure 5b and correspondingchemical abundances with and without H − opacity. (d) Figure showing emission spectra using P - T profiles shown in Figure 5b andcorresponding chemical abundances with and without H − opacity. also drastically decreases for P < − bar, however, is stillsubstantial in the deeper atmosphere probed by emissionspectrum. Inclusion of thermal ionic species also has effectson the transmission spectra, where the narrow Na and Kfeatures (cores) seen in the model spectra without thermalionic species, disappear in the model spectra with thermalionic species as shown in Figure 4b. We note that the equi-librium abundance of H O at very high temperatures andlow pressures as for WASP-121b is almost similar (see Fig-ure 4a), with and without thermal ionic species, because,thermal decomposition of H O is taken care of in the equi-librium chemistry computation (by neutral products H andO ), even if ions are not included in the computation. − opacity H − opacity contributes to the absorption of radiation in hotJupiters via bound-free and free-free cross-sections as ex-plained in Appendix A2. There is also a strong observationalevidence for H − opacity in Mikal-Evans et al. (2019). To un-derstand the effect of H − opacity we compute P - T profileswith and without H − opacities included in the model. Wealso don’t include Fe opacity specifically for models in thistests, to isolate the effects of H − opacity. Figure 5a showthese P - T profiles at 0.5 f c with solar metallicity and C/Oratio for WASP-121b. It can be noticed from the P - T pro-files that H − opacity tends to cool the deeper atmosphere( > c value of 1 (not shown here). This can be attributed toan increase in H − abundance in the lower atmosphere ( > c value, as the temperature increases.In Figure 5b the P - T profile obtained using a f c value of MNRAS , 1–26 (2019) Goyal et al. (a) (b)(c)
Figure 6. (a)
Figure showing RCE P - T profiles without (blue) and with (red) Fe opacity included in the model for WASP-121b at solarmetallicity, solar C/O ratio and 0.5 f c . (b) Figure showing transmission spectra using P - T profiles shown in Figure 6a and correspondingchemical abundances with and without Fe opacity. (c) Figure showing emission spectra using P - T profiles shown in Figure 6a andcorresponding chemical abundances with and without Fe opacity. − opacity. Figure 5b shows that there is a substantialdifference in P - T profiles with and without H − opacity.Without H − opacity there is a weak temperature inver-sion as compared to that with H − opacity. At high C/O ra-tios ( >
1) as shown in Figure 14b, the abundance of TiO/VOdecreases dramatically, the major absorbers likely to causean inversion in extremely irradiated hot Jupiters like WASP-121b. Therefore, other species start contributing to form atemperature inversion. Without H − opacity the strong inver-sion is not sustained but there is a weak inversion due to Naand K (as shown in Molli`ere et al. 2015) discussed in detailin Section 5.3.3.2. With H − opacity the strength of inver-sion increases dramatically at f c = 1.0 and C/O ratio of 1.5as shown in Figure 5b, because the H − abundance betweenpressure levels ∼ − bar increases (see Figure 14b fortrends even though at f c = 0.5), such that its opacity cancreate an inversion similar to TiO/VO. However, thermalinversion due to H − opacity lies deeper (higher pressure) in the atmosphere ( ∼ − bar), in comparison to the in-version due to TiO/VO ( ∼ − to 10 − bar). To investigatethe potential of H − opacity by its own to form temperatureinversions at different C/O ratios, we performed some modelsimulations by removing dominant optical absorbers such asTiO, VO, Na, K, Li, Rb, Cs, Fe and FeH. We find H − opacityis able to create a strong thermal inversion for C/O ratios ≥
1, we also see a very weak temperature inversion ( ∼
100 K) atC/O ratio of 0.75 and almost negligible at solar C/O ratio(0.55), highlighting the C/O ratio dependency of H − opacityto create thermal inversions.The effect of H − opacity on the transmission spectrumis also substantial as shown in the Figure 5c where it tendsto obstruct the deeper atmosphere due to its high opacityas shown for a high C/O ratio case for WASP-121b. In thiscase it tends to mute the wings of Na and K mimickingthe effect of cloud at optical wavelengths. Figure 5d showsthe emission spectrum for WASP-121b with and without H − opacity using the P - T profile shown in Figure 5b. Figure 5dshows that there is a substantial difference in the emission MNRAS000
100 K) atC/O ratio of 0.75 and almost negligible at solar C/O ratio(0.55), highlighting the C/O ratio dependency of H − opacityto create thermal inversions.The effect of H − opacity on the transmission spectrumis also substantial as shown in the Figure 5c where it tendsto obstruct the deeper atmosphere due to its high opacityas shown for a high C/O ratio case for WASP-121b. In thiscase it tends to mute the wings of Na and K mimickingthe effect of cloud at optical wavelengths. Figure 5d showsthe emission spectrum for WASP-121b with and without H − opacity using the P - T profile shown in Figure 5b. Figure 5dshows that there is a substantial difference in the emission MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres spectrum with and without H − opacity, due to difference in P - T profiles. Gaseous iron (Fe) opacity dramatically effects the P - T pro-files of extremely irradiated hot Jupiters (Lothringer et al.2018). It tends to heat the upper, lower pressure, atmosphereas shown in the Fig. 6a and cool the lower, high pressure,atmosphere. The cross-section of Fe is quite large in the op-tical leading to strong absorption and therefore the heatingin the upper atmosphere. This blocking of radiation higherup in the atmosphere is one of the causes of the coolingin the deeper atmosphere similar to H − . The transmissionspectra in Figure 6b, shows that Fe opacity is important inthe optical part of the spectrum, generally dominated byRayleigh scattering slope, with very sharp spectral features.The emission spectrum in Figure 6c with and without Feopacity, shows that the strength of the thermal inversionin the emission increases after adding Fe opacity. Thus Feopacity can play an important role in creating secondary in-versions, but in the lower pressure regions ( ∼ − or TiO/VO opacity (seeSection 5.2.4.2 for more details). The absence of H O dueto thermal dissociation also contributes to this secondaryinversion at extremely low pressures, as there is no stronginfrared emitting species available to re-emit the energy ab-sorbed by Fe. The difference between the emission spectrumshown in Figure 6c is mainly due to the increase in the size ofemission features, due to a larger temperature difference be-tween the lower (high pressure) and the upper (low pressure)atmosphere in simulations including Fe opacity, as comparedto those without Fe opacity.
The formation of temperature inversion in a irradiated plan-etary atmosphere is governed by the interplay between ab-sorbed stellar radiation and planetary emission. The pres-ence of temperature inversions in hot Jupiter exoplanet at-mospheres have been predicted for a long time (Hubeny et al.2003; Fortney et al. 2008), primarily due to TiO/VO opac-ities, as shown in Figure 8a. The presence of temperatureinversion due to TiO/VO also leads to substantial changesin the emission spectrum of the planet as shown in Figure8b. However, it is only very recently that a definitive evi-dence of an inversion layer has been seen in the atmosphereof an ultra-hot Jupiter WASP-121b (Evans et al. 2017). Al-though, there is a tentative evidence of VO in the trans-mission spectrum of WASP-121b (Evans et al. 2018), it isstill unclear what opacity source is causing this additionalabsorption creating a temperature inversion in WASP-121b,Therefore, in this section, the opacity required to producean inversion, its impact on the P - T profile and thereby theemission spectra is investigated. − opacity: Following Burrows et al. (2008) and Spiegel et al.(2009), we add an arbitrary grey absorbing opacity acrossthe optical wavelengths (0.44 - 1 µ m ) throughout the atmo-sphere (all model layers) of WASP-121b with 0.8 f c , solar metallicity and C/O ratio. Varying the magnitude of thisopacity then allows us to explore the evolution of the P - T profile from being non-inverted to being inverted as a func-tion of opacity, along with the evolution of the emission spec-trum for these different atmospheric structures. The valueof 0.8 f c is chosen as the best fit value to observations inEvans et al. (2017). For this particular test along with agrey absorbing opacity in the optical, only the H -H andH -He CIA, and H O, CO , CO, CH , NH , Na, K, Li, Rb,Cs opacities were used for simplicity. Figure 7a and 7b showthe P - T profile and emission spectra, respectively, for vary-ing levels of grey opacity for WASP-121b. We note that wehave omitted TiO/VO opacity in this model simulation. Itcan be seen that as the grey opacity increases from 0.002 to0.02 cm /g the P - T profile changes from being non-invertedto inverted. We also compute the ratio γ = κ vis κ IR , (4)where κ vis and κ IR are the mean opacities in the visi-ble and IR wavelengths, as used in previous works (Molli`ereet al. 2015; Gandhi & Madhusudhan 2019), to quantify thestrength of the inversion. We compute κ IR using the Planckmean opacity for the temperature of each atmospheric level,whereas κ vis is computed using the Planck mean opacityat the stellar effective temperature of WASP-121, which is ∼ ∼ γ valuesare 4.78, 5.5, 6.06 and 8.3 for grey opacity values of 0.002,0.004, 0.006 and 0.02 cm /g, respectively. The strength ofthe inversion increases as the value of γ increases. However,we note that this method to quantify strength of inversioncan be too simplistic, especially when comparing strength ofinversion caused by different species, mainly due to two rea-sons. Firstly, the altitude/pressure of the inversion can varydepending on the RCE P - T profile and the correspondingchemical equilibrium abundances, therefore using the γ valueat one particular pressure level may not be an accurate wayto compare strength of inversions. Secondly, for hot planetslike WASP-121b there will be some overlap between the visi-ble (stellar spectrum) and infrared (planet spectrum), whichagain means this simplistic approach is not likely to provideaccurate measure of the strength of the inversion.The change in the emission spectrum is more interest-ing where the H O absorption feature at 1.4 µ m graduallychanges into an emission feature, as the amount of grey opac-ity is increased. Moreover, with 0.006 cm /g grey opacity thespectrum almost resembles a blackbody spectrum indicatingan isothermal atmosphere, which can be seen in Figure 7a.As discussed in detail in Section 5.2.2 and shown inFigure 5b, H − opacity which almost acts like a grey opacityin the optical can produce a strong inversion in the absenceof TiO/VO opacities, which only happens at high C/O ratios( > − opacity could possibly be the opacity source that leads toinversion in the atmosphere of WASP-121b and many otherultra hot Jupiter planets. Iron (Fe) has very strong opacity in the UV and the opticalpart of the spectrum. Therefore, we investigated whether Fecan lead to inversions without TiO/VO in extremely irradi-ated hot Jupiter such as WASP-121b. For this we removed
MNRAS , 1–26 (2019) Goyal et al. (a) (b)
Figure 7. (a)
Figure showing P - T profiles for WASP-121b with 0.8 f c , solar metallicity and solar C/O ratio, with different amountof optical grey opacity added throughout the atmosphere. (b) Figure showing emission spectra with different amount of optical greyopacity using P - T profiles shown in Figure 7a.(a) (b) Figure 8. (a)
Figure showing RCE P - T profiles with all opacities (blue) including Fe and without TiO/VO opacities (red), at solarmetallicity and solar C/O ratio with 0.5 f c for WASP-121b. (b) Figure showing emission spectra using P - T profiles shown in Figure 8awith all opacities (blue) including Fe and without TiO/VO opacities (red) for WASP-121b. TiO/VO opacities from the model while computing RCE P - T profiles. We found that the Fe opacity we include is unableto produce a strong inversion like TiO/VO at solar metallic-ity as shown in Figure 8. Even if we increase the metallicityto 200 times solar, leading to an increase in Fe abundance toabout ∼ × than that at solar metallicity, it does not leadto an inversion. Fe opacity however, leads to a sharp increasein the temperature at lower pressures ( ∼ − bar like a ther-mospheric secondary inversion). The primary reason behindthis secondary inversion at low pressures is the low abun-dance of species that emit strongly in the infrared (for e.gthermal decomposition of H O), which reduces atmosphericcooling (see Figure 14b). We also observe this secondary in-version due to various other strong optical absorbers such asNa and K, when the abundance of strong infrared emitterssuch as H O or CH decreases. This overall result due to Fe opacity might seem to con-tradict that of Lothringer et al. (2018), where they see aninversion due to Fe opacity at around 10 − bar (10 mbar).However, Lothringer et al. (2018) used a fiducial model witha planet at 0.025 au from a star with effective tempera-ture of 7200 K, about ∼
750 K hotter than WASP-121. More-over, they include bound-free Fe opacity in their model sim-ulations which becomes important for wavelengths shorterthan 0.2 µ m (Sharp & Burrows 2007). The combination ofall these factors may have led to differences between our re-sults, alongside other factors such as the equilibrium chem-ical abundances of Fe as well as the treatment of condensa-tion. However, in KELT-9b the planet with highest equilib-rium temperature in our library of models, Fe opacity leadsto formation of a strong temperature inversion starting at ∼ MNRAS000
750 K hotter than WASP-121. More-over, they include bound-free Fe opacity in their model sim-ulations which becomes important for wavelengths shorterthan 0.2 µ m (Sharp & Burrows 2007). The combination ofall these factors may have led to differences between our re-sults, alongside other factors such as the equilibrium chem-ical abundances of Fe as well as the treatment of condensa-tion. However, in KELT-9b the planet with highest equilib-rium temperature in our library of models, Fe opacity leadsto formation of a strong temperature inversion starting at ∼ MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b)(c) (d)(e) (f) Figure 9. (a)
Figure showing P - T profiles for a range of f c values (0.25, 0.5, 0.75 and 1) at solar metallicity and solar C/O ratio (0.55)for WASP-121b (b) Figure showing equilibrium chemical abundances for some important species for various f c values obtained using P - T profiles shown in Figure 9a. (c) Figure showing transmission spectra for various f c values obtained using P - T profiles shown in Figure9a and corresponding equilibrium chemical abundances shown in Figure 9b. (d) Figure showing planetary emission spectra for variousf c values obtained using P - T profiles shown in Figure 9a and corresponding equilibrium chemical abundances shown in Figure 9b. (e) Figure showing normalized contribution function at 1.7 µ m for a range of f c values for emission spectra as shown in Figure 9d. (f) Sameas Figure 9e but at 1.4 µ m .MNRAS , 1–26 (2019) Goyal et al.
TiO/VO/H − . Thus, the capability of Fe opacity to form atemperature inversion is system specific showing a strongdependance on the host star effective temperature.We note that there are many other potential speciessuch as AlO, CaO, SiO, NaH, AlH, SiH, MgH etc. shownin recent studies (Lothringer et al. 2018; Malik et al. 2019;Gandhi & Madhusudhan 2019) with strong optical opacitiesthat could lead to the formation of an inversion in ultra-hotJupiters. However, these opacities have not been includedin the current version of our library. Among these speciesthere have been indications of AlO in some of the planets(von Essen et al. 2019; Chubb et al. 2020). Therefore, someof these opacities will be considered in the future version ofthe library. In this section we show the sensitivity of the model simula-tion, i.e P - T profiles and the spectra, to all the grid parame-ters, namely recirculation factor, metallicity and C/O ratioacross their full range used in this library, using WASP-17band WASP-121b as test cases. The recirculation factor (f c ) described in Section 2.2 governsthe efficiency of re-distribution of energy (by winds) receivedfrom the host star in a column. The value of 1 correspondsto no-redistribution, with an increase in redistribution asthis factor decreases. Here, we show the effect of varyingthe recirculation factor on the P - T profiles and thereby thechemical abundances and spectra, using the extremely ir-radiated hot Jupiter WASP-121b as an example. As can inseen in the P - T profiles in Figure 9a for WASP-121b, thestrength of the atmospheric temperature inversion increaseswith f c as expected, since more energy is available to createan inversion at higher values of f c . At 0.25 f c the inversion isabsent in the P - T structure due to reduced irradiation (en-ergy). Absorption due to TiO/VO is the primary reason forthe inversion, but surprisingly the abundance of TiO/VOstarts decreasing, as the inversion is formed and increasesin strength, as can be seen in Figure 9b for increasing f c .However, the abundance of H − and Fe increases with in-creasing f c . This increase in H − maintains the temperatureinversion even though the abundance of TiO/VO decreases,as described in in Section 5.2.2 and also Section 5.3.3.2.The transmission spectrum of WASP-121b in Figure9c, shows that the strength of the H O features decreaseswith increasing f c as H O abundance decreases in the re-gion where transmission spectra probes ( ∼ O starts becoming thermally unstable with increasingtemperatures. However, CO features start appearing near ∼ µ m and broadband CO features between 4 to 6 µ m . Thestrength of these CO features increases with increasing f c . Asexpected, the flux in the planetary emission spectrum shownin Figure 9d increases with increasing f c as the temperatureof emission increases. The P - T profile at 0.25 f c is very closeto isothermal, therefore its emission spectrum also resem-bles a blackbody curve, with small dips in the strong watervapour absorption bands at 1.4, 2 and 3 µ m . In contrast, P - T profiles at other f c values have temperature inversions, thus leading to a bump instead of dip in the strong H O and COabsorption bands.The normalised contribution functions (NCF) at 1.7and 1.4 µ m are shown in Figure 9e and 9f, respectively, forWASP-121b. At 1.7 µ m , the NCF peaks deeper in the atmo-sphere as compared to that at 1.4 µ m , indicating emissionat 1.7 µ m is from comparatively deeper parts of the atmo-sphere, since 1.7 µ m is at the edge of strong water absorptionband centred at 1.4 µ m . For the profiles with a temperatureinversion (f c = 0.5, 0.75, 1.0), the deeper and cooler isother-mal part (not the inversion) is primarily probed at 1.7 µ m ascompared to 1.4 µ m which probes the inversion layer, thusleading to a emission feature (bump) instead of a absorptionfeature (dip) in the emission spectrum from 1.2 to 1.7 µ m .This also happens for other strong water absorption bandsas shown in the emission spectra. The 1.4 µ m emission fea-ture has been detected in the atmosphere of WASP-121b(Evans et al. 2017), but other such potential emission fea-tures indicative of inversion for wavelengths > µ m are stillto be detected for WASP-121b and can only be possible withJWST.At 0.25 f c the inversion is absent as we reduce the ir-radiation received from the host star to 25% of its origi-nal value, mimicking the transport of energy by advection(strong winds). This also motivates accurate 3D modelling ofextremely irradiated hot Jupiter exoplanets to predict inver-sions as well as to infer wind velocities based on the presenceor absence of inversions. Metallicity fundamentally effects the chemistry of the atmo-sphere and thereby its P - T structure and observed spectrum.The effect of metallicity on the P - T structure, chemistry,transmission and emission spectra for two different planetsis discussed in this section. WASP-17b is a hot Jupiter planetwith an equilibrium temperature of 1755 K. Adopting avalue of 0.5 for the f c the transmission spectra for this planetshows TiO/VO features due to hotter P - T structure as com-pared to that using 0.25 f c . However, observations from Singet al. (2016) shows the absence of TiO/VO features, there-fore we restrict the following analysis to simulations adopt-ing an f c of 0.25 (although all values are available in themodel grid). The C/O ratio is fixed to the solar value andthe metallicity varied from across the grid range to investi-gate the effect of metallicity. For this planet, an increasingmetallicity leads to an increase in the temperature through-out the atmosphere as shown in Figure 10a. This is a resultof increased absorption of radiation at lower pressures, dueto increased opacity, as the mean molecular weight of the at-mosphere increases, driven by an increase in the abundancesof species heavier than H and He, namely H O, CO andNa as shown in Figure 10b. A sharp increase in temperaturefor sub-solar metallicity can be seen at pressures less than ∼ − bar, but it is observationally insignificant either intransmission or emission spectra, due to the low atmosphericdensity at these pressures.The effect of varying the metallicity on the transmis-sion of WASP-17b is shown in Figure 10c. The transmission MNRAS , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b)(c) (d)(e) (f) (g) (h) Figure 10. (a)
Figure showing P - T profiles for a range of metallicities at 0.25 f c and a solar C/O ratio (0.55) for WASP-17b. (b) Figureshowing equilibrium chemical abundances for some important species for various metallicity values obtained using P - T profiles shown inFigure 10b. (c) Figure showing transmission spectra for WASP-17b for different values of metallicity obtained using P - T profiles shownin Figure 10a and corresponding equilibrium chemical abundances shown in Fig. 10b. (d) Figure showing emission spectra for WASP-17bfor different values of metallicity obtained using P - T profiles shown in Figure 10a and corresponding equilibrium chemical abundancesshown in Fig. 10b. (e, f, g, h) Figures e, f, g, h showing normalised contribution function at 2.25, 2.8, 3.8 and 4.5 µ m for a range ofmetallicity values for emission spectra shown in Figure 10d.MNRAS , 1–26 (2019) Goyal et al. spectra are primarily dominated by Na, K and narrow Li fea-tures in the optical for all metallicities, with weaker TiO/VOfeatures as metallicity increases. The infrared part of thespectrum is primarily dominated by H O features for allmetallicities. The size of the H O features initially increaseswith an increase in metallicity as H O abundance increasesshown in Figure 10b, but then again decreases with increas-ing metallicity. This is caused by the increase in the meanmolecular weight of the atmosphere, leading to a decreaseof the atmospheric scale height, which, in turn, shrinks thespectral features in transmission. Pressure broadened wingsof Na and K are also effected by change in metallicity. Dueto decreasing scale height associated with increasing metal-licity, transmission spectra probes high pressure levels of theatmosphere, resulting in enhanced broadening of Na and Kline wings with increasing metallicity. The CO feature near4.5 µ m and 2.5 - 3 µ m increases in amplitude, which can alsobe seen in the emission spectrum, primarily due to a rapidincrease in the CO abundances. This shows that even un-der chemical equilibrium conditions the atmosphere rapidlytends to migrate towards a CO abundant atmosphere withincreasing metallicity (Moses et al. 2013), offering potentialreasons for the CO dominated compositions of Mars andVenus in our Solar system. Even Earth in the past may havehad a CO dominated atmosphere, currently captured inthe oceans and rocks by various geological processes (Zahnleet al. 2010). The transmission spectra can also be comparedwith Figure 12a in Goyal et al. (2019a) which uses isothermal P - T profiles. The comparison might not be completely accu-rate as the RCE P - T profiles shown here are overall coolerthan the equilibrium temperature of WASP-17b (1755 K) inthe transmission spectra probed region ( ∼ P - T profiles shown in Fig. 10a increases with in-creasing metallicity. This increase in temperature combinedwith the increase in abundances of species such as H O andCO , with increasing metallicity, leads to deeper absorptionfeatures. Similar to the transmission spectrum, the emissionspectrum is also dominated by water absorption features forWASP-17b in the infrared with CO features around 4.5 and2.5 - 3 µ m region for metallicities greater than 10 times so-lar value. The atmospheric level which contributes most tothe emission at different wavelengths can be found using theNCF. The increase in the overall temperature of the P - T profile causes the NCF to consistently shifts towards lowerpressure with increase in metallicity as shown in Figures 10e,10f, 10g and 10h. The NCF at the core of the CO absorp-tion band at 4.5 µ m shown in the Fig. 10h, peaks at lowerpressures ( < ∼ µ m as shown in the Figure 10g. The dramatic drop in theemission flux between these two wavelengths is also shown inthe emission spectra for metallicities greater than 50 timessolar. The NCF for the 2.8 µ m H O absorption band alsoshows similar effect as 4.5 µ m CO absorption band, shownin Figures 10e and 10f, for 2.25 and 2.8 µ m , respectively. The atmospheric level probed by emission spectrum shiftsto lower pressure levels with increasing metallicity, as shownby contribution functions in the H O and CO bands. Thewings and cores of absorption/emission bands also probe dif-ferent atmospheric layers for a given metallicity. Therefore,the absorption/emission features of various species can beused to constrain metallicity, as well as the P - T tempera-ture structure of the atmosphere. For some cases (for e.gFig. 10h) particularly at high metallicity, NCF shows thatthe emission spectrum is probing quite high in the atmo-sphere ( ∼ − bar). In such cases, photochemistry can alterthe emission spectrum via the formation of photochemicalproducts and change in chemical abundances (and therebythe P - T profile) at high altitudes (P < ∼ − bar) (Madhusud-han et al. 2016; Hobbs et al. 2019). However, since photo-chemistry is a dis-equilibrium effect, it is not considered inthis work and is part of our future work as discussed in theconclusions. WASP-121b is an extremely irra-diated hot Jupiter planet with an equilibrium temperature(T eq ) of ∼ P - T structure, chemical abundances, trans-mission and emission spectra, respectively for WASP-121bat 0.5 f c and solar C/O ratio. Figures 11e, 11f, 11g and 11hshow the contribution function at 2.25, 2.8, 3.8 and 4.5 µ m ,respectively.For WASP-121b we see a temperature inversion in the P - T profile, which moves towards higher pressure levels withincreasing metallicity, primarily driven by TiO/VO absorp-tion. At sub-solar metallicity the inversion is very weak, dueto the low abundance of TiO/VO, seen in Figure 11b. The Feabundance is also substantial, mainly contributing to upperatmosphere heating, as the Fe absorption cross-sections arelargest in the UV-Optical spectrum. This upper atmosphereheating leads to the formation of a second inversion layerbut with weak observational signatures due to the very lowdensity of the atmosphere in this region.The transmission spectra shown in Figure 11c is domi-nated by TiO/VO features in the optical, the size of whichdecreases with increasing metallicity due to a reduction inthe atmospheric scale height. Sharp Fe features dominatethe optical spectrum short-ward of ∼ µ m with H O fea-tures in the infrared. The CO features are also seen in thetransmission spectrum particularly around 2.5 and 4-6 µ m ,which can also be seen in the emission spectrum in Fig. 11d.In the emission spectra shown in Figure 11d for WASP-121b, due to an inversion layer in the P - T profile, most of themolecular features are seen as emission features as opposedto the absorption features seen for WASP-17b. The ampli-tude of the CO features increases with increasing metallicity.The TiO/VO features can also be seen as emission featuresin the emission spectra in the optical. The H O emissionfeatures dominate the infrared, where the 1.4 µ m feature hasled to the detection of an inversion layer for the first time inan exoplanet atmosphere (Evans et al. 2017). It can also benoticed from the NCF that the wings of strong absorptionbands at 2.25 (H O) and 3.8 µ m (CO) shown in Fig. 11e and11g, respectively, mainly probe the region below the inver-sion layer, while the cores of absorption bands at 2.8 and4.5 µ m shown in Fig. 11f and 11h probe the inversion layer. MNRAS000
Figure showing P - T profiles for a range of metallicities at 0.25 f c and a solar C/O ratio (0.55) for WASP-17b. (b) Figureshowing equilibrium chemical abundances for some important species for various metallicity values obtained using P - T profiles shown inFigure 10b. (c) Figure showing transmission spectra for WASP-17b for different values of metallicity obtained using P - T profiles shownin Figure 10a and corresponding equilibrium chemical abundances shown in Fig. 10b. (d) Figure showing emission spectra for WASP-17bfor different values of metallicity obtained using P - T profiles shown in Figure 10a and corresponding equilibrium chemical abundancesshown in Fig. 10b. (e, f, g, h) Figures e, f, g, h showing normalised contribution function at 2.25, 2.8, 3.8 and 4.5 µ m for a range ofmetallicity values for emission spectra shown in Figure 10d.MNRAS , 1–26 (2019) Goyal et al. spectra are primarily dominated by Na, K and narrow Li fea-tures in the optical for all metallicities, with weaker TiO/VOfeatures as metallicity increases. The infrared part of thespectrum is primarily dominated by H O features for allmetallicities. The size of the H O features initially increaseswith an increase in metallicity as H O abundance increasesshown in Figure 10b, but then again decreases with increas-ing metallicity. This is caused by the increase in the meanmolecular weight of the atmosphere, leading to a decreaseof the atmospheric scale height, which, in turn, shrinks thespectral features in transmission. Pressure broadened wingsof Na and K are also effected by change in metallicity. Dueto decreasing scale height associated with increasing metal-licity, transmission spectra probes high pressure levels of theatmosphere, resulting in enhanced broadening of Na and Kline wings with increasing metallicity. The CO feature near4.5 µ m and 2.5 - 3 µ m increases in amplitude, which can alsobe seen in the emission spectrum, primarily due to a rapidincrease in the CO abundances. This shows that even un-der chemical equilibrium conditions the atmosphere rapidlytends to migrate towards a CO abundant atmosphere withincreasing metallicity (Moses et al. 2013), offering potentialreasons for the CO dominated compositions of Mars andVenus in our Solar system. Even Earth in the past may havehad a CO dominated atmosphere, currently captured inthe oceans and rocks by various geological processes (Zahnleet al. 2010). The transmission spectra can also be comparedwith Figure 12a in Goyal et al. (2019a) which uses isothermal P - T profiles. The comparison might not be completely accu-rate as the RCE P - T profiles shown here are overall coolerthan the equilibrium temperature of WASP-17b (1755 K) inthe transmission spectra probed region ( ∼ P - T profiles shown in Fig. 10a increases with in-creasing metallicity. This increase in temperature combinedwith the increase in abundances of species such as H O andCO , with increasing metallicity, leads to deeper absorptionfeatures. Similar to the transmission spectrum, the emissionspectrum is also dominated by water absorption features forWASP-17b in the infrared with CO features around 4.5 and2.5 - 3 µ m region for metallicities greater than 10 times so-lar value. The atmospheric level which contributes most tothe emission at different wavelengths can be found using theNCF. The increase in the overall temperature of the P - T profile causes the NCF to consistently shifts towards lowerpressure with increase in metallicity as shown in Figures 10e,10f, 10g and 10h. The NCF at the core of the CO absorp-tion band at 4.5 µ m shown in the Fig. 10h, peaks at lowerpressures ( < ∼ µ m as shown in the Figure 10g. The dramatic drop in theemission flux between these two wavelengths is also shown inthe emission spectra for metallicities greater than 50 timessolar. The NCF for the 2.8 µ m H O absorption band alsoshows similar effect as 4.5 µ m CO absorption band, shownin Figures 10e and 10f, for 2.25 and 2.8 µ m , respectively. The atmospheric level probed by emission spectrum shiftsto lower pressure levels with increasing metallicity, as shownby contribution functions in the H O and CO bands. Thewings and cores of absorption/emission bands also probe dif-ferent atmospheric layers for a given metallicity. Therefore,the absorption/emission features of various species can beused to constrain metallicity, as well as the P - T tempera-ture structure of the atmosphere. For some cases (for e.gFig. 10h) particularly at high metallicity, NCF shows thatthe emission spectrum is probing quite high in the atmo-sphere ( ∼ − bar). In such cases, photochemistry can alterthe emission spectrum via the formation of photochemicalproducts and change in chemical abundances (and therebythe P - T profile) at high altitudes (P < ∼ − bar) (Madhusud-han et al. 2016; Hobbs et al. 2019). However, since photo-chemistry is a dis-equilibrium effect, it is not considered inthis work and is part of our future work as discussed in theconclusions. WASP-121b is an extremely irra-diated hot Jupiter planet with an equilibrium temperature(T eq ) of ∼ P - T structure, chemical abundances, trans-mission and emission spectra, respectively for WASP-121bat 0.5 f c and solar C/O ratio. Figures 11e, 11f, 11g and 11hshow the contribution function at 2.25, 2.8, 3.8 and 4.5 µ m ,respectively.For WASP-121b we see a temperature inversion in the P - T profile, which moves towards higher pressure levels withincreasing metallicity, primarily driven by TiO/VO absorp-tion. At sub-solar metallicity the inversion is very weak, dueto the low abundance of TiO/VO, seen in Figure 11b. The Feabundance is also substantial, mainly contributing to upperatmosphere heating, as the Fe absorption cross-sections arelargest in the UV-Optical spectrum. This upper atmosphereheating leads to the formation of a second inversion layerbut with weak observational signatures due to the very lowdensity of the atmosphere in this region.The transmission spectra shown in Figure 11c is domi-nated by TiO/VO features in the optical, the size of whichdecreases with increasing metallicity due to a reduction inthe atmospheric scale height. Sharp Fe features dominatethe optical spectrum short-ward of ∼ µ m with H O fea-tures in the infrared. The CO features are also seen in thetransmission spectrum particularly around 2.5 and 4-6 µ m ,which can also be seen in the emission spectrum in Fig. 11d.In the emission spectra shown in Figure 11d for WASP-121b, due to an inversion layer in the P - T profile, most of themolecular features are seen as emission features as opposedto the absorption features seen for WASP-17b. The ampli-tude of the CO features increases with increasing metallicity.The TiO/VO features can also be seen as emission featuresin the emission spectra in the optical. The H O emissionfeatures dominate the infrared, where the 1.4 µ m feature hasled to the detection of an inversion layer for the first time inan exoplanet atmosphere (Evans et al. 2017). It can also benoticed from the NCF that the wings of strong absorptionbands at 2.25 (H O) and 3.8 µ m (CO) shown in Fig. 11e and11g, respectively, mainly probe the region below the inver-sion layer, while the cores of absorption bands at 2.8 and4.5 µ m shown in Fig. 11f and 11h probe the inversion layer. MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b)(c) (d)(e) (f) (g) (h) Figure 11. (a)
Figure showing P - T profiles for a range of metallicity at 0.5 f c and a solar C/O ratio (0.55) for WASP-121b. (b) Figureshowing equilibrium chemical abundances for some important species for various metallicity values obtained using P - T profiles shownin Figure 11a. (c) Figure showing transmission spectra for WASP-121b for different values of metallicity obtained using P - T profilesshown in Figure 11a and corresponding equilibrium chemical abundances shown in Fig. 11b. (d) Figure showing emission spectra forWASP-121b for different values of metallicity obtained using P - T profiles shown in Figure 11a and corresponding equilibrium chemicalabundances shown in Fig. 11b. (e, f, g, h) Figures e, f, g, h showing normalised contribution function at 2.25, 2.8, 3.8 and 4.5 µ m for arange of metallicity values for emission spectra shown in Figure 11d.MNRAS , 1–26 (2019) Goyal et al. (a) (b)(c) (d)
Figure 12. (a)
Figure showing P - T profiles for a range of C/O ratios at 0.5 f c and solar metallicity for WASP-17b. (b) Figure showingequilibrium chemical abundances for some important species for various C/O values obtained using P - T profiles shown in Figure 12a. (c) Figure showing transmission spectra for WASP-17b for different values of C/O ratios obtained using P - T profiles shown in Figure 12aand corresponding equilibrium chemical abundances shown in Fig. 12b. (d) Figure showing emission spectra for WASP-17b for differentvalues of C/O ratios obtained using P - T profiles shown in Figure 12a and corresponding equilibrium chemical abundances shown in Fig.12b. The P - T profiles for WASP-17b fora range of C/O ratios are shown in Fig. 12a at 0.5 f c andsolar metallicity. We choose to show simulations with 0.5f c instead of 0.25 f c as one of the models with 0.25 f c anda C/O ratio of 1.0 failed to converge in the grid. It canbe seen that with increasing C/O ratio the P - T structureconsistently cools for P ≤ − bar. However, for P ≥ − bar the P - T structure first cools up-to C/O ratio of 0.75 andthen the temperature increases for a C/O ratio of 1 and 1.5.The sharp heating at around 10 − bar is due to Fe opacityas explained earlier in Section 5.2.4.2.The change in the equilibrium chemical abundances dueto the change in the C/O ratio is drastic, as it effects allthe major carbon and oxygen bearing molecules. As ex-pected the abundances of H O drop with increasing C/O ratio. Although CO bears a carbon atom it needs two oxy-gen atoms per carbon atom, therefore the equilibrium abun-dance of CO also drops with increasing C/O ratio, but insmaller increments as compared to H O. The abundance ofcarbon bearing species such as CH , HCN, C H increaseswith increasing C/O ratio, while the abundance of CO isalmost constant, since it has one atom of carbon and oxy-gen each. This transition from H O dominated spectra, tospectra dominated by various carbon bearing species occursbetween C/O ratios of 0.75 and 1, slightly higher than thatfound with isothermal P - T profiles where it was between0.7-0.75 as shown in Goyal et al. (2018). However, this valuemight change with change in the f c value as the C/O transi-tion point is a strong function of temperature (Molli`ere et al.2016; Goyal et al. 2018; Molaverdikhani et al. 2019).This C/O transition is also seen in the transmissionspectrum shown in Fig. 12c, where the spectrum transitions MNRAS000
Figure showing P - T profiles for a range of C/O ratios at 0.5 f c and solar metallicity for WASP-17b. (b) Figure showingequilibrium chemical abundances for some important species for various C/O values obtained using P - T profiles shown in Figure 12a. (c) Figure showing transmission spectra for WASP-17b for different values of C/O ratios obtained using P - T profiles shown in Figure 12aand corresponding equilibrium chemical abundances shown in Fig. 12b. (d) Figure showing emission spectra for WASP-17b for differentvalues of C/O ratios obtained using P - T profiles shown in Figure 12a and corresponding equilibrium chemical abundances shown in Fig.12b. The P - T profiles for WASP-17b fora range of C/O ratios are shown in Fig. 12a at 0.5 f c andsolar metallicity. We choose to show simulations with 0.5f c instead of 0.25 f c as one of the models with 0.25 f c anda C/O ratio of 1.0 failed to converge in the grid. It canbe seen that with increasing C/O ratio the P - T structureconsistently cools for P ≤ − bar. However, for P ≥ − bar the P - T structure first cools up-to C/O ratio of 0.75 andthen the temperature increases for a C/O ratio of 1 and 1.5.The sharp heating at around 10 − bar is due to Fe opacityas explained earlier in Section 5.2.4.2.The change in the equilibrium chemical abundances dueto the change in the C/O ratio is drastic, as it effects allthe major carbon and oxygen bearing molecules. As ex-pected the abundances of H O drop with increasing C/O ratio. Although CO bears a carbon atom it needs two oxy-gen atoms per carbon atom, therefore the equilibrium abun-dance of CO also drops with increasing C/O ratio, but insmaller increments as compared to H O. The abundance ofcarbon bearing species such as CH , HCN, C H increaseswith increasing C/O ratio, while the abundance of CO isalmost constant, since it has one atom of carbon and oxy-gen each. This transition from H O dominated spectra, tospectra dominated by various carbon bearing species occursbetween C/O ratios of 0.75 and 1, slightly higher than thatfound with isothermal P - T profiles where it was between0.7-0.75 as shown in Goyal et al. (2018). However, this valuemight change with change in the f c value as the C/O transi-tion point is a strong function of temperature (Molli`ere et al.2016; Goyal et al. 2018; Molaverdikhani et al. 2019).This C/O transition is also seen in the transmissionspectrum shown in Fig. 12c, where the spectrum transitions MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b) Figure 13. (a)
Figure showing transmission spectra features of each individual molecule used in
ATMO (1 to 10) for WASP-17b transmissionspectra shown in Fig. 12c at C/O ratio of 1.5. H -H (blue), H -He (green), H O (red), CO (cyan), CO (magenta), CH (yellow), NH (lightblue), Na (purple), K (brown), Li (lightgreen) and all 21 opacities (black). The lower continuum boundary in the spectrum sharplydropping around 1.6 µ m is due to H − opacity. No R p / R ? offset was applied while plotting. Individual simulations are divided into blocksof 10 while plotting for clarity. (b) Same as Figure 13a but for Rb (blue), Cs (green), TiO (red), VO (cyan), FeH (magenta), PH (yellow),H S (lightblue), HCN (purple), C H (brown), SO (lightgreen), Fe (violet) and all 21 opacities (black). from being H O dominated to being dominated by CH ,HCN and C H between a C/O ratio of 0.75 and 1. Fig. 13aand 13b show this transmission spectrum at a C/O ratio of1.5 decoupled into various molecules. It can be seen that at aC/O ratio of 1.5, the transmission spectrum is dominated byCH features in the infrared, with contributions from CO,HCN and C H . There is a strong HCN and C H featureat ∼ µ m and the most common CO feature at 4.5 µ m . Theemission spectrum shown in Fig. 12d also shows this C/Otransition between 0.75-1, from deep H O absorption fea-tures to more deeper CH absorption features, in the peakregion of emission around ∼ µ m The P - T profiles for WASP-121bfor a range of C/O ratios are shown in Fig. 14a. With in-creasing C/O ratio the major temperature inversion shiftsto higher pressures. The major temperature inversion refersto the inversion that has a potential observational signatureunlike the inversion due to Fe opacity at extremely low pres-sures ( ∼ − bar) as described in Section 5.2.3 and 5.2.4.2and also seen in Fig. 14a.The abundance of TiO/VO species which are the pri-mary absorbers for forming the temperature inversion layer,decrease with increasing C/O ratio. Their abundance at aC/O ratio of 1.0 and 1.5 is low, still the inversion layer ismaintained, albeit not as hot as at other low C/O ratios.We investigated this phenomenon by using two tests, firstremoving TiO/VO opacities and second removing Na, K,TiO and VO opacities. We found that this inversion at highC/O ratio can be maintained due to Na and K opacities inthe absence of TiO/VO opacities or their low abundance,as found by Molli`ere et al. (2015). Furthermore, H − opacityalso contributes to this inversion at high C/O ratio and highvalue of f c (1.0) more than Na and K opacities, as discussedin detail in Section 5.2.2. The increase in the H − abundance at C/O ratio of 1.5 around the photosphere region ( ∼ − opac-ity. H − features also can be clearly seen in the transmissionspectrum for C/O ratio of 1.5.At high C/O ratios it is interesting to see that the HCNabundance is substantial even in the low pressure regions(P > ∼ for WASP-17b. This shows an important re-sult that at high temperatures HCN dominates over CH inthe atmosphere at high C/O ratios. Therefore, HCN featuresprovide a very strong signature to constrain high C/O ra-tios in exoplanet atmospheres. The transition from an H Odominated spectrum to that dominated by HCN happensbetween C/O ratio of 0.75-1.0. Therefore, the temperaturedependence of the C/O transition as seen in Molli`ere et al.(2015); Goyal et al. (2018) does not seem to be holding inthis case, as the transition for WASP-17b also happens inthis C/O regime (0.75-1.0). The transmission spectrum alsoshows FeH features between 0.8 and 1.2 µ m at a C/O ratioof 1.0 and 1.5. The absence of TiO/VO features makes itpossible for FeH to appear, without being masked.In the emission spectrum shown in Fig. 14d most ofthe molecular features are seen in emission due to the pres-ence of an inversion layer, as explained before. However, be-tween a C/O ratio of 1 and 1.5 surprising differences can beseen, especially at 3.1 µ m which is the wavelength of a strongHCN absorption band. At a C/O ratio of 1 it is an emissionfeature, however it transforms to an absorption feature ata C/O ratio of 1.5. This is because at a C/O ratio of 1.5slightly cooler upper atmosphere is being probed as can beseen in the NCF at 3.1 µ m in Fig. 15d as compared to a C/Oratio of 1. Therefore, at a C/O ratio of 1.5, HCN absorbs MNRAS , 1–26 (2019) Goyal et al. (a) (b)(c) (d)
Figure 14. (a)
Figure showing P - T profiles for a range of C/O ratios at 0.5 f c and solar metallicity for WASP-121b. (b) Figure showingequilibrium chemical abundances for some important species for various C/O values obtained using P - T profiles shown in Figure 14a. (c) Figure showing transmission spectra for WASP-121b for different values of C/O ratios obtained using P - T profiles shown in Figure 14aand corresponding equilibrium chemical abundances shown in Fig. 14b. (d) Figure showing emission spectra for WASP-121b for differentvalues of C/O ratios obtained using P - T profiles shown in Figure 14a and corresponding equilibrium chemical abundances shown in Fig.14b. the radiation from the lower (high pressure atmosphere) incomparison to for a C/O ratio of 1.0, which probes deeperatmosphere where it has an inversion and leads to HCNemission. Interestingly, at 1.6 µ m HCN leads to an emissionfeature both at a C/O ratio of 1 and 1.5, since at 1.6 µ m theinversion layer is being probed at both C/O ratios as seen inthe NCF in Fig. 15c and P - T profile in Fig. 14a. Therefore,HCN should be observed in emission as well as absorption athigh C/O ratios (1.5) for extremely irradiated planets suchas WASP-121b. WASP-121b is not expected to be cloudy due to its ex-tremely high predicted dayside temperature (T eq = 2400 K). Moreover, Evans et al. (2018) showed that the extremelysteep slope in the optical is not due to enhanced Rayleighscattering from a haze. In Evans et al. (2018) observationswere interpreted using isothermal P - T profiles (see Fig. 11and 12 in Evans et al. 2018) resulting in detection of H O,evidence of VO and the possibility of SH causing significantabsorption in the UV and optical. Therefore, here we useour grid of model transmission spectra with RCE P - T pro-files and additional H − and Fe opacity, without grey cloudsand enhanced scattering, to fit the WASP-121b data fromEvans et al. (2018). We have excluded the data short-wardof 0.47 µ m while performing the fitting, since the steep slopein this region is not explained by Rayleigh scattering and islikely in part due to absorption of atomic species like Fe inthe thermospheric and higher atmospheric layers (Sing et al.2019; Gibson et al. 2020) which are not modeled here.. Fig.16a shows the best fit model transmission spectra for obser- MNRAS000
Figure showing P - T profiles for a range of C/O ratios at 0.5 f c and solar metallicity for WASP-121b. (b) Figure showingequilibrium chemical abundances for some important species for various C/O values obtained using P - T profiles shown in Figure 14a. (c) Figure showing transmission spectra for WASP-121b for different values of C/O ratios obtained using P - T profiles shown in Figure 14aand corresponding equilibrium chemical abundances shown in Fig. 14b. (d) Figure showing emission spectra for WASP-121b for differentvalues of C/O ratios obtained using P - T profiles shown in Figure 14a and corresponding equilibrium chemical abundances shown in Fig.14b. the radiation from the lower (high pressure atmosphere) incomparison to for a C/O ratio of 1.0, which probes deeperatmosphere where it has an inversion and leads to HCNemission. Interestingly, at 1.6 µ m HCN leads to an emissionfeature both at a C/O ratio of 1 and 1.5, since at 1.6 µ m theinversion layer is being probed at both C/O ratios as seen inthe NCF in Fig. 15c and P - T profile in Fig. 14a. Therefore,HCN should be observed in emission as well as absorption athigh C/O ratios (1.5) for extremely irradiated planets suchas WASP-121b. WASP-121b is not expected to be cloudy due to its ex-tremely high predicted dayside temperature (T eq = 2400 K). Moreover, Evans et al. (2018) showed that the extremelysteep slope in the optical is not due to enhanced Rayleighscattering from a haze. In Evans et al. (2018) observationswere interpreted using isothermal P - T profiles (see Fig. 11and 12 in Evans et al. 2018) resulting in detection of H O,evidence of VO and the possibility of SH causing significantabsorption in the UV and optical. Therefore, here we useour grid of model transmission spectra with RCE P - T pro-files and additional H − and Fe opacity, without grey cloudsand enhanced scattering, to fit the WASP-121b data fromEvans et al. (2018). We have excluded the data short-wardof 0.47 µ m while performing the fitting, since the steep slopein this region is not explained by Rayleigh scattering and islikely in part due to absorption of atomic species like Fe inthe thermospheric and higher atmospheric layers (Sing et al.2019; Gibson et al. 2020) which are not modeled here.. Fig.16a shows the best fit model transmission spectra for obser- MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b)(c) (d) Figure 15. (a)
Same as Fig. 13a but for WASP-121b at 0.5 f c , solar metallicity and C/O ratio of 1.5. H − opacity is quite dominantespecially between 1 and 1.4 µ m . (b) Same as Fig. 13b but for WASP-121b at 0.5 f c , solar metallicity and C/O ratio of 1.5. (c,d) Figuresc, d showing normalised contribution function at 1.6 and 3.1 µ m for a range of C/O ratios for emission spectra as shown in Figure 14d. vations from Evans et al. (2018). It shows a H O feature at1.4 µ m and features in the optical resembling TiO/VO fea-tures. The decoupled spectra in Figure 16c and 16d showsthat the optical spectra is dominated by VO features. Thisfitting result corroborates the result using isothermal P - T profiles discussed in Evans et al. (2018) and consistent withVO being present in the atmosphere of WASP-121b, sincethe limb P - T structure of this planet is in that narrow tem-perature regime where VO abundance dominates the TiOabundance, as discussed in Goyal et al. (2019b).The best fit transmission spectra model with RCE P - T profiles gives a reduced χ value of 1.37 with 74 DOF(75 data points minus 1). It gives super-solar metallicityand super-solar C/O ratio as shown in Fig. 16a (both whenvarying O/H and C/H). The “best-fit” P - T profile shown inthe sub-plot of Fig. 16a does not show a temperature inver-sion, since the limb P - T profile (in the observed region) isexpected to be cooler than the dayside P - T profile shown insub-plot of Fig. 16b. Although the 100 times solar metallic- ity case is the “best-fit” (lowest chi-squared), the 50 timessolar metallicity case also fits within 3 σ and a solar metal-licity case is consistent with the data at the 6 σ level, asshown in Figure B1 of Appendix B, which shows χ mapsfor all the model simulations in the grid for WASP-121b withconfidence intervals, similar to those described in details inGoyal et al. (2018). There are two reasons why high metallic-ities are preferred, one is the increase in the VO abundancesas metallicity increases (more than that of TiO) and secondthe decrease in the scale height compared to solar metallicitycase, both required to better fit the observations, driven bythe low R p /R s points in the optical. We also performed testswhere we excluded the optical data ( < µ m ) and just usedthe near-infrared data while fitting and in this case the sub-solar metallicity model simulation (0.1 times solar) was the“best-fit”, thus again concluding that the optical data leadsto a higher metallicity being preferred. We note that we havenot included relative levels between STIS and WFC3 as a MNRAS , 1–26 (2019) Goyal et al. (a) (b)(c) (d)
Figure 16. (a)
Figure showing best fit model transmission spectra using the grid of model transmission spectra for WASP-121b presentedin this paper and observations from Evans et al. (2018) giving χ value of 101.69 with f c = 0.25, 100 times solar metallicity and C/Oratio of 0.75. Best-Fit P - T profile is shown in the subplot. (b) Figure showing best fit model emission spectra using the grid of modelemission spectra for WASP-121b presented in this paper and observations from Evans et al. (2020) with χ value of 88.63 and f c =1.0, solar metallicity and C/O ratio of 0.75. Best-Fit P - T profile is shown in the subplot. (c) Best-fit decoupled transmission spectrasimilar to Figure 13a. The lower continuum boundary in the spectrum sharply dropping around 1.6 µ m is due to H − opacity. (d) Best-fitdecoupled transmission spectra similar to Figure 13b. free parameter while fitting, which can potentially alter theresults.These results demonstrate that a reasonably goodmatch to the observations can be achieved with self-consistent 1D models assuming chemical equilibrium for arange of plausible metallicities and C/O values. The real-ity is undoubtedly significantly more complex. In particu-lar, we have assumed a single RCE P - T profile for the entirelimb of the planet, but there should be a strong temperaturecontrast between the east and west limbs, in turn affectingwhich species are in the gas phase or condensed. However,limb to limb variations can be incorporated while fitting,simply by the linear combination of transmission spectrafrom our library for a specific planet (MacDonald et al.2020). The “best-fit” limb P - T profile of WASP-121b is coldenough for Fe to rainout from the atmosphere, at least in theregion of the atmosphere where Local Thermodynamic Equi- librium (LTE) can be assumed. However, Sing et al. (2019);Gibson et al. (2020) detected the presence of Fe II and Fe I inUV and optical high resolution observations of WASP-121b,which probes much higher altitudes than the optical trans-mission spectrum and may well be in the non-LTE region ofthe atmosphere. The deep interior temperature may also behotter (Thorngren et al. 2019; Sing et al. 2019) than assumedin our work (T int =100 K), which can prevent Fe from rain-ing out of the atmosphere. The other possibility is that thetrue planet limb P - T profile is much hotter than our “best-fit” limb P - T profile, since we have not modeled the trans-mission spectrum of WASP-121b short-ward of 0.47 µ m forthis fitting and not considered inter-terminator variations,as detailed earlier.Fig. 16b shows the best fit model emission spectra forobservations from Evans et al. (2020), with a χ value of88.63 and reduced χ value of 1.81 with 49 DOF. The best MNRAS000
Figure showing best fit model transmission spectra using the grid of model transmission spectra for WASP-121b presentedin this paper and observations from Evans et al. (2018) giving χ value of 101.69 with f c = 0.25, 100 times solar metallicity and C/Oratio of 0.75. Best-Fit P - T profile is shown in the subplot. (b) Figure showing best fit model emission spectra using the grid of modelemission spectra for WASP-121b presented in this paper and observations from Evans et al. (2020) with χ value of 88.63 and f c =1.0, solar metallicity and C/O ratio of 0.75. Best-Fit P - T profile is shown in the subplot. (c) Best-fit decoupled transmission spectrasimilar to Figure 13a. The lower continuum boundary in the spectrum sharply dropping around 1.6 µ m is due to H − opacity. (d) Best-fitdecoupled transmission spectra similar to Figure 13b. free parameter while fitting, which can potentially alter theresults.These results demonstrate that a reasonably goodmatch to the observations can be achieved with self-consistent 1D models assuming chemical equilibrium for arange of plausible metallicities and C/O values. The real-ity is undoubtedly significantly more complex. In particu-lar, we have assumed a single RCE P - T profile for the entirelimb of the planet, but there should be a strong temperaturecontrast between the east and west limbs, in turn affectingwhich species are in the gas phase or condensed. However,limb to limb variations can be incorporated while fitting,simply by the linear combination of transmission spectrafrom our library for a specific planet (MacDonald et al.2020). The “best-fit” limb P - T profile of WASP-121b is coldenough for Fe to rainout from the atmosphere, at least in theregion of the atmosphere where Local Thermodynamic Equi- librium (LTE) can be assumed. However, Sing et al. (2019);Gibson et al. (2020) detected the presence of Fe II and Fe I inUV and optical high resolution observations of WASP-121b,which probes much higher altitudes than the optical trans-mission spectrum and may well be in the non-LTE region ofthe atmosphere. The deep interior temperature may also behotter (Thorngren et al. 2019; Sing et al. 2019) than assumedin our work (T int =100 K), which can prevent Fe from rain-ing out of the atmosphere. The other possibility is that thetrue planet limb P - T profile is much hotter than our “best-fit” limb P - T profile, since we have not modeled the trans-mission spectrum of WASP-121b short-ward of 0.47 µ m forthis fitting and not considered inter-terminator variations,as detailed earlier.Fig. 16b shows the best fit model emission spectra forobservations from Evans et al. (2020), with a χ value of88.63 and reduced χ value of 1.81 with 49 DOF. The best MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres fit model has solar metallically and C/O ratio of 0.75, withf c value of 1.0, indicative of very low energy redistributionin the atmosphere. The dayside best fit P - T profile in thesub-plot of Fig. 16b shows a temperature inversion, whilethe limb P - T profile obtained using the transmission spectrafit (see Fig. 16a ) is cooler without a temperature inversion,again supporting very low energy redistribution in the at-mosphere of WASP-121b. It shows a 1.4 µ m H O emissionfeature, indicative of inversion layer, as explained in previoussections.
The approximation of an isothermal P - T profile has manylimitations for a real planetary atmosphere and is a rea-sonable approximation only to generate model transmis-sion spectra, which probes a very small part of the over-all atmosphere. Therefore, in this work we create a libraryof radiative-convective equilibrium P - T profiles and cor-responding equilibrium chemical abundances, transmissionspectra, emission spectra and contribution functions, fora range of observationally significant exoplanets. Unlike astatic table of chemical abundances used in various models,these P - T profiles (and all models in this grid) are consistentwith equilibrium chemical abundances, meaning P - T profileand chemical abundances are tied together during each iter-ation, making it a state of the art model grid. The libraryof models presented in this work also included H − and Feopacity, in addition to opacities included in previous libraryof models presented in Goyal et al. (2018) and Goyal et al.(2019b). The major conclusions from this work are dividedinto three parts, first the sensitivity to model choices, sec-ond the sensitivity to grid parameters and third the generalconclusions. We have to make different model choices while interpretingthe observations of exoplanet atmospheres, such as the typeof condensation, opacities to be included, source of line-list,line-broadening profile etc. Here we conclude on the effectof these different model choices. • The investigation of differences in RCE model simu-lations with local and rainout condensation revealed thatadopting different condensation approaches can result insubstantial differences in the resulting P - T profiles andthereby the model spectra, for a typical hot Jupiter planetlike WASP-17b. • Inclusion of thermal ionic species reduces the abun-dance of Na and K at atmospheric temperatures greater than ∼ < ∼ − bar), as they are ion-ized to form Na + and K + . Therefore, Na and K features areabsent in the transmission spectrum at these temperatures.It also allows formation of other ions with significant opac-ities such as H − . Thermal decomposition leads to reductionin the H O abundance for planets such as WASP-121b, butonly in the region of the atmosphere probed by transmissionspectrum and not the emission spectrum. • Iron (Fe) opacity leads to very sharp inversion at the topof the model atmosphere ( ∼ − to 10 − bar). However, it is unable to produce a temperature inversion in the region ofthe atmosphere being probed by emission spectrum observa-tions even at 200 × solar metallicity, as produced by TiO/VOor H − opacities for WASP-121b. Moreover, Fe opacity tendsto cool the P - T profile for P > ∼ µ m . However, Fe opacityis sufficient to create a strong thermal inversion in KELT-9b, the planet with the highest equilibrium temperature inthis library of models, even at solar metallicity and withoutTiO/VO/H − opacities. Thus, the capability of Fe opacity toform a temperature inversion is system specific showing astrong dependance on the host star effective temperature. • H − opacity plays an important role in shaping the P - T profile, transmission and emission spectrum, at tempera-tures greater then ∼ − opacity leads to cooling in the deeperatmosphere (P > ≥
1, H − opacityleads to formation of a strong thermal inversion layer, butnot at solar C/O ratio even if TiO/VO is absent. Thermalinversion due to H − opacity lies deeper (higher pressure) inthe atmosphere ( ∼ − bar), in comparison to the inver-sion due to TiO/VO opacities ( ∼ − to 10 − bar). In thetransmission spectrum, H − opacity tends to mute the linewings of Na, K and all features up-to 1.6 µ m (limit of H − bound free absorption) mimicking the effect of grey clouddeck opacity. The effect of H − opacity on P - T profiles alsosubstantially alters the emission spectrum, with increase inpeak planet flux due to thermal inversion.Adopting different line wing profiles of Na and K, led todifferences of ∼ P - T profiles and the spectra between the sim-ulations, varying C/O ratio by varying O/H and those byvarying C/H, shown in the online supplementary material,revealed some differences within the range of C/O ratioadopted in the library, but to a lesser extent compared toother parameters in the library and other model choices. The library of simulations presented in this work was devel-oped for four different recirculation factors, six metallicitiesand six C/O ratios for 89 hot Jupiter and warm Neptune ex-oplanets with equilibrium temperatures greater than 1200 K.The effect of varying the recirculation factor, metallicity andC/O ratio were investigated and shown for WASP-17b andWASP-121b in Sections 5.3, showing the variation of the P - T profile, equilibrium chemical abundances and thereby thetransmission and the emission spectrum. The major conclu-sion from these sensitivity tests for different grid parametersare: • The increase in recirculation factor (lower redistributionof energy) leads to transitioning of the P - T profile from with-out a temperature inversion to isothermal to a profile withtemperature inversion for WASP-121b, which is also appar-ent in the emission and transmission spectrum. Therefore,emission spectrum and to a lesser extent transmission spec- MNRAS , 1–26 (2019) Goyal et al. trum (due to other degeneracies) can be used to constrainthe energy redistribution for all the planets presented in thisgrid. • The increase in metallically leads to the P - T profile be-coming hotter for both WASP-17b and WASP-121, due tothe increase in the total opacity, driven by the increase inthe mean molecular weight of the atmosphere. The increasein metallicity leads to an increase in the size of the trans-mission spectral features at first (up to 10 × solar metallic-ity) due to higher abundances and higher temperatures, butthen they decrease again as the scale height of the atmo-sphere decreases (due to increased mean molecular weight)with increased metallicity. However, this effect is not seen inthe emission spectrum where absorption/emission featuresincrease with increasing metallicity, since emission spectralfeatures do not have scale height dependance as transmissionspectral features. The shift in the atmospheric level probedby emission spectrum to lower pressure levels with increasingmetallicity, as shown by contribution functions in the H Oand CO bands, as well as the difference in the level probedby the wings and cores of absorption/emission bands for agiven metallicity, both can be used to constrain metallicityand the P - T profile of the atmosphere. • Increasing the C/O ratio leads to a cooling of P - T pro-file for WASP-17b, with a transition seen from a H O domi-nated spectrum to a spectrum dominated by carbon bearingspecies (primarily CH ) between C/O ratios of 0.75 and 1.For WASP-121b, the strength of the temperature inversiondecreases as the abundance of TiO/VO decreases with in-creasing C/O ratio. At a C/O ratio greater than 1 eventhough TiO/VO abundances are low, a weak temperatureinversion is maintained in the atmosphere due to Na and Kat f c value of 0.5 as shown by previous works. Whereas,for a f c value of 1 (hotter P - T profile) H − opacity con-tributes substantially to the development of an inversion. In-terestingly, extremely irradiated exoplanet atmospheres likeWASP-121b show a spectrum dominated by HCN featuresat infrared wavelengths for high C/O ratios ( >
1) in compar-ison to comparatively cooler planets like WASP-17b whichare dominated by CH features. HCN and H − features canbe seen as an emission as well as absorption feature at differ-ent wavelengths in their emission spectrum. Therefore, HCNand H − features for these planets can be used to constraintheir C/O ratios as well as their thermal structure. The interpretation of observations using the library of mod-els with RCE P - T profiles presented in this work was demon-strated using WASP-121b observations. The transmissionspectra probing the planetary atmospheric limb reveal H Ofeatures in the infrared with evidence of VO in the optical.The best fit model indicates super-solar metallicity drivenby optical observations and VO opacity, with non-invertedlimb P - T profile. The emission spectra probing the daysideof the planetary atmosphere reveals a H O feature in emis-sion giving evidence of a potential temperature inversion andvery low energy redistribution in the atmosphere.One of the major limitations of the model simulationspresented in this paper is that they are 1-dimensional. Ide-ally 2D or 3D approaches would more realistically representa planetary atmosphere. However, 1D models allow us to explore a very large parameter space in chemistry and ra-diative transfer for a large number of planetary systems, notpossible currently using 2D or 3D approaches due to compu-tational limitations. Moreover, the combination of different P - T profiles, transmission and emission spectra for a givenplanet can be used to represent different parts of the at-mosphere (see for e.g MacDonald et al. 2020), thus pavingthe way to interpret 2D or 3D observations, like for exam-ple using spectral phase curves. We have also not modeleddis-equilibrium processes such as photochemistry and verti-cal mixing in this library of simulated atmospheres, whichis planned for the future development. The current modelspectra in the library has a resolution of R ∼ µ m decreasing to R ∼
35 at 30 µ m, which cannot be used tointerpret high resolution observations. However, the modelatmospheric RCE P - T profiles and the corresponding chem-ical abundances from our library can be used to generatesynthetic high resolution spectra (transmission or emission),which can then be used to interpret high resolution obser-vations. We also plan to update the spectra in our libraryonline, to achieve the highest possible JWST resolution oversome specific wavelength ranges.The library of models presented in this work can be usedto plan and interpret a broad range of transiting exoplanetobservations with current and future facilities such as HSTand JWST, since it covers the wavelength range from 0.2to 30 µ m . It represents a valuable resource to guide choicesof observational targets and instrument modes. The libraryof models can also be used to initialize retrieval models aswell as to constrain priors in them. Our development of anexpansive grid of thermochemically consistent 1D modelsfor exoplanet atmospheres provides the community with an-other tool with which to tackle our theoretical understandingof hot Jupiter atmospheres and interpret current and futureobservations of these planets. ACKNOWLEDGEMENTS
We would like to thank the anonymous referee for theirdetailed and constructive comments, that improved theclarity and quality of this manuscript. J.M.G and N.Macknowledges funding by a Leverhulme Trust ResearchProject Grant and University of Exeter College of Engineer-ing, Mathematics and Physical Sciences PhD studentship.M.W. P. acknowledges support through a UKRI-STFC stu-dentship. This work used the DiRAC Complexity system,operated by the University of Leicester IT Services, whichforms part of the STFC DiRAC HPC Facility. This work alsoused the University of Exeter Supercomputer, a DiRAC Fa-cility jointly funded by STFC, the Large Facilities CapitalFund of BIS and the University of Exeter.
DATA AVAILABILITY
The data underlying this article are currently avail-able publicly here https://drive.google.com/drive/folders/1zCCe6HICuK2nLgnYJFal7W4lyunjU4JE andhere https://noctis.erc-atmo.eu:5001/fsdownload/hq0z4udQJ/goyal2020
MNRAS , 1–26 (2019) ibrary of Exoplanet Atmospheres References
Alam M. K., et al., 2018, AJ, 156, 298Allard N. F., Allard F., Hauschildt P. H., Kielkopf J. F., MachinL., 2003, A&A, 411, L473Allard F., Homeier D., Freytag B., 2012, Philosophical Transac-tions of the Royal Society of London Series A, 370, 2765Amundsen D. S., 2015, PhD ThesisAmundsen D. S., Baraffe I., Tremblin P., Manners J., Hayek W.,Mayne N. J., Acreman D. M., 2014, A&A, 564, A59Arcangeli J., et al., 2018, ApJ, 855, L30Baraffe I., Homeier D., Allard F., Chabrier G., 2015, A&A, 577,A42Baudino J.-L., Molli`ere P., Venot O., Tremblin P., B´ezard B.,Lagage P.-O., 2017, ApJ, 850, 150Bell K. L., Berrington K. A., 1987, Journal of Physics B AtomicMolecular Physics, 20, 801Burgasser A. J., Kirkpatrick J. D., Liebert J., Burrows A., 2003,ApJ, 594, 510Burrows A., Sharp C. M., 1999, ApJ, 512, 843Burrows A., et al., 1997, ApJ, 491, 856Burrows A., Marley M. S., Sharp C. M., 2000, ApJ, 531, 438Burrows A., Ram R. S., Bernath P., Sharp C. M., Milsom J. A.,2002, ApJ, 577, 986Burrows A., Budaj J., Hubeny I., 2008, ApJ, 678, 1436Carter A. L., et al., 2020, MNRAS, 494, 5449Chamberlain J. W., Hunten D. M., 1987, Theory of planetaryatmospheres. An introduction to their physics andchemistry..Vol. 36Chubb K. L., Min M., Kawashima Y., Helling C., Waldmann I.,2020, arXiv e-prints, p. arXiv:2004.13679Drummond B., Tremblin P., Baraffe I., Amundsen D. S., MayneN. J., Venot O., Goyal J., 2016, A&A, 594, A69Drummond B., Mayne N. J., Manners J., Baraffe I., Goyal J.,Tremblin P., Sing D. K., Kohary K., 2018, ApJ, 869, 28Drummond B., Carter A. L., H´ebrard E., Mayne N. J., Sing D. K.,Evans T. M., Goyal J., 2019, MNRAS, 486, 1123Evans T. M., et al., 2017, Nature, 548, 58Evans T. M., et al., 2018, AJ, 156, 283Fortney J. J., 2005, MNRAS, 364, 649Fortney J. J., Marley M. S., 2007, ApJ, 666, L45Fortney J. J., Marley M. S., Barnes J. W., 2007, ApJ, 659, 1661Fortney J. J., Lodders K., Marley M. S., Freedman R. S., 2008,ApJ, 678, 1419Fortney J. J., et al., 2016, preprint, ( arXiv:1602.06305 )Gandhi S., Madhusudhan N., 2017, MNRAS, 472, 2334Gandhi S., Madhusudhan N., 2019, MNRAS, 485, 5817Gibson N. P., et al., 2020, MNRAS, 493, 2215Goyal J. M., 2019, University of ExeterGoyal J. M., et al., 2018, MNRAS, 474, 5158Goyal J. M., et al., 2019a, MNRAS, p. 722Goyal J. M., Wakeford H. R., Mayne N. J., Lewis N. K., Drum-mond B., Sing D. K., 2019b, MNRAS, 482, 4503Guillot T., Showman A. P., 2002, A&A, 385, 156Heiter U., et al., 2008, in Journal of Physics Conference Series. p.012011, doi:10.1088/1742-6596/130/1/012011Heiter U., et al., 2015, Phys. Scr., 90, 054010Heng K., Kitzmann D., 2017, preprint, ( arXiv:1702.02051 )Hobbs R., Shorttle O., Madhusudhan N., Rimmer P., 2019, MN-RAS, 487, 2242Hubeny I., Burrows A., Sudarsky D., 2003, ApJ, 594, 1011John T. L., 1988, A&A, 193, 189Knutson H. A., et al., 2009, ApJ, 690, 822Kreidberg L., et al., 2018, AJ, 156, 17Lecavelier Des Etangs A., Pont F., Vidal-Madjar A., Sing D.,2008, A&A, 481, L83Lodders K., Fegley B., 2002, Icarus, 155, 393Lothringer J. D., Barman T., Koskinen T., 2018, ApJ, 866, 27 MacDonald R. J., Goyal J. M., Lewis N. K., 2020, arXiv e-prints,p. arXiv:2003.11548Madhusudhan N., 2012, ApJ, 758, 36Madhusudhan N., Ag´undez M., Moses J. I., Hu Y., 2016, SpaceSci. Rev., 205, 285Malik M., Kitzmann D., Mendon¸ca J. M., Grimm S. L., MarleauG.-D., Linder E. F., Tsai S.-M., Heng K., 2019, AJ, 157, 170Mansfield M., et al., 2018, AJ, 156, 10Marley M. S., Robinson T. D., 2015, Annual Review of Astronomyand Astrophysics, 53, 279Marley M. S., Saumon D., Guillot T., Freedman R. S., HubbardW. B., Burrows A., Lunine J. I., 1996, Science, 272, 1919Mikal-Evans T., et al., 2019, MNRAS, 488, 2222Molaverdikhani K., Henning T., Molli`ere P., 2019, ApJ, 873, 32Molli`ere P., van Boekel R., Dullemond C., Henning T., MordasiniC., 2015, ApJ, 813, 47Molli`ere P., van Boekel R., Bouwman J., Henning T., Lagage P.-O., Min M., 2016, preprint, ( arXiv:1611.08608 )Moses J. I., Madhusudhan N., Visscher C., Freedman R. S., 2013,ApJ, 763, 25Nikolov N., et al., 2018, Nature, 557, 526Parmentier V., et al., 2018, A&A, 617, A110Rajpurohit A. S., Reyl´e C., Allard F., Homeier D., Schultheis M.,Bessell M. S., Robin A. C., 2013, A&A, 556, A15Rau A. R. P., 1996, Journal of Astrophysics and Astronomy, 17,113Rybicki G. B., Lightman A. P., 1986, Radiative Processes in As-trophysicsSauval A. J., Tatum J. B., 1984, ApJS, 56, 193Seager S., Sasselov D. D., 1998, ApJ, 502, L157Sharp C. M., Burrows A., 2007, ApJS, 168, 140Sing D. K., et al., 2016, Nature, 529, 59Sing D. K., et al., 2019, AJ, 158, 91Southworth J., 2011, MNRAS, 417, 2166Spiegel D. S., Silverio K., Burrows A., 2009, ApJ, 699, 1487Sudarsky D., Burrows A., Hubeny I., 2003, ApJ, 588, 1121Thorngren D., Gao P., Fortney J. J., 2019, ApJ, 884, L6Tremblin P., Amundsen D. S., Mourier P., Baraffe I., Chabrier G.,Drummond B., Homeier D., Venot O., 2015, ApJ, 804, L17Tremblin P., Amundsen D. S., Chabrier G., Baraffe I., DrummondB., Hinkley S., Mourier P., Venot O., 2016, ApJ, 817, L19Tremblin P., et al., 2017, ApJ, 841, 30Visscher C., Lodders K., Fegley Jr. B., 2006, ApJ, 648, 1181Wakeford H. R., et al., 2018, AJ, 155Woitke P., Helling C., Hunter G. H., Millard J. D., Turner G. E.,Worters M., Blecic J., Stock J. W., 2018, A&A, 614, A1Zahnle K., Schaefer L., Fegley B., 2010, Cold Spring Harb Per-spect Biol, 2, a004895Zhang M., Chachan Y., Kempton E. M. R., Knutson H. A., 2019,PASP, 131, 034501von Essen C., Mallonn M., Welbanks L., Madhusudhan N., PinhasA., Bouy H., Weis Hansen P., 2019, A&A, 622, A71
APPENDIX A: HIGH TEMPERATUREADDITIONSA1 Thermal Ionization
Thermal ionic species were recently included in ATMO tocompute the chemical equilibrium abundance of H + , H − ,Na + , K + , Ca + , Si + and e − . This was simply done by includ-ing thermodynamic data of these species in our databaseand using Gibbs energy minimization to compute the equi-librium abundances in each layer of the atmosphere, includ-ing the ionic species. The equilibrium chemical abundancesof ionic species from ATMO were validated by comparing MNRAS , 1–26 (2019) Goyal et al.
Figure A1.
Figure showing validation of ATMO chemical equi-librium abundances of ionic species with GGChem (Woitke et al.2018) at 3000 K. with those from the GGchem model (Woitke et al. 2018) at2000, 3000 and 4000 K as shown in Figure A1 for 3000 K.We used the same input P - T profile for both ATMO andGGchem for this validation. It can be seen that there is avery good agreement between the abundances from both themodels. Only small differences exist in the deeper parts ofthe atmosphere, currently not probed by either emission ortransmission spectra. A2 Implementation and Validation of H − opacity Many publications highlight the importance of H − opacityin the atmosphere of extremely irradiated hot Jupiters (e.gArcangeli et al. 2018; Mansfield et al. 2018; Kreidberg et al.2018; Parmentier et al. 2018). We also included H − opaci-ties in ATMO and investigated its effects on the P - T profilesand thereby the spectra. The formation of species H − (hy-drogen anion) is basically a result of electron attachment,driven by the presence of abundant hydrogen (H) and lowenergy electrons in the ionised atmospheres of stars or hotJupiters (Rau 1996). The absorption of electromagnetic ra-diation by H − is driven by photo-detachment (bound-free)and free-free transition processes. These are computed us-ing the analytical equations of John (1988) derived from theoriginal derivation of free-free transition in Bell & Berring-ton (1987).The photo-detachment process of H − absorption is givenby h ν + H − −−−→ H + e − , (A1)where h is the Planck’s constant and ν is the frequencyof radiation. In this process H − ions absorbs radiation offrequency ν , to form atomic hydrogen and an electron. Asshown in John (1988) for wavelengths ( λ ) less than the ion-isation threshold λ of H − ( λ < µ m) this is computedusing, k bf ( λ ) = − λ (cid:18) λ − λ (cid:19) / f ( λ ) , (A2)where , f ( λ ) = (cid:213) n = C n (cid:20) λ − λ (cid:21) ( n − )/ , where k bf ( λ ) is the bound-free cross-section of H − inunits of cm , λ is the wavelength, λ = 1.6419 µ m is thethreshold wavelength, C n are the coefficients for n differentvalues given in the Table 2 of John (1988). The bound-freeabsorption cross-section above the threshold λ of 1.6419 µ mis zero. The total opacity due to bound-free absorption isthen computed using, κ bf = k bf ( λ, T ) A [ H − ] n d ρ , (A3)where κ bf is the total bound-free opacity, A [ H − ] is theabundance of H − (mixing ratio), n d is the atmospheric num-ber density (cm − ) and ρ is the atmospheric mass density( g / cm ).The free-free transition process of H − is given by h ν + e − + H −−−→ H + e − . (A4)In this reaction photons can be absorbed by electronsinteracting with neutral hydrogen atom across the wholespectral range (0 < λ < ∞ ). This process is solely responsiblefor H − opacity beyond the ionisation threshold wavelength(1.6419 µ m). This is computed using k f f ( λ, T ) = − ˝ n = (cid:18) T (cid:19) ( n + )/ ( λ A n + B n + C n / λ + D n / λ + E n / λ + F n / λ ) , (A5)where k f f ( λ, T ) is the free-free cross-section of H − inunits of cm / d y ne and T is the temperature. A n , B n , C n ,D n , E n and F n are coefficients as given in table 3a and 3bof John (1988) for λ > µ m and 0.1823 < λ < µ m, respectively. By multiplying equation A5 by the Boltz-mann’s constant (1.38 × − erg/s) and the temperature, k f f ( λ, T ) is obtained in the units of cm . The total opacitydue to free-free absorption is then computed using, κ f f = k f f ( λ, T ) A [ H ] n d ρ A [ e − ] n d , (A6)where κ f f is the total free-free opacity, A [ H ] is the abun-dance of neutral hydrogen (mixing ratio) and A [ e − ] is theabundance of electron (mixing ratio). The total opacity ofthe H − ion ( κ tot ) due to bound-free and free-free transitionsis then given by κ tot = κ bf + κ f f .We validate the abundance weighted H − opacity bycomparing with the results from Parmentier et al. (2018) andMansfield et al. (2018). Figure 4 of Parmentier et al. (2018)shows the abundance weighted absorption cross-section ofH − (cm /molecule) as a function of wavelength at the P - T point of 0.042 bar and 3100 K. We also compute the abun-dance weighted absorption cross-section of H − at this P - T point within ATMO using κ tot × µ mean N A , where κ tot is the to-tal opacity of the H − ion computed as shown in the previous MNRAS000
Figure showing validation of ATMO chemical equi-librium abundances of ionic species with GGChem (Woitke et al.2018) at 3000 K. with those from the GGchem model (Woitke et al. 2018) at2000, 3000 and 4000 K as shown in Figure A1 for 3000 K.We used the same input P - T profile for both ATMO andGGchem for this validation. It can be seen that there is avery good agreement between the abundances from both themodels. Only small differences exist in the deeper parts ofthe atmosphere, currently not probed by either emission ortransmission spectra. A2 Implementation and Validation of H − opacity Many publications highlight the importance of H − opacityin the atmosphere of extremely irradiated hot Jupiters (e.gArcangeli et al. 2018; Mansfield et al. 2018; Kreidberg et al.2018; Parmentier et al. 2018). We also included H − opaci-ties in ATMO and investigated its effects on the P - T profilesand thereby the spectra. The formation of species H − (hy-drogen anion) is basically a result of electron attachment,driven by the presence of abundant hydrogen (H) and lowenergy electrons in the ionised atmospheres of stars or hotJupiters (Rau 1996). The absorption of electromagnetic ra-diation by H − is driven by photo-detachment (bound-free)and free-free transition processes. These are computed us-ing the analytical equations of John (1988) derived from theoriginal derivation of free-free transition in Bell & Berring-ton (1987).The photo-detachment process of H − absorption is givenby h ν + H − −−−→ H + e − , (A1)where h is the Planck’s constant and ν is the frequencyof radiation. In this process H − ions absorbs radiation offrequency ν , to form atomic hydrogen and an electron. Asshown in John (1988) for wavelengths ( λ ) less than the ion-isation threshold λ of H − ( λ < µ m) this is computedusing, k bf ( λ ) = − λ (cid:18) λ − λ (cid:19) / f ( λ ) , (A2)where , f ( λ ) = (cid:213) n = C n (cid:20) λ − λ (cid:21) ( n − )/ , where k bf ( λ ) is the bound-free cross-section of H − inunits of cm , λ is the wavelength, λ = 1.6419 µ m is thethreshold wavelength, C n are the coefficients for n differentvalues given in the Table 2 of John (1988). The bound-freeabsorption cross-section above the threshold λ of 1.6419 µ mis zero. The total opacity due to bound-free absorption isthen computed using, κ bf = k bf ( λ, T ) A [ H − ] n d ρ , (A3)where κ bf is the total bound-free opacity, A [ H − ] is theabundance of H − (mixing ratio), n d is the atmospheric num-ber density (cm − ) and ρ is the atmospheric mass density( g / cm ).The free-free transition process of H − is given by h ν + e − + H −−−→ H + e − . (A4)In this reaction photons can be absorbed by electronsinteracting with neutral hydrogen atom across the wholespectral range (0 < λ < ∞ ). This process is solely responsiblefor H − opacity beyond the ionisation threshold wavelength(1.6419 µ m). This is computed using k f f ( λ, T ) = − ˝ n = (cid:18) T (cid:19) ( n + )/ ( λ A n + B n + C n / λ + D n / λ + E n / λ + F n / λ ) , (A5)where k f f ( λ, T ) is the free-free cross-section of H − inunits of cm / d y ne and T is the temperature. A n , B n , C n ,D n , E n and F n are coefficients as given in table 3a and 3bof John (1988) for λ > µ m and 0.1823 < λ < µ m, respectively. By multiplying equation A5 by the Boltz-mann’s constant (1.38 × − erg/s) and the temperature, k f f ( λ, T ) is obtained in the units of cm . The total opacitydue to free-free absorption is then computed using, κ f f = k f f ( λ, T ) A [ H ] n d ρ A [ e − ] n d , (A6)where κ f f is the total free-free opacity, A [ H ] is the abun-dance of neutral hydrogen (mixing ratio) and A [ e − ] is theabundance of electron (mixing ratio). The total opacity ofthe H − ion ( κ tot ) due to bound-free and free-free transitionsis then given by κ tot = κ bf + κ f f .We validate the abundance weighted H − opacity bycomparing with the results from Parmentier et al. (2018) andMansfield et al. (2018). Figure 4 of Parmentier et al. (2018)shows the abundance weighted absorption cross-section ofH − (cm /molecule) as a function of wavelength at the P - T point of 0.042 bar and 3100 K. We also compute the abun-dance weighted absorption cross-section of H − at this P - T point within ATMO using κ tot × µ mean N A , where κ tot is the to-tal opacity of the H − ion computed as shown in the previous MNRAS000 , 1–26 (2019) ibrary of Exoplanet Atmospheres (a) (b) Figure A2. (a)
Figure showing abundance weighted cross-section of H − at 0.042 bar and 3100 K from Figure 4 of Parmentier et al.(2018) (green) and from ATMO (blue). (b) Figure showing abundance weighted cross-section of H − at 0.084 bar and 2756 K from Figure7 of Mansfield et al. (2018) (green) and from ATMO (blue). section, µ mean is the mean molecular weight of the atmo-sphere and N A is the Avogadro’s constant. The comparisonis shown in Figure A2a, demonstrating that the agreementis good and even the equilibrium chemical abundances atthis P - T point are similar in ATMO and Parmentier et al.(2018) (from Figure 3 in their paper), thus validating theimplementation of H − opacity in ATMO.Figure 7 of Mansfield et al. (2018) shows the abundanceweighted absorption cross-section of H − at a P - T point of0.084 bar and 2756 K. When compared with this, there is asubstantial difference between the abundance weighted ab-sorption cross-section of H − as shown in Figure A2a. Theprimary reason being the difference in equilibrium chemi-cal abundances at this P - T point, which is ∼ − from both models, there is a good agreement (not shownhere). The reason for differences in equilibrium chemicalabundances is still unclear and can be due to many factors,such as the differences in input elemental abundances, poly-nomial coefficients etc. as shown in Goyal et al. (2019a).We note that the equilibrium chemistry scheme used inATMO has been validated by comparing to various numeri-cal and analytical equilibrium chemistry models, with localand rainout condensation (Drummond et al. 2016; Goyalet al. 2019a). A3 Fe Absorption cross-sections
Absorption cross-sections of gaseous iron (Fe) have beenincluded in ATMO using the Fe line list from the VALDdatabase (Heiter et al. 2008, 2015) and the partition func-tion from Sauval & Tatum (1984). The H and He pres-sure broadening line-widths for Fe have been computed us-ing the van der Waals coefficient contained within the VALDdatabase and using Equation 23 in Sharp & Burrows (2007). Figure B1.
Figure showing χ map for WASP-121b for the trans-mission spectra fitting described in Section 6. Contours of χ areshown for all the combinations of grid parameters. Metallicity isalso log-scaled, 0 being solar metallicity and 2 being 100 timessolar metallicity. Colours indicate confidence intervals as shownin colormap to the right. See Goyal et al. (2018) for more details. The absorption cross-sections of Fe included in ATMO havealso been validated by comparing with the absorption cross-sections of Sharp & Burrows (2007).
APPENDIX B: WASP-121B χ MAP
This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS , 1–26 (2019)NRAS , 1–12 (0000) Preprint August 6, 2020 Compiled using MNRAS L A TEX style file v3.0
Supplementary Material
August 6, 2020
To identify the features of various absorbing/emittingspecies in the emission spectrum, we compute the spectrumby removing the opacity contribution due to one species ata time, which we term the decoupled emission spectrum.In the emission spectrum as the radiation travelling radi-ally outward from the planetary atmosphere is measured,spectral features are indicated by a dip due to absorption asopposed to in a transmission spectrum, unless there is an in-version, in which case it shows an emission feature (bump).We show decoupled spectra for two planets, first is WASP-17b, a hot Jupiter with T eq = ∼ eq = ∼ O, since whenH O is removed while computing the emission spectrum asshown in Figure 1a most of the absorption features van-ish as compared to where all opacities sources are included(black). The absence of H O also allows probing the hotterand deeper regions of the atmospheres, as can be seen fromhigher flux for models without H O opacity. There is alsoa strong CO absorption feature at 4.5 µ m . The P - T profileused to generate the spectrum for WASP-17b is shown inFigure 3a (Rainout Condensation) in the main paper.Figure 2a and 2b show the decoupled spectra for WASP-121b with the corresponding P - T profile shown in Figure 9a(0.5 f c ) in the main paper. For WASP-121b also it can beseen that most of the contribution to the emission spec-trum is from H O since when the opacity of H O is re-moved, shown in Figure 2a most of the emission featuresvanish when compared to the spectrum including all opac-ity sources (black). However, it is interesting to note thatdue to the temperature inversion in the simulated atmo-sphere of WASP-121b the H O features are seen in emis-sion, as opposed to absorption as in the case of WASP-17b.There is also a decrease in the overall flux after removal ofH O opacity as emission is now from the deeper regions ofthe atmosphere which are cooler. The emission from CO canalso be noticed near ∼ µ m . The optical spectrum is dom-inated by emission features of TiO as seen in Figure 2b. Itmust be noted here that we remove TiO only while comput-ing emission spectra for this test shown in Figure 2b, notwhile computing the RCE P - T profile used to generate theemission spectrum. Figure 3a shows the Na and K cross-sections at 1000 K and1 mbar with line profiles from Burrows et al. (2000) whichare primarily Lorentzian and from Allard et al. (2007) whichuses more detailed quantum mechanical calculations. It canbe noticed from this figure that the differences are primarilyin the pressure broadened wings.The effect of these line profiles on the RCE P - T pro-files, transmission and emission spectra are shown in Figure3b, 3c and 3d, respectively, for WASP-17b at 0.25 f c , solarmetallicity and solar C/O ratio. The differences are negligi-ble and likely not to be detectable with current observations,in all cases. In the emission spectrum, adopting a profilefrom Allard et al. (2007) henceforth “Allard Profile” leadsto a slightly higher flux than when adopting a profile fromBurrows et al. (2000) henceforth “Burrows profile”, due to aslight increase in temperature for the case using the Allardprofile between 100 to 0.1 mbar, as shown in Figure 3b. Vanadium Oxide (VO) has been predicted to be the majorabsorber in the atmosphere of WASP-121b leading to an in-version, with the hints of VO features detected in the trans-mission and emission spectrum of WASP-121b (Evans et al.2017, 2018). In ATMO we initially included the VO line-list from Plez (1999) (PLEZ), this was updated to new hightemperature VO line-list from Exomol named as VOMYT(McKemmish et al. 2016). Figure 4a show the differences inthe cross-sections computed using both line-lists. It can beseen that the new line-list (VOMYT) is more complete, es-pecially in the infrared. Surprisingly, there is also a strongVO absorption band in the infrared between 10-12 µ m in thenew VO line list (McKemmish et al. 2016) in comparison tothe old line-list. There are two important peaks one near3 µ m and other a broad band peak between 10-12 µ m , offer-ing a potential wavelength region to detect VO using JWST.The effect of using different line-lists on the RCE P - T pro-files is shown in Figures 4b at 200 times solar metallicity forWASP-121b. At solar metallicity and solar C/O ratio with0.5 f c , there is no difference in the RCE P - T profiles gener-ated using the two different line-lists (not shown here), dueto the comparatively low abundance of VO. However, whenthe metallicity is increased to 200x solar, the abundance ofVO increases, Goyal et al. (see Figure 13b in 2019) rising to © a r X i v : . [ a s t r o - ph . E P ] A ug (a) (b) Figure 1.
Figure showing WASP-17b emission spectrum with 0.25 f c , solar metallicity and solar C/O ratio, when removing opacitycontributions of single species at a time from the calculation, shown by their respective colours. Emission spectrum including all 21opacities is shown in black. (a) Emission Spectrum when removing opacity due to species H -H (blue), H -He (green), H O (red), CO (cyan), CO (magenta), CH (yellow), NH (lightblue), Na (purple), K (brown), Li (lightgreen) and Rb (violet). (b) Same as 1a but whenremoving opacity due to species Cs (blue), TiO (green), VO (red), FeH (cyan), PH (magenta), H S (yellow), HCN (lightblue), C H (purple), SO (brown) and Fe (lightgreen)(a) (b) Figure 2. (a)
Same as Figure 1a but for WASP-121b, at solar metallicity and solar C/O ratio with 0.5 f c . (b) Same as 1b but forWASP-121b, at solar metallicity and solar C/O ratio with 0.5 f c . ∼ P - T profiles obtained using the two different line-lists.Moreover, retrieval models have also predicted the presenceof substantially large abundances of VO ( ∼ × solar metallicity,the P - T profile obtained using the VOMYT line-list is hotterby ∼
50 K around 1 millibar region, but this absorption ofradiation in the upper atmosphere leads to cooling in thedeeper atmosphere from 0.1 to 10 bar by about 100 K.The effect of different VO line-lists on the transmissionand emission spectra of WASP-121b are shown in Figure 4cand 4d, respectively. In the transmission spectra the differ- ences are only in the size of the features which is a combina-tion of differences in P - T profiles, abundances and small dif-ferences in line-lists. In the emission spectra, the difference isa result of differences in the P - T profile. As the temperaturein the region of the inversion which is probed by emissionspectra is higher for VOMYT than PLEZ, it leads to highervalue of F p (planetary flux), thus producing differences. The differences in the P - T profiles and the spectra betweenthe simulations, varying C/O ratio by varying O/H andthose by varying C/H, are shown here for WASP-17b. We MNRAS000
50 K around 1 millibar region, but this absorption ofradiation in the upper atmosphere leads to cooling in thedeeper atmosphere from 0.1 to 10 bar by about 100 K.The effect of different VO line-lists on the transmissionand emission spectra of WASP-121b are shown in Figure 4cand 4d, respectively. In the transmission spectra the differ- ences are only in the size of the features which is a combina-tion of differences in P - T profiles, abundances and small dif-ferences in line-lists. In the emission spectra, the difference isa result of differences in the P - T profile. As the temperaturein the region of the inversion which is probed by emissionspectra is higher for VOMYT than PLEZ, it leads to highervalue of F p (planetary flux), thus producing differences. The differences in the P - T profiles and the spectra betweenthe simulations, varying C/O ratio by varying O/H andthose by varying C/H, are shown here for WASP-17b. We MNRAS000 , 1–12 (0000) upplementary Material (a) (b)(c) (d) Figure 3. (a)
Figure showing absorption cross-sections (cm /molecule) of Na and K using two different pressure broadening treatmentsfrom Allard et al. (2007) and Burrows et al. (2000) (b) Figure showing RCE P - T profiles using two different pressure broadeningprofiles (Allard and Burrows) for Na and K, shown in Figure 3a, for WASP-17b at solar metallicity and solar C/O ratio with 0.25 f c . (c) Transmission spectra for WASP-17b using P - T profiles shown in Figure 3b, and two different pressure broadening profiles, namely,Allard and Burrows. (d) Emission spectra for WASP-17b using P - T profiles shown in Figure 3b, and two different pressure broadeningprofiles, namely, Allard and Burrows. note that when we vary C/H or O/H we keep the abundancesof other species to their solar value or to a metallicity scaledvalue.Figures 5a shows the P - T profiles at a C/O ratio of 0.35resulting from varying O/H and C/H for WASP-17b. We cansee there are differences of the order of 50 K between the twoprofiles. The differences can also be seen in the equilibriumchemical abundances shown in 5b. The abundances of H O,CO and CO are slightly larger when O/H is varied, com-pared to the same C/O ratio model where C/H is varied.This is because for C/O ratios less than 1, abundances ofthese species are limited by the carbon abundance (more sofor CO as it is the dominant molecule), therefore when O/His varied to reach a C/O ratio of 0.35, O/H is increased thusfavouring an increase in oxygen bearing species. On the con-trary if C/H is varied, it has to be decreased (keeping O/Hconstant) to reach a C/O ratio of 0.35 thus limiting (de- creasing) the formation of carbon bearing species. There isalso an effect caused by the changing of P - T profile whichcan be seen for CH as its abundances are mainly differentin the region where there are larger differences in P - T pro-files, between simulations varying either O/H or C/H, at thesame C/O ratio. The changing P - T profile will also have aneffect on other species. These differences can also be seen inthe transmission and emission spectra shown in Fig. 5c and5d, respectively, primarily at 4.5 µ m due to CO.Figures 5e and Figures 5f show the P - T profiles andequilibrium chemical abundances similar to Fig. 5a and 5b,respectively, but at a C/O ratio of 1.5. At a C/O ratio of 1.5differences can again be seen in the P - T profiles and abun-dances. However, in this case since the C/O ratio is greaterthan 1, the abundances are limited by the O/H abundance.Therefore, the abundance of carbon bearing species is largerwhen C/H is varied as compared to when O/H is varied at MNRAS , 1–12 (0000) (a) (b)(c) (d)
Figure 4. (a)
Figure showing absorption cross-sections (cm /molecule) of VO using different two different line-lists VOMYT (McKem-mish et al. 2016) and PLEZ (Plez 1999) (b) Figure showing RCE P - T profiles using different VO line-list named PLEZ and VOMYTfor WASP-121b at 200x solar metallicity and solar C/O ratio with 0.5 f c . (c) Transmission spectra for WASP-121b using P - T profilesshown in Figure 4b, and two different VO line-lists. (d) Emission spectra for WASP-121b using P - T profiles shown in Figure 4b, andtwo different VO line-lists. C/O ratios >
1. However, it must be noted that the effectof changing P - T profiles is also embedded in this difference.In this section we presented the differences in the P - T profiles and the spectra, at extreme values of C/O ratioparameter space in the grid (0.35 and 1.5) by adopting twodifferent approaches, one by varying O/H and other by vary-ing C/H. Although there are some differences in the resultsobtained using these two different methodologies, in the pa-rameter space we consider, they are smaller compared tothe effects of other parameters in the grid and other modelchoices (for e.g. local or rainout condensation). The effectsof varying C/O ratio by varying O/H across the parameterspace is shown in Section 5.3.3 of the main paper. MNRAS000
1. However, it must be noted that the effectof changing P - T profiles is also embedded in this difference.In this section we presented the differences in the P - T profiles and the spectra, at extreme values of C/O ratioparameter space in the grid (0.35 and 1.5) by adopting twodifferent approaches, one by varying O/H and other by vary-ing C/H. Although there are some differences in the resultsobtained using these two different methodologies, in the pa-rameter space we consider, they are smaller compared tothe effects of other parameters in the grid and other modelchoices (for e.g. local or rainout condensation). The effectsof varying C/O ratio by varying O/H across the parameterspace is shown in Section 5.3.3 of the main paper. MNRAS000 , 1–12 (0000) upplementary Material (a) (b)(c) (d)(e) (f) Figure 5. (a)
Figure showing P - T profiles with C/O ratio of 0.35 by varying C/H (red) and O/H (blue) relative to solar C/O ratio(0.55) at 0.25 f c and solar metallicity for WASP-17b. (b) Figure showing equilibrium chemical abundances for P - T profiles shown in Fig.5a by varying O/H (solid) and C/H (dashed) (c) Figure showing transmission spectra using P - T profiles shown in Fig. 5a and chemicalabundances shown in Fig. 5b (d) Figure showing emission spectra using P - T profiles shown in Fig. 5a and chemical abundances shownin Fig. 5b (e) Same as Fig. 5a but for C/O ratio of 1.5. (f)
Same as Fig. 5bbut for C/O ratio of 1.5.MNRAS , 1–12 (0000)
Species Line list Partition FunctionH O Barber et al. (2006) Barber et al. (2006)CO Tashkun & Perevalov (2011) Rothman et al. (2009)CO Rothman et al. (2010) Rothman et al. (2009)CH Yurchenko & Tennyson (2014) Yurchenko & Tennyson (2014)NH Yurchenko et al. (2011) Sauval & Tatum (1984)Na VALD3 Sauval & Tatum (1984)K VALD3 Sauval & Tatum (1984)Li VALD3 Sauval & Tatum (1984)Rb VALD3 Sauval & Tatum (1984)Cs VALD3 Sauval & Tatum (1984)Fe VALD3 Sauval & Tatum (1984)TiO Plez (1998) Sauval & Tatum (1984)VO McKemmish et al. (2016) Sauval & Tatum (1984)FeH Wende et al. (2010) Wende et al. (2010)PH Sousa-Silva et al. (2014) Sousa-Silva et al. (2014)HCN Harris et al. (2006) Harris et al. (2006)Barber et al. (2014) Barber et al. (2014)C H Rothman et al. (2013) Rothman et al. (2013)H S Rothman et al. (2013) Rothman et al. (2013)SO Underwood et al. (2016) Underwood et al. (2016)H -H CIA Richard et al. (2012) N/AH -He CIA Richard et al. (2012) N/AH − John (1988); Bell & Berrington(1987) (Analytical) N/A
Table 1.
Line list (opacity) sources of different species used in this library. Pressure broadening sources are shown in Table 2. Heiter et al. (2008, 2015); Ryabchikova et al. (2015) ( http://vald.astro.uu.se/~vald/php/vald.php ). Figure 6.
Figure showing best fit model transmission spectrausing the grid of model transmission spectra for WASP-17b pre-sented in this paper and observations from Sing et al. (2016) giv-ing χ value of 64.64 (reduced χ = 1.7) with f c = 0.25, solarmetallicity and C/O ratio of 0.35 (sub-solar). Best-Fit P - T pro-file is shown in the subplot. MNRAS000
Figure showing best fit model transmission spectrausing the grid of model transmission spectra for WASP-17b pre-sented in this paper and observations from Sing et al. (2016) giv-ing χ value of 64.64 (reduced χ = 1.7) with f c = 0.25, solarmetallicity and C/O ratio of 0.35 (sub-solar). Best-Fit P - T pro-file is shown in the subplot. MNRAS000 , 1–12 (0000) upplementary Material Molecule Broadener Line Width Source Exponent SourceH Gamache et al. (1996) Gamache et al. (1996)H O He Solodov & Starikov (2009); Steyert et al. (2004) Gamache et al. (1996)H Padmanabhan et al. (2014) Sharp & Burrows (2007)CO He Thibault et al. (1992) Thibault et al. (2000)H R´egalia-Jarlot et al. (2005) Le Moal & Severin (1986)CO He BelBruno et al. (1982); Mantz et al. (2005) Mantz et al. (2005)H Pine (1992); Margolis (1993) Margolis (1993)CH He Pine (1992) Varanasi & Chudamani (1990)H Hadded et al. (2001); Pine et al. (1993) Nouri et al. (2004)NH He Hadded et al. (2001); Pine et al. (1993) Sharp & Burrows (2007)H Allard et al. (1999, 2003, 2007) Sharp & Burrows (2007)Na He Allard et al. (1999, 2003, 2007) Sharp & Burrows (2007)H Allard et al. (1999, 2003, 2007) Sharp & Burrows (2007)K He Allard et al. (1999, 2003, 2007) Sharp & Burrows (2007)H Allard et al. (1999) Sharp & Burrows (2007)Li, Rb, Cs He Allard et al. (1999) Sharp & Burrows (2007)H Sharp & Burrows (2007) Sharp & Burrows (2007)TiO, VO He Sharp & Burrows (2007) Sharp & Burrows (2007)H Sharp & Burrows (2007) Sharp & Burrows (2007)FeH, Fe He Sharp & Burrows (2007) Sharp & Burrows (2007)H Bouanich et al. (2004) Levy et al. (1994)PH He Salem et al. (2005) Levy et al. (1994)H Landrain et al. (1997) Sharp & Burrows (2007)HCN He Landrain et al. (1997) Sharp & Burrows (2007)C H ,H S, SO Air Rothman et al. (2009) Rothman et al. (2009)
Table 2.
Type and source of pressure broadening for all opacities used in this library.MNRAS , 1–12 (0000) S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) - C n c - e . . . . . . . . . . . W i nn e t a l. ( ) D e m o r y e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) N i k o l o v e t a l. ( ) HA T - P - . . . . . . . . . . . K o v ´a c s e t a l. ( ) S o u t h w o r t h ( b ) HA T - P - . - . . . . . . . . . . N o y e s e t a l. ( ) S o u t h w o r t h ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) S o u t h w o r t h e t a l. ( ) HA T - P - . . . . . . . . . . . Q u i nn e t a l. ( ) Q u i nn e t a l. ( ) HA T - P - . . . . . . . . . . . J o hn s o n e t a l. ( ) J o hn s o n e t a l. ( ) HA T - P - . - . . . . . . . . . . H a r t m a n e t a l. ( ) T r e g l oa n - R ee d e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) H D - . . . . . . . . . . . S a t o e t a l. ( ) C a r t e r e t a l. ( ) H D - . . . . . . . . . . . H e n r y e t a l. ( ) S o u t h w o r t h ( ) K E L T - . - . . . . . . . . . . E a s t m a n e t a l. ( ) E a s t m a n e t a l. ( ) K E L T - . - . . . . . . . . . . C o lli n s e t a l. ( ) C o lli n s e t a l. ( ) K E L T - . . . . . . . . . . . B i e r y l a e t a l. ( ) B i e r y l a e t a l. ( ) K E L T - . . . . . . . . . . . F u l t o n e t a l. ( ) F u l t o n e t a l. ( ) K E L T - . - . . . . . . . . . . G a ud i e t a l. ( ) G a ud i e t a l. ( ) K E L T - . . . . . . . . . . . K uhn e t a l. ( ) K uhn e t a l. ( ) K E L T - . . . . . . . . . . . P e pp e r e t a l. ( ) B e a tt y e t a l. ( ) K E L T - . . . . . . . . . . . R o d r i g u eze t a l. ( ) R o d r i g u eze t a l. ( ) K E L T - . - . . . . . . . . . . Z h o u e t a l. ( ) Z h o u e t a l. ( ) K E L T - . . . . . . . . . . . M c L e o d e t a l. ( ) M c L e o d e t a l. ( ) K e p l e r - . . . . . . . . . . . F o r t n e y e t a l. ( ) S o u t h w o r t h ( ) T r E S - . . . . . . . . . . . M a ndu s h e v e t a l. ( ) S o zze tt i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) M a c i e j e w s k i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . - . . . . . . . . . . W il s o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e bb e t a l. ( ) C o lli n s e t a l. ( ) W A S P - . . . . . . . . . . . S k ill e n e t a l. ( ) S o u t h w o r t h ( ) MNRAS000
Type and source of pressure broadening for all opacities used in this library.MNRAS , 1–12 (0000) S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) - C n c - e . . . . . . . . . . . W i nn e t a l. ( ) D e m o r y e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) N i k o l o v e t a l. ( ) HA T - P - . . . . . . . . . . . K o v ´a c s e t a l. ( ) S o u t h w o r t h ( b ) HA T - P - . - . . . . . . . . . . N o y e s e t a l. ( ) S o u t h w o r t h ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) S o u t h w o r t h e t a l. ( ) HA T - P - . . . . . . . . . . . Q u i nn e t a l. ( ) Q u i nn e t a l. ( ) HA T - P - . . . . . . . . . . . J o hn s o n e t a l. ( ) J o hn s o n e t a l. ( ) HA T - P - . - . . . . . . . . . . H a r t m a n e t a l. ( ) T r e g l oa n - R ee d e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) H D - . . . . . . . . . . . S a t o e t a l. ( ) C a r t e r e t a l. ( ) H D - . . . . . . . . . . . H e n r y e t a l. ( ) S o u t h w o r t h ( ) K E L T - . - . . . . . . . . . . E a s t m a n e t a l. ( ) E a s t m a n e t a l. ( ) K E L T - . - . . . . . . . . . . C o lli n s e t a l. ( ) C o lli n s e t a l. ( ) K E L T - . . . . . . . . . . . B i e r y l a e t a l. ( ) B i e r y l a e t a l. ( ) K E L T - . . . . . . . . . . . F u l t o n e t a l. ( ) F u l t o n e t a l. ( ) K E L T - . - . . . . . . . . . . G a ud i e t a l. ( ) G a ud i e t a l. ( ) K E L T - . . . . . . . . . . . K uhn e t a l. ( ) K uhn e t a l. ( ) K E L T - . . . . . . . . . . . P e pp e r e t a l. ( ) B e a tt y e t a l. ( ) K E L T - . . . . . . . . . . . R o d r i g u eze t a l. ( ) R o d r i g u eze t a l. ( ) K E L T - . - . . . . . . . . . . Z h o u e t a l. ( ) Z h o u e t a l. ( ) K E L T - . . . . . . . . . . . M c L e o d e t a l. ( ) M c L e o d e t a l. ( ) K e p l e r - . . . . . . . . . . . F o r t n e y e t a l. ( ) S o u t h w o r t h ( ) T r E S - . . . . . . . . . . . M a ndu s h e v e t a l. ( ) S o zze tt i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) M a c i e j e w s k i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . - . . . . . . . . . . W il s o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e bb e t a l. ( ) C o lli n s e t a l. ( ) W A S P - . . . . . . . . . . . S k ill e n e t a l. ( ) S o u t h w o r t h ( ) MNRAS000 , 1–12 (0000) upplementary Material S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . . . . . . . . . . . L i s t e r e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) S o u t h w o r t h e t a l. ( b ) W A S P - . . . . . . . . . . . H e bb e t a l. ( ) M a n c i n i e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) E v a n s e t a l. ( ) W A S P - . - . . . . . . . . . . B o u c h y e t a l. ( ) C i ce r i e t a l. ( ) W A S P - . . . . . . . . . . . E n o c h e t a l. ( b ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) L e h m a nn e t a l. ( ) W A S P - . . . . . . . . . . . S m a ll e y e t a l. ( ) S m a ll e y e t a l. ( ) W A S P - . - . . . . . . . . . . E n o c h e t a l. ( ) E n o c h e t a l. ( ) W A S P - . . . . . . . . . . . M a x t e d e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . H e lli e r e t a l. ( ) G ill o n e t a l. ( ) W A S P - . - . . . . . . . . . . L e nd l e t a l. ( ) L e nd l e t a l. ( ) W A S P - . . . . . . . . . . . H ´ e b r a r d e t a l. ( ) M a n c i n i e t a l. ( ) W A S P - . . . . . . . . . . . F a e d i e t a l. ( ) F a e d i e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . H ´ e b r a r d e t a l. ( ) H ´ e b r a r d e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( b ) A nd e r s o n e t a l. ( b ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) W e s t e t a l. ( ) W A S P - . - . . . . . . . . . . S m a ll e y e t a l. ( ) B r o w n e t a l. ( ) W A S P - . . . . . . . . . . . S m a ll e y e t a l. ( ) B r o w n e t a l. ( ) W A S P - . - . . . . . . . . . . T r i a ud e t a l. ( ) T r i a ud e t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) S m i t h ( ) W A S P - . - . . . . . . . . . . D e l r eze t a l. ( ) D e l r eze t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) W e s t e t a l. ( ) W A S P - . . . . . . . . . . . H a y e t a l. ( ) H a y e t a l. ( ) W A S P - . . . . . . . . . . . N e v e u - V a n M a ll ee t a l. ( ) N e v e u - V a n M a ll ee t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . G ill o n e t a l. ( ) S o u t h w o r t h & E v a n s ( ) W A S P - . . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) MNRAS , 1–12 (0000) S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) W A S P - . . . . . . . . . . . B a rr o s e t a l. ( ) B a rr o s e t a l. ( ) W A S P - . . . . . . . . . . . H a y e t a l. ( ) M oˇ c n i k e t a l. ( ) W A S P - . . . . . . . . . . . D e l r eze t a l. ( ) D e l r eze t a l. ( ) W A S P - . . . . . . . . . . . T u r n e r e t a l. ( ) T u r n e r e t a l. ( ) W A S P - . . . . . . . . . . . T u r n e r e t a l. ( ) T u r n e r e t a l. ( ) W A S P - . - . . . . . . . . . . M a x t e d e t a l. ( ) M a x t e d e t a l. ( ) W A S P - . . . . . . . . . . . M a x t e d e t a l. ( ) M a x t e d e t a l. ( ) W A S P - . - . . . . . . . . . . L a m e t a l. ( ) L a m e t a l. ( ) W A S P - . - . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) X O - . . . . . . . . . . . M c C u ll o u g h e t a l. ( ) S o u t h w o r t h ( ) X O - . . . . . . . . . . . B u r k ee t a l. ( ) D a m a ss o e t a l. ( ) T a b l e . A ll t h e s t e ll a r a ndp l a n e t a r y p a r a m e t e r s a d o p t e d f r o m T EP C a t( S o u t h w o r t h ) d a t a b a s e , f o r t h e m o d e l s i m u l a t i o n s o f e x o p l a n e t s i n t h e g r i d a r e li s t e dh e r e . F i r s t c o l u m n s h o w s p l a n e t n a m e s w i t h ’ b ’ o m i tt e d i nd i c a t i n g fi r s t p l a n e t o f t h e s t e ll a r s y s t e m a s i n T EP C a t d a t a b a s e . Sub s e q u e n t c o l u m n ss h o w , s t e ll a r t e m p e r a t u r e ( T s t a r ) i n K e l v i n , s t e ll a r m e t a lli c i t y ( [ F e / H ] s t a r ) , s t e ll a r m a ss ( M s t a r ) i nun i t s o f s o l a r m a ss , s t e ll a rr a d i u s ( R s t a r ) i nun i t s o f s o l a rr a d i u s ,l oga r i t h m i c ( b a s e ) s t e ll a r g r a v i t y ( l ogg s t a r ) i n m / s , s e m i - m a j o r a x i s ( a ) i n AU , p l a n e t a r y m a ss ( M p ) i nun i t s o f J up i t e r m a ss , p l a n e t a r y r a d i u s ( R p ) i nun i t s o f J up i t e rr a d i u s , p l a n e t a r y s u r f a ce g r a v i t y ( g p ) i n m / s , p l a n e t a r y e q u ili b r i u m t e m p e r a t u r e ( T e q p ) i n K e l v i n a ss u m i n g0a l b e d oa nd e ffi c i e n t r e d i s t r i bu t i o n , V m ag n i t ud e ( V m ag ) o f t h e h o s t s t a r , d i s c o v e r y p a p e rr e f e r e n ce ( D i s c o v e r y P a p e r ) a ndfin a ll y t h e m o s t upd a t e d r e f e r e n ce . MNRAS000
Type and source of pressure broadening for all opacities used in this library.MNRAS , 1–12 (0000) S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) - C n c - e . . . . . . . . . . . W i nn e t a l. ( ) D e m o r y e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) N i k o l o v e t a l. ( ) HA T - P - . . . . . . . . . . . K o v ´a c s e t a l. ( ) S o u t h w o r t h ( b ) HA T - P - . - . . . . . . . . . . N o y e s e t a l. ( ) S o u t h w o r t h ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) S o u t h w o r t h e t a l. ( ) HA T - P - . . . . . . . . . . . Q u i nn e t a l. ( ) Q u i nn e t a l. ( ) HA T - P - . . . . . . . . . . . J o hn s o n e t a l. ( ) J o hn s o n e t a l. ( ) HA T - P - . - . . . . . . . . . . H a r t m a n e t a l. ( ) T r e g l oa n - R ee d e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . B a k o s e t a l. ( ) B a k o s e t a l. ( ) HA T - P - . . . . . . . . . . . H a r t m a n e t a l. ( ) H a r t m a n e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) HA T S - . . . . . . . . . . . B h a tt i e t a l. ( ) B h a tt i e t a l. ( ) H D - . . . . . . . . . . . S a t o e t a l. ( ) C a r t e r e t a l. ( ) H D - . . . . . . . . . . . H e n r y e t a l. ( ) S o u t h w o r t h ( ) K E L T - . - . . . . . . . . . . E a s t m a n e t a l. ( ) E a s t m a n e t a l. ( ) K E L T - . - . . . . . . . . . . C o lli n s e t a l. ( ) C o lli n s e t a l. ( ) K E L T - . . . . . . . . . . . B i e r y l a e t a l. ( ) B i e r y l a e t a l. ( ) K E L T - . . . . . . . . . . . F u l t o n e t a l. ( ) F u l t o n e t a l. ( ) K E L T - . - . . . . . . . . . . G a ud i e t a l. ( ) G a ud i e t a l. ( ) K E L T - . . . . . . . . . . . K uhn e t a l. ( ) K uhn e t a l. ( ) K E L T - . . . . . . . . . . . P e pp e r e t a l. ( ) B e a tt y e t a l. ( ) K E L T - . . . . . . . . . . . R o d r i g u eze t a l. ( ) R o d r i g u eze t a l. ( ) K E L T - . - . . . . . . . . . . Z h o u e t a l. ( ) Z h o u e t a l. ( ) K E L T - . . . . . . . . . . . M c L e o d e t a l. ( ) M c L e o d e t a l. ( ) K e p l e r - . . . . . . . . . . . F o r t n e y e t a l. ( ) S o u t h w o r t h ( ) T r E S - . . . . . . . . . . . M a ndu s h e v e t a l. ( ) S o zze tt i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) M a c i e j e w s k i e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . - . . . . . . . . . . W il s o n e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) S o u t h w o r t h ( ) W A S P - . . . . . . . . . . . H e bb e t a l. ( ) C o lli n s e t a l. ( ) W A S P - . . . . . . . . . . . S k ill e n e t a l. ( ) S o u t h w o r t h ( ) MNRAS000 , 1–12 (0000) upplementary Material S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . . . . . . . . . . . L i s t e r e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) S o u t h w o r t h e t a l. ( b ) W A S P - . . . . . . . . . . . H e bb e t a l. ( ) M a n c i n i e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) E v a n s e t a l. ( ) W A S P - . - . . . . . . . . . . B o u c h y e t a l. ( ) C i ce r i e t a l. ( ) W A S P - . . . . . . . . . . . E n o c h e t a l. ( b ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) W A S P - . . . . . . . . . . . C o lli e r C a m e r o n e t a l. ( ) L e h m a nn e t a l. ( ) W A S P - . . . . . . . . . . . S m a ll e y e t a l. ( ) S m a ll e y e t a l. ( ) W A S P - . - . . . . . . . . . . E n o c h e t a l. ( ) E n o c h e t a l. ( ) W A S P - . . . . . . . . . . . M a x t e d e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . H e lli e r e t a l. ( ) G ill o n e t a l. ( ) W A S P - . - . . . . . . . . . . L e nd l e t a l. ( ) L e nd l e t a l. ( ) W A S P - . . . . . . . . . . . H ´ e b r a r d e t a l. ( ) M a n c i n i e t a l. ( ) W A S P - . . . . . . . . . . . F a e d i e t a l. ( ) F a e d i e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) S o u t h w o r t h e t a l. ( ) W A S P - . - . . . . . . . . . . H ´ e b r a r d e t a l. ( ) H ´ e b r a r d e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( b ) A nd e r s o n e t a l. ( b ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) W e s t e t a l. ( ) W A S P - . - . . . . . . . . . . S m a ll e y e t a l. ( ) B r o w n e t a l. ( ) W A S P - . . . . . . . . . . . S m a ll e y e t a l. ( ) B r o w n e t a l. ( ) W A S P - . - . . . . . . . . . . T r i a ud e t a l. ( ) T r i a ud e t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) S m i t h ( ) W A S P - . - . . . . . . . . . . D e l r eze t a l. ( ) D e l r eze t a l. ( ) W A S P - . . . . . . . . . . . W e s t e t a l. ( ) W e s t e t a l. ( ) W A S P - . . . . . . . . . . . H a y e t a l. ( ) H a y e t a l. ( ) W A S P - . . . . . . . . . . . N e v e u - V a n M a ll ee t a l. ( ) N e v e u - V a n M a ll ee t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . G ill o n e t a l. ( ) S o u t h w o r t h & E v a n s ( ) W A S P - . . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) W A S P - . - . . . . . . . . . . A nd e r s o n e t a l. ( ) A nd e r s o n e t a l. ( ) MNRAS , 1–12 (0000) S y s t e m T s t a r [ F e / H ] s t a r M s t a r R s t a r l ogg s t a r a M p R p g p T e q p V m ag D i s c o v e r y P a p e r U pd a t e d R e f e r e n ce ( K )( M s un )( R s un )( m / s )( AU )( M j up )( R j up )( m / s )( K ) W A S P - . . . . . . . . . . . B a rr o s e t a l. ( ) B a rr o s e t a l. ( ) W A S P - . . . . . . . . . . . H a y e t a l. ( ) M oˇ c n i k e t a l. ( ) W A S P - . . . . . . . . . . . D e l r eze t a l. ( ) D e l r eze t a l. ( ) W A S P - . . . . . . . . . . . T u r n e r e t a l. ( ) T u r n e r e t a l. ( ) W A S P - . . . . . . . . . . . T u r n e r e t a l. ( ) T u r n e r e t a l. ( ) W A S P - . - . . . . . . . . . . M a x t e d e t a l. ( ) M a x t e d e t a l. ( ) W A S P - . . . . . . . . . . . M a x t e d e t a l. ( ) M a x t e d e t a l. ( ) W A S P - . - . . . . . . . . . . L a m e t a l. ( ) L a m e t a l. ( ) W A S P - . - . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) W A S P - . . . . . . . . . . . H e lli e r e t a l. ( ) H e lli e r e t a l. ( ) X O - . . . . . . . . . . . M c C u ll o u g h e t a l. ( ) S o u t h w o r t h ( ) X O - . . . . . . . . . . . B u r k ee t a l. ( ) D a m a ss o e t a l. ( ) T a b l e . A ll t h e s t e ll a r a ndp l a n e t a r y p a r a m e t e r s a d o p t e d f r o m T EP C a t( S o u t h w o r t h ) d a t a b a s e , f o r t h e m o d e l s i m u l a t i o n s o f e x o p l a n e t s i n t h e g r i d a r e li s t e dh e r e . F i r s t c o l u m n s h o w s p l a n e t n a m e s w i t h ’ b ’ o m i tt e d i nd i c a t i n g fi r s t p l a n e t o f t h e s t e ll a r s y s t e m a s i n T EP C a t d a t a b a s e . Sub s e q u e n t c o l u m n ss h o w , s t e ll a r t e m p e r a t u r e ( T s t a r ) i n K e l v i n , s t e ll a r m e t a lli c i t y ( [ F e / H ] s t a r ) , s t e ll a r m a ss ( M s t a r ) i nun i t s o f s o l a r m a ss , s t e ll a rr a d i u s ( R s t a r ) i nun i t s o f s o l a rr a d i u s ,l oga r i t h m i c ( b a s e ) s t e ll a r g r a v i t y ( l ogg s t a r ) i n m / s , s e m i - m a j o r a x i s ( a ) i n AU , p l a n e t a r y m a ss ( M p ) i nun i t s o f J up i t e r m a ss , p l a n e t a r y r a d i u s ( R p ) i nun i t s o f J up i t e rr a d i u s , p l a n e t a r y s u r f a ce g r a v i t y ( g p ) i n m / s , p l a n e t a r y e q u ili b r i u m t e m p e r a t u r e ( T e q p ) i n K e l v i n a ss u m i n g0a l b e d oa nd e ffi c i e n t r e d i s t r i bu t i o n , V m ag n i t ud e ( V m ag ) o f t h e h o s t s t a r , d i s c o v e r y p a p e rr e f e r e n ce ( D i s c o v e r y P a p e r ) a ndfin a ll y t h e m o s t upd a t e d r e f e r e n ce . MNRAS000 , 1–12 (0000) upplementary Material References
Allard N. F., Royer A., Kielkopf J. F., Feautrier N., 1999, Phys.Rev. A, 60, 1021Allard N. F., Allard F., Hauschildt P. H., Kielkopf J. F., MachinL., 2003, A&A, 411, L473Allard N. F., Spiegelman F., Kielkopf J. F., 2007, A&A, 465, 1085Anderson D. R., et al., 2010, ApJ, 709, 159Anderson D. R., et al., 2011, A&A, 531, A60Anderson D. R., et al., 2014a, preprint, ( arXiv:1410.3449 )Anderson D. R., et al., 2014b, MNRAS, 445, 1114Anderson D. R., et al., 2015, A&A, 575, A61Bakos G. ´A., et al., 2007, ApJ, 656, 552Bakos G. ´A., et al., 2009, ApJ, 707, 446Bakos G. ´A., et al., 2016, preprint, ( arXiv:1606.04556 )Barber R. J., Tennyson J., Harris G. J., Tolchenov R. N., 2006,MNRAS, 368, 1087Barber R. J., Strange J. K., Hill C., Polyansky O. L., MellauG. C., Yurchenko S. N., Tennyson J., 2014, MNRAS, 437,1828Barros S. C. C., et al., 2016, A&A, 593, A113Beatty T. G., et al., 2017, AJ, 154, 25BelBruno J. J., Gelfand J., Radigan W., Verges K., 1982, Journalof Molecular Spectroscopy, 94, 336Bell K. L., Berrington K. A., 1987, Journal of Physics B AtomicMolecular Physics, 20, 801Bhatti W., et al., 2016, preprint, ( arXiv:1607.00322 )Bieryla A., et al., 2015, AJ, 150, 12Bouanich J.-P., Salem J., Aroui H., Walrand J., Blanquet G.,2004, J. Quant. Spectrosc. Radiative Transfer, 84, 195Bouchy F., et al., 2010, A&A, 519, A98Brown D. J. A., et al., 2017, MNRAS, 464, 810Burke C. J., et al., 2007, ApJ, 671, 2115Burrows A., Marley M. S., Sharp C. M., 2000, ApJ, 531, 438Carter J. A., Winn J. N., Gilliland R., Holman M. J., 2009, ApJ,696, 241Ciceri S., et al., 2013, A&A, 557, A30Collier Cameron A., et al., 2007, MNRAS, 375, 951Collier Cameron A., et al., 2010, MNRAS, 407, 507Collins K. A., et al., 2014, AJ, 147, 39Collins K. A., Kielkopf J. F., Stassun K. G., 2017, AJ, 153, 78Damasso M., et al., 2015, A&A, 575, A111Delrez L., et al., 2014, A&A, 563, A143Delrez L., et al., 2016, MNRAS, 458, 4025Demory B.-O., et al., 2016, Nature, 532, 207Eastman J. D., et al., 2016, AJ, 151, 45Enoch B., et al., 2011a, AJ, 142, 86Enoch B., et al., 2011b, MNRAS, 410, 1631Evans D. F., Southworth J., Smalley B., 2016, ApJ, 833, L19Evans T. M., et al., 2017, Nature, 548, 58Evans T. M., et al., 2018, AJ, 156, 283Faedi F., et al., 2013, A&A, 551, A73Fortney J. J., et al., 2011, ApJS, 197, 9Fulton B. J., et al., 2015, ApJ, 810, 30Gamache R. R., Lynch R., Brown L. R., 1996, J. Quant. Spec-trosc. Radiative Transfer, 56, 471Gaudi B. S., et al., 2017, Nature, 546, 514Gillon M., et al., 2012, A&A, 542, A4Gillon M., et al., 2014, A&A, 562, L3Goyal J. M., et al., 2019, MNRAS, p. 722Hadded S., Aroui H., Orphal J., Bouanich J.-P., Hartmann J.-M.,2001, Journal of Molecular Spectroscopy, 210, 275Harris G. J., Tennyson J., Kaminsky B. M., Pavlenko Y. V., JonesH. R. A., 2006, MNRAS, 367, 400Hartman J. D., et al., 2011, ApJ, 742, 59Hartman J. D., et al., 2012, AJ, 144, 139Hartman J. D., et al., 2014, AJ, 147, 128Hartman J. D., et al., 2016, AJ, 152, 182 Hay K. L., et al., 2016, MNRAS, 463, 3276Hebb L., et al., 2009, ApJ, 693, 1920Hebb L., et al., 2010, ApJ, 708, 224H´ebrard G., et al., 2013, A&A, 549, A134Heiter U., et al., 2008, in Journal of Physics Conference Series. p.012011, doi:10.1088/1742-6596/130/1/012011Heiter U., et al., 2015, Phys. Scr., 90, 054010Hellier C., et al., 2009, ApJ, 690, L89Hellier C., et al., 2011, A&A, 535, L7Hellier C., et al., 2012, MNRAS, 426, 739Hellier C., et al., 2014, MNRAS, 440, 1982Hellier C., et al., 2015, AJ, 150, 18Hellier C., et al., 2017, MNRAS, 465, 3693Henry G. W., Marcy G. W., Butler R. P., Vogt S. S., 2000, ApJ,529, L41John T. L., 1988, A&A, 193, 189Johnson J. A., et al., 2011, ApJ, 735, 24Kov´acs G., et al., 2007, ApJ, 670, L41Kuhn R. B., et al., 2016, MNRAS, 459, 4281Lam K. W. F., et al., 2017, A&A, 599, A3Landrain V., Blanquet G., Lep`ere M., Walrand J., Bouanich J.-P.,1997, Journal of Molecular Spectroscopy, 182, 184Le Moal M. F., Severin F., 1986, J. Quant. Spectrosc. RadiativeTransfer, 35, 145Lehmann H., Guenther E., Sebastian D., D¨ollinger M., HartmannM., Mkrtichian D. E., 2015, A&A, 578, L4Lendl M., et al., 2012, A&A, 544, A72Lendl M., et al., 2016, A&A, 587, A67Levy A., Lacome N., Tarrago G., 1994, Journal of Molecular Spec-troscopy, 166, 20Lister T. A., et al., 2009, ApJ, 703, 752Maciejewski G., et al., 2014, Acta Astron., 64, 11Mancini L., et al., 2013, MNRAS, 436, 2Mancini L., et al., 2017, MNRAS, 465, 843Mandushev G., et al., 2007, ApJ, 667, L195Mantz A. W., Malathy Devi V., Chris Benner D., Smith M. A. H.,Predoi-Cross A., Dulick M., 2005, Journal of Molecular Struc-ture, 742, 99Margolis J. S., 1993, J. Quant. Spectrosc. Radiative Transfer, 50,431Maxted P. F. L., et al., 2011, PASP, 123, 547Maxted P. F. L., et al., 2016, A&A, 591, A55McCullough P. R., et al., 2006, ApJ, 648, 1228McKemmish L. K., Yurchenko S. N., Tennyson J., 2016, MNRAS,463, 771McLeod K. K., et al., 2017, AJ, 153, 263Moˇcnik T., Hellier C., Anderson D. R., Clark B. J. M., South-worth J., 2017, MNRAS, 469, 1622Neveu-VanMalle M., et al., 2014, A&A, 572, A49Nikolov N., et al., 2014, MNRAS, 437, 46Nouri S., Orphal J., Aroui H., Hartmann J.-M., 2004, Journal ofMolecular Spectroscopy, 227, 60Noyes R. W., et al., 2008, ApJ, 673, L79Padmanabhan A., Tzanetakis T., Chanda A., Thomson M. J.,2014, J. Quant. Spectrosc. Radiative Transfer, 133, 81Pepper J., et al., 2017, AJ, 153, 215Pine A. S., 1992, J. Chem. Phys., 97, 773Pine A. S., Markov V. N., Buffa G., Tarrini O., 1993, J. Quant.Spectrosc. Radiative Transfer, 50, 337Plez B., 1998, A&A, 337, 495Plez B., 1999, in Le Bertre T., Lebre A., Waelkens C., eds, IAUSymposium Vol. 191, Asymptotic Giant Branch Stars. p. 75Quinn S. N., et al., 2012, ApJ, 745, 80R´egalia-Jarlot L., Thomas X., von der Heyden P., Barbe A., 2005,J. Quant. Spectrosc. Radiative Transfer, 91, 121Richard C., et al., 2012, J. Quant. Spectrosc. Radiative Transfer,113, 1276Rodriguez J. E., et al., 2016, AJ, 151, 138MNRAS , 1–12 (0000) Rothman L. S., et al., 2009, J. Quant. Spectrosc. Radiative Trans-fer, 110, 533Rothman L. S., et al., 2010, J. Quant. Spectrosc. Radiative Trans-fer, 111, 2139Rothman L. S., et al., 2013, J. Quant. Spectrosc. Radiative Trans-fer, 130, 4Ryabchikova T., Piskunov N., Kurucz R. L., Stempels H. C.,Heiter U., Pakhomov Y., Barklem P. S., 2015, Phys. Scr.,90, 054005Salem J., Bouanich J.-P., Walrand J., Aroui H., Blanquet G.,2005, Journal of Molecular Spectroscopy, 232, 247Sato B., et al., 2005, ApJ, 633, 465Sauval A. J., Tatum J. B., 1984, ApJS, 56, 193Sharp C. M., Burrows A., 2007, ApJS, 168, 140Sing D. K., et al., 2016, Nature, 529, 59Skillen I., et al., 2009, A&A, 502, 391Smalley B., et al., 2011, A&A, 526, A130Smalley B., et al., 2012, A&A, 547, A61Smith A. M. S., 2015, Acta Astron., 65Solodov A. M., Starikov V. I., 2009, Molecular Physics, 107, 43Sousa-Silva C., Al-Refaie A. F., Tennyson J., Yurchenko S. N.,2014, VizieR Online Data Catalog, 744Southworth J., 2010, MNRAS, 408, 1689Southworth J., 2011a, MNRAS, 417, 2166Southworth J., 2011b, MNRAS, 417, 2166Southworth J., 2012, MNRAS, 426, 1291Southworth J., Evans D. F., 2016, MNRAS, 463, 37Southworth J., Bruni I., Mancini L., Gregorio J., 2012a, MNRAS,420, 2580Southworth J., et al., 2012b, MNRAS, 426, 1338Southworth J., et al., 2013, MNRAS, 434, 1300Southworth J., et al., 2014, MNRAS, 444, 776Southworth J., et al., 2016, MNRAS, 457, 4205Sozzetti A., et al., 2015, A&A, 575, L15Steyert D. W., Wang W. F., Sirota J. M., Donahue N. M., ReuterD. C., 2004, J. Quant. Spectrosc. Radiative Transfer, 83, 183Tashkun S. A., Perevalov V. I., 2011, J. Quant. Spectrosc. Radia-tive Transfer, 112, 1403Thibault F., Boissoles J., Le Doucen R., Bouanich J. P., ArcasP., Boulet C., 1992, J. Chem. Phys., 96, 4945Thibault F., Calil B., Boissoles J., Launay J. M., 2000, PhysicalChemistry Chemical Physics (Incorporating Faraday Trans-actions), 2, 5404Tregloan-Reed J., et al., 2018, MNRAS, 474, 5485Triaud A. H. M. J., et al., 2017, MNRAS, 467, 1714Turner O. D., et al., 2016, PASP, 128, 064401Underwood D. S., Tennyson J., Yurchenko S. N., Huang X.,Schwenke D. W., Lee T. J., Clausen S., Fateev A., 2016, MN-RAS, 459, 3890Varanasi P., Chudamani S., 1990, J. Quant. Spectrosc. RadiativeTransfer, 43, 1Wende S., Reiners A., Seifahrt A., Bernath P. F., 2010, A&A,523, A58West R. G., et al., 2009, AJ, 137, 4834West R. G., et al., 2016, A&A, 585, A126Wilson D. M., et al., 2008, ApJ, 675, L113Winn J. N., et al., 2011, ApJ, 737, L18Yurchenko S. N., Tennyson J., 2014, MNRAS, 440, 1649Yurchenko S. N., Barber R. J., Tennyson J., 2011, MNRAS, 413,1828Zhou G., et al., 2016, AJ, 152, 136This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000