Cloud property trends in hot and ultra-hot giant gas planets (WASP-43b, WASP-103b, WASP-121b, HAT-P-7b, and WASP-18b)
Ch. Helling, D. Lewis, D. Samra, L. Carone, V. Graham, O. Herbort, K. L. Chubb, M. Min, R. Waters, V. Parmentier, N. Mayne
AAstronomy & Astrophysics manuscript no. aanda-forarX © ESO 2021February 24, 2021
Cloud property trends in hot and ultra-hot giant gas planets(WASP-43b, WASP-103b, WASP-121b, HAT-P-7b, and WASP-18b)
Ch. Helling , , , D. Lewis , , D. Samra , , L. Carone , V. Graham , O. Herbort , , , K. L. Chubb , M. Min , R.Waters , , V. Parmentier , N. Mayne Centre for Exoplanet Science, University of St Andrews, North Haugh, St Andrews, KY169SS, UKe-mail: [email protected] SUPA, School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews, KY169SS, UK SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, NL Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany School of Earth & Environmental Studies, University of St Andrews, Irvine Building, St Andrews, KY16 9AL, UK School of Physics and Astronomy, University of Glasgow, University Avenue, Glasgow, G12 8QQ, UK Institute for Mathematics, Astrophysics & Particle Physics, Department of Astrophysics, Radboud University, P.O. Box 9010, MC62, NL-6500 GL Nijmegen, The Netherlands Department of Physics, University of Oxford, Parks Rd, Oxford, OX1 3PU, UK Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, EX4 4QL, UKReceived September 15, 2996; accepted March 16, 2997
ABSTRACT
Context.
Ultra-hot Jupiters are the hottest exoplanets discovered so far. Observations begin to provide insight into the composition oftheir extended atmospheres and their chemical day / night asymmetries. Both are strongly a ff ected by cloud formation. Aims.
We explore trends in cloud properties for a sample of five giant gas planets: the hot gas giant WASP-43b and the four ultra-hotJupiters WASP-18b, HAT-P-7b, WASP-103b, and WASP-121b. This provides a reference frame for cloud properties for the JWSTtargets WASP-43b and WASP-121b. We further explore chemically inert tracers to observe geometrical asymmetries of ultra-hotJupiters, and if the location of inner boundary of a 3D GCM matters for the clouds that form.
Methods.
A homogeneous set of 3D GCM results is used as input for a kinetic cloud formation code to evaluate the cloud opacityand gas parameters like C / O, mean molecular weight, and degree of ionisation. We cast our results in terms of integrated quantities toenable a global comparison between the sample planets.
Results.
The large day / night temperature di ff erences of ultra-hot Jupiters cause large chemical asymmetries: cloud-free days butcloudy nights, atomic vs. molecular gases and respectively di ff erent mean molecular weights, deep thermal ionospheres vs. low-ionised atmospheres, undepleted vs enhanced C / O. WASP-18b, as the heaviest planet in the sample, has the lowest global C / O. Conclusions.
The global climate may be considered as similar amongst ultra-hot Jupiters, but di ff erent to that of hot gas giants.The local weather, however, is individual for each planet since the local thermodynamic conditions, and hence the local cloud andgas properties, di ff er. The morning and the evening terminator of ultra-hot Jupiters will carry signatures of their strong chemicalasymmetry such that ingress / egress asymmetries can be expected. An increased C / O ratio is a clear sign of cloud formation, makingcloud modelling a necessity when utilizing C / O (or other mineral ratios) as tracer for planet formation. The changing geometricalextension of the atmosphere from the day to the nightside may be probed through chemically inert species like helium. Ultra-hotJupiters are likely to develop deep atmospheric ionospheres which may impact the atmosphere dynamics through MHD processes.
Key words. exoplanets – chemistry – cloud formation
1. Introduction
Ultra-hot Jupiters provide the unique opportunity to study awide range of atmospheric regimes in one object due to theirstrong day-night temperature di ff erence of > ffi cient heat redistribution from the day- to the nighside(Perez-Becker & Showman 2013). For one of the hottest knownultra-hot Jupiters, KELT-9b, several indicators for a very high-temperature dayside have been found: Ca II (Turner et al. 2020)as well as Fe and Fe + (Hoeijmakers et al. 2018) at the limb,in addition to an extended hydrogen-envelope (Yan & Henning2018) prompting investigations into the atmospheric mass lossof KELT-9b (e.g. Wyttenbach et al. 2020). Fossati et al. (2020)discuss the di ff erences in the H α and H β lines as observed by dif- ferent groups with di ff erent instruments and di ff erent reductionpipelines. Employing non-LTE radiative transfer, a temperatureof 10 . . . . × K is retrieved to be consistent with the PEPSItransmission spectra. The first CHEOPS science paper by Lendlet al. (2020) presents WASP-189b with an global dayside tem-perature of ≈ ffi -cient heat redistribution. Also WASP-121b shows less extremetemperatures than KELT-9b such that the presence of neutralatoms like Mg, Na, Ca, Cr, Fe and also Ni and V have been in-ferred from observations of the terminator regions (Hoeijmakerset al. 2020). However, Hoeijmakers et al. (2020) did not detect Tiand TiO on WASP-121b which may be an indication for cloud-depleted Ti abundances at the cold evening terminator similar toWASP-18b or HAT-P-7b (Helling et al. 2019a,b). Gibson et al.(2020) detect Fe I in WASP-121b applying VLT / UVES transit
Article number, page 1 of 38 a r X i v : . [ a s t r o - ph . E P ] F e b & A proofs: manuscript no. aanda-forarX observations. Partial coverage of WASP-121b by aerosols wassuggest along the terminator for WASP-121b by Kempton et al.(2017) based on phase equilibrium considerations. Ehrenreichet al. (2020) present ESPRESSO / VLT observations of the ultra-hot Jupiter WASP-78b showing a day / night terminator asymme-try as suggested for WASP-18b or HAT-P-7b. Neutral iron hasbeen suggested to be present on the hot morning terminator butnot on the colder evening terminator, leading the authors to claimthat iron rain should form on the nightside of WASP-78b. Basedon detailed cloud modelling, Helling et al. (2019a,b) show thatthe dayside of the ultra-hot Jupiters WASP-18b and HAT-P7bare likely to be cloud free while the nightside will be covered inclouds. In comparison, hot giant gas planets, like HD 189733b,HD 209458b and WASP-43b, have a global day / night cloud cov-erage over a large pressure range (Lee et al. 2015a, 2016; Lineset al. 2018; Helling et al. 2020) due to their smaller day-nighttemperature di ff erences.The theoretical modelling of exoplanet atmospheres hasreached a level that may allow to study a set of ultra-hot Jupitersand hot giant gas planets with respect to their potential trends incloud properties. In this paper, we consider the ultra-hot JupitersWASP-103b, WASP-121b, HAT-P-7b, and WASP-18b, and thehot giant gas planet WASP-43b. WASP-43b and WASP-18bare ERS JWST targets (program 1366). WASP-43b (program1224), and WASP-121b (program 1201) are GTO JWST tar-gets . The ultra-hot Jupiters in our sample have a global temper-ature of T eq > T eq < P / T eq and the T e ff / T eq diagrams. As a comparison, we add theclose-in sub-Neptune HD 86226c (Teske et al. 2020) which hasa global temperature similar to those of hot gas giants, and fallsinto the giant gas planet g P / T eq corner of Fig. 1 (top left). Cross-field et al. (2020) show that the IRAC2 (4.5 µ m) irradiation tem-perature of the hot Neptune LTT 9779b is roughly comparableto that of HAT-P-7b, and generally consistent with that of giantgas planets.For our comparison study, we use results from 3D GCMs asinput for our kinetic cloud formation code in order to study dif-ferences and similarities of the cloud coverage of these planets.The atmosphere dynamics enters our simulation only indirectlydue to its e ff ect on the local thermodynamic properties. Startingfrom the global temperature / pressure / velocity structure, cloudproperties like cloud particle formation rate, mean particle size,material compositions, the dust-to-gas ratio are investigated, andalso characteristic gas-phase properties like C / O, mean molecu-lar weight and degree of ionisation which all provide insight intovarious processes beyond cloud formation. C / O (and also othermineral ratios like Si / O, Fe / O, Helling et al. 2019a) are usedas potential markers for planet formation scenarios (e.g. Hellinget al. 2014; Cridland et al. 2019), the mean molecular weightis important to guide our understanding of atmospheric exten-sions, and the degree of ionisation shows in how far electrostaticor electromagnetic processes require attention in exoplanet at-mospheres (e.g. Rodríguez-Barrera et al. 2015). The latter is anessential step towards magnetosphere studies of exoplanets (forexample, Varela et al. 2018; Selhorst et al. 2020)The paper is structured as follows. After the introduction(Sect. 1), Sect. 2 outlines our modelling approach to studythe cloud properties and some key gas characteristic for the https: // / jwst / observing-programs / program-information five gas planets in our sample listed in black colour in Ta-ble 1. Section 3 summarises the input. Section 4 compares thecloud properties of the di ff erent planets. Section 5 compares theplanets with respect to the cloud feedback on the atmosphericgas (C / O), the mean molecular weight, and also the degree ofionisation. Section 6 looks at how the inner boundary of theGeneral Circulation Model (GCM) a ff ects the (T gas (z), p gas (z),v z ( x , y , z ))-profiles and consequently the possible cloud proper-ties for WASP-43b. Observational implications are explored inSect. 7, Sect. 8 presents our discussion and Sect. 9 presents ourconclusions.
2. Approach
We adopted a two-step approach in order to examine the cloudstructures of five gas planets in comparisons, similar to workson the hot Jupiters HD 189733b, HD 209458b and WASP-43b(Lee et al. 2015a; Helling et al. 2016), and the ultra-hot JupitersWASP-18b (Helling et al. 2019a) and HAT-P-7b (Helling et al.2019b; Molaverdikhani et al. 2020): The first modelling stepproduced pre-calculated 3D GCM results. These results wereused as input for the second modelling step which was a kineticcloud formation model consistently combined with equilibriumgas-chemistry calculations. We utilised 16 1D (T gas (z), p gas (z),v z ( x , y , z ))-profiles for all planets in our ensemble (Fig. 2). Theseprofiles probe specific locations (incl. morning and evening ter-minators, substellar and antistellar point) on the planetary globeand were distributed as depicted in Fig. 1 in Helling et al.(2019a). The same longitudes, φ , and latitudes, θ , are sampledfor all ensemble planets studied here. The sampled longitudesare φ = o , o , o , o , − o , − o , − o with φ < θ = o and θ = o in the northern hemisphere. The 3D simulations assume that thesouthern hemisphere is similar to the northern hemisphere. Thesubstellar point is ( θ, φ ) = (0 o , o ) (black dashed), the antistel-lar point is ( θ, φ ) = (0 o , − o ) (black dash-dot), the terminatorsare at φ = o , − o (grey lines in Fig. 2). T gas (z) is the localgas temperature [K], p gas (z) is the local gas pressure [bar], andv z (x,y,z) is the local vertical velocity component [cm s − ]. Weuse the solar element abundances from Asplund et al. (2009) forthe undepleted element abundances.This two-step approach has the limitation of not explicitlytaking into account the potential e ff ect of horizontal winds oncloud formation, nor the opacity of the cloud particles on theatmospheric structure. However, processes governing the forma-tion of mineral clouds are determined by local thermodynamicproperties which are the result of 3D dynamic atmosphere simu-lations. Cloud particle properties such as particle size or particlecomposition should be smeared out in longitude compared to theresults shown here. We note that comparing Lee et al. (2015a)(without horizontal advection) and Lee et al. (2016) (includ-ing horizontal advection), the non-coupled problem is both morecomputationally feasible, easier to interpret and provides rea-sonable first order insights into the expected atmospheric cloudproperties. The situation is somewhat di ff erent for photochem-ically triggered cloud formation. Photochemical hydrocarbon-haze production, for example, is determined by the external ra-diation field. We did, however, show that in the case of e ffi cientmineral cloud formation, that hydrocarbon hazes play no role forthe cloud opacity on the nightside and the terminator (Hellinget al. 2020). The dayside of all the ultra-hot Jupiters will be toohot for hydrocarbon hazes to be thermally stable. Article number, page 2 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters
Stellar Parameters WASP-103 WASP-18 WASP-121 HAT-P-7 T e ff [K] 6100 ± ± ± ± Mass [M
Sun ] 1.220 ± ± ± ± Radius [R
Sun ] 1.436 ± ± ± ± Spectral Type F8V F6V F6V F8Metallicity [Fe / H][dex] 0.06 ± ± ± ± Orbital Parameters WASP-103b WASP-18b WASP-121b HAT-P-7b
Semi-Major Axis [AU] 0.01985 ± ± ± ± Orbital Period [days] 0.92554 ± ± ± Planetary Parameters T eq [K] 2500 ± ± ± ± Mass [M
Jup ] 1.49 ± ± ± ± Radius [R
Jup ] 1.528 ± ± ± ± Density [g cm − ] 0.554 ± ± ± ± g [g Jup ] 0.638 ± ± ± ± log (g [cm s − ]) 3.219 ± ± ± ± Stellar Parameters HD 209458 WASP-43 HD 189733 HD 86226 T e ff [K] 6100 ± ± ± ± Mass [M
Sun ] 1.119 ± ± ± ± Radius [R
Sun ] 1.155 ± ± ± ± Spectral Type G0V K7V K1.5V G2VMetallicity [Fe / H][dex] 0.00 ± -0.01 ± -0.03 ± ± Orbital Parameters HD 209458b WASP-43b HD 189733b HD 86226c
Semi-Major Axis [AU] 0.04707 ± ± ± ± Orbital Period [days] 3.524746 ± ± Planetary Parameters T eq [K] 1500 ± ± ± ± Mass [M
Jup ] 0.685 ± ± ± ± [M E ] or 0.023 M Jup
Radius [R
Jup ] 1.359 ± ± ± ± [R E ] or 0.193 R Jup
Density [g cm − ] 0.362 ± ± ± ± g [g Jup ] 0.371 ± ± ± ± log (g [cm s − ]) 2.983 ± ± ± ± Table 1: Physical parameters of the exoplanets, their host star and of the orbit. The equilibrium temperature given in the literaturehave been rounded to the next 100K as it in unrealistic to expect that it can be determined to a precision of 1K or 10K.
Top:
Ultra-hotJupiters.
Bottom: hot giant gas planets and HD 86226c, a close-in sub-Neptune. Grayed planets are used for comparison only, blackcoloured planets are composing the gas giant sample studied here.
References : Delrez et al. (2016), Van Eylen et al. (2012), Pál (2009), Gillon et al. (2014), Hellier et al. (2009), Pearson (2019), Sheppard et al. (2017), Torres et al. (2008), Gillon et al. (2012), This Work (calculated using the referenced data), Teske et al.(2020).
3D GCM input:
We utilize the 3D thermal structures ofWASP-43b, HAT-P-7b, WASP-18b, WASP-103b, and WASP-121b as described in Parmentier et al. (2018); Mansfield et al.(2018) as input for our kinetic cloud-formation simulation.These 3D GCM structures were obtained with the cloud-freeSPARC / MITgcm (Showman et al. 2009) and was run for 300Earth days, with the last 100 days used to calculate time averagedquantities. The pressure range covered is 2 · − bar . . . Kinetic cloud formation:
To preserve consistency for WASP-43b, HAT-P-7b, WASP-18b, WASP-103b, and WASP-121b, weapply the same set-up of our kinetic cloud formation model(nucleation, growth, evaporation, gravitational settling, elementconsumption and replenishment) and equilibrium gas-phase cal-culations as in Sect 2.1 in Helling et al. (2019b). Insight intonumerical aspects of the solution can be found in Sect. 2.4 inWoitke & Helling (2004). Cloud particle formation depletes thelocal gas phase, and gravitational settling causes these elements to be deposited, for example, in the inner (high pressure) at-mosphere where the cloud particles evaporate. We use the lo-cal vertical velocity to calculate the necessary mixing timescale, τ mix ∝ v z ( r ) − as outlined in Sect. 2.4 in Lee et al. (2016). Hence, τ mix ∝ K − (cid:44) const along the probed atmospheric profiles.We acknowledge that this approach may introduce limitationswhich, however, will a ff ect all planets in our sample similarly.Our comparative study therefore remains valid.Seed forming species (TiO , SiO) also need to be consideredas surface growth material, since both processes (nucleation andgrowth) compete for the participating elements (Ti, Si, O, C, K,and Cl in this work). We consider the formation of 16 bulk ma-terials ([s] = TiO [s], Mg SiO [s], MgSiO [s], MgO[s], SiO[s],SiO [s], Fe[s], FeO[s], FeS[s], Fe O [s], Fe SiO [s], Al O [s],CaTiO [s], CaSiO [s], C[s], KCl[s]) that form from 11 elements(Mg, Si, Ti, O, Fe, Al, Ca, S, C, K and Cl) by 128 surface reac-tions. The abundance of these 11 elements will decrease if cloudparticles are forming (nucleation, growth) and increase if cloudparticles evaporate. Sulfur has not been included in our present Article number, page 3 of 38 & A proofs: manuscript no. aanda-forarX eq [K]02468 g [ g J u p ] WASP-121bWASP-103bWASP-18bHAT-P-7bWASP-43bHD 189733bHD 209458bHD 86226c eq [K]40005000600070008000900010000 T e ff [ K ] WASP-121bWASP-103bWASP-18b HAT-P-7bWASP-43bHD 189733b HD 209458bHD 86226c
Metallicity [Fe/H][dex] p [ g c m ] WASP-121bWASP-103bWASP-18bHAT-P-7bWASP-43bHD 189733bHD 209458bHD 86226c eff [K]0246810 p [ g c m ] WASP-121bWASP-103bWASP-18bHAT-P-7bWASP-43bHD 189733bHD 209458bHD 86226c
Fig. 1: Relationship between selected system properties for hot giant Jupiters (WASP-43b, HD 189733b, HD 209458b) and ultra-hotJupiters (HAT-P-7b, WASP-18b, WASP-103b, WASP-121b). The two classes of giant gas planets are clearly separated with respectto their global planetary temperature, T eq [K] and the planets’ surface gravity, g [g Jup ]. There is not as clear a separation betweenthe hot giant gas planets and ultra-hot Jupiters regarding their host star’s e ff ective temperature, T e ff [K], bulk planetary density ρ p ,and stellar metallicity [Fe / H]. The ultra-hot Jupiters are shown by circle markers, the giant-gas planets by the square markers anda sub-Neptune (HD 86226c) by the diamond marker. We also include the sample of hot and the ultra-hot Jupiters from Table 1 inBaxter et al. (2020) in the T e ff vs T eq plot (top right) as smaller light gray points.mineral cloud model. Sulfuric materials in form of S[s], FeS[s],MgS[s] would contribute by less than 10% in volume fraction ina solar element abundance gas (see Fig. 6 in Helling 2019).Other kinetic cloud models emphasise the importance of theKelvin e ff ect on cloud formation (e.g. Powell et al. 2018; Zhang2020). The Kelvin e ff ect refers to the decreasing thermal sta-bility with increasing surface curvature, hence, with decreasingparticle sizes. The Figures 3 in Goeres (1996) and in Helling& Fomins (2013) visualise the need for a super-cooling belowthermal stability as result of the decreased surface binding en-ergy with increasing surface curvature for small particles. Thee ff ect of the resulting changing thermal stability is taken into ac-count in our nucleation model by determining the stable molec-ular clusters and deriving a surface tension as outlined in Leeet al. (2015b).
3. The different atmosphere structures
Figure 2 summarises the 1D atmospheric ( T gas , p gas )-profilesfor the hot giant gas planet WASP-43b, and the four ultra-hot Jupiters WASP-18b, HAT-P-7b, WASP-103b, WASP-121b.This sample of giant gas planets is homogeneous in that all( T gas , p gas )-profiles result from the same 3D GCM code. All dif-ferences that will be explored in this paper will therefore becaused by the local thermodynamic conditions, and will not be caused by di ff erences in numerical methods or other assump-tions made in di ff erent hydrodynamic simulations. Section 6will, however, address the e ff ect of the inner boundary for the ex-ample of WASP-43b based on results from di ff erent 3D GCMs.Figure 2 shows that hot giant gas planets and the ultra-hot Jupiters have substantially di ff erent day / night ( T gas , p gas )-structures. The largest di ff erence occurs on the dayside betweenthese two sub-classes of gas giants. The nightsides appear moresimilar. All ultra-hot Jupiters sampled reach maximum gas tem-peratures of ≈ ff er, but all ultra-hot Jupiters have a comparably low nightside temperature.Figure 2 (right lower panel) provides a comparison of theday- and the nightside averaged profiles (excluding the termi-nator regions). All sampled planets have a hotter dayside witha temperature inversion occurring at p gas ∼ − . . . − bar forthe ultra-hot Jupiters. These gas temperature inversions typicallydisplay a change of 1500-2000K. Hot giant gas planets have amuch less pronounced temperature inversion happening deeperin the atmosphere than the ultra-hot Jupiters, at about 1 bar, witha range of only less than 500K. In the low pressure regimes, thedayside profiles from our simulations of the ultra-hot Jupiters lieat 2700K, whereas the dayside profiles of the hot giant gas plan- Article number, page 4 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) T ga s ( K ) WASP-43b
Day-sideNight-sideSubstellar pointAnti-stellar point Evening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) T ga s ( K ) WASP-103bDay-sideNight-sideSubstellar pointAnti-stellar point Evening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) T ga s ( K ) WASP-18b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) T ga s ( K ) HAT-P-7b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) T ga s ( K ) WASP-121b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) T ga s ( K ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7bHD 189733bHD 209458b
Fig. 2: The 16 1D ( T gas , p gas )-profiles of the hot giant gas planet WASP-43b, and the ultra-hot Jupiters WASP-18b, HAT-P-7b,WASP-103b, and WASP-121b. The day- and nightside average profiles (lower right panel) exclude the terminators. The samelongitudes, φ , and latitudes, θ , are sample for each planets. The sampled longitudes are φ = o , o , o , o , − o , − o , − o ( φ < θ = o and θ = o in the northern hemisphere. The substellar point is ( θ, φ ) = (0 o , o )(black dashed), the antistellar point is ( θ, φ ) = (0 o , − o ) (black dash-dot), the terminators are at φ = o , − o (grey lines).Day / night temperature di ff erences of ≈ . . . − bar and 100 bar within the GCM mod-elling framework utilised here. An average dayside profile of hotgiant gas planets (now including WASP-43b, HD 189733b andHD 209458b for comparison) are a lot cooler than those of theultra-hot Jupiters in our sample but exact di ff erences vary across pressure ranges (Fig. 2, lower right panel). The average nightsidetemperatures of the ultra-hot Jupiters are in the temperature andpressure ranges of the average dayside profiles of the hot giantgas planets in our sample for p gas < . Article number, page 5 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) WASP-43bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) WASP-103b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) WASP-18bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) HAT-P-7b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) WASP-121b Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. 3: Total nucleation rate J ∗ = (cid:80) J i [cm − s − ] for the 1D ( T gas , p gas )-profiles (Fig. 2) for the hot giant gas planets WASP-43b, andthe ultra-hot Jupiters WASP-18b, HAT-P-7b, WASP-103b, and WASP-121bs. The colour code is similar to Fig. 2. The lower rightpanel shows the day (solid lines) and nightside (dashed lines) averaged seed formation rates, excluding the terminator profiles. Alldepicted planets show seed formation on the nightside. Only WASP-43b enables the nucleation process on the dayside e ffi ciently.
4. Comparing cloud properties
The nucleation rate, J ∗ [cm − s − ], is an essential measure forthe e ffi ciency with which cloud formation occurs, hence, withwhich e ffi ciency the gas is depleted and is undergoing a phasetransition leading to the formation of cloud particles. Here weconsider the formation of mineral cloud particles which is trig-gered by the nucleation of mainly TiO and SiO. We analyse thecloud formation e ffi ciency for individual profiles first (Fig. 3),before we proceed to integrated properties (Fig. 4) as the base for comparing column integrated nucleation rates for di ff erentplanets according to their T eq and g P (Fig. 5).Figure 3 demonstrates that the nightside gas temperaturesare low enough that nucleation takes place for all exoplanets ofour sample, hot giant gas planets and ultra-hot Jupiters. We mayconclude that most if not all ultra-hot Jupiters will have cloudsforming on their nightsides.
Averaging over all nightside pro-files (Fig. 3, lower right panel) suggests the most e ffi cient forma-tion of cloud condensation nuclei occurring on WASP-18b andWASP-43b with average values of J ∗ ≈ . . . cm − s − ,and the least e ffi cient nucleation on the nightside of WASP-43b Article number, page 6 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) WASP-43b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) WASP-103b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) WASP-18b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) HAT-P-7b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) WASP-121b
Day-sideNight-sideSub/Anti-stellar pointTerminator
Fig. 4: Column-integrated total nucleation rates (cid:82) z max z min J ∗ ( z ) dz [cm − s − ] for the sample planets WASP-43b, WASP-18b, HAT-P-7b,WASP-103b, and WASP-121b. WASP-103b has the highest integrated nucleation e ffi ciency, HAT-P-7b the lowest in the nightside. T eq [K] − − − − l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) Day-sideNight-sideSub/Anti-stellar pointTerminatorWASP-103bWASP-121bWASP-18bWASP-43bHAT-P-7b g[g
Jup ] − − − − l og ( R z m a x z m i n J ∗ ( z ) d z [ c m − s − ] ) Day-sideNight-sideSub/Anti-stellar pointTerminatorWASP-103bWASP-121bWASP-18bWASP-43bHAT-P-7b
Fig. 5: The range of column-integrated nucleation rates from Fig. 4 shown for T eq [K] (left) and g [g Jup ] (right) for the giant gasplanet WASP-43b, and the ultra-hot Jupiters HAT-P-7b, WASP-18b, and WASP-103b, WASP-121b. The WASP-18b T eq is o ff set by +
200 K to avoid overlap. No one value su ffi ces to describe the rate at which cloud particles form. Article number, page 7 of 38 & A proofs: manuscript no. aanda-forarX with values of J ∗ ≈ − . . . cm − s − in the upper atmo-sphere. The least e ffi cient nightside nucleation in the upper at-mosphere occurs in HAT-P7b. The details of the nucleation pro-files depend on the local thermodynamic conditions. The night-side averaged values are higher than those retrieved with ARCiSby Min et al. (2020) for the 10 hot giant gas planets published inSing et al. (2016). Both samples contain di ff erent planets, how-ever.Therefore, the only planet forming a substantial amount ofcloud particles on the dayside within our sample is the hot gi-ant gas planet WASP-43b, and a tiny nucleation peak occursin deeper, high-pressure atmospheric regions on the dayside ofWASP-121b (Fig. 3). This will have implications for the cloudparticle sizes in Sect. 4.2. We have demonstrated (Lee et al.2015a, 2016; Helling et al. 2016; Lines et al. 2018) that both thehot giant gas planets HD 189733b and HD 209458b form cloudson the day and on the nightside. It might therefore be reasonableto conclude that hot giant gas planets can form clouds that coverthe entire globe and that occupy a substantial pressure range.
To be able to compare the cloud formation e ffi ciency in theglobal atmospheres of our sample planets, column integrated nu-cleation rates (cid:82) z max z min J ∗ ( z ) dz [cm − s − ] are considered (Fig. 4).The left half of the plot shows the equatorial values ( θ = o ) andthe right half showing northern hemisphere values ( θ = o ). Theorder of profiles is starting at sub-stellar point ( φ, θ ) = (0 o , o ),move around from East to West at the equator θ = o (left half ofthe plot) and then the same for θ = o . We note that these valuesaverage out all local information as discussed before (Figure 3)and should be considered as guiding rather then absolute values.The colour code is the same as in Fig. 3. Nucleation is gener-ally less e ffi cient (on hot giant gas planets) or completely absent(ultra-hot Jupiters) on the dayside. Nucleation is more e ffi cientin the non-equatorial hemispheres for some planets (WASP-43b,WASP-103b, WASP-121b). Nucleation is generally less e ffi cientin the terminator regions for the ultra-hot Jupiters. The maxi-mum nucleation e ffi ciency is very individual for every planet.Figure 5 (left) shows the much larger spread of nucleation val-ues for globally hotter ultra-hot Jupiters compared to the shownhot giant gas planet. This suggests that the cloud particle popu-lation will be more diverse in size on ultra-hot Jupiters than onhot giant gas planets. The cloud particle size, a [cm], is an essential value entering theopacity calculation and shows how e ffi cient surface growth de-pletes the gas phase through the growth of Mg / Si / O / Fe / Ti / Al / containing minerals. For our purpose, we show the surface av-eraged mean particle size, (cid:104) a (cid:105) A [cm], which we will use for ouropacity calculation in Sect. 7, (cid:104) a (cid:105) A = (cid:114) π L L , (1)with the dust moments L and L , (Eq.A.1 in Helling et al. 2020).Further discussion of the di ff erent definitions of the mean parti-cle size can be found in Appendix A of Helling et al. (2020).Similar to Sect. 4.1, we first present details of surface av-eraged mean particle size, (cid:104) a (cid:105) A , in Fig. 6, before we proceedto integrated properties (Fig. 7), namely the integrated numberdensity weighted surface averaged mean particle size, (cid:104)(cid:104) a (cid:105) A (cid:105) = (cid:82) z max z min n d ( z ) (cid:104) a (cid:105) A ( z ) dz (cid:82) z max z min n d ( z ) dz with n d ( z ) = ρ ( z ) L ( z )4 π (cid:104) a ( z ) (cid:105) / ff erent planet parameter, T eq and g P (Fig. 8).Across both sides of the planets, the mean particle size, (cid:104) a (cid:105) A ,increases with pressure, as surface growth e ffi ciency increaseswith increasing gas density (Fig. 6). Small cloud condensationseeds nucleate in the cool upper atmosphere. Due to gravita-tional settling these fall through the atmosphere, growing fasterthe deeper they fall. Both night and day show an increase in meanparticle size with increasing pressure with dayside profiles al-ways showing a larger particle radius than the nightside. Cloudparticles of the size of (cid:104) a (cid:105) ≈ . µ m reside about 2h in theatmosphere where p gas ≈ − bar in the terminator region ofWASP-43b, but remains for 170h on the nightside which has asomewhat less extended atmosphere of higher density.The mean particles sizes (plotted as number densityweighted surface averaged, column integrated mean particlesizes, (cid:104)(cid:104) a (cid:105) A (cid:105) , in Fig, 7) are biggest in atmospheric regions oflow nucleation e ffi ciency. This results in a factor of 10 di ff er-ence in size between day and nightside on the hot giant gasplanets WASP-43b, but causes the formation of cm-sized cloudparticles at some terminator and dayside locations on the ultra-hot Jupiters. Figure 8 suggests that low-mass ultra-hot Jupitershave the widest range of cloud particles sizes across their at-mospheres, indicating a strong spatial in-homogeneity of theseatmospheres. This includes the JWST target WASP-121b, but notthe much heavier WASP-18b.
The dust-to-gas ratio, ρ d /ρ ( ρ d – cloud particle mass density, ρ –gas mass density), shows where the largest cloud particle massis located in the atmosphere, or in broader terms, where mostof the condensed mass is located. It therefore makes little senseto discuss column integrated values here. In other areas of as-trophysics, ρ d /ρ , is used to measure the enrichment of gaseousenvironments with solid particles, like in planet forming disks,commentary tails, the ISM, AGB star winds, super novae ejects.The general shape of the day- and nightside ρ d /ρ -profiles inour sample of giant exoplanets (Figs. 9, A.1) are similar, all in-creasing to a maximum before falling back to zero at the inneratmosphere. The nightside of all low-mass ultra-hot Jupiters inour sample (WASP-103b, WASP-121b, HAT-P7b) have a steepincrease of the atmospheric cloud particle mass load at the cloudtop, reaching the maximum ρ d /ρ within a very narrow pres-sure interval. Amongst the ultra-hot Jupiters, WASP-18b standsout with a shallower increase of the cloud particle mass loadat the cloud top more comparable to the dayside of the gas gi-ant WASP-43b. Figure 9 provides day- (solid line) and nightside(dashed lines) averaged ρ d /ρ values without the terminators forthe planet ensemble considered here.For the hot giant gas planet WASP-43b in our sample, thenightside always displays a higher dust-to-gas ratio than the day-side. This is consistent with the lower nightside mean particlesize. The dust-to-gas ratio sharply increases up to 4 . · − whereit stays fairly level before beginning to decrease at ∼ . . . . ρ d /ρ values is reached if all elements like Mg / Si / O / Fehave condensed (Woitke et al. 2018), indicating that these atmo-spheric parts have achieved thermal equilibrium. Figure A.1 incomparison to Fig 3 shows that, after a brief period of nucleation(which does not occur under thermal equilibrium) in the very up-per atmosphere, the nightside is almost completely covered bya thick cloud at all lat / long profiles, with the cloud continuingdeep into the atmosphere. Most cloud particles have evaporated Article number, page 8 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) WASP-43bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) WASP-103bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) WASP-18bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) HAT-P-7bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) WASP-121bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − l og ( h a i A [ µ m ] ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. 6: Surface averaged mean particle size, (cid:104) a (cid:105) A [ µ m] (Eq. 2), for the hot giant gas planet WASP-43b, and the ultra-hot JupitersWASP-18b, HAT-P-7b, WASP-103b, and WASP-121b. The lower right panel shows the day (solid lines) and nightside (dashed lines)averaged surface averaged mean particle size. The cloud particles sizes vary throughout the atmospheres with the largest particlesoccurring in the high-pressure, inner cloud layers. Cloud particles as large as 1cm may occur in low numbers in the inner daysidecloud layers of ultra-hot Jupiters where nucleation is very ine ffi cient, but present.at 1bar for the ultra-hot Jupiters, except for WASP-18b and thehot gas giant WASP-43b.The northern morning terminator point, ( φ, θ ) = ( − o , o ),of WASP-43b (Fig. A.1) displays a short, sharp peak in dust-to-gas ratio of almost 6 · − at 10 − bar, being considerably higherthan the other profiles. This peak coincides with an influx of coldgas at the terminator which boosts cloud particle formation. Sim-ilar peaks of often lower ’amplitude’ occur for all other planetsof our sample for the morning terminator. We note that substan-tial cloud particle mass is present at the evening terminator (grey dotted lines in the detailed plots of Fig. A.1) of some planets inour sample.There are generally less extended (for hot giant gas planets)or no (for ultra-hot Jupiters) clouds on the dayside, shown bya lower dust-to-gas ratio, but this thinner cloud is still presentacross all dayside profiles and even continues deep into the at-mosphere for WASP-43b. Dips in ρ d /ρ are consistent with thedayside temperature inversions. Article number, page 9 of 38 & A proofs: manuscript no. aanda-forarX ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) − − − hh a i A i [ µ m ] WASP-43b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) − − − − hh a i A i [ µ m ] WASP-103b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) − − − hh a i A i [ µ m ] WASP-18b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) − − − hh a i A i [ µ m ] HAT-P-7b
Day-sideNight-sideSub/Anti-stellar pointTerminator ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) ( φ , θ ) = ( − . ◦ , . ◦ ) − − − hh a i A i [ µ m ] WASP-121b
Day-sideNight-sideSub/Anti-stellar pointTerminator
Fig. 7: Integrated, number density weighted surface averaged mean particle size, (cid:104)(cid:104) a (cid:105) A (cid:105) = (cid:82) z max z min n d ( z ) (cid:104) a (cid:105) A ( z ) dz (cid:14) (cid:82) z max z min n d ( z ) dz , forthe giant gas planet WASP-43b and the ultra-hot Jupiters WASP-18b, HAT-P-7b, WASP-103b, and WASP-121b. T eq [K] − − − − hh a i A i [ µ m ] Day-sideNight-sideSub/Anti-stellar pointTerminatorWASP-103bWASP-121bWASP-18bWASP-43bHAT-P-7b g[g
Jup ] − − − − hh a i A i [ µ m ] Day-sideNight-sideSub/Anti-stellar pointTerminatorWASP-103bWASP-121bWASP-18bWASP-43bHAT-P-7b
Fig. 8: The range of integrated, number density weighted surface averaged mean particle size from Fig. 7 shown for T eq [K] (left)and g [g Jup ] (right). The largest range of integrated cloud particles sizes occurs for ultra-hot Jupiters with small surface gravity, onebeing the JWST target WASP-121b. The WASP-18b T eq is o ff est by +
200 K to avoid overlap.
Article number, page 10 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) ρ d / ρ × − Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. 9: The day (solid lines) and nighside (dashed lines) averageddust-to-gas ratios, ρ d /ρ , for the giant gas planet WASP-43b, andthe ultra-hot Jupiters WASP-18b, HAT-P-7b, WASP-103b, andWASP-121b. The detailed results are in Fig. A.1. The material composition of the cloud particles gives insight intothe changing chemical composition of the atmosphere in whichthe cloud particles form, and through which they fall while theycontinue to grow. The 16 bulk materials considered for bulkgrowth are listed in Section 2. Here we split these materials intofive categories of condensates: high temperature condensates,metal oxides, silicates, carbon and salts. The chemical speciescontained within each group are listed in Table 2. The modelsfor WASP-18b and HAT-P-7b do not include KCl[s]. The indi-vidual material volume fractions can be found in Section A, themain text focuses on the material groups only.Figure 10 shows the variation of the volume fraction foreach of the material categories for each of the planets at fourkey points: the sub-stellar point ( φ, θ ) = (0 o , o ), the anti-stellarpoint ( φ, θ ) = ( − o , o ), the equatorial morning termina-tor ( φ, θ ) = ( − o , o ), and the equatorial evening terminator( φ, θ ) = (90 o , o ). For the giant-gas planet WASP-43b, the up-per atmosphere is dominated by silicates, making up ∼
50% ofthe cloud particle volume. The next most common are metaloxides at ∼ ∼ ∼
10% be-ing made up by carbon materials. In the very upper atmosphereat the anti-stellar point, carbon material volume fractions arehigher than high-temperature condensate volume, but decreasesteadily as pressure increases from 0.01 mbar. Deeper in the at-mosphere, between 10 mbar and 1 bar the fraction of metal ox-ides increases, and the fraction of silicates decreases as silicatesevaporate. After a small increase the high temperature conden-sates remain constant comprising ∼
20% of the total material vol-ume. At 10 bar the material composition becomes dominated byhigh temperature condensates, with the remaining groups com-prising around 5% of the composition in total.The material volume fractions of the anti-stellar point(WASP-103b, WASP-121b and HAT-P-7b) and the equatorialevening terminator (WASP-103b, WASP-121b, HAT-P-7b andWASP-18b) follow similar variations throughout the atmosphereas seen for the same points on WASP-43b. The upper atmo-sphere, above 1 mbar, of the anti-stellar point of WASP-18b is Condensate group Materials includedMetal Oxides SiO[s], SiO [s], MgO[s],FeO[s], Fe O [s]Silicates MgSiO [s], Mg SiO [s],CaSiO [s], Fe SiO [s]Carbon C[s]High TemperatureCondensates TiO [s], Fe[s], Al O [s],CaTi [s], FeS[s]Salts KCl[s]Table 2: The 16 bulk materials considered in our model aregrouped in 6 categories. [s] indicates condensate materials.dominated by metal oxides and there is a small fraction of carbonbetween 0.1 mbar and 1 bar. At the evening terminator there arecondensates from approximately at 1 mbar (10 mbar for WASP-18b) to pressures of 0.1 bar for WASP-121b and WASP-103b, 1bar for HAT-P-7b and WASP-18b, and 10 bar for WASP-43b atwhich the temperature inversion occurs. Salt species are negli-gible for all planets in our sample. No clouds are forming at thesub-stellar point and at the equatorial morning terminator for allthe ultra-hot Jupiters (hence, the respective panels are empty).Figure 10 also allows to see the pressure range, and thus howmuch of the atmosphere, over which cloud condensates are form-ing in the frame of our model. There are cloud particles formingthroughout most of the atmosphere of WASP-43b, ranging from p ≈ . − .
01 mbar . . .
10 bar, for all four atmosphere pro-files. For the ultra-hot Jupiters WASP-121b, WASP-103b andHAT-P-7b the anti-stellar point shows clouds forming between p ≈ . − .
01 mbar . . . . p ≈ . − . . . . p ≈ −
10 bar.The material volume fractions for all planets ’oscillate’ be-tween groups as pressure is increased. This is caused by a’switching’ back and forth associated with the evaporation of in-dividual species, which frees up elements that are then consumedby thermally stable species in other condensate groups: The tran-sition between Fe SiO [s] and Fe[s] as can be seen more clearlyin Figs. A.2 to A.5. As a general rule, the volume fractions ofsilicates and carbon decrease whereas volume fractions of metaloxides and high temperature condensates increase as pressure in-creases as result of their thermal stability. In all profiles, metaloxides become more common than silicates at higher pressures.
Figure 11 shows the normalised column integrated volumefractions, (cid:104) V (cid:105) norm = (cid:82) z max z min V s ( z ) V tot ( z ) dz (cid:80) i (cid:82) z max z min V i ( z ) V tot ( z ) dz , (3)where i runs through each of the condensate groups listed in Ta-ble 2, for the same four points as shown in Fig.10. These valuesprovide an average cloud composition at this particular point,however it does not contain the details on the local pressure andmaterial composition variation and so should be used only as aguiding value. Both the anti-stellar point and the morning termi-nator of all planets show that metal oxides and silicates togetherdominate the cloud composition making up between ∼ Article number, page 11 of 38 & A proofs: manuscript no. aanda-forarX . . . . . . WASP-43b φ = 0.0 θ = 0.0 WASP-43b φ = -180.0 θ = 0.0 − − − − − . . . . . . WASP-43b φ = 90.0 θ = 0.0 − − − − − WASP-43b φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t . . . . . . WASP-103b φ = 0.0 θ = 0.0 WASP-103b φ = -180.0 θ = 0.0 − − − − − . . . . . . WASP-103b φ = 90.0 θ = 0.0 − − − − − WASP-103b φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t . . . . . . WASP-18b φ = 0.0 θ = 0.0 WASP-18b φ = -180.0 θ = 0.0 − − − − − . . . . . . WASP-18b φ = 90.0 θ = 0.0 − − − − − WASP-18b φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t . . . . . . HAT-P-7b φ = 0.0 θ = 0.0 HAT-P-7b φ = -180.0 θ = 0.0 − − − − − . . . . . . HAT-P-7b φ = 90.0 θ = 0.0 − − − − − HAT-P-7b φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t . . . . . . WASP-121b φ = 0.0 θ = 0.0 WASP-121b φ = -180.0 θ = 0.0 − − − − − . . . . . . WASP-121b φ = 90.0 θ = 0.0 − − − − − WASP-121b φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t Fig. 10: The volume fractions V s / V tot of the material groups as defined in Table 2 (blue: high temperature condensates, red: metaloxides, orange: silicates, grey: carbon, olive: salts). Sub-stellar point: ( φ, θ ) = (0 . o , . o ), Anti-stellar point: ( φ, θ ) = ( − . o , . o ),Equatorial Morning Terminator: ( φ, θ ) = ( − . o , . o ), Equatorial Evening Terminator: ( φ, θ ) = (90 . o , . o ). There are no saltcondensate species included for WASP-18b and HAT-P-7b due to their very low abundance. Empty panels represent profiles withoutcloud formation.shows metal oxides and silicates comprise approximately ∼ ∼
40% be-ing high temperature condensates. The high temperature conden-sates, metal oxides and silicates are almost equal in their contri-bution to the volume of WASP-43b’s evening terminator clouds.
5. The comparison of characteristic global gasphase properties
The carbon-to-oxygen ratio is often used in astrophysics to de-cide if an object is carbon rich, i.e. has more carbon than oxygen,or oxygen rich. Most of the exoplanet host stars will be oxygen-rich as the majority of stars in the universe are main sequencestars today. Once low-mass stars develop into AGB stars, the starwill become carbon-rich. The measurement of the stellar carbon
Article number, page 12 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters . . . . . . . h V i n o r m ( φ,θ ) = (0 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) ( φ,θ ) = (90 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) WASP-43b
High Temperature CondensatesMetal OxidesSilicatesCarbonSalts . . . . . . . h V i n o r m ( φ,θ ) = (0 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) ( φ,θ ) = (90 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) WASP-103b
High Temperature CondensatesMetal OxidesSilicatesCarbonSalts . . . . . . . h V i n o r m ( φ,θ ) = (0 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) ( φ,θ ) = (90 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) WASP-18b
High Temperature CondensatesMetal OxidesSilicatesCarbon . . . . . . . h V i n o r m ( φ,θ ) = (0 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) ( φ,θ ) = (90 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) HAT-P-7b
High Temperature CondensatesMetal OxidesSilicatesCarbon . . . . . . . h V i n o r m ( φ,θ ) = (0 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) ( φ,θ ) = (90 . ◦ , . ◦ ) ( φ,θ ) = ( − . ◦ , . ◦ ) WASP-121b
High Temperature CondensatesMetal OxidesSilicatesCarbonSalts
Fig. 11: The normalised column integrated volume fractions (cid:104) V (cid:105) norm = (cid:82) z max z min V s ( z ) V tot ( z ) dz (cid:46) (cid:80) i (cid:82) z max z min V i ( z ) V tot ( z ) dz where s is the given materialgroup and i runs over all the material groups as defined in Table 2 (blue: high temperature condensates, red: metal oxides, orange:silicates, grey: carbon, olive: salts). Sub-stellar point: ( φ, θ ) = (0 . o , . o ), Anti-stellar point: ( φ, θ ) = ( − . o , . o ), EquatorialMorning Terminator: ( φ, θ ) = ( − . o , . o ), Equatorial Evening Terminator: ( φ, θ ) = (90 . o , . o ). The relative abundance of themetal oxides, silicates and high temperature condensates is comparable for the substellar point of the ultra-hot Jupiters WASP-103b,HAT-P-7b and WASP-121b.and the oxygen abundance relies on high-resolution spectra, atechnique which has only recently begun to be available in ex-oplanet research through instruments like CARMENES, PEPSI,and CRIRES + . So far, however, only the mere presence of atomshas been shown (e.g., Casasayas-Barris et al. 2019; Yan et al.2020) and detailed abundance measurements are compromisedby atmospheric clouds (e.g., Nikolov et al. 2018; Carter et al.2020). Here we focus on the local C / O which is determinedby how much oxygen is locked in cloud particle materials likeMgSiO3[s], MgO[s], Al O [s] etc. A similar exercise can beconducted for other element (or mineral) ratios as for exampleshown in Helling et al. (2019a) (their Figs. A.3. ff .). As demonstrated in Figure 12 (top) all cloud-forming pro-files have on average a C / O ratio larger than the undepleted, solarvalue of 0.55 in the upper atmosphere indicating oxygen deple-tion by cloud particle condensation. This result holds also forthe individual 1D profiles of the 3D atmospheres (Figure A.6).The atmosphere turns more oxygen-rich at ∼ ffi -ciently evaporate and, hence, enrich the local gas phase with allelements previously locked within the cloud materials, includ-ing oxygen. Hence, cloud particle transport elements into thedeeper atmosphere. The strongest enrichment occurs for WASP- Article number, page 13 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) . . . . . . . . . C / O Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b − − − − − − log (p gas [bar]) . . . . . . . µ Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b − − − − − − log (p gas [bar]) − − − l og ( f e ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b f e = 1 × − Fig. 12: The carbon-to-oxygen ratio (C / O, top), atmosphericmean molecular weight, µ (middle), the degree of thermal ioni-sation, f e = p e / (cid:16) p gas + p e (cid:17) (bottom) for the hot giant gas planetWASP-43b, and the ultra-hot Jupiters WASP-18b, HAT-P-7b,WASP-103b, and WASP-121b. The solar value C / O = f e = × − as a threshold for plasma behaviour (bottom). Allultra-hot Jupiters have dayside thermal ionisation f e > − sug-gesting an extended dayside ionosphere. The detailed results forthe individual planets are provided in Figs. A.1 – A.8.43b, WASP-103b and HAT-P-7b for the dayside profiles with asmall number of big cloud particles evaporating.All planets in our sample can be expected to have a largerange of C / O values from 0.54 to 0.75 on the nightside (bluelines in Fig. A.6). The average nightside C / O values (Fig. 12, top) are similar among the ultra-hot Jupiters, except for WASP-18b which is the most massive planet with a larger bulk densitythan any of the other gas planets in our sample.Transmission spectra probe the terminator regions of the at-mosphere which, according to our study, are very likely to di ff erin the C / O (grey dashed and grey dotted lines in Fig. A.6).
Espe-cially when considering the asymmetry in clouds, thus compar-ing the C / O for just above the opaque cloud level shows that 1Dretrievals will fail to capture the global C / O ratio.
Our computations confirm the conclusion by Baxter et al.(2020) that both, hot and ultra-hot Jupiters are likely to haveC / O < / O. The solar (or original) C / O can only beexpected for the cloud free parts of the dayside. Lower than so-lar C / O would either point to an e ff ective mass transport throughthe atmosphere (see C / O spikes < The mean molecular weight, µ , defined as the mean mass of aparticle in a gas, is an important quantity to know as it can beused to transform the local gas pressure into the local gas den-sity via the ideal gas law. It, hence, enters calculations of trans-mission depth being expressed in terms of pressure scale heights( H = k B T eq / ( µ g P ); e.g. Alexoudi et al. 2020) or for deriving acloud top pressure for defining an isothermal transit radius (Heng2019). A constant value of µ is often assumed when running a3D GCM (see introduction in Drummond et al. 2018) as it is ben-eficial computationally. Zhang & Showman (2017) show that achanging bulk composition of the atmosphere (hence, a chang-ing mean molecular weight) leads to a decreasing zonal wind ve-locity with increasing µ , causing the planetary atmosphere to de-velop a more banded structure and a larger day / night temperaturecontrast. We demonstrate here that assuming a constant atmo-spheric bulk composition ( µ = const) globally may not be valid inall cases. Figure 12 (middle) summarises the results in terms ofdayside and nightside averaged mean molecular weights (termi-nators excluded) for the hot Jupiter WASP-43b, and for the ultra-hot Jupiters WASP-103b, WASP-121b, HAT-P-7b, and WASP-18b. Figure A.7 provides the detailed results for each planet in-dividually.For WASP-43b, the hot giant gas panet in our sample, themean molecular weight remains approximately constant ( µ = . . . . . ff erent story with the day- and nightside value of µ vary-ing substantially across the global atmosphere. In the upper at-mosphere, above 1 mbar, of the ultra-hot Jupiters the nightsidevalue is µ ≈ .
3, whereas the dayside has a value of µ ≈ . ff erence is caused by the large temperature di ff erence be-tween the day and night sides of the planet seen in Fig. 2 whichleads the dayside being highly ionised, in addition to molecularhydrogen being unabel to form.The changing mean molecular weight which results fromthe local temperature e ff ect on the gas-phase composition, re-sults in substantial changes in the geometrical extension of theatmosphere around the globe. The details are summarised in Article number, page 14 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters A − − − − − − log (p gas [bar]) T ga s ( K ) Day-sideNight-sideSubstellar pointAnti-stellar point Evening terminatorMorning terminatorDay-side averageNight-side average − − − − log (p gas [bar]) T ga s ( K ) Day-sideNight-sideSubstellar pointAnti-stellar point Evening terminatorMorning terminatorDay-side averageNight-side average − − − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − log (p gas [bar]) − − − − l og ( J ∗ [ c m − s − ] ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − log (p gas [bar]) − − − − l og ( h a i A [ µ m ] ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) ρ d / ρ × − Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − log (p gas [bar]) ρ d / ρ × − Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator
Fig. 13: The e ff ect of the inner boundary of the 3D GCM models on the ( T gas , p gas )-profiles and the local cloud properties J ∗ , (cid:104) a (cid:105) A ,and ρ d /ρ for the giant gas planet example WASP-43b. Left: based on the 1D thermodynamic profiles from Parmentier et al.
Right: based on the 1D thermodynamic profiles from Carone et al.Appendix B where the substantial e ff ect of the changing meanmolecular weight on the hydrostatic pressure scale height isshown. The degree of ionisation (Fig. 12 (bottom) and Fig. A.8), f e = n e / n tot ( n tot - total gas number density, n e - electron numberdensity), provides a first insight into potential plasma behaviourwithin the atmospheres of exoplanets, including the possibility Article number, page 15 of 38 & A proofs: manuscript no. aanda-forarX . . . . . . φ = 0.0 θ = 0.0 φ = -180.0 θ = 0.0 − − − − − . . . . . . φ = 90.0 θ = 0.0 − − − − − φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t . . . . . . φ = 0.0 θ = 0.0 φ = -180.0 θ = 0.0 − − − − . . . . . . φ = 90.0 θ = 0.0 − − − − φ = -90.0 θ = 0.0 log (p gas [bar]) V s / V t o t − − − − − − log (p gas [bar]) . . . . . . . C / O Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − log (p gas [bar]) . . . . . . . C / O Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) − − − − l og ( f e ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − log (p gas [bar]) − − − − l og ( f e ) Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − Fig. 14: The e ff ect of the inner boundary of the 3D GCM models on the grouped V s / V tot , the local C / O, and the degree of ionisationfor the giant gas planet example WASP-43b.
Left:
Parmentier et al.
Right:
Carone et al. The di ff erences in the cloud particlesmaterial fractions result from the di ff erent local temperatures of the two GCM models, with the Carone model nightside being coolerthan the Parmentier model nightside.of forming an ionosphere and a magnetosphere in the presenceof a potential magnetic field. A value of f e > − is postulatedas a threshold for transitioning from gas to plasma behaviour(Rodríguez-Barrera et al. 2015). Here, we consider thermal ion-isation for the calculation of f e only.The high gas temperatures on the dayside of the ultra-hotJupiters results in a highly ionised upper atmosphere with f e ap-proaching almost 1, and a less ionised lower atmosphere with f e = − . . . − . The nightside gas temperatures of the ultra-hot Jupiters are su ffi cient for a partially ionised atmospherewhere f e ≈ − . . . − , where the increasing thermal ioni-sation is in line with the increased gas temperature deeper inthe atmosphere. The giant gas planet WASP-43b has daysideand nightside gas temperatures ∼ − ∼ f e ≈ − throughout the entire atmosphere and the nightsidehas f e = − − − increasing with atmospheric depth.The daysides of all the ultra-hot Jupiters (WASP-103b,WASP-121b, HAT-P-7b, WASP-18b) and the giant gas planetWASP-43b are su ffi ciently ionised by thermal processes suchthat an extended ionosphere is present. Such an ionosphere isgeometrically more extended for ultra-hot Jupiters compared tohot giant gas planets according to the geometrical extension ofthe atmosphere (Appendix B). The degree of ionisation will fur-ther be enhanced on the dayside by the XUV radiation and stellarenergetic particles of the host stars which will a ff ect the outer-most layers of the atmosphere. The nightside will not be a ff ectedby the stellar XUV and SEPs, but by the galactic cosmic rays.CRs have little e ff ect in the atmospheric ionisation (Rimmer &Helling 2013), but can open kinetic pathways to form complexhydrocarbon molecules (Rimmer et al. 2014; Barth et al. 2020). Article number, page 16 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters
Koskinen et al. (2014) demonstrate that the outer atmosphere ofthe hot gas giant HD 209458b is magnetically coupled to a globalmagnetic field that may be present. The magnetic coupling am-plifies with height in HD 209458b due to the increasing e ff ectof photoionisation. Barth et al. (2020) show that photochemistryamplifies the day / night asymmetry due to the high host star’s ra-diation flux (XUV, FUV, SEPs) for tidally locked, close-in plan-ets. Therefore, in the presence of a magnetic field (Zaghoo &Collins 2018; Cauley et al. 2019), a magnetosphere may a ff ectthe atmosphere of hot giant gas planets globally (as on WASP-43b and HD 209733b), but it will have a strongly asymmetric af-fect on the atmosphere of ultra-hot Jupiters due to their stronglyasymmetric ionosphere (as on WASP-103b, WASP-121b, HAT-P-7b, WASP-18b). The asymmetry of an extended magneto-sphere may be detectable as a bow shock as result of the interac-tion with the host-star wind (Lai et al. 2010; Vidotto et al. 2010,2011) or through radio transit observation (Selhorst et al. 2020)in the future.The best candidates for detecting a magnetosphere could bethe ultra-hot Jupiters WASP-103b, WASP-121b and HAT-P-7bif using the hydrostatic scale height as a first guiding estimate(Fig. B.1). Taking into account the interaction with the stellarwind, Vidotto et al. (2011) proposes WASP-18b (amongst oth-ers) as target for detecting a bow-shock. The coupling of theionised part of a globally circulating atmosphere with a poten-tially existing exoplanet magnetic field may cause a current sys-tem to emerge that reduces the angular velocity at high latitudesand generate an auroral emission comparable to what has beensuggested for brown dwarfs (Nichols et al. 2012). Rogers (2017)present MHD simulations for a giant gas planet with a day / nighttemperature di ff erence of ∆ T =
6. The effect of the inner boundary on GCM resultsfor the example of WASP-43b
Simulations using GCMs requires extensive computational re-sources, in particular if the radiation hydrodynamics is solvedconsistently with the gas chemistry and actual cloud formationmodelling. Therefore, it is unsurprising that all exoplanet mod-els apply a cloud parameterisation of some sort (Dobbs-Dixon& Agol 2013; Charnay et al. 2018; Mendonça et al. 2018; Lineset al. 2019; Roman et al. 2020; Parmentier et al. 2021). Gridsof GCM simulations are often run as completely cloud free oras opacity species only with cloud properties derived in post-processing (e.g., Kataria et al. 2015; Parmentier et al. 2018).Consequently, little time has been a ff orded to run extensive teston other assumptions, for example, the inner boundary. Recently,Carone et al. (2020) proposed that very deep layers (down to700 bar) need to be considered to fully capture the emergenceof waves that sculpt the observable climate in hot Jupiters thatrotate faster than 1.5 days. This situation may be the case forWASP-43b but also generally for ultra-hot Jupiters (see Table 1,most tidally locked ultra-hot Jupiter are expected to have rota-tion periods faster than 1.5 days). The possible importance to re-solve deeper layers and a su ffi ciently long simulation times hasbeen further confirmed by Wang & Wordsworth (2020); Show-man et al. (2020). Here we take the opportunity to o ff er a firstdiscussion on what e ff ect the choice of the inner boundary may have on the cloud coverage of the hot giant gas planets, WASP-43b.In what follows, we compare the WASP-43b results from two3D GCM simulations: Parmentier’s version of SPARC / MITgcm(see Sect. 2) and Carone 3D GCM. We follow the same ap-proach as outlines in Sect 2, but additionally utilize the inputdata from the Carone 3D GCM simulations (Carone et al. 2020)for WASP-43b. We will point out di ff erences between the two 3DMITgcm versions below. However, an understanding of why themodels di ff er in detail will require a more extensive comparisonstudy which is outwith the scope of this paper. We demonstratethat shifting the inner boundary does extend the cloud layer intodeeper, high pressure regimes. This raises the question about ad-ditional heating by backwarming from the cloud later which will,in turn, a ff ect the thermal ionisation of the gas.Also the Carone 3D GCM simulation for WASP-43b iscloud-free. It uses simplified radiative transfer via Newtonaniancooling compared to a non-grey binned radiative transfer in Par-mentier et al. (2018). Thus, the temperature in the Carone modelis less well constrained with a temperature uncertainty of up to100 K. Carone et al. (2020) has a dynamically active atmospherethat extends deeper downward to pressures of 700 bar, allowingfor the formation of deep wind jets. Carone et al. (2020) usesseveral additional measures to stabilize the lower boundary at p >
10 bar. These are: temperature convergence to the interioradiabat, a shorter convergence time scale τ conv = s and dragbetween 550 and 700 bar (Carone et al. 2020, Section 2.3). Thesemeasures are chosen ensure that the atmosphere is in a dynami-cal steady state from the top to the bottom.The SPARC / MITgcm runs of WASP-43b used here use a freeslip, impermeable boundary condition situated at 200 bars andno drag other than numerical dissipation is added (see Showmanet al. 2009, for the detailed setup used). Because of the compu-tational cost of running non-grey radiative transfer compared tothe much faster newtonian cooling, the models are integrated for300 days, which is shorter than the 2000 days of Carone et al.(2020). With such a short integration timescale, the deep layersof the model are not yet equilibriated. The statistical steady-statereached at the photosphere is therefore dependent on the assump-tion that whatever circulation would develop in the deep layersof the planet is not strongly a ff ecting the photospheric flow, anassumption recently challenged by Carone et al. (2020).Di ff erent conditions in the deep atmosphere are proposedto induce a di ff erent climate regime compared to the thermalphotosphere. Waves can travel upwards from the optically thickto the optically thin atmosphere regime. The di ff erent climateregime naturally leads to a larger day-to-night side temperaturecontrast and much colder (cloud free) night side temperaturescompared to other GCMs. Thus, despite the di ff erent level ofapproximations chosen in the Paramentier SPARC / MITgcm andin the Carone GCM, we investigate if the proposed wave con-nection between the atmosphere at greater depth ( >
100 bar) af-fect cloud formation and chemistry higher up in the atmospherewhere these e ff ects maybe observable. We explore this question by comparing our cloud formation re-sults for the Paramentier SPARC / MITgcm and the Carone GCM.We also explore the e ff ect on C / O and on the local thermal ioni-sation as direct e ff ects of cloud formation and thermodynamics.Figure 13 (top) shows the two sets of ( T gas , p gas )-profiles, bothshowing temperature inversions at p gas ∼ . Article number, page 17 of 38 & A proofs: manuscript no. aanda-forarX log Pressure [bar] T e m p e r a t u r e [ K ] T i O [ s ] S i O [ s ] S i O [ s ] C a T i O [ s ] C a S i O [ s ] F e [ s ] F e O [ s ] F e S [ s ] F e O [ s ] F e S i O [ s ] A l O [ s ] K C l[ s ] saturation curves MgO[s]MgSiO [s]Mg SiO [s] Fig. 15: The sub-stellar ( T gas , p gas )-profiles from the Carone(blue, extended inner boundary) and the Parmentier (red, stan-dard inner boundary) GCM runs for WASP-43b. The compari-son to the thermal stability curves (supersaturation ratio S = ff erences at p gas ≈ ff erences be-tween the two models (Fig. 14). We note that the S = ρ d /ρ (Fig. 13, 4th row).The cloud formation on the dayside di ff ers more betweenthe two models than on the night side, reflecting the daysidedi ff erences in the ( T gas , p gas ) profiles. The inner dayside cloud(p gas > . ffi ciently in the Carone model,hence, more cloud particles form such that they remain smallerup to p gas ≈ ffi cient in the Carone model (Fig. 13,right column) than in the Parmentier models (Fig. 13, left col-umn) as the local densities are simply higher, hence the innercloud has more and bigger cloud particles in the Carone modelon the dayside and on the nightside.Figure 14 (top) shows that the thermodynamics of the atmo-sphere a ff ects also the material compositions of the cloud par-ticles (for more details see Appendix B.1), suggesting that it isimportant to extend the 3D GCM models not only into lower at-mospheric pressure regions where the stellar irradiation will af-fect the gas phase photo-chemically, but also toward higher pres-sures at the inner boundary. The cloud particle material compo-sition will a ff ect the element depletion of the gas phase locally,which we represent here in terms of the carbon-to-oxygen ratio (Fig. 14, 2nd row). Overall, the C / O values are comparable oreven similar, but can di ff er in detail. For example is C / O < p gas ≈ − bar at the substellar point in the Carone model butC / O ≈ .
68 in the Parmentier model at the same pressure. Thereason is that the element depletion is a ff ected by the dynamicsof the cloud particle formation which is determined by the cloudparticle history in that a smaller particle will fall less fast into anatmosphere than a bigger particle.Both models predict a partially ionised dayside through ther-mal ionisation (Fig. 14, 3rd row), but little ionisation on thenightside, hence, a magnetosphere should only be expected toform on the dayside from both models. We conclude this com-parison by noting that the geometrical extension and hence themean molecular weight are comparable in both models for agiven pressure level (Fig. B.5).In this section, we studied how the treatment of the innerboundary and that of the inner atmosphere will e ff ect the cloudproperties, the C / O and the thermal degree of ionisation.
We con-clude that the qualitative findings such as the presence of clouds,average C / O or degree of ionisation are in reasonable agreementbetween the two 3D atmosphere simulations.
While the results discussed above remain qualitatively thesame, the details of the material composition of the clouds (seetop row of Fig. B.5) appears significantly di ff erently for boththe anti-stellar and sub-stellar point. Here, the temperature anddensity di ff erences are the largest between the Parmentier andCarone model (Fig. 14 top row). Thus, the night side clouds arecomposed of metal oxides and are geometrically more extendedin the Carone model, whereas in the Parmentier model the cloudsare composed of silicates and are thinner.There also appears to be a di ff erence for the substellarpoints of the two models. For pressures greater than ∼ − bar this di ff erence is easily explained by the di ff erences be-tween the thermal profiles of the models, with the Parmen-tier model being warmer in this region. However, for pres-sures between 10 − − − bar the two models have tem-peratures within 100 K of one another for the same pres-sure. Thus it is surprising that in this region the Caronemodel produces clouds dominated by high-temperature conden-sates, whereas the clouds in the Parmentier model are mostlymade of silicates and metal oxides. To explore this Figure 15shows the S = [s], Mg SiO [s] aswell as that of Fe and SiO[s], which make up the ma-jority of the cloud material in the Parmentier models (Fig.B.3). This leaves only the high-temperature condensates ofTiO [s], CaSiO [s], CaTiO [s], Al O [s] to be thermally stable.This explains the high-temperature condensate peak before thedrop in temperature at 0.1 bar in the Carone model, as here onlyCaTiO [s] and Al O [s]. Although we stress here the resultsshown in Fig 15 are for solar abundances at all temperatures andpressures, and do not reflect our full kinetic model, where cloudformation depletes the gas phase of certain elements and hencechanges the supersaturation ratios of condensate species bearingthese elements.As a summary, we note that generally the night sides oftidally locked exoplanets are the most susceptible to e ff ects ofthe inner boundary. The nightside temperatures are set by the in-terior temperature and horizontal heat transport originating fromthe irradiated day side (Thorngren et al. 2019). Since horizontal Article number, page 18 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters heat transport is less e ffi cient for ultra-hot Jupiters (Komacek &Showman 2016; Komacek et al. 2017), assumptions about the in-terior temperature and thus the lower boundary will become im-portant for these planets. Recently, the temperature of the deepinterior (at 200 bar) was invoked to explain observations of Feand Mg in the ultra-hot WASP-121b, which led to constraints ofthe interior temperature T int =
500 K (Sing et al. 2019, Fig.13).An important next step to shed further light on model dif-ferences would be to set up both 3D GCMs with the very samenumerical parameters for the inner boundary and the radiativetransfer treatment of the atmosphere. This is, however, outwiththe scope of this paper.
7. Observational implications
We now take a look at the spectroscopic properties of the cloudsfor each of four ultra-hot Jupiters (WASP-18b, WASP-103b,WASP-121b, and HAT-P-7b) and one gas giant planet (WASP-43b), at four points around the equator ( θ = . ◦ ), the sub-stellarand anti-stellar points ( φ = . ◦ , . ◦ ), and the morning andevening terminators ( φ = ◦ , − ◦ ). The terminator profilesare indicative of what could be seen in emission for secondaryeclipse, and in transmission spectroscopy. The anti-stellar pointis di ffi cult to observe, but is representative of nightside condi-tions, which is where cloud formation is very e ffi cient and themost similarity in cloud structure between the planets occur. Toinvestigate the atmosphere observable for both of these tech-niques (transmission and emission) we must know what pressurelevels are optically thin, i.e. τ <
1; for example in transmission,the atmosphere deeper than this level is not visible to observers.The optical depth along some path from z to z for a givenwavelength is defined as τ ( λ, z − z ) = (cid:90) zz κ ( λ, z (cid:48) ) ρ ( z (cid:48) )d z (cid:48) (4)where κ is the extinction coe ffi cient per unit atmospheric mass.For our atmospheres we use cloud spectral properties along ver-tical profiles, hence z = τ = ffi cients for the cloudparticles are calculated using Mie theory (Mie 1908; Bohren &Hu ff man 1983) using the surface average particle radius from themoments as defined in Eq. 1 with corresponding number densityas discussed in Helling et al. (2020): n d , A = ρ L L . (5)Mixed material refractive indices are determined using e ff ec-tive medium theory with the Bruggeman mixing rule (Brugge-man 1935). Individual cloud species refractive indices are thesame as in Helling et al. (2019b), with the addition of KCl from(Palik 1985) for all planets except WASP18-b and HATP-7b. Toaccount for the e ff ects of non-spherical cloud particles we in-clude a Distribution of Hollow Spheres (DHS) (Min et al. 2005;Samra et al. 2020). Hollow spheres are defined by a structureof a vacuous core and a mantle containing the material volumeof a compact sphere of radius (cid:104) a (cid:105) A , with volume fractions ofmaterials as appropriate for that atmospheric layer. A distribu-tion of these particles with di ff erent fractions of volume beingthe vacuum core are then averaged over. This represents well the distributions of irregularly shaped particles for protoplane-tary disks, both in the Rayleigh regime and for larger particles(Min et al. 2003, 2008; Min 2015), and has now also been im-plemented in atmospheric models ATRES (Stolker et al. 2017),PetitCODE (Mollière et al. 2015; Mollière et al. 2017), ARCiS(Ormel & Min 2019; Chubb et al. 2020) and also in retrievalsPetitRADTRANS (Mollière et al. 2019).For ultra-hot Jupiter exoplanets there is significant di ff erencein extension between the day and the nightside of the planet (seeAppendix B), furthermore as the stellar light passes through theatmosphere at a slant geometry (Fortney 2005), there is a non-zero width of atmosphere probed around the terminator. The an-gle (in longitude) to which transit spectra are sensitive has beendetermined in recent works using both a parameterised estima-tion (Caldas et al. 2019), and by examining the impact of a fullradiative transfer model (Lacy & Burrows 2020; Pluriel et al.2020), both found the angle for these planets to vary between10 ◦ − ◦ , i.e between ± ◦ − ◦ around the terminator. From ourstudied sample, WASP-18b representing the lower end of thisrange and HAT-P-7b and WASP-103b representing the upper end(see Lacy & Burrows (2020), their Figure 3 top left). As our ap-proach produces 1D cloud profiles of selected longitude-latitudepoints, with a spacing in longitude of 45 ◦ , our grid spacing istoo wide to meaningfully integrate along line-of-sight trajecto-ries through the atmosphere. We therefore chose to use verticallyintegrated optical depth of the clouds and apply a correction forthe e ff ect of slant geometries. In order to take into account the ef-fect of slant geometry we use an correction factor calculated fora hydrostatic atmosphere, using the work of Fortney (2005), theslant geometry method of determining the optical depth adjuststhe vertically integrated τ to τ s = τ (cid:115) π R p H p , (6)where R p is the radius of the planet, and H p is the hydrostaticpressure scale height, H p = ( kT ) / ( µ m H (cid:49) ), with k the Boltzmannconstant, m H the atomic mass unit, (cid:49) the gravitational accelera-tion of the planet, and µ the mean molecular weight, for whichwe use µ = . µ = . ff erent from points probed in the opticallythin atmosphere along the line-of-sight. This has been previouslybeen investigated for more dense grids of longitude and lati-tudes (for example for HAT-P-7b in Helling et al. (2019b) andfor WASP-43b in Helling et al. (2020)), with especially rapidchange in cloud properties around the terminators of ultra-hotJupiters. Particularly at the morning terminator the pressure atwhich clouds form is a function of angle from the morning ter-minator, with the further day-ward points having clouds only atdeeper levels and higher pressures, thus the optical depths ofthese profiles are likely a ff ected by our assumption here. Forcalculations of transmission spectra it is clear that a fully threedimensional calculation is necessary as shown in Pluriel et al.(2020) and Lacy & Burrows (2020), we leave such a full analy-sis to future works as previously noted, because of our wide gridspacing. Article number, page 19 of 38 & A proofs: manuscript no. aanda-forarX p ( τ s ( λ ) = -levels for a hot gas giants and fourultra-hot Jupiters Figures 16 shows the results of optical thick pressure levels in-cluding the e ff ect of slant geometry for compact (solid) and non-spherical (dashed) cloud particles. Full plots for vertically inte-grated optical depth alongside the slant values for each planetare found in Figure A.9. Only WASP-43b is su ffi ciently coolon the dayside to have clouds present at the sub-stellar point,and as it is substantially di ff erent from all of the other plan-ets, it will be discussed separately in Sect. 7.2. For the ultra-hot Jupiters, the ine ffi cient heat re-distribution from the daysideto the nightside along with global circulation initiated by plan-etary rotation causes the evening terminators to be too hot forcloud formation, in addition to the nightside. Evidence for thee ff ects of partial cloud coverage around the terminator has beenfound in retrievals (Line & Parmentier 2016; Lacy & Burrows2020). Clouds are present at the morning terminator (( φ, θ ) = ( − o , o )) in all ultra-hot Jupiters (Fig. 16, top left panels), butremain confined by the temperature inversion to deeper atmo-spheric levels of p > − bar such that the atmosphere abovewould not be a ff ected by cloud opacity. This results in cloudparticles sizes of 10 . . . µ m at τ s = λ < µ m in theultra-hot Jupiters in comparison to 0 . . . . . µ m at τ s = λ < µ m for the hot giant WASP-43b according to our presentmodels. The material properties vary in accordance to the lo-cal temperatures. For WASP-103b, HAT-P-7b, WASP-18b andWASP-121b, the optically thick pressure level appears wave-lengths independent up to ≈ µ m at the morning terminator.Whilst the optically thick pressure is constant at short wave-lengths for each planet, the specific pressure varies between themfrom 10 − . . . − bar, due to the di ff erent geometric extensions.At the morning terminator (( φ, θ ) = ( − . ◦ , . ◦ ), top right inFigures 16), p ( τ s ( λ ) =
1) di ff ers considerably between the hotgas giants and the ultra-hot Jupiters at λ < µ m. Beyond this,all planets show a trend of increasing transparency of clouds atlonger wavelengths (i.e. increasing pressure at which τ s = ff ected by the details of thecloud micro-physics (see Sect 7.3). For the anti-stellar points(( φ, θ ) = ( − . ◦ , . ◦ )), all ultra-hot Jupiters show a consis-tent increase in pressure where τ s ( λ ) = − µ m.Hence, the atmospheric gas will be observable to greater depthand higher temperatures at these wavelengths. Strong silicateresonant features at 10 µ m and 20 µ m are prominent for all plan-ets at the nightside, compared with only for WASP-43b at themorning terminator. Figure 16 represent the maximum atmo-spheric depth that can be probed remotely. Additional gas opac-ity may cut the observable atmosphere to lower pressure levelsthan those depicted.The distinct opacity di ff erence between the morning and theevening terminator of ultra-hot Jupiters may be probed by dis-tinct asymmetries of the ingress and the egress in transmissionlight curves. Such an ingress / egress asymmetry e ff ect due toclouds should be wavelength independent up to λ ≈ µ m ac-cording to Fig. 16. An observational signature of the eveningterminator would furthermore be a clear atmosphere such thatthe molecules in the atmosphere could be easily observable, andin the morning terminator one would see a much subdued spec-tral signature of gas phase molecules. The large di ff erence intemperature between the two terminators will also play a roleand will determine which gas species are present. WASP-43b stands out amongst the selected planets as, in com-parison to the ultra-hot Jupiter results, clouds form around theentire equator, thus observations both in transmission and emis-sion will be significantly a ff ected by cloud. It is worth noting thatthe sub-stellar point is not the hottest point on WASP-43b, due tothe super-rotating equatorial jet, this is located at about φ = ◦ (Fig. 2 in Helling et al. 2020). For all profiles WASP-43b showssignificant silicate spectral features at ∼ − µ m wavelengths,although the sub-stellar point displays a very di ff erent featureshape in this spectral region. The morning and evening termi-nators for WASP-43b, in contrast to the ultra-hot Jupiters, areboth virtually identical to the anti-stellar point, with strong sili-cate features and a marginally lower pressure for optically thickclouds at all wavelengths. This provides a key di ff erence for hotgiant gas planets vs ultra-hot Jupiters with total cloud cover ofthe terminators vs patchy cloud cover of only the morning ter-minator. A further notable di ff erence for the sub-stellar point, isthe total lack of Fe SiO [s] which may explain the di ff erentcesin spectral features. For the the sub-stellar point, using verticallyintegrated optical depth (Figure A.9) results in almost none orvery weak silicate features, and look much more like the morn-ing terminator points for the ultra-hot Jupiters.We previously investigated the optical depth of aerosols inWASP-43b in (Helling et al. 2020), for which the compact, ver-tically integrated clouds are identical. However, in (Helling et al.2020) we calculated tholin haze optical depths, we found thathaze would be optically thin in the atmosphere of WASP-43b.Regardless of if compact or non-spherical shapes were consid-ered for the haze, the clouds dominate the aerosol opacity.WASP-43b is also a key target with JWST, full phase curveobservations are planned with MIRI as part of the communityearly release science (Program No. 1366; PI: N. Batalha and Co-PIs: J. Bean, K. Stevenson; Bean et al. (2018)), followed by aNIRspec phase curve as part of GTO Program 1224 (PI: S. Birk-mann). Previous observations of WASP-43b include full phasecurves with Spitzer at 3 . µ m and 4 . µ m (Stevenson et al. 2017)and Hubble / WFC3 (Stevenson et al. 2014) across 1 . . . . . µ m .Both sets of observations produced low nightside emission pos-sibly due to poor heat redistribution (Kataria et al. 2015), ordisequilibrium chemistry and clouds (Mendonça et al. 2018).However Chubb et al. (2020) did not find statistical evidencefor inclusion of clouds in their retrievals, further Venot et al.(2020) point out di ff erentiating cloud scenarios is di ffi cult usingHubble / WFC3 data. Venot et al. (2020) included cloud micro-physics in some of their modelling, where they assume that mag-nesium silicates are composed of Mg SiO [s] (forsterite) overMgSiO [s] (enstatite) and in addition including Fe[s] , Cr[s] ,MnS[s] , and Na S[s] . Overall they find that dayside magne-sium silicate cloud species would be cold-trapped below 100 bar,and nightside cloud opacity dominated by MnS[s] and Na S[s]shortward of 7 µ m and forsterite at longer wavelengths. Howeverwe find that clouds should be optically thick in the near-infraredacross the planet at pressures as low as 0.1 mbar. At Spitzerwavelengths we only see minor di ff erences between the profilesaround the equator. As we do not include MnS or Na S com-parison of models is di ffi cult, but NIRSpec phase curve observa-tions will provide details requiring consistent cloud chemistry.In MIRI observations Fig.16 shows that (using the Parmentiermodel) we expect to see silicate features consistent around theequator of the planet, although variable cloud abundance withlatitude would still a ff ect the strength of these features in phasecurve observations, particularly for dayside emission. Article number, page 20 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − − l og ( p ( τ s = ) [ b a r ] ) MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ − MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = − . ◦ , θ = 0 . ◦ WASP-121bWASP-103bWASP-18bHAT-P-7bWASP-43b (Parmentier)WASP-43b (Carone) − log ( λ [ µ m]) − − − − − − l og ( p ( τ s = ) [ b a r ] ) MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 0 . ◦ , θ = 0 . ◦ − log ( λ [ µ m]) MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ MIRINIRCamNIRSpecNIRISS φ = 90 . ◦ , θ = 0 . ◦ Compact h a i A CloudsHollow Spheres h a i A Clouds
Fig. 16: Wavelength-dependent pressure level where the giant gas planets WASP-43, WASP-103b, WASP-121b, HAT-P-7b, andWASP-18b become optically thick due to cloud particles of di ff erent sizes and mixed materials forming inside these atmospheres,i.e. where p gas = p ( τ s ( λ ) = T gas , p gas )-structures, except forWASP-43b where we include both models (Parmentier GCM in green and Carone GCM in grey). When clouds remains opticallythin such that τ s ( λ ) <
1, the pressure for the bottom of the atmosphere (p ≈ . bar in the Parmentier GCMs) is returned (hencethe lines for the sub-stellar points where there is no cloud are outside the plotted range).Every attempt to derive spectral information from modelswill depend on the computational domain for which the mod-els are simulated. Utilising the two di ff erent GCM solution forWASP-43b we show the e ff ect on the pressure level where τ s ( λ ) = ff ect the location and the extension of the cloud layer resultingin some lack of features to be explained by material compositionof cloud, such as the sub-stellar point. The two models occupydi ff erent pressure domains: TOA(Parmentier) less than 10 − bar,TOA Carone only to 10 − bar. The clouds based for the CaroneGCM results have larger particles sizes in their upper cloud duethe higher density supporting a higher surface growth e ffi ciency,which flatten the wavelength-dependence of the optical depthsubstantially. The morning terminator is comparable to that ofthe ultra-hot Jupiter in our sample, but for a di ff erent reason:The large particle sizes in UHJs are cause by the low nucleationrate due to their locally higher gas temperatures. The e ff ects of non-spherical cloud particles are captured by aDistribution of Hollow Spheres (DHS) (Sect. 7) and are notmeant to be physical interpretations of the cloud particles, butinstead by averaging over a distribution of these particles, thespectroscopic e ff ects of a distribution of irregularly shaped cloudparticles are well represented. The e ff ects of non-sphericity aresurprisingly limited for the case of ultra-hot Jupiters. In Samraet al. (2020) we found that the wavelength at which clouds wereno longer optically thick was increased with a DHS, howeverin these atmospheres (where they form) the clouds are nevertransparent at any wavelength. For profiles with strong silicatefeatures, e ff ects are largely limited to less than half an order ofmagnitude higher optically thick pressure levels for wavelengthslonger than the silicate features, well outside the scope of whatwill be observable with JWST. Article number, page 21 of 38 & A proofs: manuscript no. aanda-forarX
Fig. 17: The cumulative, height-integrated number density of He, (cid:82) z( τ s = = n(z) dz [cm − ], in the optically thin region of the atmo-sphere p < p ( τ s ( λ ) =
1) for the sub-stellar, anti-stellar and equa-torial morning and evening terminator points for λ = µ m, 1.0 µ m, 10.5 µ m and 107 µ m.For profiles with subdued features (i.e. WASP-43b sub-stellar point) a DHS does enhance the silicate features,marginally. For short wavelengths (0 . − µ m) there is practicallyno di ff erence between the spherical and DHS case for all profilesand planets. For profiles where the optically thick level is flatto 25 µ m (e.g. morning terminators for HAT-P-7b and WASP-103b) the DHS increases the optical depth for all longer wave-lengths, where compact particles become increasingly transpar-ent. However, for all the Ultra-hot Jupiter morning terminators,in the slant geometry a DHS does not impact the optical depthfor wavelengths observable by JWST, at these wavelengths thecloud deck is flat regardless of the micro-physics. The changing day / night mean molecular weights (Fig. 12, A.7),being representative of a H / H dominated atmosphere gas in thecases studied here, respectively, leads to a 8 . . .
10 times moregeometrically extended dayside compared to the nightside, ifmeasured in hydrostatic pressure scale heights (Fig. B.1). Thevertical extension of the 3D GCM causes a factor of 2 (Fig. B.2),which is not caused by the changing chemistry as the meanmolecular weight is kept constant in these simulations. The ef-fect of geometrical asymmetry is also present in the terminatorregions. Such geometrical e ff ects may be traced by observing achemically inert species, which is not a ff ected by element deple-tion / enrichment by cloud formation, and possibly also not bychanges of the ionisation state.Helium (He) maybe such a species and Fig. 17 shows the cu-mulative number density of He in the optically thin atmosphere(i.e. above the clouds) for the sub-stellar, anti-stellar and equa-torial morning and evening terminator points at four selectedwavelengths ( λ = µ m, 1.0 µ m, 10.5 µ m and 107 µ m) to matchcurrent and future observational capabilities. CARMENES canobserve at 1.0 µ m and JWST will be capable of observing atboth 1.0 µ m and 10.5 µ m. The column density of He changes with wavelength in Fig. 17 as the pressure level p ( τ s ( λ ) = p < p ( τ s ( λ ) = p = p ( τ ( s λ ) = . . . cm − ). On the nightside (Fig. 17, topleft), it follows the wavelength-dependent slope of p = p ( τ s ( λ ) =
1) for all sampled planets as shown in Fig. 16 (top left). The low-est He column density ( ≈ cm − ) occurs in the optical, thehighest in the IR on the nightside ( ≈ . . . cm − ).
8. Discussion
If two planets have a similar host star, similar orbital periods,radii, masses and similar undepeleted element abundances, theoutcome of cloud formation should be largely similar, includ-ing certainly general trends such as clouds forming on the day-side or not. Skaf et al. (2020) used HST / WCF3 data to studythree (WASP-127b, WASP-79b, WASP-62b) hot gas giants thatare somewhat comparable to WASP-43b. Opaque clouds wereretrieved at ≈ − bar (10 Pa) for WASP-127b, no clouds orat p > − bar (10 Pa) for WASP-79b, and at ≈ − . bar forWASP-62b, hence, at much greater depth than what our mod-els predict. Alam et al. (2020) use HST-WCF3 data for HAT-P-32Ab retrieveing a (isothermal) limp temperature of ≈ ≈ − . bar and a C / O = τ s ( λ = . . . µ m =
1) at p ≈ − bar at the terminators with T gas ≈ . . . (cid:104) a (cid:105) A ≈ − µ m but (cid:104) a (cid:105) A ≈ − µ m at the dayside at the samepressure level (Fig. 6). The particles are made of a mix of metaloxides and silicates. The retrieved mean molecular weights are2.34, 2.38, and 2.39, respectively. The values for WASP-127b,WASP-79b, WASP-62b, also within the unrealistically preciseerror bars, are consistent with an oxygen-depleted gas due tocloud formation. The values suggest a higher oxygen depletionthan what is derived from our model for the comparable hot gi-ant WASP-43b (Fig. A.7, top left panel). This may be consis-tent with the formation of bigger cloud particles that can falldeeper into the atmosphere and consume more material. How-ever, a quantitative comparison can only be made if similar un-depleted element abundances and a similarly complete gas-phasechemistry is used. Alam et al. (2020) derive a very low C / O ratiofor HAT-P-32Ab, and a high metallicity for the host star. Un-less these values are plagued by the retrieval approach, the lowC / O may point to either a carbon depletion and / or an initiallyhigh oxygen abundance as result of the planet formation and / orevolution processes.The non-detection of TiO and VO on WASP-121b (Merrittet al. 2020) may be related to cloud formation at the evening ter-minator and to TiO / VO being thermally unstable, hence, Ti / Vwould be most abundant in their atomic (or ionic) form. Ed-wards et al. (2020) argue for hints of TiO and VO in combi-nation with a grey cloud layer based on HST / WFC3 data forthe ultra-hot Jupiter WASP-76b which has a equilibrium tem-perature comparable to HAT-P-7b. This would suggest that thecloudy evening terminator dominates the transmission spectrum.Gibson et al. (2020) present the VLT / UVES detection of Fe I inWASP-121b and retrieve the presence of a cloud later at p ≈ . . . . . . . . Article number, page 22 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters mation impossible, and may suggest that a continuum opacitysource is missing in the retrieval.As pointed out in previous works such as Venot et al. (2020),it is di ffi cult to di ff erentiate between a cloudy and cloud-freemodel by retrieving HST / WFC3 data alone. The influence oncloud modelling for retrievals of hot Jupiters HD 189733 b andHD 209458 b has been studied in detail by Barstow (2020). Theyfind strong observational evidence that aerosols on HD 209458 bcover less than half of the terminator region, with unclear find-ings for HD 189733b. As demonstrated by the present work,there are di ff erences between the morning and evening termi-nators, in terms of pressure-temperature structure, clouds, andchemistry. A 1D transmission retrieval assumes that the two ter-minator regions are identical. Works such as MacDonald et al.(2020) point out the requirements for multi-dimensional retrievaltechniques, which are starting to be developed, in particular foranalysis of emission spectra (see, for example, Irwin et al. 2020).
9. Conclusion
Our modelling work for a sample of ultra-hot Jupiters suggeststhat these exoplanets have a large day / night cloud and gas-phaseasymmetry which causes characteristic di ff erences of their meanmolecular weight, C / O (and other element ratios), and degree ofionisation. Similar properties di ff er less for hot giant gas planets.In conclusion, we identify the following trends: – In ultra-hot Jupiter atmospheres where p < µ ≈ . dominating, whereas the dayside has avalue representing an atomic gas like µ ≈ . ff erencebetween the day- and nightsides of these exoplanets. Thedayside is therefore highly thermally ionised, in addition tomolecular hydrogen being thermally unstable. – A larger mean molecular weight of µ = . – The day / night mean molecular weight di ff erences cause ageometrically asymmetry between day- and nightsides inparticular on tidally locked planets. We suggest a chemicallyinert species like He to probe this geometrical asymmetry. – The immense atmospheric day / night temperature di ff erenceson ultra-hot Jupiters cause thermal ionisation to change sub-stantially from the day- to the nightside. The thermal ioni-sation of the dayisde of > − is su ffi cient to argue for thepresence of very extended, thermally driven electrically con-ducting daysides, namely an atmospheric ionosphere. – The atmospheric ionosphere suggests electromagneticcoupling to a potential planetary magnetic field whichmaybe observable through auroral emission or a bow-shockas result of the magnetosphere - stellar wind interaction. – Ultra-hot Jupiters can be expected to have cloud-free day-sides and cloudy nightsides, in comparison to hot gas giantswhich have cloud-covered day- and nightsides. – The detailed material composition is determined locally, butmineral silicate clouds made of Mg / Si / Fe / O may dominatethe outer cloud layers, and high-temperature condensateswill dominate the inner, warmer cloud layers. Photochemi-cal hazes may also be present but will not a ff ect the opticaldepth significantly on ultra-hot Jupiters. – Exoplanet clouds may extend further inwards than previ-ously assumed due to the increased thermal stability for in-creasing gas pressures. – The global atmosphere circulation results in cloud formationbeing more likely at the less-extended morning terminator,but not in the geometrically more extended, warmer eveningterminator regions in ultra-hot Jupiters. – Transmission spectra of ultra-hot Jupiters may be a ff ectedby cloud opacity at the morning terminator, but by atomicand / or ionic opacity sources at the evening terminator. Thiswill a ff ect the retrieval of mineral ratios like C / O / , Mg / Si etc. – The di ff erent cloud properties at the morning terminator ofhot giant gas planets like WASP-43b and ultra-hot Jupiterslike WASP-103b, WASP-121b, WASP18b, and HAT-P-7bcause their spectral features to di ff er characteristically. Acknowledgements.
Ch.H. and M.M. acknowledge funding from the Euro-pean Union H2020-MSCA-ITN-2019 under Grant Agreement no. 860470(CHAMELEON). D.S. acknowledges financial support from the Science andTechnology Facilities Council (STFC), UK. for his PhD studentship (project ref-erence 2093954), and O.H. acknowledges the PhD stipend from the Universityof St Andrews’ Centre for Exoplanet Science. V.G. acknowledges the hospitalityof the School of Physics & Astronomy at the University of St Andrews and thesummer student funding from the Royal Astronomical Society.
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Article number, page 24 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters
Appendix A: Cloud properties and gas-phaseparameters (C/O, µ , f e ) In order to enable model comparability, we provide here thedetailed results of the cloud complex for the ultra-hot Jupiterswhich form the base for the more condensed representationwithin the main text body. Figure A.1 provides all the dust-to-gas ratio, ρ d /ρ , profiles clearly indicating where in these atmo-sphere most of the cloud particle mass is located according to ourmodel. Figures A.2 – A.5 provide the details of the 16 consid-ered bulk growth materials as part of our kinetic cloud formationmodel for the equatorial nightside and the morning terminatoronly. Mineral clouds do not form on the dayside and the eveningterminator due to unfavourably high local gas temperatures. Pan-els appear empty where no cloud particle formation occurs; thisresults from profiles where no nucleation seeds form. Figure A.6– A.8 provide the detailed results of the carbon-to-oxygen ra-tio (C / O), the mean molecular weight, µ , and the thermal degreeof ionisation, f e as data input for the averaged values shown inprevious sections.Figure A.9 provides the individual plots for the pressurewhere optical depth of unity (both vertical and slant geometry)is reached for the five sample planets, the hot giant gas planetslike WASP-43b and ultra-hot Jupiters like WASP-103b, WASP-121b, WASP18b, and HAT-P-7b. Article number, page 25 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) ρ d / ρ × − WASP-43b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) ρ d / ρ × − WASP-103b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) ρ d / ρ × − WASP-18b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) ρ d / ρ × − HAT-P-7b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) ρ d / ρ × − WASP-121b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) − − − l og ( h a i A [ µ m ] ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. A.1: Dust-to-gas ratio, ρ d /ρ , for the giant gas planet WASP-43b, and the ultra-hot Jupiters WASP-18b, HAT-P-7b, WASP-103b,and WASP-121b. Article number, page 26 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-121b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-121b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. A.2: Individual bulk material volume fractions WASP-121b. Anti-stellar point: ( φ, θ ) = ( − . o , . o ) and Equatorial MorningTerminator: ( φ, θ ) = ( − . o , . o ). − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-103b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-103b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. A.3: Individual bulk material volume fractions WASP-103b. Anti-stellar point: ( φ, θ ) = ( − . o , . o ) and Equatorial MorningTerminator: ( φ, θ ) = ( − . o , . o ). − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-18b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-18b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. A.4: Individual bulk material volume fractions WASP-18b. Anti-stellar point: ( φ, θ ) = ( − . o , . o ) and Equatorial MorningTerminator: ( φ, θ ) = ( − . o , . o ). Article number, page 27 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) . . . . . . V s / V t o t HAT-P-7b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t HAT-P-7b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. A.5: Individual bulk material volume fractions HAT-P-7b. Anti-stellar point: ( φ, θ ) = ( − . o , . o ) and Equatorial MorningTerminator: ( φ, θ ) = ( − . o , . o ).) Article number, page 28 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) . . . . . . . C / O WASP-43bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) . . . . . . . . C / O WASP-103bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) . . . . . . . . C / O WASP-18bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) . . . . . . . . . C / O HAT-P-7bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) . . . . . . . C / O WASP-121bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminatorC/O = 0.54 − − − − − − log (p gas [bar]) . . . . . . . . . C / O Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. A.6: The carbon-to-oxygen ratio (C / O) for the giant gas planet WASP-43b, and the ultra-hot Jupiters WASP-18b, HAT-P-7b,WASP-103b, and WASP-121b. The solar value C / O = Article number, page 29 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) . . . . . . µ WASP-43bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . µ WASP-103bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . µ WASP-18bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . µ HAT-P-7bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . µ WASP-121bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . µ Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. A.7: The atmospheric mean molecular weight, µ , for the giant gas planet WASP-43b, and the ultra-hot Jupiters WASP-18b,HAT-P-7b, WASP-103b, and WASP-121b. The ultra-hot Jupiters show significant di ff erences in µ between the dayside and nightsideof the planets, whereas WASP-43b shows an approximately constant value around µ ≈ . Article number, page 30 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) − − − − l og ( f e ) WASP-43bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − − − log (p gas [bar]) − − − − l og ( f e ) WASP-103bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − − − log (p gas [bar]) − − − − − − − l og ( f e ) WASP-18bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − − − log (p gas [bar]) − − − − − − − l og ( f e ) HAT-P-7bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − − − log (p gas [bar]) − − − − l og ( f e ) WASP-121bDay-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator f e = 1 × − − − − − − − log (p gas [bar]) − − − l og ( f e ) Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b f e = 1 × − Fig. A.8: Degree of thermal ionisation, f e = p e / (cid:16) p gas + p e (cid:17) . The dash-dot purple line shows f e = × − as a threshold for plasmabehaviour. All ultra-hot Jupiters have dayside thermal ionisation f e > − suggesting an extended dayside ionosphere. Most of thecloud-forming nightsides are little a ff ected by thermal ionisation. Article number, page 31 of 38 & A proofs: manuscript no. aanda-forarX
Fig. A.9: Wavelength-dependent pressure level, p gas = p ( τ =
1) where atmospheric gas above the clouds become optically thick(where τ = τ = τ s Eq. 6) and plane-parallel geometry (dashed) as comparison.When the optical depth of clouds never reaches 1, the pressure for the bottom of the atmosphere (here p ≈ . bar) is returned(hence the lines for the sub-stellar points where there is no cloud). Article number, page 32 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters
Appendix B: Global atmosphere heightasymmetries and hydrostatic pressure scaleheight
We consider the (vertical) geometrical extension of the atmo-sphere (Fig. B.2), and provide a comparison to the hydrostaticpressure scale height for completeness (Fig. B.1). This geometricheight is of interest as it gives an indication for the asymmetry ofthe atmosphere. For example, have Salz et al. (2018) observe anasymmetric transit in the He I line at 0.1083Å with CARMENESin conjunction with a net blue shift of − . ± . − . Oneinterpretation is a geometrical day / night asymmetry of 0.2 R P .Figure B.2 demonstrates that the atmosphere of close-in planetsare not spherical symmetric. The day / night geometric extensionfor the ultra-hot Jupiters in our sample is ≈
2, but this is not a re-sult of the changing mean molecular weight as a constant meanmolecular weight is assumed in the 3D GCMs utilised here. Ta-ble B.1 presents the e ff ect of the changing geometrical extensionin terms of a potential transit depth δ transit = (( R P + z ) / R star ) ( z -vertical extension of the atmosphere,Fig. B.2).The e ff ect of the changing mean molecular weight is betterseen in considering the hydostatic pressure scale height whichwas derived after the gas-phase chemistry was solved within ourcloud formation model (Fig. B.1). Clearly visible in all plots isthe onset of the thermal inversions, which produces an increasein the rate at which the vertical extent of the atmosphere growsat higher altitudes (moving left in the Fig. B.2). This change ismost noticeable for the ultra-hot Jupiters, for the terminators asthey have the steepest inversions. The terminator profiles ini-tially have atmospheric extensions similar to nightside profilesbut around the millibar level they switch to a gradient parallelto the dayside profiles. The lower right of figure shows the dif-ference between average the dayside and nightside profiles, withthe general trend that in the deep atmosphere the extension is thesame, but at higher altitudes diverges, this altitude similarly cor-responds with the drop in mean molecular weight (see bottomright Fig. A.7. It also shows that the e ff ect is most prominent forplanets with low surface gravities; WASP-18b shows little dif-ference in extension despite being an ultra-hot Jupiter as it has asignificantly higher surface gravity). Multiple studies have nowinvestigated the a ff ects of di ff erent extensions on the day- andnightsides in transmission spectra, (Caldas et al. 2019; Plurielet al. 2020) found changes in temperature and compositional gra-dient across the terminator region can bias results of retrievals,and further that this is dependent on the gradient of the changeas this a ff ects the extent of the atmosphere and thus the amountof the dayside that the light ray passes through.Figure B.5 provides the detailed results on the mean molecu-lar weight, µ , and geometric extension for the Parmentier / Caronein order to enable comparison with future simulations.
Article number, page 33 of 38 & A proofs: manuscript no. aanda-forarX − − − − − log (p gas [bar]) . . . . . . . . . H p × [ c m ] WASP-43b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − log (p gas [bar]) H p × [ c m ] WASP-103b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − log (p gas [bar]) . . . . . . . H p × [ c m ] WASP-18b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − log (p gas [bar]) H p × [ c m ] HAT-P-7b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − log (p gas [bar]) H p × [ c m ] WASP-121b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) H p × [ c m ] Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. B.1: Hydrostatic pressure scale height (H p = (kT)( µ m H g)) for the giant gas WASP-43b, and the ultra-hot Jupiters HAT-P-7b, WASP-18b, and WASP-103b, WASP-121b. The changing pressure scale height is caused by the temperature-dependent meanmolecular weight, µ ( T ), that changes from the day- to the nightside due to the large di ff erences in gas temperatures (see Fig. A.7). Planet WASP-103b WASP-18b WASP-121b HAT-P-7b WASP-43b
Average dayside maximum extension [R P ] 0.10777 0.0126 0.16558 0.07815 0.02856Average nightside maximum extension [R P ] 0.05244 0.0055 0.09582 0.04561 0.00214Day- / nightside ratio 2.055 2.294 1.728 1.713 1.334 δ transit [%] 1.141 0.834 1.548 1.725 2.432Table B.1: The maximum average dayside and nightside extensions in terms of planetary radius, the day-to-nightside extensionratio and the expected transit depth calculated as δ transit = (( R P + z ) / R star ) . We use the R p and R star given in Table 1, and the verticalextension of the atmosphere z (Fig. B.2). Article number, page 34 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) . . . . . . z × [ c m ] WASP-43b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) z × [ c m ] WASP-103b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . . z × [ c m ] WASP-18b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) z × [ c m ] HAT-P-7b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) z × [ c m ] WASP-121b
Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) z × [ c m ] Day-side averageNight-side averageWASP-121bWASP-103bWASP-43bWASP-18bHAT-P-7b
Fig. B.2: Geometric atmosphere height, z [cm], calculated by summing the change in height dz between successive pressure layersstarting from the inner boundary where z = Article number, page 35 of 38 & A proofs: manuscript no. aanda-forarX
Appendix B.1: Supplementary details on the WASP-43bsimulations results by Parmentier and Carone
The detailed cloud modelling results regarding the cloud mate-rial volume fractions, V s / V tot , and the results for the mean molec-ular weight , µ , and the vertical, geometric extension, z , for thecomparative study if the e ff ect of the inner boundary for the ex-ample of WASP-32b in Sect. 6 are provided. Article number, page 36 of 38h. Helling et. al.: Trending clouds in hot giant gas planets and ultra-hot Jupiters − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = 0.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = 90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. B.3: Individual bulk material volume fractions WASP-43b (based on the 1D thermodynamic profiles from Parmentier etal.). Sub-stellar point: ( φ, θ ) = (0 . o , . o ), Anti-stellar point: ( φ, θ ) = ( − . o , . o ), Equatorial Morning Terminator: ( φ, θ ) = ( − . o , . o ), Equatorial Evening Terminator: ( φ, θ ) = (90 . o , . o ).) − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = 0.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = -180.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = 90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] − − − − log (p gas [bar]) . . . . . . V s / V t o t WASP-43b φ = -90.0 θ = 0.0 TiO [s]SiO[s]SiO [s]CaTiO [s]CaSiO [s]MgO[s]MgSiO [s]Mg SiO [s]Fe[s]FeO[s]FeS[s]Fe O [s]Fe SiO [s]Al O [s]C [s] Fig. B.4: Individual bulk material volume fractions WASP-43b (based on the 1D thermodynamic profiles from Carone et al.). Sub-stellar point: ( φ, θ ) = (0 . o , . o ), Anti-stellar point: ( φ, θ ) = ( − . o , . o ), Equatorial Morning Terminator: ( φ, θ ) = ( − . o , . o ),Equatorial Evening Terminator: ( φ, θ ) = (90 . o , . o ).) Article number, page 37 of 38 & A proofs: manuscript no. aanda-forarX − − − − − − log (p gas [bar]) . . . . . . µ Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − log (p gas [bar]) . . . . . . µ Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − − − log (p gas [bar]) . . . . . . z × [ c m ] Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator − − − − log (p gas [bar]) . . . . . . z × [ c m ] Day-sideNight-sideSubstellar pointAnti-stellar pointEvening terminatorMorning terminator
Fig. B.5: The e ff ect of the inner boundary of the 3D GCM models on the mean molecular weight, µ , and the geometric atmosphereextension for the giant gas planet example WASP-43b. Right: based on the 1D thermodynamic profiles from Parmentier et al.
Right: based on the 1D thermodynamic profiles from Carone et al. There is a di ff erence of ∼ × cm between the day and nightgeometric extensions, of the same profiles, between the two models.cm between the day and nightgeometric extensions, of the same profiles, between the two models.