Beyond Equilibrium Temperature: How the Atmosphere/Interior Connection Affects the Onset of Methane, Ammonia, and Clouds in Warm Transiting Giant Planets
Jonathan J. Fortney, Channon Visscher, Mark S. Marley, Callie E. Hood, Michael R. Line, Daniel P. Thorngren, Richard S. Freedman, Roxana Lupu
DDraft version November 3, 2020
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Beyond Equilibrium Temperature: How the Atmosphere/Interior Connection Affects the Onset ofMethane, Ammonia, and Clouds in Warm Transiting Giant Planets
Jonathan J. Fortney, Channon Visscher,
2, 3
Mark S. Marley, Callie E. Hood, Michael R. Line, Daniel P. Thorngren, Richard S. Freedman,
4, 7 and Roxana Lupu Department of Astronomy & Astrophysics, University of California, Santa Cruz, CA 95064, USA Chemistry & Planetary Sciences, Dordt University, Sioux Center, IA 51250, USA Space Science Institute, Boulder, CO 80301, USA NASA Ames Research Center Moffett Field, Mountain View, CA 94035, USA School of Earth & Space Exploration, Arizona State University, Tempe AZ 85287, USA Institute for Research on Exoplanets, Universit´e de Montr´eal, Montr´eal, Qu´ebec, H3T 1J4, Canada SETI Institute, Mountain View, CA 94043, USA BAER Institute, NASA Research Park, Moffett Field, CA 94035, USA
ABSTRACTThe atmospheric pressure-temperature profiles for transiting giant planets cross a range of chemicaltransitions. Here we show that the particular shape of these irradiated profiles for warm giant planetsbelow ∼ O, CO, CH , CO , and NH inJupiter- and Neptune-class planets. We show the cooling history of a planet, which depends mostsignificantly on planetary mass and age, can have a dominant effect on abundances in the visibleatmosphere, often swamping trends one might expect based on T eq alone. The onset of detectable CH in spectra can be delayed to lower T eq for some planets compared to equilibrium, or pushed to higher T eq . The detectability of NH is typically enhanced compared to equilibrium expectations, which isopposite to the brown dwarf case. We find that both CH and NH can become detectable at around thesame T eq (at T eq values that vary with mass and metallicity) whereas these “onset” temperatures arewidely spaced for brown dwarfs. We suggest observational strategies to search for atmospheric trendsand stress that non-equilibrium chemistry and clouds can serve as probes of atmospheric physics. Asexamples of atmospheric complexity, we assess three Neptune-class planets GJ 436b, GJ 3470b, andWASP-107, all around T eq = 700 K. Tidal heating due to eccentricity damping in all three planetsheats the deep atmosphere by thousands of degrees, and may explain the absence of CH in these coolatmospheres. Atmospheric abundances must be interpreted in the context of physical characteristicsof the planet. INTRODUCTION1.1.
Atmospheric Characterization
Even 25 years after the discovery of gas giant exo-planets (Mayor & Queloz 1995) we are still in our in-fancy in characterizing the atmospheres of these worlds.Over the past two decades, astronomers have made fan-tastic strides to obtain spectra of exoplanets, but westill have much to do. In the realm of transiting plan-ets, observers have often been hindered by instrumentsaboard space- and ground-based telescopes that were
Corresponding author: Jonathan J. [email protected] never designed for precision time series spectrophotom-etry. Even as dozens of planets have been seen in trans-mission spectroscopy (e.g., Sing et al. 2016) and occulta-tion spectroscopy or photometry (e.g., Kreidberg et al.2014; Garhart et al. 2020) our ability to understandthe physics and chemistry of hydrogen-dominated atmo-spheres has been limited, principally by low signal-to-noise observations and limited wavelength coverage. Onthe side of the directly imaged planets, telescopes likeKeck, VLT, and Gemini have allowed more robust atmo-spheric spectroscopy, but with a sample size that is sofar limited in number (e.g., Konopacky et al. 2013; Mac-intosh et al. 2015; Gravity Collaboration et al. 2019).It is with brown dwarfs, now numbering over 1000,with temperatures down to 250 K (Luhman 2014; Ske- a r X i v : . [ a s t r o - ph . E P ] O c t Fortney et al. mer et al. 2016) where robust atmospheric character-ization has taken place over the past 25 years. Themajor transitions in atmospheric chemistry and cloudopacity have now been unveiled (Burrows et al. 2001;Kirkpatrick 2005; Helling & Casewell 2014; Marley &Robinson 2015), although major open questions still ex-ist on the role of clouds in shaping the spectra acrossa range of T eff and surface gravity. However, it shouldbe clear that relying solely on the classic “stellar” fun-damental quantities of T eff , log g , and metallicity hasalready shown its faults for these objects. For instance,time-variability can reach tens of percent, and effectsdue to rotation rate (Artigau 2018) and viewing anglehave now been seen as important to take into accountfor atmospheric characterization (Vos et al. 2017).To understand the atmospheres of giant planets wewill certainly need a larger sample size than the browndwarfs, for a similar level of understanding, as planetshave many additional complicating factors (Marley et al.2007). For instance, substantial recent work has goneinto assessing the Spitzer
IRAC 3.6/4.5 colors of coolertransiting planets, in order to better assess atmosphericmetallicity and the role of CH and CO absorption (Tri-aud et al. 2015; Kammer et al. 2015; Wallack et al. 2019;Dransfield & Triaud 2020). The wide diversity of colorsat a given T eq , much wider than is seen in brown dwarfsat a given T eff (Beatty et al. 2014; Dransfield & Triaud2020), has been interpreted as needing a large dispersionin atmospheric metallicity and potentially C/O ratio.Planets present additional complicating physics, suchas heating from above, across a range of incident stel-lar spectral types (Molli`ere et al. 2015), in addition to arange of UV fluxes. The planets will have diverse day-night contrasts and circulation regimes, likely with verywide range of atmospheric metallicities (Fortney et al.2013; Kreidberg et al. 2014) and non-solar abundanceratios ( ¨Oberg et al. 2011; Madhusudhan et al. 2014; Es-pinoza et al. 2017). The cooling of the interiors of giantplanets – even the cooler giant planets not affected bythe hot Jupiter radius anomaly – is also still not fully un-derstood (e.g., Vazan et al. 2015; Berardo & Cumming2017)Key science goals of the James Webb Space Telescope ( JWST ) and
ARIEL are to obtain spectra of a widerange of planetary atmospheres (Beichman et al. 2014;Greene et al. 2016; Tinetti et al. 2018). In the realm oftransiting giant planets, which have predominantly ac-creted their atmospheres from the proto-stellar nebula,one aspect of this science will be characterizing planetsover a wide range of temperatures, to sample a widerange of transitions in atmospheric chemistry and cloudformation. A significant amount of previous theoreti- cal and modeling work have gone into trying to predictand understand trends in the atmospheres of these plan-ets, going back to important early works such as Marleyet al. (1999) and Sudarsky et al. (2000), supplementedby later works like Fortney et al. (2008), Madhusudhanet al. (2011a), and Molli`ere et al. (2015). Most of thesepapers have pointed to planetary equilibrium tempera-ture, T eq , as the dominant physical parameter that de-termines atmospheric physics and chemistry, somewhatakin to T eff in stars. While there are good reasons tothink that this is indeed true, there are equally goodreasons to think that T eq is only a starting point, andthat other physical parameters can have a crucial effecton determining the atmospheric spectra that we will see.Of course T eq is only part of the energy budget, andit is well-understood that T = T + T , with T int parameterizing the intrinsic flux from the planetary in-terior, and T eq from thermal balance with the parentstar. In Jupiter, for instance, T eq and T int are simi-lar, with neither dominating the energy budget (Pearl& Conrath 1991; Li et al. 2018). Recently, Thorngrenet al. (2019, 2020) pointed out that the radii of “hot”and “warm” Jupiter population can be used to assessthe intrinsic flux coming from planetary interiors. Of-ten Jupiter-like values of T int (100 K) had been chosenfor convenience, but the inflated radius of a typical hotJupiter goes hand-in-hand with a hotter interior andmuch higher T int values (assuming convective interiors).This work gives us the ability to better assess thedepth of the radiative-convective boundary (RCB) inthese strongly irradiated planets. A key finding ofThorngren et al. (2019) was the T int values are typi-cally larger (sometimes much larger) than previous ex-pectations, which moves the RCB to lower pressures. Ahigher T int can remove or weaken cold traps in these at-mospheres, which can alter atmospheric abundances andthe depth at which clouds form. Much additional workneeds to be considered for these hot planets, perhapsmuch of it in the 3D context, given the large day-nighttemperature contrasts (Parmentier & Crossfield 2018).The role of the current paper is to serve as a comple-ment, of sorts, and extension to, the work of Thorngrenet al. (2019), but mostly for cooler planets. For planetsbelow T eq ∼ ransiting Planet Atmosphere/Interior Connection T eff , provid-ing strong evidence for a detached radiative zone, belowthe visible atmospheres, long predicted in these atmo-spheres (Marley et al. 1996; Burrows et al. 1997). Is isthese disequilibrium tracers which we turn to next, inmore detail.1.2. “Hidden” Atmospheric Chemistry Due to non-equilibrium chemistry via vertical mix-ing, deep atmosphere temperatures can matter as muchas temperatures in the visible atmosphere in determin-ing observable abundances. This well-understood pro-cess affects abundances when the mixing timescale fora parcel of gas, t mix , it shorter than the chemical con-version timescale, t chem , for a given chemical reaction.Well-studied reactions are CO to CH and N to NH .These timescales can be so long that the gas in thevisible atmosphere (at say, 1 mbar) will be represen-tative of pressure-temperature ( P–T ) conditions at ∼ T eq from CO–dominated to CH –dominated atmospheres, an area ofactive study already with Hubble and
Spitzer (Stevensonet al. 2010; Morley et al. 2017a; Kreidberg et al. 2018;Benneke et al. 2019).We can first look at an illustrative example of whyvertical mixing from different atmospheric depths canstrongly affect observed abundances and spectra, by ex-ploring the behavior of CO, CH , and H O. Figure 1shows the atmospheric pressure-temperature (
P–T ) pro-file for a planet at 0.15 AU from the Sun, with T eq = 710K. Five models are shown, with decreasing T int , lead-ing to cooler interior adiabats. Underplotted in lightgray are curves of constant volume mixing ratio (molefraction) for CO, to the lower left, following the chemi-cal equilibrium calculations of Visscher et al. (2010) andVisscher (2012). Underplotted in dark gray is the samefor CH , to the upper right. The dashed thick blackcurve shows the equal-abundance boundary, where themixing ratio of CO=CH :log P ≈ . − . /T + 0 . , (1)for P in bar, T in K, and [Fe/H] as the metallicity(Visscher 2012). When we turn to nitrogen chemistryin Section 4.2, we will use the analogous N =NH equalabundance curve:log P ≈ . − . /T + 0 . Fortney et al.
Table 1.
Guide to Model Parameters
Fig. T eq (K) T int (K) M J g (m s − ) m age (Gyr)1 710 60, 100, 200, 300, 400 1 25 10 ×
4, 23 710 52, 77, 117, 182, 333 0.1, 0.3, 1, 3, 10 5.8, 9.8, 24, 65, 225 10 ×
37, 13 1120 to 180 75 0.3 10 10 ×
39, 15 870, 380, 180 52, 117, 333 0.1, 1, 10 5.8, 24, 225 10 × × × Note —In each figure, a range of planetary models is considered explored across different planetary parameters. The metallicity factor m is defined as m = 10 [Fe/H] . equal to T eff , a good representation of the mean ther-mal photosphere in emission. Points 1 and 2 are in theCH -dominated region, with point 2 having ∼ × moreCO. Moving down to point 3, all profiles are now in theCO-dominated regime, where the CH abundance fallsoff dramatically with temperature. Point 4 is deeper inthe atmosphere along the hottest adiabat, in the CO-rich region, with a decrease in CH compared to point3. Points 5 and 6 are along cooler adiabats, with 5 hav-ing abundances quite similar to point 3. Point 6 is quiteinteresting, in that, while it is in the deep part of the at-mosphere, it is clearly within the CH -dominant region,and has the same CH and CO abundances as point 2.This complexity should be contrasted with the profile ofa T eff = 1000 K, log g =5 brown dwarf, plotted in thickorange. For the brown dwarf, as a parcel of gas movesalong from high pressure to low, there is a monotonicincrease in CH and decrease in CO.As one would expect, the spectra that use thequenched abundances, brought up to the visible atmo-sphere from the black points of Figure 1, vary consider-ably as the abundances of CO and CH vary by orders ofmagnitude. In addition, the abundance of H O changesdepending on whether CO is present as well. We demon-strate this for 5 different models shown in Figure 2. Forpoints to the “right” of the CO/CH equal-abundancecurve, like 3, 5, and especially 4, the CO band is muchstronger, and CH weaker. The spectra from points 1and 6 are substantially similar, given their relatively po-sitions in CO/CH phase space. The lack of monotonicbehavior in the mixing ratio (and observability) of CH as a function of the quench pressure was also pointedout for by Molaverdikhani et al. (2019, see their Figure2), although they did not explore variations in the lowerboundary condition, which is our focus here.Such a wide range of internal adiabats, for a given up-per atmosphere, is quite possible due to the differencesin cooling histories in giant planets. It is by now widelyappreciated that giant planets cool over time, most dra- matically at young ages, and that more massive planetstake longer to cool (Marley et al. 1996; Burrows et al.1997; Chabrier & Baraffe 2000). For reference, in Fig-ure 3 we plot cooling tracks for planets from 10 M J to0.1 M J (32 M ⊕ ) for ages from 10 to 10 years, usingthe models of Fortney et al. (2007) and Thorngren et al.(2016). At an age of 3 Gyr, for instance, T int values of50 K to 350 K span the population. Such model planetswould in reality all have different surface gravities, whichwould then yield different P–T profile shapes, even at
500 1000 1500 2000 2500T (K)20-2-4-6 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . C H D e c r ea s i ng C O D e c r e a s i n g Figure 1.
Model pressure-temperature profiles for a 10 × solar atmosphere at 0.15 AU from the Sun. The five profilesall have T eq = 710 K and show (alternating red and blue)five values of T int , at 60, 100, 200, 300, and 400 K and aJupiter-like gravity of 25 m s − . Also shown in thick orangeis a T eff of 1000 K brown dwarf with a gravity of 1000 ms − . Equal-abundance contours for CH are shown in darkgray, and show the log (base 10) of volume mixing ratiosof CH that fall off by many orders of magnitude towardsthe upper right. Correspondingly, light gray contours showthe same for CO, toward the lower left, where CH is thedominant absorber. CO and CH have an equal abundanceat the dashed thick black curve. These mixing ratio contoursassume equilibrium chemistry. The numbered black dots arecalled out specifically in the text. ransiting Planet Atmosphere/Interior Connection T r an s i t D ep t h ( % ) COCO CO H O CH CH CH H OCH H O CH H O Figure 2.
The corresponding transmission spectra for the
P–T profiles and chemical abundance points from Figure 1.The main absorption features of H O, CO, CH , and CO are labeled. Transmission spectra that use the “quenched”chemical abundances from points 1, 3, 4, 5, and 6 are labeledwith arrows. Spectra are normalized to wavelengths whereH O is the main absorber, to show the relative roles of COand CH in shaping spectra. The transit models assume 1 R J at a pressure of 1 kbar, a gravity of 25 m s − , and stellarradius of the Sun. Time (years)1001000 T i n t ( K ) M J M J . M J Figure 3.
Thermal evolution of giant planets at 0.1 AUfrom the Sun, after Fortney et al. (2007) and Thorngrenet al. (2016). Plotted are the intrinsic effective temperature, T int , for models at 10, 3, 1, 0.3, and 0.1 M J (32 M ⊕ ), fromtop to bottom. For reference, Jupiter today has T int = 99 K.A wide range of T int values are possible at old ages, given arange of planetary masses, and a wide range of T int valuesare possible at a given mass, over time. for H/He-dominated atmospheres. The aim then is toshow that a range of factors other than equilibrium tem-perature can have significant impacts, even dominant impacts, on atmospheric abundances and spectra. Wealso explore how non-equilibrium chemistry can serve asa tracer for understanding the deep temperature struc-ture for these atmospheres, at pressures far below whereone can probe directly. After describing our methods ina bit more detail, we investigate these factors, first forwell-known transiting Neptune-class planets GJ 436b,GJ 3470b, and WASP-107. After that we will explorecarbon chemistry more generally, followed by nitrogenchemistry more generally, before our Discussion (withcaveats), and Conclusions. MODEL DESCRIPTION2.1.
Atmospheric Structure and Spectra
The model atmosphere methods used here have pre-viously been extensively described in the literature. Wecompute planet-wide average (“4 π re-radiation of ab-sorbed stellar flux”) 1D radiative-convective equilibriummodels using the model atmosphere code described inthe papers of Marley & McKay (1999), Marley et al.(1996), Fortney et al. (2005), Fortney et al. (2008),and the general review of Marley & Robinson (2015).The radiative transfer methods are described in McKayet al. (1989). The model uses 90 layers, typically evenlyspaced in log pressure from 1 microbar to 1300 bars.
500 1000 1500 2000T (K)20-2-4-6 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . Figure 4.
Model pressure-temperature profiles (with T eq =710 K) for a 10 × solar atmosphere at 0.15 AU from theSun, this time based on thermal evolution models. The fiveprofiles (alternating red and blue) show five values of T int , at52, 77, 117, 182, and 333 K, as respective surface gravities g =5.8, 9.8, 24, 65, and 225 m s − . Equal-abundance contoursfor CH are shown in black, and light gray contours showthe same for CO. CO and CH have an equal abundance atthe dashed thick black curve. These mixing ratio contoursassume equilibrium chemistry. Fortney et al.
The equilibrium chemical abundances follow the workof Lodders & Fegley (2002), Visscher et al. (2006, 2010)and Visscher (2012). The opacity database is describedin Lupu et al. (2014) and Freedman et al. (2014). Trans-mission spectra are calculated using the 1D code de-scribed in Morley et al. (2017b).2.2.
Interiors and Tidal Heating
As already mentioned, the giant planet thermal evo-lution models use the methods of Fortney et al. (2007)and Thorngren et al. (2016). These thermal evolu-tion calculations use an extensive grid of 1D non-graysolar-composition radiative-convective atmosphere mod-els, which serve at the upper boundary condition. Theinterior H/He equation of state is that of Saumon et al.(1995). We make the standard, typical assumption ofa fully-convective H/He envelope, and these evolutionmodels also have a 10 M ⊕ ice/rock core.Tidal heating, to be investigated in a Section 3,uses the extensive tidal evolution equations derived inLeconte et al. (2010). We determine the tidal heatingrate (in energy per second) with equation (13) in thiswork. We will show that for some planets this tidalheating flux from the interior can be orders of magni-tude higher than that calculated from normal secularcooling of the interior.2.3. Nonequilibrium Chemistry
When treating non-equilibrium chemistry, an impor-tant topic in this paper, we make extensive use of thefindings of Zahnle & Marley (2014). These authors pro-vide quenching relations that are derived by fitting tothe complete chemistry of a full ensemble of 1D kineticchemistry models. We use the standard “quench pres-sure” formalism, where we assume chemical equilibriumwhere the chemical conversion time, t chem , is shorterthan the vertical mixing time, t mix . The local values of t mix along a P–T profile use the standard assumptionthat t mix = L /K zz , where L a length scale of interest,here assumed to be the local pressure scale height, H ,and K zz is the vertical diffusion coefficient. Other, po-tentially smaller values of L could be used (Smith 1998;Visscher & Moses 2011), however, as we discuss below,uncertainties in K zz dwarf any uncertainty in L , so, fol-lowing Zahnle & Marley (2014), we make the simplestchoice.For these strongly irradiated planets, atmospheres canbe radiative until depths of tens of bars, even beyond ∼ T int . The lower thevalue of T int , the deeper the radiative zone, as shown inFigure 1. While in convective zones mixing length the-ory can be used as a guide to values of K zz (Gierasch & Conrath 1985), in radiative regions no such readily us-able theory exists, although it is generally expected thatradiative regions will have orders of magnitude lower K zz values.Some 3D circulation model simulations of hot Jupitershave attempted to gauge reasonable K zz values. Par-mentier et al. (2013) suggested a fit to models of planetHD 209458b that yielded K zz = 5 × / √ P bar cm s − . They suggest that cooler planets, like the onestreated here, should have slower vertical wind speedsand smaller values of K zz . More recent work has triedto estimate K zz from first-principles (Zhang & Showman2018a,b; Menou 2019).The chemical kinetics literature for irradiated plan-ets shows a range of K zz choices. These include basingvalues tightly on 3D simulations, but more commonly,choosing a wide-range of constant-with-altitude K zz val-ues, to bracket a reasonable parameter space. It is thisbracketing choice that we make here, as we aim to makethe point that non-equilibrium chemistry must be im-portant for a wide range of objects. For calculations forparticular planets of interest it may be worthwhile togenerate K zz predictions from GCM simulations. Wereturn to this point in Section 5. Followup work thatcouples planetary temperature structures with detailedpredictions of K zz profiles (Zhang & Showman 2018a,b;Menou 2019), to predict atmospheric abundances, wouldbe important and fruitful work.Before exploring a wide range of planets, we first inves-tigate how our models can be used to understand the at-mospheric abundances of three (relatively) well-studiedNeptune-class transiting planets, which have been thetargets of many observations with Spitzer and
Hubble . THE ATMOSPHERES OF THREENEPTUNE-CLASS PLANETS: GJ 436B, GJ3470B, WASP-107BOur first foray into why T eq is not enough will be forthe Neptune-class exoplanets, GJ 436b, GJ 3470b, andWASP-107b. These three planets have been the tar-gets of extensive observational campaigns, in particularfor GJ 436b, as it was the first transiting Neptune-classplanet found (Gillon et al. 2007). The work on emis-sion and transmission observations and their interpre-tation for this planet is large and difficult to conciselysummarize. A recent review can be found in Morleyet al. (2017a). The most significant finding, going backto Stevenson et al. (2010), is the suggestion that theplanet’s atmosphere is far out of chemical equilibrium,with little CH absorption and a likely high abundanceof CO and/or CO . An upper limit on the CH abun-dance is published in Moses et al. (2013). ransiting Planet Atmosphere/Interior Connection seen. And a transmission spectrum ofWASP-107b by Kreidberg et al. (2018) finds no sign ofCH in the near infrared. For both planets, these papersinclude CH abundance upper limits.While these three planets have masses and radii thatdiffer by a factor of around 2, they share some interest-ing similarities. Perhaps most strikingly, they have T eq values that all within ∼
100 K of each other. This may suggest that the planets could have similar atmosphericproperties. Another, perhaps surprisingly fact, is thatall three planets are on eccentric orbits. Most impor-tant to our current discussion is that we find all threeplanets are currently undergoing significant eccentricitydamping today.Figure 5 shows model
P–T profiles for all three plan-ets, with GJ 436b in blue, GJ 3470b in red, and WASP-107b in orange. For simplicity, all are at 100 × solar,a value similar to the carbon abundance inferred forUranus and Neptune. We note that retrieval work forGJ 436b (Morley et al. 2017a) suggests a metallicityhigher than this value, retrievals for GJ 3470b suggesta metallicity lower than this (Benneke et al. 2019), andpreliminary structure models (that did not take into ac-count tidal heating) for WASP-107b also suggested alower metallicity (Kreidberg et al. 2018). Our aim hereis not to find best fits for the spectra of each planet, butto suggest that tidal heating in the interior plays a largerole in altering atmospheric abundances. We thereforefeel that a simple, but plausible metallicity, can serve asan illustrative example.A cursory glance shows that all 3 planets reside ina remarkably similar P–T space. For these planets 4adiabats are shown. First we will examine the coolestadiabats (lowest specific entropy), which are for modelswith no tidal heating ( T int = 60K), and then 3 warmeradiabats that assume log Q = 6, 5, and 4, from colder tohotter, as a lower Q means more tidal heating (Leconteet al. 2010). Tidal heating for these planets has a dra-matic effect, warming the interior by hundreds to thou-sands of K at a given pressure.All three planets have three sets of solid dots on theirprofiles that show the quench pressure level for log K zz = 4, 8, and 12 cm s − . For the quench pressure for log K zz = 4, very sluggish mixing, tidal heating has a mod-est impact in shifting the expected chemical abundances log K zz ∼ .
500 1000 1500 2000T (K)20-2-4-6 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . GJ 3470b, 100xGJ 436b, 100xWASP-107b, 100x
Figure 5.
Atmospheric
P–T profiles for planets GJ 436b,GJ 3470b, and WASP-107b all at 100 × solar abundances.The light and dark gray equal-abundance curves are similarto those in Figure 1, although here we plot 100 × solar. Foreach planet, 4 interior adiabats are shown, for the case ofno tidal heating (coolest), and Q = 10 , 10 and 10 , fromcooler to warmer. The sets of solid dots show the quenchpressure for log K zz = 4, 8, 12, where larger K zz valuesprobe deeper. to CO-richer and CH -poorer territory, compared to,say, equilibrium chemistry at 1 mbar. However, for thedepths probed at log K zz = 8 and 12, the atmospheremodels are significantly warmer, and draw from a regionof much higher CO and lower CH if heating is present.We can explore and quantify this effect for a subset ofmodels, which are shown in Figure 6, where each planethas its own panel. Abundances at 1 mbar are plotted forequilibrium chemistry and log K zz = 4, 8, and 12. Thinlines are for no tidal heating, while thick lines includetidal heating, with Q = 10 – a reasonable estimate forNeptune (Zhang & Hamilton 2008) – for GJ 3470b andWASP-107b, and Q = 10 for GJ 436b, based on a fit tothe planet’s thermal emission spectrum (Morley et al.2017a). At our assumed 100 × abundances with equi-librium chemistry, for all three planets CH would beexpected to be abundant, and even the dominant car-bon carrier in GJ 436b and WASP-107b. The retrieved1 σ CH upper limits, from free retrievals from all threeatmospheres (Moses et al. 2013; Kreidberg et al. 2018;Benneke et al. 2019), are shown as dashed black lines.There are two main effects to be seen in Figure 6. Firstin the large change in abundances for CH – falling offdramatically, and CO – increasing, but more modestly,just in going from equilibrium chemistry to log K zz = 4.Another striking effect is the divergence in the behaviorof the CH abundance at log K zz = 8 and 12, between theno tidal heating model (thin lines) and the model withtidal heating. Based on the P–T profiles in Figure 5 we
Fortney et al. can see that no-heating models bring up CH -rich gas,while the tidal heating models bring up CH -poor gas.This is a dramatic effect in all three planets. Large K zz values, driven by strong convection caused by ongoingtidal dissipation, can drive the CH abundance to lowvalues, in the range constrained by observations to date.This strongly suggests that nonequilibrium chemistryand tidal heating conspire to drive the atmosphericabundances far from simple expectations. We shouldof course be a bit wary about treating the three plan-ets as carbon copies however. With no theory to guidethe strength of tidal heating, Q for the planets couldbe quite different for all three. The expected mass frac-tion of H/He in WASP-107b is far larger than for GJ3470b, for instance. Similarly, with little theory to guidevertical mixing strength, this could also be quite dif-ferent among the planets, as they have quite differentsurface gravities. Additionally, they have been modeledwith relatively simple chemical abundances (100 × solar,with a solar C/O ratio), and the actual planets couldreadily have more complex, and different, base elemen-tal abundances. Of note, the planet WASP-80b, about100 −
150 K warmer than this trio, but on a circular orbit(Triaud et al. 2015), has a
Spitzer
IRAC 3.6/4.5 µ m ra-tio in thermal emission that is similar to early T-dwarfs.Triaud et al. (2015) suggest this IRAC color could po-tentially be due to some CH absorption in the planet’satmosphere, which seems quite viable, as we describe inthe next section.As Morley et al. (2017a) suggested for GJ 436b, a di-rect sign of tidal heating would be a high thermal fluxfrom the planet’s interior, which could be observed viaa secondary eclipse spectrum or thermal emission phasecurve. Future observations with JWST , including thosewhere tidal heating are not at play, may allow for a cou-pled understanding of atmospheric abundances, temper-ature structure at a variety of depths, vertical mixingspeed, and tidal heating. These three planets, all in asimilar
P–T space, motivate a wider investigation. THE PHASE SPACE OF CHEMICALTRANSITIONSIn the face of vertical mixing altering chemical abun-dances, mixing ratios in the visible atmosphere are tiedto atmospheric temperatures at depth, as described inthe previous section. This complicates the goal of deriv-ing a straightforward understanding of chemical transi-tions. We aim to show that, even at a given metallicityand K zz , this transition will depend on the cooling his-tory (hence, mass and age) of any planet. We refer backto Figure 3 which showed models of the thermal evo-lution of giant planets. These model planets are all at Eq 4 6 8 10 12log K zz (cm s -1 )10 -7 -6 -5 -4 -3 -2 -1 M i x i ng R a t i o CH H OCOCO GJ Eq 4 6 8 10 12log K zz (cm s -1 )10 -7 -6 -5 -4 -3 -2 -1 M i x i ng R a t i o CH H OCOCO GJ Eq 4 6 8 10 12log K zz (cm s -1 )10 -7 -6 -5 -4 -3 -2 -1 M i x i ng R a t i o CH H OCOCO WASP-107b, 100x, Q=10 Figure 6.
Top: Chemical abundances at 1 mbar for 3 mod-els of GJ 436b. H O is blue, CO is orange, CO is red,and CH is green. Plotted are abundances for equilibriumchemistry, and log K zz = 4, 8, and 12. Thin lines show notidal heating, while thick lines use Q = 10 . With tidalheating, the higher the K zz , the higher the CO/CH ratio.The dashed black line shows the CH mixing ratio upperlimit. Middle: A very similar plot for GJ 3470b, again show-ing how nonequilibrium chemistry and tidal heating enhancethe CO/CH ratio, but with Q = 10 . Bottom: Anothersimilar plot for WASP-107b, with Q = 10 . Tidal heatingand high K zz can plausibly explain all observations. ransiting Planet Atmosphere/Interior Connection T int , how changing incident flux(hence, T eq ) does or does not lead to changes in chemicalabundances in the visible atmosphere. We first explorecarbon chemistry.4.1. CO-CH Transitions
In Section 3 we examined the CO-CH boundary forspecific tidally-heated Neptune-class planets. Objectswith tidal heating are special cases, but certainly willbe common enough that they cannot simply be ignored,when looking at general trends. But here we can exam-ine the general trends in the absence of tidal heating, fora range of planet masses and ages. As we will see, therange of cooling histories, and lack of clarity with howvertical mixing will change with planet mass, can leadto important complexities.4.1.1. Effects of T eq and Vertical Mixing We first examine the general case of a Saturn-like ex-oplanet as a function of distance from a Sunlike star.Here we have chosen a 10 × solar atmosphere, surfacegravity of 10 m s − , and T int = 75 K, representative of aseveral gigayear-old Saturn-mass exoplanet. We choosethis as our “base planet” since these kinds of giant plan-ets would be excellent targets for atmospheric charac-terization via transmission. Atmospheric P–T profilesare shown in Figure 7, for planets from 0.06 AU to 2AU. The three sets of black dots show quench pressurescorresponding to log K zz values of 4, 8, and 11. Mostimportantly, at lower pressures, the atmospheres divergequiet widely, owing to the factor of ∼ g/T int pairs, and one could make a plot like thisfor any Jupiter-like planet, super-Jupiter, or sub-Saturn.Why this behavior occurs requires some discussion. Toour knowledge this effect was first noted in Figure 3 ofFortney et al. (2007), who described the effects of these“bunched up” deep profiles on the mass-radius relationfor warm transiting giant planets, but they did not iden-tify a cause for the similarity of the deep temperatures.A study of the gray analytic temperature profiles ofGuillot (2010) suggests, via their Equation (29), a rela-tion between the temperature ( T ) and optical depth τ that is a function of only three quantities: the irradia-tion temperature (which is directly related to T eq ), T int ,and γ , the ratio of the visible to thermal opacities. If γ is P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . Figure 7.
Atmospheric
P–T profiles for old, Saturn-likeplanets ( T int = 75K, g = 10m s − , assuming 10 × metallicity.The models are a 9 incident flux levels, at 0.06, 0.07, 0.1,0.15, 0.2, 0.3, 0.5, 1, 2 AU from the Sun. Three sets of blackdots show the depth of vertical mixing with log K zz of 4, 8,and 11 cm s − . At higher pressures, note that the spreadbetween all profiles is lessened, both in temperature, andin reference to the CH (black) and CO (grey) abundancecurves.) relatively constant, and at a given T int value, decreasing T eq cools the entire atmosphere at every τ , including thedeep region that here transitions to an adiabat. How-ever, if γ were to dramatically decrease with decreasing T eq , the deep T − − τ profile (analogous to our deep T–P profile) could remain nearly constant at depth with anupper atmosphere that was colder with decreasing T eq .Indeed, Figure 5 of Freedman et al. (2014) shows a fac-tor ∼
60 falloff in γ from ∼ γ rel-atively constant at hotter and colder temperatures. This700-1400 K temperature range corresponds reasonablywell to what is seen in our Figure 7 and “middle region”of Figure 3 of Fortney et al. (2007). Therefore, we sug-gest that this change in visible opacity is the dominantphysical effect the keeps the deep atmosphere tempera-tures relatively constant across this T eq range. However,additional work on this point is surely needed.Of particular interest is that the coldest profiles aremostly in the CH -dominant region at lower pressures,but along the atmospheric adiabat, as one reaches hotterlayers, one finds gradually more CO. This is the “typi-cal” case for brown dwarfs (Saumon et al. 2003; Phillipset al. 2020) and for Jupiter as well (Prinn & Barshay1977; Lodders & Fegley 2002). However, for the hottestmodels, this typical trend is reversed, and when oneprobes quite deeply, one reaches more CH -rich gas, inparticular at P >
Fortney et al.
We can examine how atmospheric abundances are af-fected by making plots of volume mixing ratio as a func-tion of planetary T eq . Such a plot is shown in Figure 8,and includes all the profiles shown in Figure 7. The mix-ing ratios at 1 mbar for H O, CO, and CH are plotted,for equilibrium chemistry and for log K zz of 4 and 8.In the equilibrium chemistry case (dashed curves), thechangeover from CO-dominant to CH dominant is atabout T eq = 850 K. As one goes cooler, this also leads toan increase in the H O abundance, as oxygen is liberatedfrom CO (and CO ).If we include quite sluggish vertical mixing, with log K zz = 4 (thin solid line), this boundary shifts dramati-cally left, to a much lower T eq value of only 475 K. Theslopes of the CH and CO curves, vs. T eq , are both quiteshallow compared to the equilibrium chemistry case andone might readily expect both molecules to be seen from ∼
800 to 200 K. Of course how “detectable” a molecule isdepends strongly on the wavelength being investigated,the spectral resolution, and the impact on other opacitysources, like clouds. Given the non-detections of CH with HST at mixing ratios of ∼ − in the Neptune-class planets (See Section 3), here we suggest ∼ − . .However, he 3.3 and 7.8 µ m bands of CH and 4.5 µ mband of CO are strong and could likely yield detectionsat lower mixing ratios, in particular at high spectral res-olution.Interestingly, a look back to Figure 7 might suggestthat log K zz = 8 case might be a bit less extreme in al-tering abundances, even though we are mixing up fromeven hotter layers. The modest pinching together ofthe P–T profiles yields a behavior in Figure 8 (solidline) that is intermediate between the two previous be-haviors, with a crossover T eq of 680 K. Both CO andCH may be seen from T eq ∼
900 to 400 K. The upshothere is that the value of K zz in these atmospheres, andits depth dependence, which is currently unknown, willhave a significant effect on the atmospheric abundancesas a function of T eq , and a wide range of behavior is ex-pected. As discussed later, given that K zz is unlikely tobe constant with altitude, more realistic mixing furthercomplicates this picture.4.1.2. Effects of Planet Mass at a Given Age
In the previous section we examined one particularplanet, a Saturn-like object at different distances fromthe Sun. However, we have already discussed in some de-tail in the Introduction that planets of different massesare expected to have quite different cooling histories(Figure 3).We can begin to address the question of planet masswith three disparate planet examples, with planets of eq (K)-8-7-6-5-4-3-2-1 l og ( V o l u m e M i x i ng R a t i o ) CH H OCO
EqChemK zz =10 K zz =10 Detectable
Figure 8.
The 9
P–T profiles from Figure 7 are plottedat 9 T eq values across the x-axis, with chemical abundancesalong the y-axis. “EqChem” gives the chemical equilibriumabundances at 1 mbar (dashed), while log K zz = 4 and 8are shown as thin solid and thick solid, respectively. In equi-librium, at T eq <
800 K, the CO mixing ratio falls off pre-cipitously, while for log K zz = 4 this falloff is delayed until ∼
500 K cooler. At log K zz = 8 the weakening of CO is alsodelayed and the change in CO abundance with T eq is much“shallower.” The corresponding increases in CH abundancewith lower T eq is again “shallower” for non-equilibrium chem-istry. The loss of H O in the coolest (equilibrium) model isdue to loss of water vapor into water clouds. M J (a super-Jupiter), 1 M J and 0.1 M J (32 M ⊕ , asuper-Neptune). For now we limit ourselves to the same10 × atmospheric metallicity, so as to not change toomany parameters at once. Similar to Figure 7 above,we have computed a range of atmospheric P–T profilesfor these 3 planets, at different distances from the Sun,assuming an age of 3 Gyr and the T int values from Fig-ure 3. These profiles are shown in Figure 9. For clar-ity, profiles are only shown at three distances, 0.1, 0.5,and 2 AU. Along each profile, colored dots, from lowerto higher pressure, show log K zz of 4, 8, and 11, re-spectively. The more massive the planet, the higher thesurface gravity, and the higher pressure at a given tem-perature, in the outer atmosphere. This, however, is re-versed in the deep atmosphere and interior as the highermass planets take longer to cool, so they have a higher T int (333 K, 117 K, and 52 K, respectively for the 10, 1,0.1 M J models) and “hotter” (higher specific entropy)interior adiabat. The much larger scale heights for thelow gravity models means greater physical distances formixing, thus longer mixing times for a fixed K zz , andhence, lower quench pressures.What we are particularly interested in here is howthe role of surface gravity and cooling history work todramatically change the ratio of CO/CH in these at- ransiting Planet Atmosphere/Interior Connection P ( ba r) J J
10 M J Figure 9.
Atmospheric
P–T profiles for 3-Gyr-old plan-ets at 0.1 (red), 1 (blue), and 10 (orange) M J , at 10 × solar.The CO/CH equal-abundance curve is in dashed black. Themodels are at 0.1, 0.5, and 2 AU from the Sun. The color-coded dots show the quench pressure for log K zz = 4, 8,and 11. Higher gravity models have higher pressure photo-spheres, but also have hotter interiors, which causes signifi-cant crossing of profiles. The much larger scale heights forthe low gravity models means greater physical distances formixing, and hence, lower quench pressures. mospheres. We address this scenario in Figure 10. Thisabundance ratio is plotted vs. planetary T eq and we willfirst examine the abundances for equilibrium chemistryat 1 mbar. The “transition” T eq value is 950 K at 10 M J , and 850 K at 1 and 0.1 M J . With sluggish verticalmixing (log K zz = 4), the story becomes more complex,however. The 10 M J planet has a relatively hot interioradiabat, which is essentially the same for all values of T eq , as seen in orange in Figure 9. For such a large valueof T int , the smaller values of T eq becomes essentially ir-relevant. For the lower mass planets, the transition T eq is much lower than in the equilibrium case, reaching 500K. For more vigorous mixing (log K zz = 8), more CH -rich gas is brought up, leading to a hotter transitiontemperature, at 700 K.4.1.3. Effects of Planet Age at a Given Mass
Up until this point, we have examined “old” plane-tary systems that to date make up the vast majority ofthe transiting population. However, studying youngertransiting planets to better understanding evolutionaryhistories is extremely important. First, this would yieldconnections to the directly imaged self-luminous planets,which are predominantly young (Bowler 2016). Second,understanding atmospheric abundances as a function ofplanet age would give us new insight into planetary ther-mal evolution. Third, since parent stars are much more eq (K)-6-4-20246 l og ( C O / CH R a t i o ) J J
10 M J EqChemK zz =10 K zz =10 Figure 10.
The log of the CO/CH ratio for 5 values of T eq for 0.1, 1, and 10 M J model planets, where a subset of theprofiles are shown in Figure 9. In equilibrium (at 1 mbar),the transition T eq for CO/CH =1 (log=0, shaded grey) is at ∼ T eq lower for the 0.1 and 1 M J mod-els. The 10 M J model quenches from CH -richer gas, at high T eq , which yields the opposite behavior. For all three modelplanets, CO and CH exist together in detectable amountsfor a wide swath of T eq values. active when they are young, high XUV fluxes for youngsystems could drive quite interesting photochemistry.In the absence of tidal heating giant planet interiorsinexorably cool as they age, meaning cooler interior adi-abats and lower T int values. In the face of vertical mix-ing, we should expect atmospheric abundances to changethen as well. We examine the effect on a range of P–T profiles for a Jupiter-like example (1 M J , 3 × solar)at 0.15 AU in Figure 11. The values of T int are takenfrom every half-dex in planetary thermal evolution froman age of 10 Myr to 10 Gyr, yielding 7 models from T int of 501 K to 84 K. For moderately irradiated plan-ets like these, the cooling of the interior has little effecton the upper atmosphere (Sudarsky et al. 2003), but weshould expect quite different atmospheric abundanceswhen including vertical mixing. The 3 sets of black dotsin Figure 11 show log K zz of 4, 8, and 11.In Figure 12 we examine the corresponding chemicalabundances for equilibrium and the 3 values of verti-cal mixing strength, as a function of planetary age. Inequilibrium at 1 mbar, the atmosphere is CH domi-nated, and the CO mixing ratio is nearly off the bottomof the plot. However, even very modest vertical mix-ing (log K zz = 4, thin lines) changes the picture. Theatmosphere becomes modestly CO-dominated, and welose essentially all sensitivity to the deeper atmosphereof the planet – the abundances depend very little on2 Fortney et al.
500 1000 1500 2000T (K)20-2-4 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . Figure 11.
Atmospheric
P–T profiles for a 1 M J planet at0.15 AU from the Sun, assuming 3 × solar metallicity. Sevenages, every half dex from 10 Myr to 10 Gyr, with seven valuesof T int (501, 383, 283, 212, 156, 117, 84 K) are shown. Theplanetary surface gravity also changes among the models.The three collections of black dots show quench pressuresfor log K zz = 4, 8, and 11. At depth, hotter profiles areclearly CO rich, while cooler profiles are CH -rich. T int . However with more vigorous vertical mixing, wesee a picture emerge that has much in common with ourunderstanding of non-equilibrium chemistry in browndwarfs. Higher T int values and hotter interiors lead tomore CO and less CH . The plot shows a changeoverfrom CO-dominated to CH -dominated at ∼
200 Myr,at a T int value of ∼
250 K. Again, this is generic be-havior, as more massive objects would transition laterin life (but at higher T int values given their higher pres-sure photospheres and the positions of the CO and CH iso-composition curves), and less massive objects earlier(but at higher T int values, given their lower pressure pho-tospheres). While we expect building up a large sampleof atmospheric spectra size a function of planetary agewill be a challenge, it will be rewarding to have a statis-tical sample to compared to the typical several-Gyr-oldsystems. This could yield important insights into plan-etary cooling history and the vigor of vertical mixingwith age. 4.2. N -NH Transitions
Nitrogen chemistry is predominantly a balance be-tween N and NH , and has been explored and validatedin the brown dwarf context (e.g., Saumon et al. 2000,2003; Cushing et al. 2006; Hubeny & Burrows 2007;Zahnle & Marley 2014). N is favored at high temper-atures (and low pressures) while NH is favored at lowtemperatures (and high pressures). The transition fromN to NH at cooler temperatures has a similar characterto that of CO converting to CH , but it occurs at lower Age (yr)-7-6-5-4-3-2 l og ( V o l u m e M i x i ng R a t i o ) CH H O CO
EqChemK zz =10 K zz =10 K zz =10 Figure 12.
Atmospheric abundances at 1 mbar as func-tion of planetary age, for the
P–T profiles shown in Figure11. In equilibrium (dashed), the cooling of the planet’s in-terior has no effect on the atmospheric abundances, as thetemperatures of the upper atmosphere are essentially con-stant, and the atmosphere could be CH -rich and quite CO-poor. Modest vertical mixing (log K zz =4) yields a muchhigher CO/CH ratio, but abundances that again are es-sentially constant with time. More vigorous mixing, fromhigher quench pressures, samples a much wider range rangeof CO and CH abundances. As the interior cools off theatmosphere transitions from CO-rich to CH rich. temperatures. Understanding non-equilibrium nitrogenchemistry in brown dwarfs has typically been hamperedby two constraints. The first is that N , with no per-manent dipole, has no infrared absorption features, un-like CO. The second is that NH iso-composition curveshave slopes that lie nearly along interior H/He adiabats,meaning that one typically cannot assess a given atmo-sphere’s quench pressure, as all pressures along the adi-abat correspond to nearly the same NH mixing ratio.However, in some sense irradiated planets have the ad-vantage of having relatively more isothermal P–T pro-files, which can remain non-adiabatic to pressure of ∼ if these predominantly radiative at-mospheres have K zz values less than their mostly con-vective brown dwarf cousins, then it may be these moreisothermal radiative parts of the atmosphere where onemay quench the chemistry. We can examine this withthe same Saturn-like P–T profiles we first examined inFigure 7. These profiles, but now with quench pres-sures for N -NH chemistry (Zahnle & Marley 2014),are shown in Figure 13.Underplotted in black are curves of constant NH abundance, falling off at higher temperature and lowerpressure. Underplotted in grey are curves of constant N abundance, falling off at lower temperature and higherpressure. A detailed look at Figure 13, compared to ransiting Planet Atmosphere/Interior Connection iso-composition curves aremore “spread out” than similar curves for CH , suggest-ing a more gradual change in nitrogen chemistry, withtemperature, than for carbon. As the chemical conver-sion times for N → NH are longer than for CO → CH ,the corresponding quench pressures for log K zz = 4, 8,and 11 cm s − are at somewhat higher pressures. Whilefor vigorous mixing (log K zz = 11), all profiles convergeto the same quench pressure (and hence changes in T eq across this range would yield no change in the NH abun-dance, there are a broad ranges of N and NH mixingratios for the log K zz = 4 and K zz = 8 cases.
500 1000 1500 2000T (K)20-2-4-6 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . Nitrogen
Figure 13.
Atmospheric
P–T profiles for old, Saturn-likeplanets ( T int = 75K, g = 10m s − , assuming 10 × metallicity.The models are a 9 incident flux levels, at 0.06, 0.07, 0.1,0.15, 0.2, 0.3, 0.5, 1, 2 AU from the Sun. Three sets of blackdots show the nitrogen quench pressure for log K zz of 4, 8,and 11 cm s − . At higher pressures, note that the spreadbetween all profiles is lessened, both in temperature, andin reference to the NH (black) and N (grey) abundancecurves. Figure 14 shows the mixing ratios of N and NH asa function of planetary T eq . Equilibrium chemistry (at1 mbar) shows a crossover from N -dominant to NH dominant at around 475 K. However, even sluggish ver-tical mixing keeps all of these atmospheres N dominant,while also increasing the NH mixing ratio for all T eq val-ues >
600 K. More vigorous mixing (log K zz = 8) furtherflattens the slope of the NH curve, leading to relativelyabundant NH at essentially all T eq values, as expectedfrom the grouping of most of the log K zz = 8 black dotsin Figure 13. Across the entire phase space, the NH mixing ratios are similar to those of CH (see Figure 8),and are actually even higher for NH than for CH forthe higher T eq values. This suggests that onset of de-tectable CH is these planets should be accompanied byNH as well – one will not need to wait for particularly cold temperatures, compared to the brown dwarfs. Forthose interested in determining the relative abundancesof C, N, and O, to compare to Jupiter’s values (Wonget al. 2004), we note that in these models NH neverbecomes the dominant nitrogen carrier compared to N ,such that the nitrogen abundance determined from NH would only be a lower limit. eq (K)-8-7-6-5-4-3-2-1 l og ( V o l u m e M i x i ng R a t i o ) NH N EqChemK zz =10 K zz =10 Detectable
Figure 14.
The 9
P–T profiles from Figure 13 are plottedat 9 T eq values across the x-axis, with chemical abundancesalong the y-axis. “EqChem” gives the nitrogen chemicalequilibrium abundances at 1 mbar (dashed), while log K zz = 4 and 8 are shown as thin solid and thick solid, respec-tively. In equilibrium, at T eq ∼
480 K, the N and NH mixing ratios crossover, while for all models with verticalmixing, this crossover does not happen. The more vigorousthe vertical mixing, generally, the higher NH mixing ratio,except for the coldest models. Effects of Planet Mass at a Given Age
Previously, in Section 4.1.2 and Figures 9 and 10 weinvestigated the role that surface gravity and cooling his-tory have for the planets. Here, we examine the sameprofiles, but for nitrogen chemistry. Figure 15 showsthese sample
P–T profiles for the 0.1, 1.0, and 10 M J planets, with log K zz = 4, 8, and 11. Compared to thecarbon example from Figure 9, the quench pressures arehigher. For the high gravity (10 M J ) planet in par-ticular, the quench pressure is within the deep atmo-sphere adiabat for log K zz = 8 and 11, and near it forlog K zz = 4. We might expect that the NH abundancewill change little with K zz , similar to a brown dwarfcase (Zahnle & Marley 2014). The deeper one probes,the closer one comes to these adiabats, which lie nearlyparallel to curves of constant NH abundance. Instead,the NH mixing ratio is in some sense a probe of the cur-rent specific entropy of the adiabat, which could proveuseful in constraining thermal evolution models.4 Fortney et al. P ( ba r) J J
10 M J Figure 15.
Atmospheric
P–T profiles for 3-Gyr-old planetsat 0.1 (red), 1 (blue), and 10 (orange) M J , at 10 × solar.The N /NH equal-abundance curve is shown in black. Themodels are at 0.1, 0.5, and 2 AU from the Sun. The color-coded dots show the nitrogen quench pressure for log K zz = 4, 8, and 11. Higher gravity models have higher pressurephotospheres, but also have hotter interiors, which causessignificant crossing of profiles. The much larger scale heightsfor the low gravity models means greater physical distancesfor mixing, and hence, lower quench pressures. Comparedto Figure 9, the nitrogen chemistry quench pressures are athigher pressures than for carbon chemistry. For high gravityand/or cool models, the quench pressure is near or withinthe deep atmosphere adiabat. We can examine the N /NH ratio as a function of T eq for these three planets in Figure 16. The crossover T eq for nitrogen chemistry, in equilibrium, would be ∼
550 Kat 10 M J , 500 K at 1 M J , and 475 K at 0.1 M J . How-ever, even modest vertical mixing dramatically changesthis picture. As the T eq decreases, the quench pressurefalls near or into the deep atmosphere adiabat, even atlow gravity. On Figure 15 this manifests as the N /NH ratio asymptoting to values that depend solely on thespecific entropy of the adiabat, as one might have ex-pected for the specific cases investigated for the Saturn-like planet in Figure 14. Much like the brown dwarfs, atcool temperatures (and especially at high surface grav-ity) planets here are insensitive to K zz .4.2.2. Effects of Planet Age at a Given Mass
Previously in Section 4.1.3 and Figures 11 and 12 wefound that planet age, and hence, the cooling historyand specific entropy of the interior adiabat, can havedramatic effects on the carbon chemistry. Young plan-ets would have quite different abundances (richer in CO)than older planets at the same T eq , all things beingequal. We can investigate the role of cooling historyon the nitrogen chemistry with these same profiles. InFigure 17 we plot the 1 M J profiles from 10 Myr to 10 eq (K)-6-4-20246 l og ( N / NH R a t i o ) J J
10 M J EqChemK zz =10 K zz =10 Nitrogen
Figure 16.
The log of the N /NH ratio for 5 values of T eq for 0.1, 1, and 10 M J model planets, where a subsetof the profiles are shown in Figure 15. In equilibrium (at1 mbar), the transition T eq for CO/CH =1 (log=0, shadedgrey) is at ∼ ∼ exists in detectable amounts for a wide swath of T eq values. Gyr, this time with the nitrogen quench pressures la-beled. The figure is quite similar to 11, but with higherquench pressures, at hotter temperatures. At log K zz = 4, the levels are in the radiative part of the atmo-sphere, but are relatively pinched together. At log K zz = 8 and 11, we find all quench pressure in or very nearthe deep atmosphere adiabats.The effect on the atmospheric mixing ratios of N andNH , shown in Figure 18, are quite straightforward, butdifferent than that found for the carbon chemistry inFigure 12. In equilibrium at 1 mbar, as the atmospherechanges negligibly in temperature, the NH mixing ratio(dashed line) changes little with age. The same is true atlog K zz = 4, albeit it at a higher NH abundance. Sinceboth the log K zz = 8 and 11 quench pressures samplethe deep adiabat, which are nearly parallel NH abun-dance curves, we find essentially the same behavior ofmixing ratio as a function of age, independent of (high) K zz . This is essentially the same as the well-understoodbrown dwarf behavior.4.3. Effect of a Mass-Metallicity Relation on Carbonand Nitrogen
So far we have aimed, as much as possible, to inves-tigate the physical and chemical effects of only alter-ing one or two quantities at a time, including distancefrom the Sun, surface gravity, and T int . Atmospheric ransiting Planet Atmosphere/Interior Connection
500 1000 1500 2000T (K)20-2-4 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . Nitrogen
Figure 17.
Atmospheric
P–T profiles for a 1 M J planet at0.15 AU from the Sun, assuming 3 × solar metallicity. Sevenages, every half dex from 10 Myr to 10 Gyr, with seven valuesof T int (501, 383, 283, 212, 156, 117, 84 K, from Figure 3)are shown. The three collections of black dots show nitrogenquench pressures for log K zz = 4, 8, and 11. At depth, allprofiles are within the N rich region of P–T space, and theadiabats lie parallel to curves of constant NH abundance. Age (yr)-7-6-5-4-3-2 l og ( V o l u m e M i x i ng R a t i o ) NH N EqChemK zz =10 K zz =10 K zz =10 Figure 18.
Atmospheric N and NH abundances at 1 mbaras function of planetary age, for the P–T profiles shownin Figure 17. In equilibrium (dashed), the cooling of theplanet’s interior has almost no effect on the atmosphericabundances, as the temperatures of the upper atmosphereare essentially constant, and the atmosphere would be N rich. Modest vertical mixing (log K zz $ =4) yields a slightlyhigher NH abundance, but still essentially constant withtime. More vigorous mixing, from higher quench pressures(log K zz or 8 and 11), samples progressively more NH -richgas. However, there is little sensitively in these models. metallicity will also play an important role in alteringthese boundaries. This chemistry has certainly be ex-plored before, or a very wide range of compositions (e.g., Moses et al. 2013). In this section we attempt to explorea composition phase space, but in a more narrow sense.It is strongly suggested from the bulk densities of tran-siting giant planets that there is a bulk “mass-metallicityrelation” for the planets (Thorngren et al. 2016), withthe lower mass giant planets being more metal-rich. Theeffect of such a relation at atmospheric abundances isnot yet clear (Kreidberg et al. 2014; Wakeford et al.2017; Welbanks et al. 2019), but there is such a relationin the solar system for carbon (e.g., Atreya et al. 2016),and from standard models of core-accretion planet for-mation theory, albeit with a large spread (Fortney et al.2013).For both the carbon and nitrogen chemistry discussedin Section 4.1.2 and 4.2.1, for the 3 planet masses at 10 × solar, we can examine how an increasing metallicity withlower planet masses may alter the previously examinedtrends. Figure 19 shows P–T profiles for planets at 0.5and 2 AU from the Sun, with the upper panel showingcarbon quench pressures and the lower panel nitrogenquench pressures. The profiles themselves differ some-what from those shown in Figure 9 and 15 as the modelshere use 50 × solar (0.1 M J ), 3 × solar (1 M J ), and 1 × (10 M J ). Since the plots use 3 different metallicities,we also show three different CO/CH equal-abundancecurves (dashed).Compared to our previous investigations into chem-istry at 10 × solar metallicity (Figures 10 and 16), thetwo panels in Figure 20 show a much wider range of be-havior. At higher metallicity, the cooler models “hangon” to CO and N to much cooler T eq values. In equilib-rium the carbon transitions would occur between 1100and 700 K in these models. Even sluggish vertical mix-ing shows a large impact. For instance, with more vig-orous mixing (log K zz = 8), these three transition T eq values are ∼ /NH ratio as a function of T eq for these three planets in Figure 19. The crossover T eq for nitrogen chemistry, in equilibrium, would be ∼
600 Kat 10 M J , 530 K at 1 M J , and 420 K at 0.1 M J . How-ever, even modest vertical mixing dramatically changesthis picture. As the T eq decreases, the quench pressurefalls near or into the deep atmosphere adiabat, even atlow gravity. On Figure 15 this manifests as the N /NH ratio asymptoting to values that depend solely on themetallicity and the specific entropy of the adiabat, asone might have expected for the specific cases investi-gated for the Saturn-like planet in Figure 14.4.4. Putting it Together: The Onset of CH and NH We can summarize, at least for the “old” 3-Gyr plan-ets that have been the baseline for many of calculations,6
Fortney et al. P ( ba r) J J J P ( ba r) J J J Figure 19.
Atmospheric
P–T profiles for 3-Gyr-old plan-ets at 0.1 (red, 50 × ), 1 (blue, 3 × ), and 10 (orange, 1 × ) M J .The CO/CH (upper) and N /NH (lower) equal-abundancecurves at these 3 metallicity values are shown in dashedcurves with the same 3 colors. The models are at 0.1 and0.5 AU from the Sun. The color-coded dots show the quenchpressures for log K zz = 4, 8, and 11 for carbon (upper panel)and nitrogen (lower panel). The nitrogen chemistry quenchpressures are at higher pressures than for carbon chemistry.For high gravity and/or cool models, the quench pressure isnear or within the deep atmosphere adiabat, in particular fornitrogen. the expected rise of detectable CH and NH abun-dances. It is by now well-understood that for the at-mospheres of brown dwarfs that the onset of CH andNH are well-separated in T eff -space. Indeed, the rise ofnear-infrared CH and NH define the T and Y spec-tral classes, at ∼ ∼
600 K respectively (Kirk-patrick 2005; Stephens et al. 2009; Line et al. 2017),although the much stronger mid-IR bands can appearat 1700 K (CH at 3.3 µ m) and 1200 K (NH at 10.5 µ m).However, significantly different P–T profiles of irradi-ated giant planets leads to much different behavior. This eq (K)-6-4-20246 l og ( C O / CH R a t i o ) J J J EqChemK zz =10 K zz =10 Carbon0 200 400 600 800 1000 1200 1400T eq (K)-6-4-20246 l og ( N / NH R a t i o ) J J J EqChemK zz =10 K zz =10 Nitrogen
Figure 20.
The log of the CO/CH ratio (upper panel)N /NH ratio (lower panel) for 5 values of T eq for 0.1, 1,and 10 M J model planets, where a subset of the profiles areshown in Figure 19. In equilibrium (at 1 mbar), the tran-sition T eq for N /NH =1 (log=0, shaded grey, lower panel)is at ∼ ∼ exists in detectable amounts for a wide swathof T eq values. is shown in Figure 21, both for planets at a fixed 10 × solar metallicity (top panel) and for planets that use thenotional mass-metallicity relation (bottom panel), withboth panels using log K zz of 8. For the higher gravityplanets with a large thermal reservoir in their interior,the giant planet behavior is at least similar to that ofbrown dwarfs, with CH coming on for T eq a few hun-dred K hotter for the 1 × solar case at 10 M J (bottompanel). However, beyond that example, a different andricher behavior, driven mostly by the altered tempera-ture structure of irradiated planets, is seen. For all other ransiting Planet Atmosphere/Interior Connection and NH onset isat a similar T eq , and at the higher metallicities (bottompanel) NH can arise at warmer T eq values than CH .Figure 21 is in some ways the central prediction ofthe paper, albeit for a relatively constrained example,as we describe at some length in the Discussion section.The oddly shaped and radiative P–T profiles lead to anexpectation of significantly different behavior than thatalready known for brown dwarfs.
All 10x Solar eq (K)-8-7-6-5-4-3-2-1 l og ( V o l u m e M i x i ng R a t i o ) CH NH J J J
10 M J Detectable
Detectable
With Mass-Metallicity Relation eq (K)-8-7-6-5-4-3-2-1 l og ( V o l u m e M i x i ng R a t i o ) CH NH J J J
10 M J Figure 21.
The log of the CH and NH mixing ratios asa function of T eq for models at 0.1, 0.3, 1, and 10 M J modelplanets at an age of 3 Gyr. The upper panel shows calcu-lations where 10 × solar abundances are used for all models,while the lower panel assumes the mass-metallicity relation(50, 10, 3, and 1 × solar) for the 4 masses, respectively. Forthe range of models, and unlike in brown dwarfs, the onsetof NH is nearly coincident with the onset of CH , and forthe lower masses ( < . M J ), NH onset occurs for warmer T eq values than CH . In this figure log K zz = 8 is assumed. Cloud Formation and Cold Traps
A lesson well-learned from observations of transitingplanet atmospheres to date is that clouds and hazes can readily obscure molecular absorption features. This hastypically been thought of as a hindrance. However, earlywork in this field suggested that the atmospheres of gi-ant planets could potentially be classified based on thepresence or absence of clouds (Marley et al. 1999; Su-darsky et al. 2000, 2003). In the end, it seems likely thatsome mixture will be true – in some ways clouds will helpus understand temperature structures and transport inthese atmospheres, but will also obscure features due toatoms and molecules.However, it seems clear that the role of clouds will notbe a simple function of T eq , as cloud condensation curvescan be crossed at a variety of pressures. At a low pres-sure, perhaps little condensible material will exist. At ahigh pressure, perhaps all cloud material in an opticallythick cloud will be below the visible atmosphere. Theseeffects will depend on the shape of the atmospheric P–T profile, and hence on the specific entropy of the adia-bat (which depends on planet mass and age), in addi-tion to the role of atmospheric metallicity (more metalsmeans more cloud-forming material), and even the spec-tral type of the parent star, which can also alter profileshapes, as discussed below.In some ways this topic is beyond the scope of the pa-per, which is focused on 1D models, but we can motivatethat there will be a diversity in behavior at a given plan-etary T eq with plots that focus on P–T profiles and con-densation curves. First we will examine our trio of warmNeptunes, GJ 436b, GJ 3470b, and WASP-107b. InFigure 22 we replot the same
P–T profiles from Figure5, with chemical information removed, but now includ-ing radiative-convective boundary depths (RCBs) withsquares, and condensation curves for potential cloud-forming materials. These “cooler” clouds, for planetscooler than the hot Jupiters, have been studied in Mor-ley et al. (2012, 2013). Note, however, that Gao et al.(2020) have suggested that most of these cloud species(save KCl) may not nucleate and form. Lee et al. (2018)suggest that Cr, KCl, and NaCl (instead of Na S) willform across this temperature range. These predictionscan be corroborated by future detailed spectroscopic ob-servations of brown dwarfs and planets.The KCl and ZnS cloud bases move little with or with-out tidal heating, as the upper atmospheres change lit-tle. The Na S cloud base, however, can move dramat-ically. Without tidal heating, the cloud base would bearound ∼
300 bars in all three planets. However, fortidal heating with Q = 10 , the Na S cloud base movesto ∼ P–T profiles at 0.15 AU from the Sun. Figure8
Fortney et al.
500 1000 1500 2000T (K)20-2-4-6 P ( ba r) KCl ZnSNa S MnSCr
GJ 3470b, 100xGJ 436b, 100xWASP-107b, 100x
Figure 22.
Atmospheric
P–T profiles for planets GJ 436b,GJ 3470b, and WASP-107b all at 100 × solar abundances,taken from Figure 5. Black dashed curves are for cloud con-densation for various elements from Morley et al. (2012). Foreach planet, 4 interior adiabats are shown, for the case of notidal heating (coolest), and Q = 10 , 10 and 10 , from coolerto warmer. Colored squares show the radiative-convectiveboundary depth. Tidal heating can push cloud formation ofNa S, MnS, and Cr, out of the deep atmosphere, into thevisible atmosphere.
23 shows the same profiles that were explored in Fig-ure 4, now with a focus on RCBs and cloud conden-sation, rather than chemical abundances. The inter-face between these profiles and condensation dependsstrongly on surface gravity. For instance, the denser,higher pressure photosphere of the highest gravity mod-els yields a detached convective zone near 0.2 bar, coin-cidentally at the region of ZnS and KCl clouds, which isnot seen in the lower gravity models. Potentially morevigorous mixing here could lead to thicker clouds andlarger particle sizes. If these profiles were calculated atgreater orbital distances, yielding cooler atmospheres,all would develop this detached convective zone (Fort-ney et al. 2007). The Na S case is also interesting forthese profiles. The cloud base is found in the deep atmo-sphere for the two higher gravity models, but at a fewtenths of bar in the three lower gravity models. Thisclearly shows that at a given T eq , the depth of cloudformation can be significantly impacted by temperatureof the deep atmosphere, which is mitigated by the inte-rior cooling. One could readily imagine other exampleswhere the cloud formation depth is affected by plane-tary age, at a given mass, as is seen in brown dwarfsand self-luminous imaged planets. DISCUSSIONWe wish to stress that the calculations shown here areonly a starting point, and we have considered only what
500 1000 1500 2000T (K)20-2-4 P ( ba r) KCl ZnS Na SMnS Cr
Figure 23.
Model pressure-temperature profile for a 10 × solar atmosphere at 0.15 AU from the Sun, The five profilesfrom Figure 4 show (alternating red and blue) five values of T int , at 52, 77, 117, 182, and 333 K, with respective surfacegravities g =5.8, 9.8, 24, 65, and 225 m s − . Thicker parts ofthe profiles show convective regions. Note that the specificentropy of the deep atmosphere adiabat can move the loca-tion of the Na S cloud into the visible atmosphere (base 1bar for the highest gravity model) or a depth (base at 300bar in the lowest gravity model). The high gravity modelalso has a detached convective zone (coincidentally) at thelocation of ZnS and KCl condensate formation. we believe will be the 1st order effects. In the interest ofbrevity we have not considered several additional factorsthat could or will play important roles in further alter-ing predicted temperature structures and atmosphericabundances. We describe these here:1. We have elected not to self-consistently recalcu-late the atmospheric
P–T profiles for each value of K zz . The altered atmospheric abundances in turnalter the radiative-convective equilibrium profile,as has been explored by several authors, with andwithout stellar irradiation (Hubeny & Burrows2007; Drummond et al. 2018a; Phillips et al. 2020).In particular Drummond et al. (2018a), for HD189733b and HD 209458b, found differences in the P–T profile of up to 100 K. For the arguments pre-sented here, tripling or quadrupling the number ofplotted
P–T profiles (one for every K zz ) would dis-tract from the main point, particularly given thelarge uncertainly today in the K zz profiles. Addi-tionally, including the cloud species discussed herewould alter P–T profiles and chemical transitions(Molaverdikhani et al. 2020).2. We have assumed a constant value of K zz withheight. Mixing length theory is an importantguide to K zz in convective regions, but it is not ransiting Planet Atmosphere/Interior Connection K zz transitions at the radiative-convective boundary, in particular given the 3Dnature of atmospheric mixing. Three-dimensionalGCM runs may be a guide for particular planets ofinterest. Work to date has suggested that as onemoves deeper, to higher pressures in the radiativeregions, that K zz should decrease. This may leadto a “quench bottle neck” of less vigorous mixingjust above the RCB.3. Our models are 1D, however 3D effects havebeen shown to be important in understanding at-mospheric abundances. As has previously beendemonstrated (Cooper & Showman 2006; Ag´undezet al. 2014; Drummond et al. 2018b, 2020), non-equilibrium chemistry is affected by day-nighttemperature differences in addition to verticalmixing. Day-night effects may be minimized forthese relatively cooler planets, compared to thehot Jupiters, as day-night temperature differencesare expected to be more modest at cooler tempera-tures (Lewis et al. 2010; Perez-Becker & Showman2013).4. Non-solar ratios of elemental abundance ratios arelikely to occur. As has been extensively mod-eled over the past decade, planet formation pro-cesses can drive atmospheres towards higher orlower C/O ratios, depending on the formation lo-cation and the relative accretion of solids and gas(e.g., ¨Oberg et al. 2011; Madhusudhan et al. 2014;Mordasini et al. 2016; Espinoza et al. 2017). Morerecently, the role of the nitrogen N ice line as asite of planet formation (Piso et al. 2016; Bosmanet al. 2019; ¨Oberg & Wordsworth 2019) and al-tered N/O and N/C ratios in giant planet atmo-spheres (Cridland et al. 2020) has been investi-gated. Previous radiative-convective atmosphericcalculations have shown that an altered C/O ratiocan alter P–T phase space of major chemical tran-sitions (e.g., Madhusudhan et al. 2011b; Molli`ereet al. 2015).5. Photochemistry will further alter atmosphericabundances. The nonequilibrium abundances thatwe find, based on timescale arguments, are merelythe “raw materials” for further chemical reactions(Zahnle et al. 2009b,a; Moses et al. 2011, 2013;Venot et al. 2020). It is well known that CH in thesolar system can be readily photolyzed, and the de-struction of CH may make it less easily observed,while increasing the abundances of other hydrocar-bons, along with photochemical hazes. We notethat signs of hazes may already be seen in the transmission spectra of the cool transiting giantplanet population (Gao et al. 2020).6. A range of parent star spectral types will be rel-evant across the planetary population. Movingfrom hot stars to cool stars, the peak of the stellarspectral energy distribution moves to redder wave-lengths, and the temperature of the incoming radi-ation field is more similar to that of the planetaryatmosphere, leading to more isothermal tempera-ture structure (Molli`ere et al. 2015), as shown inFigure 24. The range from hotter to cooler parentstars certainly spans at least the range from F toM. Temperature differences of ∼
150 K are seen atat 1-100 bars, the relevant quench pressures for log K zz =8, which straddles the CO/CH equal abun-dance curve. Interestingly, this could be a verynice probe of K zz , as for this example, as muchlower and much higher K zz values, the profiles con-verge back to similar CO/CH abundances.7. A range of planetary eccentricities can impactthe timescale arguments made here, as well asdrive tidal heating. The thermal response of theplanetary atmospheric temperatures, and hencechemistry, depends on the planetary orbit. Thetimescale over which the atmosphere heats up andcools off due to the eccentric orbit will competewith the timescales t mix and t chem that we have ex-plored here. This idea was previously explored forhighly eccentric hot Jupiters by Visscher (2012),but a new study that focuses on cooler planetsappears to be warranted. Tidal heating from theinterior, as shown for planets GJ 436b, GJ 3470b,and WASP-107b in Section 3, should be a rela-tively common process, particularly for the “in-between” planets that are not so close that theywill have circularized quickly, and are not so fartides do not affect the energy budget. Tidal heat-ing should then be investigated for any particulartarget of interest. Assessing the eccentricity of agiven planet may be difficult, if radial velocity datais sparse, or if a secondary eclipse is not detected.8. The radius-inflation mechanism that affects hotJupiters may still operate in the cooler planetswe investigate here. Since Thorngren & Fort-ney (2018) and Thorngren et al. (2019), foundno strong evidence for the mechanism affectingplanets cooler than T eq < Fortney et al. only small effects on the observed radius vs. inci-dent flux distribution, which would be currentlyundetectable in the planetary population. Andany “residual” radius inflation power could be im-portant for the Saturn- and Neptune-class planets,whose interiors would be expect to cool of signif-icantly in the absence of additional power. Thiswould lead to lower CH /CO and NH /N ratiosat a given T eq , compared to our calculations, andcould be an important probe of temperatures inthe deeper atmosphere.
500 1000 1500 2000T (K)20-2-4-6 P ( ba r) - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . M starF starThe Sun
Figure 24.
Atmospheric
P–T profiles for three planets withthe same incident stellar flux. For the profile in black, theplanet is at 0.15 AU. In red is a profile with the GJ 436bparent star (type M2.5), while in blue it is the WASP-17bparent star (type F4). Here log K zz values of 4, 8, and 11 areshown as upper, middle, and lower set of color dots, respec-tively. Large temperature differences are particularly seen atat 1-100 bars, the relevant quench pressures for log K zz =8,which straddles the CO/CH equal abundance curve (dashedblack). The N /NH equal abundance curve is shown indashed gray, for reference.6. CONCLUSIONSThrough a straightforward implementation of 1Dradiative-convective model atmospheres and non-equilibrium chemistry, we have shown that atmosphericabundances of C-, N-, and O-bearing molecules in warmtransiting planets will show a diverse and complex be-havior. This behavior will depend strongly on the cool-ing history of the planet, such that a planet’s mass, age,parent star spectral type, and any ongoing tidal dissi-pation can lead to atmospheric abundances that differfrom planet to planet at the same level of incident stellarflux.Non-equilibrium chemical abundances may then serveas a tool to probe the deeper atmosphere, similar to work recently begun for very cool brown dwarfs (Miles et al.2020). For the three Neptune-class planets discussedin Section 3 (GJ 436b, GJ 3480b, and WASP-107b),we suggest that ongoing eccentricity damping tidallyheats the deep atmospheres of the planets. This raisestemperatures by several thousand degrees and drivesstrong convective mixing, which dramatically decreasesthe CH /CO ratio in the visible atmosphere. This mayplay the dominant role in understanding their observa-tions to date.The more isothermal shape of P–T profiles in irradi-ated planets, compared to brown dwarfs, leads to theexpectation that planetary behavior will differ stronglycompared to brown dwarfs. Perhaps most strikingly, theonset of detectable CH and then NH should occur atvery similar T eq values, and for the Saturn-masses andbelow, a reversal compared to brown dwarf behavior,where NH is seen at warmer temperatures than CH .We have also shown that N will dominate over NH overa wide range of temperatures and ages, such than bulknitrogen abundances determined from NH will only belower limits.To discover the underlying physical and chemicaltrends for these atmospheres, it would likely be the moststraightforward to look for trends at a given mass andage . For instance, in mature planetary systems (say,Gyr+), the Jupiter-mass planets around Sunlike stars at T eq < T int values of ∼
100 K. One could expectto see a trend of increasing CH abundance with lower T eq , with CH becoming dominant at 800 K, as in Fig-ure 10. Note, however, that this potential trend couldreadily be disguised by mixing planets with a range ofmasses into one’s sample, as shown in that same figure.We reiterate that it is not yet known how diverse theatmospheric metallicities of those planets may be, andhow that may change with planetary mass, which wouldalso add scatter to any trend.While retrievals to constrain atmospheric abundancesand temperature structures (see Madhusudhan 2018,for a review) are likely up to the task for determin-ing abundances in planetary transmission and emission,these findings can only properly be interpreted withinthe context of the physical characteristics of the planetand its environment . In particular, since we find that T int can play a significant role in altering abundances, re-trievals that utilize deep atmospheric temperatures thatare guided by thermal (and/or tidal) evolution models,and aim to retrieve the quench pressure depth in ad-dition to molecular mixing ratios, may yield the mostrobust results. The role of planetary structure model-ing, thermal evolution modeling, and physics-driven 1D ransiting Planet Atmosphere/Interior Connection Ag´undez, M., Parmentier, V., Venot, O., Hersant, F., &Selsis, F. 2014, A&A, 564, A73,doi: 10.1051/0004-6361/201322895Artigau, ´E. 2018, Variability of Brown Dwarfs, 94,doi: 10.1007/978-3-319-55333-7 94Atreya, S. K., Crida, A., Guillot, T., et al. 2016, arXive-prints, arXiv:1606.04510.https://arxiv.org/abs/1606.04510Baraffe, I., Chabrier, G., & Barman, T. 2008, A&A, 482,315, doi: 10.1051/0004-6361:20079321Beatty, T. G., Marley, M. S., Gaudi, B. S., et al. 2019, AJ,158, 166, doi: 10.3847/1538-3881/ab33fcBeatty, T. G., Collins, K. A., Fortney, J., et al. 2014, ApJ,783, 112, doi: 10.1088/0004-637X/783/2/112Beichman, C., Benneke, B., Knutson, H., et al. 2014, PASP,126, 1134, doi: 10.1086/679566Benneke, B., Knutson, H. A., Lothringer, J., et al. 2019,Nature Astronomy, 3, 813,doi: 10.1038/s41550-019-0800-5Berardo, D., & Cumming, A. 2017, ApJL, 846, L17,doi: 10.3847/2041-8213/aa81c0Bosman, A. D., Cridland, A. J., & Miguel, Y. 2019, A&A,632, L11, doi: 10.1051/0004-6361/201936827Bowler, B. P. 2016, PASP, 128, 102001,doi: 10.1088/1538-3873/128/968/102001Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J.2001, Reviews of Modern Physics, 73, 719.http://adsabs.harvard.edu/cgi-bin/nph-bib query?bibcode=2001RvMP...73..719B&db key=ASTBurrows, A., Hubeny, I., Budaj, J., Knutson, H. A., &Charbonneau, D. 2007, ApJL, 668, L171,doi: 10.1086/522834Burrows, A., Marley, M., Hubbard, W. B., et al. 1997, ApJ,491, 856Chabrier, G., & Baraffe, I. 2000, ARA&A, 38, 337Cooper, C. S., & Showman, A. P. 2006, ApJ, 649, 1048,doi: 10.1086/506312 Cridland, A. J., van Dishoeck, E. F., Alessi, M., & Pudritz,R. E. 2020, arXiv e-prints, arXiv:2009.02907.https://arxiv.org/abs/2009.02907Cushing, M. C., Roellig, T. L., Marley, M. S., et al. 2006,ApJ, 648, 614, doi: 10.1086/505637Dransfield, G., & Triaud, A. H. M. J. 2020, arXiv e-prints,arXiv:2008.00995. https://arxiv.org/abs/2008.00995Drummond, B., Mayne, N. J., Baraffe, I., et al. 2018a,A&A, 612, A105, doi: 10.1051/0004-6361/201732010Drummond, B., Mayne, N. J., Manners, J., et al. 2018b,ApJ, 869, 28, doi: 10.3847/1538-4357/aaeb28Drummond, B., H´ebrard, E., Mayne, N. J., et al. 2020,A&A, 636, A68, doi: 10.1051/0004-6361/201937153Espinoza, N., Fortney, J. J., Miguel, Y., Thorngren, D., &Murray-Clay, R. 2017, ApJL, 838, L9,doi: 10.3847/2041-8213/aa65caFegley, B. J., & Lodders, K. 1996, ApJL, 472, L37Fortney, J. J., Lodders, K., Marley, M. S., & Freedman,R. S. 2008, ApJ, 678, 1419, doi: 10.1086/528370Fortney, J. J., Marley, M. S., & Barnes, J. W. 2007, ApJ,659, 1661, doi: 10.1086/512120Fortney, J. J., Marley, M. S., Lodders, K., Saumon, D., &Freedman, R. 2005, ApJL, 627, L69, doi: 10.1086/431952Fortney, J. J., Mordasini, C., Nettelmann, N., et al. 2013,ApJ, 775, 80, doi: 10.1088/0004-637X/775/1/80Fortney, J. J., Thorngren, D., Line, M. R., & Morley, C.2017, in AAS/Division for Planetary Sciences MeetingAbstracts Fortney et al.
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