10 Aug 2021 Ets Has Been Observed by HST for Transmission Spectra Temperate Exoplanets (Beichman Et Al

Draft version August 11, 2021 Typeset using LATEX twocolumn style in AASTeX62

Photochemistry and Spectral Characterization of Temperate and Gas-Rich Exoplanets

Renyu Hu1, 2

1Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA 2Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA

ABSTRACT Exoplanets that receive stellar irradiance of approximately Earth’s or less have been discovered and many are suitable for spectral characterization. Here we focus on the temperate planets that have massive H2-dominated atmospheres, and trace the chemical reactions and transport following the photodissociation of H2O, CH4, NH3, and H2S, with K2-18 b, PH2 b, and Kepler-167 e representing temperate/cold planets around M and G/K stars. We ﬁnd that NH3 is likely depleted by photodissociation to the cloud deck on planets around G/K stars but remains intact in the middle atmosphere of planets around M stars. A common phenomenon on temperate planets is that the photodissociation of NH3 in presence of CH4 results in HCN as the main photochemical product. The photodissociation of CH4 together with H2O leads to CO and CO2, and the synthesis of hydrocarbon is suppressed. Temperate planets with super-solar atmospheric metallicity and appreciable internal heat may have additional CO and CO2 from the interior and less NH3 and thus less HCN. Our models of K2-18 b can explain the transmission spectrum measured by Hubble, and indicate that future observations in 0.5 − 5.0 µm would provide the sensitivity to detect the equilibrium gases CH4,H2O, and NH3, the photochemical gas HCN, as well as CO2 in some cases. Temperate and H2-rich exoplanets are thus laboratories of atmospheric chemistry that operate in regimes not found in the Solar System, and spectral characterization of these planets in transit or reﬂected starlight promises to greatly expand the types of molecules detected in exoplanet atmospheres.

Keywords: Exoplanet atmospheres — Extrasolar gaseous planets — Extrasolar ice giants — Mini Neptunes — Habitable zone — Transmission spectroscopy

1. INTRODUCTION tures (Tsiaras et al. 2019; Benneke et al. 2019), and The era of characterizing temperate exoplanets has the spectrum indicates that the planet hosts an atmo- begun. Kepler, K2, and TESS missions have found a sphere dominated by H2, and has H2O and/or CH4 in few tens of exoplanets cold enough for water to con- its atmosphere (Benneke et al. 2019; Madhusudhan et al. dense in their atmospheres in transiting orbits (from the 2020; Blain et al. 2021). TOI-1231 b is another temper- NASA Exoplanet Archive). Another handful of temperate planet suitable for atmospheric studies with transits ate planets may be confirmed in the next few years with (Burt et al. 2021). With > 7 times more collecting area ongoing validation and followup of TESS planet candi- and infrared instruments, JWST will be capable of pro- dates (Barclay et al. 2018). A small subset of these plan- viding a more detailed look into the atmospheres of these arXiv:2108.04419v1 [astro-ph.EP] 10 Aug 2021 ets has been observed by HST for transmission spectra temperate exoplanets (Beichman et al. 2014). (De Wit et al. 2018; Zhang et al. 2018; Tsiaras et al. We refer to the exoplanets that receive stellar irradi- 2019; Benneke et al. 2019). For example, a transmis- ance of approximately Earth’s as “temperate exoplan- sion spectrum obtained by Hubble at 1.1 – 1.7 µm of ets” and those that receive less irradiance by approx- the temperate sub-Neptune K2-18 b shows spectral fea- imately an order of magnitude as “cold exoplanets” in this paper. Temperate and cold exoplanets include both giant planets and small planets and potentially Corresponding author: Renyu Hu have diverse atmospheric composition. Giant planets renyu.hu@jpl.nasa.gov (Jupiters and Neptunes) have massive H2/He envelopes @2021 California Institute of Technology. Government sponsorship acknowledged. (e.g., Burrows et al. 2001), and small planets (mini- Neptunes, super-Earths, and Earth-sized planets) can 2 Hu have H2/He atmospheres with variable abundances of planets and potential areas of further development; and heavy elements, steam atmospheres mostly made of wa- Section5 summarizes the key findings of this study. ter, or secondary atmospheres from outgassing (e.g., Fortney et al. 2013; Moses et al. 2013; Hu & Seager 2. METHODS 2014). In this paper, we focus on temperate/cold and gas-rich 2.1. Atmospheric Structure Model exoplanets, which include temperate/cold giant planets We use the atmospheric structure and cloud for- and mini-Neptunes. We assume that the atmospheres mation model in Hu(2019) to simulate the pressure- are H2/He-dominated and massive enough for thermo- temperature profile and potential gas depletion by con- chemical equilibrium to prevail at depths. This condi- densation in temperate and cold exoplanets. tion determines that the dominant O, C, N, S species We have updated the model with a routine to com- should be H2O, CH4, NH3, and H2S on temperate and pute the condensation of NH4SH cloud, in a similar way cold planets in most cases (e.g., Fegley Jr & Lodders as the equilibrium cloud condensation model of Atreya 1996; Burrows & Sharp 1999; Heng & Tsai 2016; Woitke & Romani(1985). In short, we compare the products et al. 2020). Thermochemical equilibrium may also pro- of the partial pressure of NH3 and H2S with the equi- duce N2 as the dominant N species and substantial abun- librium constant of the reaction that produces NH4SH dance of CO and CO2 if the planet has a hot interior solid (Lewis 1969), and partition the NH3 and H2S in ex- (e.g., Fortney et al. 2020). On temperate and cold plan- cess to form the NH4SH solid cloud in each atmospheric ets, H2O can condense to form a cloud and the above- layer. We have verified that the resulting NH4SH cloud cloud H2O is partially depleted as a result (e.g., Morley density and pressure level is consistent with the previ- et al. 2014; Hu 2019; Charnay et al. 2021). Cold planets ously published models when applied to a Jupiter-like may additionally have NH4SH (from the combination planet (e.g., Atreya et al. 1999). reaction between NH3 and H2S) and NH3 condensed to Another update is that the model now traces the con- form clouds (e.g., Lewis 1969; Atreya et al. 1999). This centration of NH3 in liquid-water cloud droplets when paper primarily concerns the photochemical processes applicable. The model of Hu(2019) has included the above the clouds, with H2O, CH4, NH3, and H2S as the dissolution of NH3 in the liquid-water droplets. By addi- feedstock. tionally tracing the concentration of NH3 in droplets, we Past work on the atmospheric photochemistry of low- have now taken into account the non-ideal effects when temperature and gas-rich planets in the exoplanet con- the NH3 solution is non-dilute. When the mass ratio be- text is rare. Moses et al.(2016) studied the thermo- tween NH3 and H2O in the droplet is > 0.05, we replace chemistry and photochemistry in directly imaged young Henry’s law with the vapor pressure of NH3 in equilib- giant planets, and discussed the photochemical produc- rium with the solution (Perry & Green 2007). The latter tion of CO2 and HCN in their atmospheres. Zahnle merges the solubility in the Henry’s law regime to that et al.(2016) showed that sulfur haze can form photo- in the Raoult’s law regime smoothly. We also apply the chemically in the young Jupiter 51 Eri b, and the level of vapor pressure of H2O in equilibrium with the solution, the sulfur haze would moves upward in the atmosphere which can be substantially smaller than that with pure when the eddy diffusion coefficient increases. Gao et al. water when the solution is non-dilute (i.e., the Raoult’s (2017) further modeled the effect of the sulfur haze on law). While the impact of these processes on the overall the reflected starlight spectra of widely separated giant atmospheric composition of the planets studied in this planets. Here we systematically study the atmospheric paper – planets warmer than Jupiter – is small, these photochemistry of H2O, CH4, NH3, and H2S in low- processes may control the mixing ratio of H2O and NH3 temperature exoplanetary atmospheres and model the in the atmospheres of even colder planets (De Pater et al. abundance of the photochemical gases to guide the fu- 1989; Romani et al. 1989). ture observations of temperate/cold and gas-rich exoplanets. 2.2. Atmospheric Photochemical Model The paper is organized as follows: Section2 describes We use the general-purpose photochemical model in the models used in this study; Section3 presents the Hu et al.(2012, 2013) to simulate the photochemical results in terms of the main behaviors of atmospheric products in the middle atmospheres of temperate and chemistry, key photochemical mechanisms, and the cor- cold exoplanets. The photochemical model includes a responding spectral features in transmission and re- carbon chemistry network and a nitrogen chemistry net- flected starlight; Section4 discusses the prospect to de- work and their interactions (Hu et al. 2012). The photo- tect photochemical gases in temperate and gas-rich exo- chemical model also includes a sulfur chemistry network 3 and calculates the formation of H2SO4 and S8 aerosols matters for long-lived species (e.g., C2H6 in Jupiter). when applicable (Hu et al. 2013). Our choice of lower boundary conditions thus results We have made several updates to the original reac- in conservative estimates of the abundance of long-lived tion network (Hu et al. 2012), and they are listed in Ta- photochemical gases. ble1. We have checked the main reactions that produce, The upper boundary is assumed at 10−4 Pa, i.e., small remove, and exchange C1 and C2 hydrocarbons in the enough so that the peaks of photodissociation of all Jovian atmosphere (Gladstone et al. 1996; Moses et al. species are well within the modeled atmosphere. Fol- 2005) and updated rate constants when more recent val- lowing Gladstone et al.(1996), we assume a zero-flux ues in the relevant temperature range are available in boundary condition for all species except for H, for which the NIST Chemical Kinetics Database. We have added we include a downward flux of 4 × 109 cm−2 s−1 (Waite low-pressure or high-pressure rate constants for three- et al. 1983) to account for ionospheric processes that body reactions if any of them were missing in the orig- produce H. This influx of H was calculated for Jupiter inal reaction rate list. Certain reactions important for and the actual flux can conceivably be different. The the hydrocarbon chemistry do not have a directly usable impact of this additional H is limited to the upper at- rate constant expression in the NIST database; rather mosphere and, in most of our cases, is swamped by the their rates are fitted on experimental data or estimated H from the photodissociation of H2O (see Section 3.4). by Moses et al.(2005). We have also added several re- Since the modeled domain of the atmosphere includes actions that involve NH because it may be produced by the stratosphere and a small section of the upper tro- NH3 photodissociation, and updated the rate constant posphere, the standard mixing-length scaling (Gierasch of an important reaction NH2 + CH4 −−→ NH3 + CH3 & Conrath 1985) is not applicable to estimate the eddy to the latest calculated value. Lastly, we have removed diffusion coefficient. We instead anchor our choice of two reactions that were incorrectly included: CH4 + the eddy diffusion coefficient on the value in the upper 3 2 −1 C2H2 −−→ C2H3 + CH3 and C2H6 + C2H2 −−→ C2H3 + troposphere of Jupiter (∼ 1 × 10 cm s , Conrath & C2H5 because the reactant should have been CH2 –C. Gierasch(1984)) and explore a larger value in the study. The photochemical model is applied to the “strato- Above the tropopause, we assume that mixing is pre- sphere” of the atmosphere, where the “tropopause” is dominantly caused by the breaking of gravity waves and defined as the pressure level where the temperature pro- the eddy diffusion coefficient is inversely proportional to file becomes adiabatic. We define the lower boundary the square root of the number density (Lindzen 1981). of the model as the pressure level 10-fold greater than Because the pressure range of the photochemical the tropopause pressure, and thus include a section of model typically includes the condensation of NH3 and the “troposphere” in the model. These choices are cus- H2O, we have added a scheme to account for the con- tomary in photochemical studies of giant planets’ at- densation of NH3 into the photochemical model, with mospheres (e.g., Gladstone et al. 1996), and reasonable that for H2O already included in the model of Hu et al. because the photochemical products in the stratosphere (2012). In addition, we have added the schemes of (and above the condensation clouds) are the objective of condensation for N2H4 and HCN, the two main photo- the study. Including a section of the troposphere makes chemical gases expected to condense in Jupiter’s upper sure that the results do not strongly depend on the lower troposphere (e.g., Atreya et al. 1977; Moses et al. 2010). boundary conditions assumed. The low-temperature vapor pressures of N2H4 and HCN We apply fixed mixing ratios as the lower boundary are adopted from Atreya et al.(1977) and Krasnopolsky conditions for H2, He, H2O, CH4, NH3, and when ap- (2009), respectively. As such, these gases are treated plicable, H2S according to assumed the elemental abun- in the photochemical model and their production and dance. When interior sources of CO, CO2, and N2 are removal paths including chemical reactions and conden- included in some scenarios (see Section 2.4 for detail), sation are self-consistently computed. This is important fixed mixing ratios are also applied to these gases at because, for example, NH3 above the clouds in Jupiter the lower boundary. We assume that all other species is expected to be completely removed by photodissocia- can move across the lower boundary (i.e., dry deposi- tion and converted to N2H4 and N2, followed by conden- tion when the lower boundary is a surface in terrestrial sation and transport to the deep atmosphere (Strobel planet models) at a velocity of Kzz/H, where Kzz is the 1973; Atreya et al. 1977; Kaye & Strobel 1983a,b; Moses eddy diffusion coefficient and H is the scale height. This et al. 2010). As we will show in Section3, the conden- velocity is the upper limit of the true diffusion velocity, sation of N2H4 and HCN limits their abundance in the which could be damped by the gradient of the mixing middle atmosphere of cold planets like Kepler-167 e. ratio (Gladstone et al. 1996); however, the velocity only For H2S, we make a binary choice: if the cloud model 4 Hu indicates NH4SH formation, we remove sulfur chemistry et al. 1984) and the radiative properties of the sulfur from the model, because NH4SH should completely se- haze particles in the same way as Hu et al.(2013). quester H2S(Atreya & Romani 1985); and we include NH4SH and HCN condensates are treated the same way the sulfur chemistry if NH4SH cloud is not formed. This as NH3 clouds. N2H4 condensates have very low abun- simplifies the calculations of sulfur photochemistry and dance in all models and do not contribute significantly is broadly valid when N/S> 1 in the bulk atmosphere. to the opacity. Thus, our model includes the absorption We calculate the cross-sections and single scattering and scattering of cloud and haze particles when calcu- albedo of ammonia and water cloud particles using their lating the radiation field that drives photochemical re- optical properties (Palmer & Williams 1974; Martonchik actions in the atmosphere.

Table 1. Reactions and rate constants updated with respect to Hu et al.(2012).

Reaction Rate Reason for Update Source

−12 0.5 H + C2H3 −−→ C2H2 + H2 1.2 × 10 T Revise rate Moses et al.(2005) −12 1.93 H + C2H4 −−→ C2H3 + H2 5.0 × 10 (T/298) exp(−6520/T ) Revise rate NIST −10 H + C2H5 −−→ 2 CH3 1.25 × 10 Revise rate NIST −11 −0.9 CH + CH4 −−→ C2H4 + H 9.1 × 10 (T/298) (T > 295 K) Revise rate NIST 1.06 × 10−10(T/298)−1.04 exp(−36/T )(T ≤ 295 K) −14 2.24 CH3 + H2 −−→ CH4 + H 2.31 × 10 (T/298) exp(−3220.0/T ) Revise rate NIST −11 C2H + CH4 −−→ C2H2 + CH3 1.2 × 10 exp(−490.7/T ) Revise rate NIST −11 0.54 C2H + C2H6 −−→ C2H2 + C2H5 2.58 × 10 (T/298) exp(180/T ) Revise rate NIST −14 2.56 C2H3 + H2 −−→ C2H4 + H 3.39 × 10 (T/298) exp(−2530.5/T ) Revise rate NIST −13 C2H3 + C2H5 −−→ 2 C2H4 8.0 × 10 Revise rate Moses et al.(2005) −13 C2H3 + C2H5 −−→ C2H2 + C2H6 8.0 × 10 Revise rate Moses et al.(2005) −12 C2H5 + C2H5 −−→ C2H6 + C2H4 2.4 × 10 Revise rate NIST −11 −0.04 NH + NH −−→ N2H2 8.47 × 10 (T/298) exp(80.6/T ) Add reaction NIST −10 −0.27 NH + NH2 −−→ N2H2 + H 1.5 × 10 (T/298) exp(38.5/T ) Add reaction NIST −10 NH + CH4 −−→ NH2 + CH3 1.49 × 10 exp(−10103/T ) Add reaction NIST −10 NH + C2H6 −−→ NH2 + C2H5 1.16 × 10 exp(−8420.3/T ) Add reaction NIST −12 0.1 NH + OH −−→ NH2 + O 2.94 × 10 (T/298) exp(−5800/T ) Revise rate NIST −11 NH2 + CH4 −−→ NH3 + CH3 5.75 × 10 exp(−6952/T ) Revise rate NIST M −33 −0.6 −32 H + H −−→ H2 k0 = min(8.85 × 10 (T/298) , 1.0 × 10 ) Revise k0; NIST −11 k∞ = 1.0 × 10 Add k∞ Moses et al.(2005) M −29 −1.8 H + CH3 −−→ CH4 k0 = 6.0 × 10 max(T/298, 1.0) Revise k0 at T ≤ 298 K; NIST; −8 −0.5 k∞ = 1.92 × 10 (max(T, 110) exp(−400/ max(T, 110)) Add k∞ Moses et al.(2005)

Fc = 0.3 + 0.58 exp(−T/800) M −18 −3.1 H + C2H −−→ C2H2 k0 = 1.26 × 10 T exp(−721/T ) Add k0 Moses et al.(2005) −10 k∞ = 3.0 × 10 M −30 H + C2H2 −−→ C2H3 k0 = 3.31 × 10 exp(−740/T ) Add k∞ NIST −11 k∞ = 1.4 × 10 exp(−1300/T )

Fc = 0.44 M −24 −1 H + C2H3 −−→ C2H4 k0 = 2.3 × 10 T Add k0; Moses et al.(2005) −10 k∞ = 1.8 × 10 Revise k∞ M −29 −30 H + C2H4 −−→ C2H5 k0 = max(1.3 × 10 exp(−380/T ), 3.7 × 10 ) Revise k0 at T ≤ 300 K; NIST; −15 1.28 k∞ = 6.6 × 10 T exp(−650/T ) Add k∞ Moses et al.(2005)

Fc = 0.24 exp(−T/40) + 0.76 exp(−T/1025) M −19 −3 H + C2H5 −−→ C2H6 k0 = 4.0 × 10 T exp(−600/T )(T > 200 K) Revise k0; Moses et al.(2005) −27 k0 = 2.49 × 10 (T ≤ 200 K) −10 k∞ = 2.0 × 10 M −32 C + H2 −−→ CH2 k0 = 6.89 × 10 Add k∞ NIST −11 k∞ = 2.06 × 10 exp(−57/T ) M −31 CH + H2 −−→ CH3 k0 = 9.0 × 10 exp(550/T ) Revise k0 and k∞ NIST −10 0.15 k∞ = 2.01 × 10 (T/298) Moses et al.(2005)

Table 1 continued 5 Table 1 (continued)

Reaction Rate Reason for Update Source

M −24 −7 CH3 + CH3 −−→ C2H6 k0 = 1.68 × 10 (T/298) exp(−1390/T )(T > 300 K) Revise k0 at T ≤ 300 K; NIST; −18 −3.5 k0 = 6.15 × 10 T (T ≤ 300 K) Add k∞ Moses et al.(2005) −9 −0.5 k∞ = 1.12 × 10 T exp(−25/T )

Fc = 0.62 exp(−T/1180) + 0.38 exp(−T/73)

3 Note—The rate constants of two-body reactions and the high-pressure limiting rate constants of three-body reactions (k∞) have a unit of cm −1 −1 6 −2 −1 molecule s , and the low-pressure limiting rate constants of three-body reactions (k0) have a unit of cm molecule s . The rates of β 2 −1 three-body reactions are k0k∞[M]/(k∞ + k0[M])Fc , where [M] is the number density of the atmosphere, and β = (1 + (log10(k0[M/k∞)) ) . Fc = 0.6 unless otherwise noted. NIST=NIST Chemical Kinetics Database (http://kinetics.nist.gov).

and HCN. The abundance of HCN is low (∼ 10−9) in the troposphere due to the photolysis of NH3 and CH4 2.3. Jupiter as a Test Case occurring at well separated pressure levels, and is limited As a test case, we have applied the coupled cloud by the cold trap near the tropopause (Figure1). These condensation and photochemical model to a Jupiter- behaviors are qualitatively similar to the past models of like planet and compared the results with the mea- Jupiter’s nitrogen photochemistry (Atreya et al. 1977; sured gas abundance in Jupiter and previous models Kaye & Strobel 1983a,b; Moses et al. 2010). of Jupiter’s stratospheric composition (Gladstone et al. Figure1 also indicates that adopting the modeled 1996; Moses et al. 2005; Atreya et al. 1977; Kaye & Stro- pressure-temperature profile that does not have a strato- bel 1983a,b; Moses et al. 2010). Figure1 shows the sphere, while preserving the overall behavior of the pressure-temperature profile, eddy diffusion coefficient, atmospheric photochemistry, would under-predict the mixing ratios of C2H6 and C2H2 by approximately half and the mixing ratios of CH4, NH3, and major photochemical gases of the test case. The atmospheric struc- an order of magnitude. We use the atmospheric structure model adequately predicts the tropospheric temper- ture model in this study for speedy exploration of the ature profile and the pressure level of the tropopause, main photochemical behavior, and one should keep this but it cannot generate a temperature inversion in the context in mind when interpreting the results shown in middle atmosphere (Figure1, panel a). We have run Section3. the photochemical model with the pressure-temperature Another interesting point to make is that the quantum profile measured in Jupiter and the modeled pressure- yield of H in the photodissociation C2H2 has been con- temperature profile (i.e., without the temperature in- vincingly measured to be 100% by recent experiments version) to see how much the photochemical gas mixing (Läuteret al. 2002). When producing the models shown ratios change. as the solid and dashed lines in Figure1, panel c, we We find that the photochemical model can predict the have applied a quantum yield of 16% so that the top- of-atmosphere rate of C2H2 + hν −−→ C2H + H would mixing ratios of C2H6,C2H2, and C2H4 measured in Jupiter’s stratosphere, and the modeled profile of HCN match with the models of Gladstone et al.(1996); Moses is consistent with the upper limit in Jupiter’s upper tro- et al.(2005). Revising the quantum yield to 100%, as posphere when the measured pressure-temperature pro- shown by the dotted lines in Figure1, panel c, slightly file is adopted (Figure1, panel c). The only exception reduces the steady-state mixing ratio of C2H6 and re- is the C H mixing ratio at ∼ 1 Pa, where the mod- duces the mixing ratio of C2H2 and C2H4 by a factor of 2 2 3 eled mixing ratio is greater than the measured value by ∼ 5 in the lower stratosphere (∼ 10 Pa). The photodis- 2 ∼ 3σ. This less-than-perfect performance may be due sociation of C2H2 is the main source of H in the lower stratosphere (e.g., Gladstone et al. 1996) and thus its to the lack of C3,C4, and higher hydrocarbons in our reaction network. For example, Moses et al.(2005) was quantum yield is important for the hydrocarbon chemistry in the lower stratosphere. However, a quantum able to fit the C2H2 mixing ratio at ∼ 1 Pa together with other mixing ratio constraints, with a more com- yield of 100% would result in poor fits to the measured plete hydrocarbon reaction network and specific choices mixing ratios of C2H2 and C2H4, and this potential dis- in the eddy diffusion coefficient profiles for Jupiter’s crepancy suggests that additional consideration of the stratosphere. In terms of nitrogen photochemistry, our atmospheric photochemistry of Jupiter might be war- ranted. We adopt the quantum yield of 100% in the photochemical model finds that NH3 is depleted by photodissociation to the cloud deck, and the vast majority subsequent models. of the net photochemical removal of NH3 becomes N2H4 2.4. Planet Scenarios and then condenses out. A small fraction becomes N2 6 Hu

10-4 10-4 (c) (a) 10-2

10 10-2

Pressure [Pa] 102

104 100 100 200 300 400 500 CH Temperature [K] 4 -4 10 C H 2 6 Pressure [Pa] -2 C H 10 102 2 2 C H 10 2 4 NH 3 2 Pressure [Pa] 10 HCN 104 104 (b) 104 106 108 -2 -1 -12 -10 -8 -6 -4 -2 Kzz [cm s ] 10 10 10 10 10 10 Mixing Ratio

Figure 1. Jupiter as a test case. The planet modeled is a Jupiter-mass and Jupiter-radius planet at a 5.2-AU orbit of a Sun-like star, having an atmospheric metallicity of 3×solar. (a) The solid line is the pressure-temperature profile adopted from Galileo probe measurements and Cassini CIRS measurements in Jupiter (the solid line; Seiff et al. 1998; Simon-Miller et al. 2006) and the dashed line is the pressure-temperature profile calculated by the atmospheric structure model. (b) The eddy diffusion coefficient profile adopted in this work. (c) The calculated mixing ratio profiles of CH4, NH3, and major photochemical products. The solid lines are the results using the measured temperature profile, the dashed lines are the results using the modeled temperature profile (i.e., without the temperature inversion), and the dotted lines are the results using the modeled temperature profile and the photodissociation quantum yield of C2H2 set to unity (see discussion in Section 2.3). In comparison are the abundance data of major hydrocarbons and HCN in Jupiter’s atmosphere, as compiled in Morrissey et al.(1995); Gladstone et al.(1996); Davis et al.(1997); Yelle et al.(2001); Moses et al.(2005). We use the temperate sub-Neptune K2-18 b as a repre- Table 2. Planetary parameters adopted in this sentative case of temperate and gas-rich planets around study. M dwarf stars, and use the gas giants PH2 b and Kepler- Planet K2-18 b PH2 b Kepler-167 e

167 e as the representative cases of temperate and cold 1 Mp (M⊕) 8.63 N/A N/A planets around G and K stars (Table2). The results for 2 3 3 Rp (R⊕) 2.61 9.40 9.96 K2-18 b are generally applicable to temperate (mini- Insolation (Earth) 1.01 1.24 0.0755 )Neptunes of M dwarf stars such as the recently de- Stellar Type MGK tected TOI-1231 b. For K2-18 b, the interior structures, Note—1Benneke et al.(2019). 2Cloutier et al.(2019). thermochemical abundances, and atmospheric circula- 3Berger et al.(2018). 4Wang et al.(2013). 5Kipping tion patterns have been studied (Benneke et al. 2019; et al.(2016). Madhusudhan et al. 2020; Piette & Madhusudhan 2020; Blain et al. 2021; Charnay et al. 2021), but the effects of atmospheric photochemistry remain to be studied. Kepler-167 e is considered a “cold” exoplanet be- The UV spectrum of K2-18 has not been measured cause it only receives stellar irradiation 7.5% of Earth’s. and so we adopt that of GJ 176, a similar M dwarf star The equilibrium cloud condensation model would pre- with the UV spectrum measured in the MUSCLES sur- dict NH3 to condense in its atmosphere and form the vey (France et al. 2016). The reconstructed Ly-α flux uppermost cloud deck, below which NH4SH solids form of GJ 176 is similar to the measured flux of K2-18 (dos and scavenge sulfur from the above-cloud atmosphere. Santos et al. 2020). We adopt the UV spectrum of the In the atmospheres of K2-18 b and PH2 b, only H2O is Sun for the models of PH2 b and Kepler-167 e, even expected to condense and forms the cloud deck – and though Kepler-167 is a K star. Figure2 shows the inci- thus the physical distinction between “temperate” and dent stellar flux at the top of the atmospheres adopted “cold”. in this study. K2-18 b, while having similar total irra- 7

0 carried to the atmosphere above the quench point by 10 vertical mixing. Figures3–5 show the pressure-temperature proﬁles of -2

/nm] 10 the three planets calculated by the atmospheric struc- 2 ture model, and the mixing ratios of major C and N

10-4 molecules at the respective quench points. We adopt the chemical lifetime of the CO ←−→ CH4 and N2 ←−→ NH3 conversions from Zahnle & Marley(2014) and estimate -6 10 the eddy diffusion coefficient in the deep troposphere us- Stellar Flux [W/m K2-18 b ing the mixing-length theory in Visscher et al.(2010). PH2 b 10-8 The eddy diffusion coefficient depends on the assumed Kepler-167 e internal heat flux and has a typical value of ∼ 104 m2 100 200 300 400 500 s−1 at the pressure of 106 −108 Pa. The quench point of Wavelength [nm] CO2 follows that of CO, and similarly, that of HCN oc- Figure 2. Incident stellar flux at the top of the atmospheres curs at a similar pressure and temperature as N2 (Zahnle adopted in this study. & Marley 2014; Tsai et al. 2018). The mixing ratios of gases at the quench points are calculated using the ther- diation as PH2 b, receives considerably less irradiation mochemical equilibrium model of Hu & Seager(2014). in the near-UV. Figure3–5 show that a solar-metallicity atmosphere For these planets, we simulate H2-dominated atmo- is likely deep in the CH4- and NH3-dominated regime spheres having 1 − 100× solar metallicities. The higher- at the quench points on all three planets. Specifically, −8 than-solar metallicity scenario may be particularly in- we find the mixing ratio of CO ≤ 10 , that of CO2 −11 teresting for sub-Neptunes like K2-18 b because of a ≤ 10 , and the mixing ratio of NH3 greater than that proposed mass-metallicity relationship that posits a less of N2 by > 10 folds. With 10×solar metallicity, the at- massive planet should have a higher metallicity (Thorn- mosphere remains CH4-dominated, but the mixing ratio gren et al. 2016). For PH2 b and Kepler-167 e, we as- of CO transported from the deep troposphere can be on sume as fiducial values a surface gravity of 25 m s−2 the order of 10−6 ∼ 10−5 and thus non-negligible. With and an internal heat flux that corresponds to Tint = 100 the assumed internal heat flux and the modeled strength K, similar to the parameters of Jupiter. Changing the of deep tropospheric mixing, the mixing ratio of N2 can surface gravity to 100 m s−2 results in slightly different be comparable to that of NH3 at the quench point. As cloud pressures and above-cloud abundance of gases on N2 does not have strong spectral features and is not a these planets, but do not change the qualitative behav- feedstock molecule for photochemistry, the effect of a iors of the atmospheric chemistry. For K2-18 b we as- hot interior would be mostly seen as a reduction of the sume an internal heat flux that corresponds to Tint = 60 mixing ratio of NH3. The impact of the hot interior is K, similar to that of Neptune. the most significant in the 100×solar-metallicity atmo- −4 In the standard models, we assume that the dominant sphere. Both CO and CO2 have mixing ratios > 10 O, C, N, and S species are H2O, CH4, NH3, and H2S at the quench point, and in the hottest case (PH2 b), at the base of the photochemical domain. Gases and the mixing ratio CO is greater than that of CH4. For aerosols produced in the photochemical domain can be nitrogen, the mixing ratio of NH3 can be reduced by a transported through the lower boundary, and thus the factor of 10 ∼ 100 at the thermochemical equilibrium in standard model setup implicitly assumes that thermo- the deep troposphere. chemical recycling in the deep troposphere effectively re- As a general trend, a higher deep-atmosphere temper- cycles the photochemical products into H2O, CH4, NH3, ature favors CO, CO2, and N2, and reduces the equi- and H2S. Here we quantitatively assess how realistic this librium abundance of NH3. We have thus run variant assumption is based on the quench-point theory (e.g., models for the 10× and 100×solar-metallicity cases, and Visscher & Moses 2011; Moses et al. 2013; Hu & Sea- used the mixing ratios of CH4, CO, CO2, NH3, and N2 ger 2014; Zahnle & Marley 2014; Tsai et al. 2018). In at the quench points as shown in Figures3–5 as the that theory, the “quench point” is defined as the pres- lower-boundary conditions. Technically the mixing ra- sure level where the chemical lifetime of a gas equals tio of deep H2O is also affected, but the photochemi- the vertical mixing timescale (typically at the pressure cal models have lower boundaries that are well above of 107 Pa or higher). The gas is close to thermochemical the base of the water cloud, and are thus immune to equilibrium at the quench point, and its mixing ratio is small changes in the input water abundance. Also, we 8 Hu

0 do not fix the lower-boundary mixing ratio of HCN in 10 these models, because the mixing ratio of HCN at the 101 quench point does not exceed the mixing ratio found by 2 the photochemical models at the lower boundary in any 10 case. We emphasize that specific quantities of the input 3 -4 10 NH3 = 2.6×10 N = 5.5×10-4 CO 2 gas abundance depend on the detailed thermal structure HCN = 2.0×10-7 CH4 104 of the interior, which is related to the thermal history N -4 2 NH3 = 2.9×10 NH -3 3 N2 = 6.3×10 -6 of the planet and exogenous factors like tidal heating, Pressure [Pa] 5 HCN = 6.1×10 10 -3 CH4 = 4.9×10 as well as the strength of vertical mixing in the interior 100× CO = 6.3×10-5 -2 CH4 = 1.7×10 10× CO = 4.5×10-7 -2 6 2 CO = 3.0×10 (Fortney et al. 2020). For example, applying an internal 10 -3 1× CO2 = 1.3×10 heat flux that corresponds to Tint = 30 K (similar to 107 Earth) largely restores the CH and NH dominance for -8 4 3 CO~10 NH /N >10 -11 3 2 CO2~10 the three planets. While these factors are likely uncer- 108 200 400 600 800 1000 1200 1400 1600 tain for many planets to be observed, the standard and Temperature [K] variant photochemical models presented in this paper give an account of the range of possible behaviors that Figure 4. The same as Figure3 but for the planetary parameters of PH2 b and an internal heat flux of Tint = 100 K manifest in the observable part of the atmosphere. (similar to Jupiter).

100 100 101 101 102

102 103

4 3 10 -4 10 CO NH3 = 5.4×10 -4 N2 = 4.0×10 CH -8 -4 CO N 4 HCN = 3.0×10 NH3 = 7.2×10

Pressure [Pa] 2 -3 CH 5 -3 N = 6.4×10 4 10 NH CH = 4.9×10 2 4 -4 3 4 -6 NH = 8.6×10 -6 HCN = 3.8×10 10 3 CO = 1.7×10 N = 2.5×10-4 -8 CH = 4.6×10-2 N2 2 CO2 = 1.8×10 4 -8 -3 HCN = 1.6×10 6 CO = 5.1×10 NH3 CH = 4.9×10-3 10 100× -4 4 -3 CO = 5.0×10 Pressure [Pa] 5 -7 NH = 1.3×10 2 CO = 4.2×10 3 10 -3 10× -9 N2 = 6.2×10 CO2 = 4.4×10 1× HCN = 3.0×10-6 7 100× -2 10 CH4 = 5.0×10 6 10× -3 CO~10-10 10 CO = 1.3×10 -12 1× CO = 1.4×10-4 CO2<10 2 108 200 400 600 800 1000 1200 1400 1600 Temperature [K] 107 CO~10-10 -12 CO2<10 Figure 3. Pressure-temperature profiles of the temperate 108 200 400 600 800 1000 1200 1400 1600 sub-Neptune K2-18 b for varied atmospheric metallicities Temperature [K] and an internal heat flux of Tint = 60 K (similar to Nep- tune). The short horizontal bars show the lower boundary Figure 5. The same as Figure3 but for the planetary of the photochemical model (i.e., the pressure level 10-fold parameters of Kepler-167 e and an internal heat flux of greater than the tropopause pressure). The green and red Tint = 100 K (similar to Jupiter). lines show the equal-abundance boundaries for major carbon and nitrogen gases in a solar-metallicity gas in thermo- pressure dependency differ significantly from model to chemical equilibrium, and the green and red dots show the model. expected quench point for CO and that for N2 respectively. The equilibrium mixing ratios of major C and N molecules K2-18 b: a temperate planet around an M star at the respective quench points are shown. 3.1.1. For K2-18 b, our model predicts that water condenses to form a cloud at the pressure of ≥ 104 Pa for the solar 3 3. RESULTS and 10×solar cases, and at the pressure of ∼ 10 Pa for the 100×solar case. Above the cloud, the mixing ratio 3.1. Main Behaviors of Atmospheric Chemistry of water is depleted by approximately one order of mag- The abundance profiles of the equilibrium gases (H2O, nitude, but not totally depleted. The pressure of cloud CH4, NH3, and H2S) and their main photochemical for the 100×solar abundance case we model is consis- products are shown in Figures6–8. In all models, we tent with predictions of a non-gray radiative-equilibrium find that the main photochemical products are C2H6, model and a 3D climate model, but those models do not C2H2, CO, CO2,N2, HCN, N2O, and elemental sul- predict a water cloud for the solar and 10×solar abun- fur haze, but the abundance of these species and their dance (Blain et al. 2021; Charnay et al. 2021). Given 9

10-2 (a) Solar

100

102 Pressure [Pa] Pressure

Sulfur Haze 104 Water Cloud

10-2 (b) 10x Solar

NH CH 3 100 4 C H N 2 6 2 C H HCN 2 2 H O CO 2 2 CO H S 10 2 2 Pressure [Pa] Pressure Sulfur Haze

104 Water Cloud

10-2 (c) 100x Solar

100 Pressure [Pa] Pressure 102 Sulfur Haze Water Cloud

10-10 10-8 10-6 10-4 10-2 100 Mixing Ratio Figure 6. Modeled abundances of main gases and photochemical products in the temperate sub-Neptune K2-18 b for varied metallicities. Solid lines show the photochemical model results and the dashed lines show the equilibrium cloud condensation model results for comparison. Dotted lines in Panels (b) and (c) show the photochemical model results that adopt the quench- point abundances of CH4, CO, CO2, NH3, and N2 (Figure3) at the lower boundary. the small degree of water depletion found in our mod- tropospheric source of CO and CO2 is applied to the els, this discrepancy does not lead to substantial errors bottom of the photochemical domain, the mixing ratio in the results of the above-cloud photochemistry. of CO at 102 Pa is ∼ 1 ppm for the 10×solar cases, but Both CH4 and H2O are photodissociated at the pres- it can reach ∼ 4000 ppm for the 100×solar case. The 2 sure of approximately 0.1 – 1 Pa. The photodissociation mixing ratio of CO2 at 10 Pa can reach ∼ 500 ppm for results in the formation of C2H6,C2H2, CO, and CO2. the 100×solar case. C2H2 has a high mixing ratio at the pressure where the NH3 is photodissociated at the pressure of 1 ∼ 10 photodissociation takes place but is quickly depleted to- Pa. The photodissociation results in the formation of wards higher pressures. In the middle atmosphere (∼ 10 N2 and HCN with similar yields. The mixing ratio of 3 2 – 10 Pa), CO, CO2, and C2H6 can have a mixing ratio HCN at ∼ 10 Pa is ∼ 6, 50, and 500 ppm for the solar, of ∼ 1 parts-per-million (ppm) for the 100×solar abun- 10×solar, and 100×solar abundance cases, respectively. dance case, and the mixing ratio of these photochemical If the mixing ratio of NH3 in the deep troposphere is ap- gases is < 1 ppm for lower metallicities. When the deep plied to the bottom of the photochemical domain, the 10 Hu

10-2 (a) Solar

100

102 Pressure [Pa]

Sulfur Haze 104 Water Cloud

10-2 (b) 10x Solar

0 CH NH 10 4 3 C H N 2 6 2 C H HCN 2 2 H O 2 CO 2 10 CO H S 2 2 Pressure [Pa] Sulfur Haze 4 10 Water Cloud

10-2 (c) 100x Solar

100

Pressure [Pa] 102

Water Cloud Sulfur Haze

10-10 10-8 10-6 10-4 10-2 100 Mixing Ratio

Figure 7. Modeled abundances of main gases and photochemical products in the temperate gas giant PH2 b for varied metallicities. Solid lines show the photochemical model results and the dashed lines show the equilibrium cloud condensation model results for comparison. Dotted lines in Panels (b) and (c) show the photochemical model results that adopt the quench- point abundances of CH4, CO, CO2, NH3, and N2 (Figure4) at the lower boundary. resulting mixing ratio of HCN does not change signiﬁ- 3.1.2. PH2 b: a temperate planet around a G/K star cantly in the 10×solar case but decreases to ∼ 100 ppm in the 100×solar case. PH2 b has a slightly higher insolation and temperature than K2-18 b, but it receives much more near-UV irra- Lastly, H2S is photodissociated at approximately the same pressure as the water cloud. The photodissociation diation (Figure2). The water condensation and small degree of depletion above the cloud, as well as the pho- leads to the formation of elemental sulfur (S8) haze, as predicted previously (Zahnle et al. 2016). The haze layer todissociation of H2S and the location of the sulfur haze extends to an altitude only slightly higher than the water layer, are similar to those predicted for K2-18 b. cloud deck. CH4 is photodissociated at the pressure of 0.1 – 1 Pa, and H2O is photodissociated at 1 – 10 Pa. The main products of these photodissociations are still C2H6, 11

10-2 (a) Solar

100

102 Pressure [Pa]

104

NH4SH Haze

10-2 (b) 10x Solar

0 10 CH 4 NH C H 3 2 6 N C H 2 2 2 HCN 2 10 CO H O CO 2 Pressure [Pa] 2

104

NH4SH Haze Water Cloud 10-2 (c) 100x Solar

100

Pressure [Pa] 102

NH4SH Haze WaterW t Cloud Cl d 10-10 10-8 10-6 10-4 10-2 100 Mixing Ratio

Figure 8. Modeled abundances of main gases and photochemical products in the cold gas giant Kepler-167 e for varied metallicities. Solid lines show the photochemical model results and the dashed lines show the equilibrium cloud condensation model results for comparison. Dotted lines in Panels (b) and (c) show the photochemical model results that adopt the quench- point abundances of CH4, CO, CO2, NH3, and N2 (Figure5) at the lower boundary.

C2H2, CO, and CO2. Instead of CO in the case of K2- As a striking diﬀerence from the M star case (K2- 18 b, CO2 is the most abundant photochemical gas in 18 b), NH3 is fully depleted by photodissociation above 3 the middle atmosphere (∼ 10 – 10 Pa), and its mixing the water cloud deck. The mixing ratio of NH3 in the ratio is 2 – 10 ppm, 5 – 40 ppm, and 40 – 200 ppm middle atmosphere is minimal. The photodissociation for the solar, 10×solar, and 100×solar abundance cases, also leads to the formation of N2 and HCN, with HCN respectively. The mixing ratio of CO is less by approx- being the most abundant photochemical product. The imately one order of magnitude, and that of C2H6 is mixing ratio of HCN in the middle atmosphere reaches ∼ 1 ppm for the 100×solar case and < 1 ppm for lower ∼ 100, 700, and 10,000 ppm for the solar, 10×solar, and metallicities. 100×solar abundance cases, respectively. 12 Hu

With a Jupiter-like internal heat flux, the equilibrium be detectable on temperate planets around M stars but chemistry in the deep troposphere may substantially not around G/K stars (see Section 3.5). change the chemical composition in the photochemical The root cause of this different behavior is the M stars domain. In the 10×solar cases, the mixing ratio of CO (represented by GJ 176 here) emit substantially lower in the middle atmosphere can reach ∼ 10 ppm and that irradiation at the near-UV wavelengths than the G/K of CO2 ∼ 60 ppm. HCN would no longer be the most stars (represented by the Sun here, Figure2). The ra- abundant nitrogen product, and its mixing ratio in the diation that dissociates NH3 in the H2-dominated at- middle atmosphere can be reduced to ∼ 40 ppm. In the mosphere is the radiation that is not absorbed by the 100×solar cases, both CO and CO2 can have very high typically more abundant CH4 and H2O. NH3 has a dis- −2 mixing ratios (> 10 , and on the same order of CH4) in sociation limit at ∼ 230 nm while CH4 at ∼ 150 nm the middle atmosphere, and the above-cloud H2O would and H2O at ∼ 240 nm, but the cross section and the be consumed by photochemistry and have a mixing ratio shielding effect of H2O is small > 200 nm (Hu et al. 2 of ∼ 10 ppm at 10 Pa. The mixing ratio of HCN would 2012; Ranjan et al. 2020). C2H2 also absorbs photons be further reduced to ∼ 10 ppm, while still marginally up to ∼ 230 nm but it typically does not strongly inter- greater than the mixing ratio at the quench point. fere with the NH3 photodissociation due to its relatively low abundance. Thus, photons in 200 – 230 nm are the 3.1.3. Kepler-167 e: a cold planet around a G/K star most relevant for the photodissociation of NH3 in K2- The atmosphere of Kepler-167 e is much colder than 18 b and PH2 b, and photons in 150 – 230 nm are the that of K2-18 b or PH2 b, and its atmospheric chemistry most relevant for Kepler-167 e. Having similar bolomet- is more akin to that of Jupiter (Gladstone et al. 1996; ric irradiation, the photon flux in 200 – 230 nm received Moses et al. 2005; Atreya et al. 1977; Kaye & Strobel by PH2 b is more than that received by K2-18 b by > 2 1983a,b; Moses et al. 2010). Both H2O and H2S are fully orders of magnitude (Figure2). The photon flux re- depleted by condensation or NH4SH formation, and the ceived by Kepler-167 e is one-order-of-magnitude more uppermost cloud predicted by the atmospheric structure than K2-18 b, and the removal of NH3 by condensa- model is NH3 ice. However, the steady-state results of tion further pushes down the pressure of photochemical the photochemical model indicate that photodissocia- depletion (see below). tion of NH3 should deplete the NH3 ice cloud. NH3 is photochemically depleted to the pressure of 7×104 – 103 3.2.1. Criterion of Photochemical Depletion Pa from the solar to 100×solar abundance cases. The How does the photon flux control the pressure of pho- main product of the photodissociation that can accumu- tochemical depletion? Guided by the numerical results, late in the middle atmosphere is N2, while the mixing here we develop a simple theory that estimates the pres- ratios of HCN and N2H4 are limited by condensation. sure of photochemical depletion. Assuming that pho- The mixing ratio of HCN can reach > 1 ppm below the todissociation is the only process that removes NH3 with condensation level in the 100×solar case. no recycling or production, its mixing ratio profile at the The main photochemical gases of carbon are C2H6 and steady state should obey the following differential equa- C2H2, with no CO or CO2 at appreciable mixing ratios. tion: d df While the mixing ratio of C2H2 strongly peaks at 0.1 KN = fNJ, (1) Pa, where the photodissociation of CH4 takes place, the dz dz mixing ratio of C2H6 can be significant in the middle at- where z is altitude, K is the eddy diffusion coefficient, 2 mosphere. At 10 Pa, the mixing ratio of C2H6 is ∼ 2, N is the total number density of the atmosphere, f is 4, and 30 ppm for the solar, 10×solar, and 100×solar the mixing ratio, and J is the photodissociation rate abundance cases, respectively. If the deep tropospheric (often referred to as the “J-value” in the atmospheric source of CO and CO2 is applied to the bottom of the chemistry literature). The number density has a scale photochemical domain, they can have substantial mix- height of H, and the equation can be rewritten as ing ratios in the 100×solar case, while the mixing ratio d2f 1 df J of C2H6 is not strongly impacted. − − f = 0. (2) dz2 H dz K 3.2. Photochemical Depletion of NH3 Assuming J, H, and K to be a constant with respect to From Figures6–8, we see that NH 3 is depleted to z, the equation above has the analytical solution as the cloud deck in temperate and cold planets around r G/K stars but remain intact in the middle atmosphere z 1 1 4J αz f = f exp − + ≡ f exp − , of temperate and cold planets around M stars. This 0 2 H H2 K 0 H finding is significant because it implies that NH3 should (3) 13

101 where f0 is the mixing ratio at the pressure of photochemical depletion (z = 0 for simplicity), and α is

r 102 1 4JH2 α = 1 + − 1 . (4) 2 K 103 Therefore, when the product 4JH2/K is small, α → 0 and the mixing ratio profile is close to a constant; and Pressure [Pa] K2-18 b 2 4 when 4JH /K is large, α can be 1 and thus the 10 PH2 b mixing ratio drops off very quickly. This explains the Kepler-167 e vertical profiles of NH3 seen in Figures6-8. 105 Going back to Equation (1), which can be integrated 1014 1015 1016 1017 1018 1019 from the pressure of photochemical depletion to the top K N f /H or I [m-2 s-1] 0 0 of the atmosphere, as Figure 9. Pressure of photochemical depletion of NH3 ∞ df df Z predicted by the criterion in Equations (9) and (10). We KN |z=∞ − KN |z=0 = n(z)J(z)dz, (5) dz dz 0 compare the left-hand side (solid line) and right-hand side (dashed line) of Equation (10), assuming a solar-abundance where n ≡ fN is the number density of NH3. Assuming atmosphere. Where the solid line and the dashed line meet that the photoabsorption of NH3 itself is the sole source defines the pressure of photochemical depletion. of opacity, J can be expressed as Z ∞ not depend on the mean cross section. Similarly, the 0 0 J(z) = J∞ exp(−σ n(z )dz ), (6) criterion will be applicable to any molecule subject to z photodissociation in a wavelength range largely free of where J∞ is the top-of-atmosphere J-value and σ is the interference by other molecules. mean cross section of NH3. The differential of Equation It should be noted that Equation (9) cannot be de- (6) is rived by requiring the pressure of photochemical deple- dJ tion to occur roughly at the optical depth of unity for the = σnJ. (7) dz photodissociating radiation. This is because the mixing Combining Equations (5) and (7), and recognizing df/dz ratio profile in Equation (3) is valid only locally and de- vanishes at z = ∞, we obtain pends on J, which in turns depends on the vertical profile of the mixing ratio. As such, one cannot integrate Z ∞ df 1 dJ J∞ − J(z = 0) Equation (3) directly to find the pressure of photochem- −KN |z=0 = dz = . (8) dz σ 0 dz σ ical depletion, and the optical-depth-of-unity condition is not as predictive as Equation (9). With J(z = 0) ∼ 0 (i.e., the J-value immediately below The left-hand side of Equation (9) can be evaluated the pressure of photochemical depletion is minimal), and locally using Equation (3), and Equation (9) becomes J∞ = σI, where I is the photon flux at the top of the αKN f atmosphere, we obtain 0 0 = I, (10) H df −KN | = I. (9) where N and f is the total number density and the dz z=0 0 0 mixing ratio at the pressure of photochemical depletion. Note that to derive Equation (9), no specific profiles for The pressure is thus P0 = N0kbT where kb is the Boltz- J or n (f) need to be assumed. mann constant and T is temperature. α can be evalu- The physical meaning of Equation (9) is that the num- ated with Equation (4) for a J value that corresponds ber of NH3 molecules that diffuse through the pressure to 5% of the top-of-atmosphere value. Equation (10) of photochemical depletion should be equal to the num- thus provides a closed-form criterion that determines ber of photons received at the top of the atmosphere. the pressure of photochemical depletion, and explains This physical condition would become evident if one re- why the pressure of photochemical depletion is sensi- gards the column of NH3 above the pressure of photo- tive to the top-of-atmosphere flux of photons that drive chemical depletion as a whole and recognizes that one photodissociation. photon dissociates one molecule. To the extent that the Figure9 shows both sides of Equation (10) for the photoabsorption of NH3 itself is the dominant source three planets modeled assuming a solar-abundance at- of opacity, the criterion expressed by Equation (9) does mosphere. We can see that the pressure of photochem- 14 Hu ical depletion implied by Equation (10) for K2-18 b is sure of photochemical depletion of H2S, the feedstock of ∼ 100 Pa, consistent with the pressure where the photo- sulfur haze, decreases for a greater eddy diffusion coef- chemical model starts to substantially deviate from the ficient. Second, a stronger eddy diffusion helps increase equilibrium cloud condensation model (Figure6). Fig- the lifetime of haze particles against falling (see the for- ure6 also shows that the mixing ratio NH 3 decreases mulation in Hu et al. 2012). For PH2 b, the extended very slowly near the pressure of the photochemical de- sulfur haze layer further keeps NH3 from photochemical pletion, but the decrease becomes faster for lower pres- depletion by absorbing the ultraviolet photons that can 2 sures, where the J value and the 4JH /K product be- dissociate NH3. come greater (see Equations3 and4). The mixing ra- The sensitivity of main photochemical gases’ abun- −6 tio of NH3 eventually drops below 10 at the pressure dance to the eddy diffusion coefficient is complex (Fig- lower than the pressure of photochemical depletion by ure 10), which indicates several factors at work. For N2 approximately one order of magnitude. The pressures and HCN (the dominant photochemical gases of nitro- of photochemical depletion implied by Equation (10) for gen), their mixing ratios at the lower boundary decrease PH2 b and Kepler-167 e are close to or below the cloud with the eddy diffusion coefficient. This is because, in deck (i.e., 104 −105 Pa), which is consistent with numer- our model, gases move across the lower boundary at a ical finding that NH3 is photodissociated to the cloud velocity that is proportional to the eddy diffusion coef- deck on these planets (Figures7 and8). Therefore, ficient, and the loss to the lower boundary is the main although Equation (10) cannot replace the full photo- loss mechanism for both N2 and HCN. Their mixing ra- chemical calculation due to the underlying assumptions tios in the middle atmosphere do not necessarily follow (e.g., no recycling or production, self-shielding only), it the same trend as that also depends on the photochem- provides a guiding estimate of whether a gas is likely de- ical production (see Section 3.3). The abundance of the pleted by photodissociation in the middle atmosphere. photochemical gases of carbon does not depend on the eddy diffusion coefficient monotonically, and this is be- 3.2.2. Sensitivity to the eddy diffusion coefficient cause the formation rates of CO, CO2, and C2H6 largely depend on the abundance of H, OH, and O, which is From the criterion of photochemical depletion (Equa- in turn controlled by the full chemical network involv- tion 10), we see that when the eddy diffusion coefficient ing the photodissociation of CH ,H O, and NH (see increases, the pressure of photochemical depletion de- 4 2 3 Section 3.4). For example, in K2-18 b with the solar creases. In other words, stronger mixing would sustain metallicity, both CO and CO have very small mixing a photodissociated gas (e.g., NH ) to a lower pressure or 2 3 ratios in the middle atmosphere in the standard case; higher altitude. We have used the photochemical model the two would be substantially more abundant in the to conduct a sensitivity study of the eddy diffusion coef- middle atmosphere with a 10-fold greater eddy diffusion ficient, and the results confirm this understanding (Fig- coefficient, and CO would become more abundant than ure 10). The most significant sensitivity happens with CO with a 100-fold greater eddy diffusion coefficient. PH2 b: the standard model predicts the photodissoci- 2 These examples highlight the richness and complexity ation would deplete NH to the cloud deck, while with 3 of atmospheric photochemistry in temperate and cold a 10-fold or 100-fold greater eddy diffusion coefficient, 2 3 planets. NH3 would be depleted at 10 ∼ 10 Pa. For Kepler- 167 e, with a 10-fold or 100-fold greater eddy diffusion coefficient, photodissociation can no longer deplete the 3.3. Photolysis of NH3 in the Presence of CH4 NH3 ice cloud, while the mixing ratio of NH3 in the mid- A common phenomenon that emerges from the pho- dle atmosphere remains small due to condensation and tochemical models is the synthesis of HCN in temper- photodissociation above the cloud deck. ate and H2-rich exoplanets. The photodissociation of The top of the sulfur haze layer moves up in the at- NH3 in Jupiter leads to N2 but not significant amounts mosphere when the eddy diffusion coefficient increases. of HCN, and this is mainly because NH3 is dissociated For both K2-18 b and PH2 b, the top of the sulfur haze at much higher pressures than CH4 (e.g., Atreya et al. would be at ∼ 103 Pa and 102 Pa for 10-fold and 100-fold 1977; Kaye & Strobel 1983a,b; Moses et al. 2010). HCN greater eddy diffusion coefficient (Figure 10). A haze in Titan’s N2-dominated atmosphere mainly comes from layer that extends to 102 Pa would greatly interfere with the reactions between atomic nitrogen and hydrocar- transmission spectroscopy and also affect the spectra of bons and the associated chemical network (Yung et al. the reflected starlight (see Section 3.5). This trend is 1984; Lavvas et al. 2008; Krasnopolsky 2014; Vuitton consistent with the findings of Zahnle et al.(2016) and is et al. 2019). Similar processes, as well as the reac- produced by two effects acting together. First, the pres- tions between CH and NO/N2O may also lead to for- 15

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K2-18 b

10-2 C H 2 6 C H 2 2 CO 100 CO 2 NH 3 N 2 102 HCN Pressure [Pa]

104

PH2 b 10-2

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102 Pressure [Pa]

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Kepler-167 e

10-10 10-8 10-6 10-4 10-2 Mixing Ratio

Figure 10. Sensitivity of the abundance profiles of NH3 and main photochemical gases to the eddy diffusion coefficient. The profiles of H2O and CH4 are not shown because their abundance in the middle atmosphere is not sensitive to the eddy diffusion coefficient. The horizontal orange lines show the top of the sulfur haze layer. The solid lines show the standard model, and the dashed and dash-dot lines show the models with 10-fold and 100-fold greater eddy diffusion coefficients, respectively. These models assume the solar abundance. A greater eddy diffusion coefficient causes the photodissociation of NH3 to occur at a lower pressure. mation of HCN on early Earth or rocky exoplanets Agúndezet al. 2014) and photochemistry (Line et al. with N2-dominated atmospheres irradiated by active 2011; Kawashima & Ikoma 2018; Hobbs et al. 2019). stars (Airapetian et al. 2016; Rimmer & Rugheimer Here we show that HCN can also build up to significant 2019). In addition, the formation of HCN has been amounts in temperate exoplanets with H2-dominated at- commonly found in warm and hot H2-rich exoplanets mospheres. (e.g., Moses et al. 2011; Line et al. 2011; Venot et al. Figure 11 shows the chemical network that starts with 2012; Agúndezet al. 2014; Mollièreet al. 2015; Moses the photodissociation of NH3 and ends with the forma- et al. 2016; Blumenthal et al. 2018; Kawashima & Ikoma tion of N2 and HCN as the main photochemical prod- 2018; Molaverdikhani et al. 2019; Hobbs et al. 2019; Lav- ucts. The key condition for the synthesis of HCN is the vas et al. 2019), and the mechanisms identified include photodissociation of NH3 in the presence of CH4 and at quench kinetics (Moses et al. 2011; Venot et al. 2012; a temperature >∼ 200 K. This condition allows CH3, 16 Hu

C2H5N whose photodissociation produces N2, or with H to re- C2H3 hv turn to NH2 (Figure 11). The other loss of NH2 is to react with CH3, CH3 hv hv NH2 CH5N HCN NH2 + CH3 −−→ CH5N, (R6) H NH2 H followed by photodissociation to form HCN, H, H2 NH3 N2H4 N2H3 hν CH5N −−→ HCN + 2 H2 · (R7) N2H3 hv N2H3 NH hv Reaction (R6) is the critical step in this HCN formation NH N2H2 N2 NH2 mechanism, and it requires the CH3 radical to be available. The CH3 in Reaction (R6) is mainly produced by Figure 11. Chemical network from the photodissociation of NH3 in temperate and H2-dominated atmospheres. Not H + CH4 −−→ H2 + CH3 · (R8) all reactions are shown, and the importance of the shown Note that the photodissociation of CH , which also reactions changes from case to case. In the presence of CH4, 4 HCN is one of the main photochemical products. produces CH3, does not contribute signiﬁcantly to the source of CH3 in Reaction (R6) because the photodisso- one of the ingredients for the synthesis of HCN, to be ciations of CH4 and NH3 typically occur at very diﬀerent pressures. Another formational path of HCN is through produced locally by the reaction between CH4 and H, and this H is produced by the photodissociation of NH3 itself. We describe the details as follows. NH2 + C2H3 −−→ C2H5N, (R9) The photodissociation of NH3 mainly produces NH2, followed by photodissociation

hν hν NH3 −−→ NH2 + H, (R1) C2H5N −−→ HCN + CH3 + H · (R10) and some of the NH2 produced is returned to NH3 via The C2H3 in Reaction (R9) is mainly produced by

M NH2 + H2 −−→ NH3 + H, (R2) H + C2H2 −−→ C2H3, (R11) and and C2H2 is ultimately produced by the photodissocia- M NH2 + H −−→ NH3 · (R3) tion of CH4 and then transported to the pressure of the photodissociation of NH . The HCN produced in Reac- Another channel of the photodissociation of NH is to 3 3 tions (R7 and R10) is photodissociated to form CN but produce NH CN quickly reacts with H2 and C2H2 to return to HCN. hν Thus, HCN does not have significant net chemical loss NH3 −−→ NH + H2 · (R4) and is transported together with N2 through the lower boundary. The NH2 channel requires photons more energetic than 230 nm and the NH channel requires photons more ener- The NH3-CH4 coupling (Reactions R6–R8) dominates getic than 165 nm. Therefore, the photons that produce the formation of HCN over the NH3-C2H2 coupling (Reactions R9–R11) in temperate H2-dominated atmo- NH is more easily shielded by H2O and CH4. For the three planets modeled, the NH channel is important in spheres by several orders of magnitude. This is because K2-18 b and Kepler-167 e, but not in PH2 b. This is the mixing ratio of C2H2 at the the pressure of NH3 photodissociation is typically very small on temperate because the photodissociation of NH3 occurs at higher pressures in PH2 b and is object to the shielding effect planets like K2-18 b and PH2 b (Figures6 and7). On colder planets like Kepler-167 e, more C2H2 is available of both H2O and CH4. The NH channel mostly leads to and the NH3-C2H2 coupling can contribute 1–10% of the N2 (Figure 11). HCN formation, consistent with the results for Jupiter The NH2 that is not recombined to form NH3 can undergo (Moses et al. 2010). We also note that past models of warm and hot H2-rich exoplanets suggested different re- NH2 + NH2 −−→ N2H4, (R5) actions to represent the NH3-CH4 coupling, including and the N2H4 produced (if not condensed out) can then NH + CH3 (Line et al. 2011) and N + CH3 (Kawashima become N2H3.N2H3 can react with itself to form N2H2, & Ikoma 2018; Hobbs et al. 2019); in our models the 17 contribution from N + CH −−→ HCN + H contributes H2O 3 2 CH CH OH to the formation of HCN less than Reactions (R6–R8) 2 H2O by > 3 orders of magnitude. H The efficacy of the NH path to produce N and HCN O H 2 2 CH3 CH2O CHO and the branching between N2 and HCN depend on the O O abundance of H and the temperature. Reaction (R8) hv has an activation energy of 33.60 kJ/mol (Baulch et al. C2H4 O H H H 1992) and does not occur at very low temperatures. At OH the pressure of NH3 photodissociation, the temperature H H, CH2 is 220 – 240 K in K2-18 b and PH2 b, 120 – 130 K in CH3CO H2CCO CO CO2 hv, S hv Kepler-167 e, and ∼ 110 K in Jupiter. This makes Re- H2 H2 O O2 action (R8) faster by six orders of magnitude in K2-18 b OH HCCO C H C and PH2 b than in Kepler-167 e or Jupiter, eventually 2 2 leading to an efficient HCN production and a high abun- CH4 dance in the middle atmosphere. This is why the HCN production mechanism (Reactions R6–R8) does not op- Figure 12. Chemical network from the photodissociations of CH and H O in temperate/cold and H -dominated atmo- erate efficiently in giant planets in the Solar System but 4 2 2 spheres. Not all reactions are shown, and the importance of can build up HCN in warmer exoplanetary atmospheres. the shown reactions changes from case to case. The dashed The abundance of H is another important control. links represent the chemical network of CH4 and hydrocar- From Figure 11, we can see that a higher abundance bons in cold and H2-dominated atmospheres, as standard of H would enhance the recycling from N2H4 to NH2, in the literature (e.g., Gladstone et al. 1996; Moses et al. 2005). The photodissociation of H O provides oxidizing rad- produce more NH3 to react with NH2, and help the re- 2 icals such as OH. When CH4 is photodissociated together turn of NH2 to NH3. In other words, a higher abundance with H O, CO and CO can be formed in addition to hydro- of H would reduce the overall efficacy of the NH path 2 2 2 carbons. but favor the branch that leads to HCN. At the pressure of NH photodissociation, the main source of H is the 3 found for PH2 b (Figures6 and7). This is because the combination of Reactions (R1 and R2), whose net result photodissociation of NH occurs at higher pressures in is the dissociation of H but not NH . The sink of H is 3 2 3 PH2 b than in K2-18 b. When abundant CO exists, the mainly Reaction (R3) and the direct recombination H + reactions CO + H −−→M HCO and HCO + H −−→ CO + H −−→M H . In high-metallicity atmospheres, another 2 H efficiently remove H. Note that the first reaction sink of H is Reaction (R5) followed by 2 in this cycle is three-body and only significant at suf- ficiently high pressures. This sink of H results in the N2H4 + H −−→ N2H3 + H2, (R12) reduction of CH3 production (Reaction R8) and thus and disfavors the branch in the NH2 path that leads to HCN. To summarize, the numerical models and the HCN N2H3 + H −−→ 2 NH2 · (R13) formation mechanism presented here indicate that HCN The net result of Reactions (R5, R12, and R13) is H + and N2 are generally the expected outcomes of the pho- H −−→ H2. Therefore, the chemical network that starts todissociation of NH3 in gaseous exoplanets that receive with the photodissociation of NH3 is both a source and stellar irradiance of approximately Earth’s, regardless of a sink of H, which feedback to determine the outcome the stellar type. of the network in a non-linear way. For example, the 3.4. Photolysis of CH4 Together with H2O NH2 channel is a minor pathway to form N2 in the solar or 10×solar abundance atmosphere of K2-18 b but The formation of CO and CO2 as the most abundant it becomes an important pathway in the 100× solar at- photochemical gases of carbon on K2-18 b and PH2 b mosphere. is another significant finding of our numerical models. The abundance of H at the pressure of NH3 photodis- The photodissociation of CH4 in colder H2-dominated sociation also explains the different sensitivity of the atmospheres – such as the giant planets’ atmospheres in HCN mixing ratio on the inclusion of deep-tropospheric the Solar System – produces hydrocarbons such as C2H6 source of CO/CO and partial depletion of NH3. For K2- and C2H2 but not oxygenated species (e.g., Gladstone 18 b, the reduction in the HCN mixing ratio is small or et al. 1996; Moses et al. 2005). This is because H2O con- proportional to the reduction in the input NH3 abun- denses out and is almost completely removed from the dance, but more reduction in the HCN mixing ratio is above-cloud atmosphere (such as in Kepler-167 e, Figure 18 Hu

8). External sources such as comets and interplanetary temperate atmospheres. Lastly, the main source of O is dust can supply oxygen to the upper atmospheres of the photodissociation of CO and CO2, which eventually Jupiter and the other giant planets (e.g., Moses et al. traces to OH and the photodissociation of water. 2005; Dobrijevic et al. 2020), but we do not include At this point we can explain the ratio between CO2 this source in the present study. For warmer planets, and CO in the middle atmosphere, which is ∼ 1 on K2- however, H2O is only moderately depleted by conden- 18 b and ∼ 10 on PH2 b (Figures6 and7). Because sation. The above-cloud water is photodissociated at Reaction (R14) is the main source of CO2 and photodis- approximately the same pressure as CH4 (Figures6 and sociation is the main sink, the number density of CO2

7). The photodissociations of CH4 and H2O together is ∼ kR14[CO][OH]/JCO2 , where k is the reaction rate in H2-dominated atmospheres produces a chemical net- constant and [] means the number density of a molecule. work beyond hydrocarbons (Figure 12) and eventually Because Reaction (R15) is the main source of OH, the lead to the formation of CO and CO2. Even warmer number density of OH is ∝ JH2O[H2O]. Therefore, the atmospheres (e.g., the atmosphere of GJ 1214 b with an ratio between CO2 and CO is ∝ JH2O[H2O]/JCO2 . For eﬀective temperature of 500 – 600 K) may also have CO any given metallicity, the abundance of H2O in the mid- and CO2 as the most abundant photochemical gases of dle atmosphere of PH2 b is 3 ∼ 5-fold greater than that carbon (e.g., Kempton et al. 2011; Kawashima & Ikoma in K2-18 b because PH2 b is slightly warmer (Figures6

2018). and7). And, JH2O at the top of the atmosphere on The photodissociation of CH4 and the subsequent PH2 b is approximately twice that on K2-18 b, while chemical reactions produce a wealth of hydrocarbons JCO2 is similar between the two planets (Figure2). To- and radicals, and many of them (e.g., C, CH, CH3, gether, this causes the [CO2]/[CO] ratio to be greater in C2H2, and C2H4) lead to chemical pathways that form the atmosphere of PH2 b than in K2-18 b by ∼ 10 folds. CO (Figure 12). Between K2-18 b and PH2 b and among This trend to maintain the [CO2]/[CO] ratio also con- the modeled metallicities, we do not see a monotonic trols how the atmosphere reacts to a deep-tropospheric trend regarding the relative contribution of these CO source of CO and CO2 that is applied as input at the forming pathways, probably due to many chemical cy- lower boundary. The input CO2 is always less than CO cles and feedback in hydrocarbon photochemistry. CO by one or more orders of magnitude (Figures3-5). On is converted to CO2 by the reaction with OH: PH2 b, photochemical processes convert CO into CO2 in the middle atmosphere (∼ 102 Pa), and cause the CO + OH −−→ CO + H · (R14) 2 steady-state mixing ratio of CO2 to be greater than that of CO. This conversion even becomes a significant sink Reaction (R14) is the dominant source of CO in all 2 of H O and causes H O to be depleted in the middle at- models, and the only significant chemical loss of CO is 2 2 2 mosphere in the 100×solar metallicity case (Figure7). to form CO via either photodissociation or the reaction The CO to CO conversion is not so strong in the at- with elemental sulfur when available (Figure 12). The 2 mosphere of K2-18 b or Kepler-167 e, and their mixing CO that is not returned to CO is then transported 2 ratios in the middle atmosphere are largely the input through the lower boundary. values at the lower boundary (Figure6). What are the sources of OH, O, and H that power the Finally, let us turn to the impact of H O and NH pho- chemical pathways shown in Figure 12? At the pressure 2 3 todissociation onto the hydrocarbon chemistry. Com- of CH and H O photodissociation, the source of OH is 4 2 pared with Kepler-167 e, the mixing ratio of C H – the the photodissociation of water, 2 6 dominant, supposedly long-lived hydrocarbon – in K2- hν 18 b and PH2 b is smaller and sometimes features an H2O −−→ H + OH, (R15) additional peak near the cloud deck (Figures6-8). Par- and the main sink is the reaction with H2, ticularly, the atmospheres of K2-18 b and PH2 b have a strong sink of C2H6 at ∼ 1−10 Pa, while the atmosphere OH + H2 −−→ H2O + H · (R16) of Kepler-167 e does not. This sink is ultimately because of the high abundance of H produced by the pho- Reaction (R16) is the main sink of OH in all models, todissociation of H O (Reactions R15 and R16). The which means that the use of OH in the chemical path- 2 detailed reaction path involves the formation of C H ways shown in Figure 12 does not usually become the 2 5 from C H (by direct reaction with H or photodissoci- dominant sink of OH. Reactions (R15 and R16) to- 2 6 ation to form C H followed by H addition), and then gether is equivalent to the net dissociation of H , which 2 4 2 C H + H −−→ 2 CH . Because of the abundance of H, overtakes the photodissociation of CH and subsequent 2 5 3 4 CH mostly combines with H to form CH , rather than hydrocarbon reactions as the dominant source of H in 3 4 19 recombines to form C2H6. It is well known that the in 1.1 – 1.7 µm, at odds with the Hubble data. Both CH4 abundance of hydrocarbons is fundamentally controlled and H2O contribute to the spectral modulations seen M by the relative strength between H + CH3 −−→ CH4 by Hubble, which may have caused the difficulties in the M identification of the gases by spectral retrieval (Tsiaras and CH3 + CH3 −−→ C2H6 (e.g. Gladstone et al. 1996; Moses et al. 2005). Here we find that the added H from et al. 2019; Benneke et al. 2019; Blain et al. 2021). HCN, one of the most abundant photochemical gases H2O photodissociation results in a net sink for C2H6 in K2-18 b and PH-2 b at ∼ 1 − 10 Pa and limits the in the middle atmosphere, is likely detectable in K2-18 b abundance of hydrocarbons in their atmospheres. This via its spectral band at ∼ 3.0 µm. The HCN is produced sink does not exist in the atmosphere of Kepler-167 e, from the photodissociation of NH3 in presence of CH4. Also at 3.0 µm are the absorption bands of NH3 and to because little H2O photodissociation occurs in its atmosphere. Additionally, near the cloud deck, the tempera- a lesser extent C2H2. It would be possible to disentangle ture is warmer, and Reaction (R8) that uses H from the these bands with a reasonably wide wavelength coverage because NH3 has multiple and more prominent bands in photodissociation of NH3 provides an additional source the mid-infrared (Figure 13), and because C2H2 should of CH3, and some of the CH3 becomes C2H6 and thus its peak near the cloud deck. The formation of hydrocar- have a minimal abundance in the middle atmosphere bons is thus strongly impacted by the water and nitrogen (Figure6) and contribute little to the transmission spec- photochemistry. tra. The spectral bands of CO2 and CO can be seen in the 3.5. Spectral Features of H2O, CH4, NH3, and modeled spectra (in 4 – 5 µm) of K2-18 b only when the Photochemical Gases atmosphere has super-solar metallicity and the trans- 3.5.1. Transmission spectra port from the deep troposphere is taken into account (Figure 13). In other words, the CO and CO that are Figures 13-15 show the transmission spectra of the 2 produced from the photodissociation of CH together temperate and cold planets K2-18 b, PH2 b, and Kepler- 4 with H O would have too low mixing ratios to be de- 167 e, based on the gas and sulfur haze profiles simulated 2 tected. The photodissociation of CH also produces by the photochemical models. These modeled spectra 4 C H . While C H has strong bands at 3.35 and 12 can be regarded as the canonical examples of a tem- 2 6 2 6 µm, they would not be detectable due to its relatively perate (Earth-like insolation) planet irradiated by an M low abundance and the strong CH and NH bands at dwarf star (K2-18 b, and also TOI-1231 b), a temperate 4 3 the same wavelength, respectively (Figure 13). (Earth-like insolation) planet irradiated by a G/K star For PH2 b, prominent spectral bands of CH ,H O, (PH2 b), and a cold (∼ 0.1× Earth insolation) planet 4 2 and the photochemical gases CO and HCN can be ex- irradiated by a G/K star (Kepler-167 e). Here we focus 2 pected (Figure 14). NH is not detectable because it on the wavelength range of 0.5 – 5.0 µm, where several 3 is depleted by photodissociation to the cloud deck (Fig- instruments on JWST will provide spectral capabilities ure7). Even though its pressure of photochemical de- (e.g., Beichman et al. 2014). pletion can be reduced to ∼ 102 Pa for a large eddy For K2-18 b, the equilibrium gases CH ,H O, and 4 2 diffusion coefficient, the sulfur haze in that case would NH , as well as the photochemical gas HCN have po- 3 mute spectral features that are generated from approx- tentially detectable spectral features in the visible to imately the same pressure levels (Figure 10) and thus mid-infrared wavelengths (Figure 13). Adding deep- cause NH to be undetectable. HCN, CO , and CO are tropospheric source of CO, CO , and N and sink of NH 3 2 2 2 3 the most abundant photochemical gases (Figure7); but does not cause a significant change of the spectrum of a the CO bands are intrinsically weaker and so CO and 10×solar metallicity atmosphere. However, a 100×solar 2 HCN are the detectable photochemical gases via their metallicity atmosphere with deep-tropospheric source spectral bands at 4.2 and 3.0 µm, respectively. Simi- and sink would be free of the spectral features of NH or 3 lar to K2-18 b, adding deep-tropospheric source of CO, HCN, but instead have potentially detectable features of CO , and N and sink of NH does not cause a signifi- CO and CO. 2 2 3 2 cant change of the spectrum of a 10×solar metallicity at- Strikingly, the models from 1× to 100× solar abun- mosphere. However, a 100×solar metellicity atmosphere dance and with the standard eddy diffusion coefficient with deep-tropospheric source and sink would not have provide good fits to the existing transit depth measure- the spectral features of H O or HCN and have more ments by K2, Hubble, and Spitzer (Tsiaras et al. 2019; 2 prominent features of CO and CO, as predicted by the Benneke et al. 2019). The models with a 100-fold greater 2 photochemical model (Figure7). eddy diffusion coefficient would have the sulfur haze layer extending to 102 Pa and mute the spectral features 20 Hu

3020 2 2 (a) CH4+ H2O Solar, = 19.7 10x Solar with Deep Troposphere, = 21.6 2 3000 10x Solar, = 21.6 100x Solar, 2 = 22.4 Benneke et al. (2019) 100x Solar witg Deep Troposphere, 2 = 22.5 2980 CH NH3 + HCN 4 2960 H2O CH4 CO 2940 CH 2 4 CH4 NH3

2920 CO

CH + NH 2900 4 3

Transit Depth [ppm] NH3 + H2O CH + H O 2880 4 2 CH + NH 4 3 HCN 2860

2840 3020 (b) 2 Standard K, = 19.672 3000 Standard K 10, 2 = 23.7643 2 2980 Standard K 100, = 29.2059

2960

2940

2920

2900 Transit Depth [ppm]

2880

2860

2840 0.5123456 Wavelength [microns]

Figure 13. Modeled transmission spectra of the temperate sub-Neptune K2-18 b for varied metallicities (a) and varied eddy diffusion coefficients at the solar metallicity (b). The dashed lines show model spectra with deep-tropospheric source of CO, CO2, and N2 and sink of NH3. All models with the standard eddy diffusion coefficient fit the observed transit depths. The equilibrium gases (CH4,H2O, and NH3) and the photochemical gas HCN are detectable in the wavelength range of 0.5 – 5.0 µm. The 100×solar metallicity atmosphere with deep-tropospheric source and sink can have detectable features of CO2 and CO.

Lastly for the cold planet Kepler-167 e, the transmis- atmosphere C2H6 has spectral bands at 3.35 and 12 µm. sion spectra will be dominated by the absorption bands The 3.35-µm band is buried by a strong CH4 band, and of CH4 (Figure 15), as H2O is completely removed by while not shown in Figure 15, the 12-µm band might condensation and NH3 by condensation and photodisso- be detectable given appropriate instrumentation with ciation. For a large eddy diffusion coefficient, the pres- the spectral capability in the corresponding wavelength sure of photochemical depletion of NH3 can be reduced range. Finally, the deep-troposphere-sourced CO2 and to ∼ 103 Pa (Figure 10) and this can produce a spec- CO in a 100×solar metallicity atmosphere may produce tral band of NH3 at ∼ 3.0 µm. Thus, a search for this detectable spectral features in 4 – 5 µm. absorption band in the transmission spectra may con- To summarize, transmission spectroscopy from the strain the eddy diffusion coefficient, although to distin- visible to mid-infrared wavelengths can provide the sen- guish it with a small peak due to the combined absorp- sitivity to detect the equilibrium gases CH4 and H2O, tion of the photochemical gases HCN and C2H2 (Fig- and the photochemical gases HCN, and in some cases ure 15) may involve quantification through photochem- CO2 in temperate/cold and H2-rich exoplanets. We do ical models. The main photochemical gas in this cold not expect C2H6 to be detectable. NH3 would be de- 21

8510 (a) Solar 10x Solar 8500 10x Solar with Deep Troposphere CH CH + H O 4 100x Solar 4 2 CH 4 100x Solar witg Deep Troposphere 8490 CO CH HCN 2 4 H O CH 2 8480 4 CH4 CO+HCN CO2 8470 Transit Depth [ppm]

CO2 H2O 8460

8450 8510 (b) Standard K Standard K 10 8500 Standard K 100

8490

8480

8470

Transit Depth [ppm] 8460

8450

8440 0.5123456 Wavelength [microns]

Figure 14. Modeled transmission spectra of the temperate gas giant PH2 b for varied metallicities (a) and varied eddy diffusion coefficients at the solar metallicity (b). The dashed lines show model spectra with deep-tropospheric source of CO, CO2, and N2 and sink of NH3. Several equilibrium gases (CH4 and H2O) and photochemical gases (HCN, CO2, and CO) are detectable in the wavelength range of 0.5 – 5.0 µm. tectable on temperate planets around M dwarf stars also be characterized in the reflected starlight by direct but not detectable on temperate planets around G/K imaging. Figure 16 shows the geometric albedo spec- stars. The deep-tropospheric source and sink can have tra of PH2 b and Kepler-167 e in the visible and near- a major impact only on the transmission spectrum of infrared wavelengths that approximately correspond to a 100×solar metallicity atmosphere, where typically the the Roman Space Telescope’s coronagraph instrument features of NH3 and HCN would be reduced and those (Kasdin et al. 2020) and its potential Starshade Ren- of CO2 and CO would be amplified. The detection dezvous (Seager et al. 2019) and the HabEx concept and non-detection of these gases will thus test the pho- (Gaudi et al. 2020). While PH2 b and Kepler-167 e tochemical model and improve our understanding of themselves are not potential targets for these missions, the photochemical mechanisms as well as tropospheric their albedo spectra broadly resemble the targets in the transport in temperate/cold and H2-dominated atmo- temperate (PH2 b) and cold (Kepler-167 e) regimes. spheres. The spectral features of CH4 and H2O can be seen in the reflected starlight of PH2 b. This ability to detect 3.5.2. Spectra of the reflected starlight H2O in giant planets warmer than Jupiter is consistent The temperate and cold planets around G/K stars with MacDonald et al.(2018). In addition to the ab- are widely separated from their host stars and may thus 22 Hu

104 1.644

(a) CH4 Solar CH 4 10x Solar 1.643 10x Solar with Deep Troposphere 100x Solar 100x Solar witg Deep Troposphere 1.642 CO2 CO CO 1.641 2

1.64 Transit Depth [ppm]

1.639

HCN + C2H2 1.638 104 1.644 (b) Standard K Standard K 10 1.643 Standard K 100

1.642

1.641

NH 3 NH 1.64 3 Transit Depth [ppm]

1.639

HCN + C2H2 1.638 0.5123456 Wavelength [microns]

Figure 15. Modeled transmission spectra of the cold gas giant Kepler-167 e for varied metallicities (a) and varied eddy diffusion coefficients at the solar metallicity (b). The dashed lines show model spectra with deep-tropospheric source of CO, CO2, and N2 and sink of NH3. With the standard eddy diffusion coefficient, CH4 is the only detectable equilibrium gas and the photochemical gases HCN and C2H2 result in a small peak at ∼ 3 µm. The 100×solar metallicity atmosphere with deep-tropospheric source and sink can have detectable features of CO2 and CO. Greater eddy diffusion coefficients can produce potentially detectable NH3. sorption features of CH4 and H2O, the albedo spectra the absorption of CH4 can be seen in the albedo spectra of PH2 b feature the absorption of the sulfur (S8) haze of Kepler-167 e, as H2O is depleted by condensation. On layer at wavelengths shorter than ∼ 0.5 µm. This re- both planets, the spectral features of NH3 are not seen sult is consistent with the findings of Gao et al.(2017). due to its weak absorption (Irwin et al. 2018) and pho- For a greater eddy diffusion coefficient, the sulfur haze tochemical depletion to the cloud deck (Figures7 and layer is higher and the spectral features of CH4 and H2O 8). The deep-tropospheric source and sink has minimal become weaker. Interestingly, the absorption features impact on the albedo spectra, unless in the 100×solar of H2O are the most prominent in the solar-abundance metallicity atmosphere on PH2 b where a reduction of case, and they are somewhat swamped by the adjacent the CH4 features can be seen. CH4 features at higher metallicities. This is because, as H2O condenses out, the above-cloud mixing ratio of 4. DISCUSSION H O only slightly increases with the metallicity, while 2 The results and analyses presented in Section3 indi- that of CH4 increases proportionally (Figure7). Only cate that the temperate and H2-rich exoplanets, partic- 23

PH2 b Kepler-167 e 0.7

H2O Solar CH + H O 4 2 10x Solar 0.6 H O 2 10x Solar with Deep Troposphere CH 100x Solar 0.5 4 100x Solar with Deep Troposphere

0.4 CH4

0.3 s8 Solar Geometric Albedo 0.2 10x Solar CH4 10x Solar with Deep Troposphere 0.1 100x Solar CH CH 4 100x Solar with Deep Troposphere 4 0 0.7 Standard K 0.6 Standard K 10 Standard K 100

0.5

0.4

0.3 s8

Geometric Albedo 0.2 Standard K Standard K 10 0.1 Standard K 100

0 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Wavelength [microns] Wavelength [microns]

Figure 16. Modeled geometric albedo spectra of the temperate gas giants PH2 b and the cold gas giant Kepler-167 e for varied metallicities and varied eddy diffusion coefficients at the solar metallicity. The dashed lines show model spectra with deep-tropospheric source of CO, CO2, and N2 and sink of NH3. All absorption features in Kepler-167 e’s spectra are due to CH4. Both H2O and CH4 can be detectable in the reflected starlight of PH2 b and only CH4 can be detectable in Kepler-167 e. ularly those orbiting M dwarf stars, provide an unprece- rent estimate of the potential “noise floor” of the near- dented opportunity to characterize the photochemical infrared instruments on JWST (<∼ 10 ppm, Schlawin mechanisms in low-temperature atmospheres. So far, et al. 2020, 2021), and are thus likely measurable. These these planets include K2-18 b, TOI-1231 b, and LHS- spectral features may also be within the reach of ARIEL 1140 b if they have H2-dominated atmospheres. H2- (Tinetti et al. 2018; Changeat et al. 2020). dominated atmospheres that receive stellar irradiation An an example, we have used PandExo (Batalha et al. as Earth are not found in the Solar System, and we 2017) to estimate the overall photometric uncertainties have shown here that this unique exoplanetary regime achieved by observing the transits of K2-18 b with the would result in mechanisms to form HCN as a uniformly G235H and G395H gratings of the NIRSpec instrument abundant product from the photodissociation of NH3 in on JWST. These two channels would cover the wave- presence of CH4, as well as detectable levels of CO2 on length range of 1.7 − 5.2 µm and thus provide the sen- planets around G/K stars from the photodissociation sitivity to the spectral features shown in Figure 13. We of CH4 together with H2O. The observations of tem- find that with two visits in G235H and four visits in perate and H2-rich exoplanets thus promise to greatly G395H, the overall photometric precision would be ∼ 20 expand the types of molecules detected in exoplanet at- ppm per spectral element at the resolution of R = 100 mospheres. Interestingly, HCN is one of the most impor- in both wavelength channels, and this precision should tant molecules for prebiotic chemistry (e.g., Patel et al. enable the detection of CH4,H2O, NH3, the photochem- 2015), and the exoplanet observations may constrain the ical gas HCN, and possibly CO2. If reducing the spec- photochemical pathways for its formation in primordial tral resolution to R = 50, the number of visits would planetary atmospheres. be halved, but this could cause spectral ambiguity be- For K2-18 b, our model predicts that the spectral fea- tween NH3 and HCN because they both have absorption tures of CH4 can have a size of ∼ 80 ppm in the transit bands at ∼ 3.0 µm (Figure 13). Spectral ambiguity in depth, and those of H2O, NH3, HCN, and CO2 (from the transmission spectra with the resolution of R ∼ 50 or the deep troposphere) would have a size of 30 ∼ 60 less has been recently shown with Hubble at 1.1−1.7 µm ppm. These quantities are substantially above the cur- (Mikal-Evans et al. 2020). 24 Hu

The size of the transmission spectral features expected We have also shown in Section3 that the deep- for temperate and cold gas giants around G/K stars, tropospheric source of CO, CO2, and N2 and sink of such as PH2 b and Kepler-167 e, is small but probably NH3 can substantially change the composition of the ob- not prohibitive. For example, our model predicts that servable part of the atmosphere – and the transmission the spectral features of CH4 can have a size of ∼ 50 ppm spectrum – if the atmosphere has 100×solar metallicity. in the transit depth, and those of H2O, CO2, and HCN The main change is the reduction of NH3 and HCN and would have a size of 20 ∼ 30 ppm. Several visits may the enhancement of CO and CO2 in the spectrum. As need to be combined to achieve the photometric pre- such, detecting and measuring the abundance of these cision to detect these gases. Complementary to trans- gases in the temperate H2-dominated atmosphere may mission spectroscopy, future direct-imaging missions can provide constraints on the temperature and the strength readily detect CH4,H2O, and clouds (e.g., Damiano & of vertical mixing in the deep troposphere (e.g., Fortney Hu 2020), as well as the sulfur haze produced by atmo- et al. 2020). One should note that modification of the spheric photochemistry. deep-tropospheric abundance of gases by photochemical While we focus on temperate and cold planets in this processes will be important in this endeavor: NH3 is paper, the photochemical mechanisms and the predic- expected to be depleted anyway and CO2 should over- tions on the gas formation and spectral features should take CO as the main carbon molecule in the middle at- remain applicable to the planets that are only slightly mosphere of temperate and H2-rich exoplanets of G/K warmer than K2-18 b and PH2 b. This is because the stars. results on these planets do not rely on the formation A recently published study of atmospheric photo- of water clouds. We suspect that the results should be chemistry in the atmosphere of K2-18 b (Yu et al. 2021) applicable as long as the dominant O, C, N, S species came to our notice during the peer-review phase of this in thermochemical equilibrium with H2 are H2O, CH4, work. The “no-surface” case in Yu et al.(2021) has NH3, and H2S and the assumptions on other atmo- a comparable physical picture as the 100×solar metal- spheric parameters (e.g., the eddy diffusion coefficient) licity case with the deep-tropospheric source and sink remain broadly valid. presented in Figure6. A common feature is that such The eddy diffusion coefficient adopted in this work an atmosphere would be rich in CO and CO2, and the corresponds to that of Jupiter (Conrath & Gierasch difference in the profiles of HCN and other photochemi- 1984) and features a minimum at the bottom of cal gases between the models may be due to the assumed the stratosphere. This minimum value is also close profile of eddy diffusivity. to the eddy diffusion coefficient at the troposphere- Lastly, we emphasize that several effects of poten- stratosphere boundary of Earth’s atmosphere (Massie tial importance have not been studied in this work. A & Hunten 1981). However, the adopted eddy diffusion more accurate pressure-temperature profile from 1D or coefficient at the bottom of the stratosphere is smaller 3D models may improve the prediction on the extent than the values used in past photochemical models of of water vapor depletion by condensation. A tempera- warmer exoplanets (e.g., GJ 1214 b and GJ 436 b, ture inversion would result in higher temperatures in the Kempton et al. 2011; Moses et al. 2013; Hu & Seager upper stratosphere than what has been adopted here, 2014) or the values derived from a 3D particulate tracer- and this may have an impact on the efficacy and rela- transport model conditioned on hot Jupiters (Parmen- tive importance of chemical pathways. A more accurate tier et al. 2013) by several orders of magnitude. We note pressure-temperature profile and vertical mixing mod- that Earth, the cold giant planets in the Solar System, eling for the deep troposphere may improve the predic- and the modeled K2-18 b (Blain et al. 2021; Charnay tion and perhaps remove the need for the endmember et al. 2021) all have temperature inversion and thus a scenarios as presented. On planets that are expected to true stratosphere, while atmosphere models of the warm be tidally locked, the transmission spectra are controlled exoplanets GJ 1214 b and GJ 436 b do not predict tem- by the chemical abundance at the limb (e.g., Steinrueck perature inversion (e.g., Kempton et al. 2011; Moses et al. 2019; Drummond et al. 2020), and thus the hori- et al. 2013). The lower temperature and the tempera- zontal transport of long-lived photochemical gases such ture inversion may both contribute to the lower eddy as HCN and CO2 may be important. Finally, we have diffusion coefficient on temperate and cold exoplanets. not included hydrocarbon haze in this study, while it Predictive models of the eddy diffusion coefficient in ex- can form with both C2H2 and HCN in the atmosphere oplanets are being developed (e.g., Zhang & Showman (Kawashima et al. 2019). We hope that the present 2018a,b) and can be tested by future observations as work will help motivate future studies to address these shown in Figures 13-15. potential effects. 25

5. CONCLUSION H2O, and the photochemical gases HCN and CO2, com- We have studied the photochemical mechanisms in plementing future spectroscopy in the reflected light by direct imaging. If the eddy diffusion coefficient is greater temperate/cold and H2-rich exoplanets. For the H2-rich planets (giants and mini-Neptunes) that receive stellar than that in Jupiter by two orders of magnitude, the irradiance of approximately Earth’s, we find that the sulfur haze layer would subdue the transmission spectral features – but this situation is unlikely for K2-18 b main photochemical gases are HCN and N2. The syn- because of the detected spectral modulation. These re- thesis of HCN requires the photodissociation of NH3 in sults are also applicable to similarly irradiated H2-rich presence of CH4 at a temperature >∼ 200 K. NH3 is dissociated near the water cloud deck and thus has a exoplanets, including TOI-1231 b and LHS-1140 b if minimal mixing ratio in the middle atmosphere (10 – they have H2-dominated atmospheres. 3 The results here indicate that the temperate/cold and 10 Pa) if the planet orbits a G/K star, but NH3 can remain intact in the middle atmosphere if the planet H2-rich exoplanets, which often represent a tempera- orbits an M star. Additional photochemical gases in- ture and atmospheric composition regime that is not found in the Solar System, likely have rich chemistry clude CO, CO2,C2H6, and C2H2. CO and CO2 are the main photochemical gas of carbon because of the pho- above clouds that leads to a potpourri of photochemical gases, some of which will build-up to the abundance todissociation of H2O together with CH4. The photodis- detectable by transmission spectroscopy soon. The de- sociation of H2O also strongly limits the abundance of photochemical hydrocarbons in the atmosphere. For the tection of atmospheric photochemical products in K2- planets that receive stellar irradiance of approximately 18 b and other temperate exoplanets would expand the 0.1× Earth’s, the formation of HCN is limited by the types of molecules detected in exoplanet atmospheres and greatly advance our understanding of the photo- low temperature, CO2 or CO is not produced due to chemical processes at works in low-temperature exoplan- nearly complete removal of H2O by condensation, and ets. the main photochemical gases are C2H6 and C2H2. The photochemical models of the temperate sub- Neptune K2-18 b assuming 1 − 100×solar abundance result in transmission spectra that fit the current mea- ACKNOWLEDGMENTS surements from K2, Hubble, and Spitzer. Both CH4 We thank Sara Seager and the anonymous referee for and H2O contribute to the spectral modulation seen helpful comments that improved the paper, Yuk Yung by Hubble. Transmission spectroscopy with JWST and and Danica Adams for providing information on the Cal- ARIEL will likely provide the sensitivity to detect the tech/JPL KINETICS code for comparison, and Mario equilibrium gases CH4,H2O, and NH3, the photochem- Damiano for advice on the PandExo simulations. This ical gas HCN, and in some cases CO2.C2H6 is unlikely work was supported in part by the NASA Exoplanets to be detectable due to its low mixing ratio and spec- Research Program grant #80NM0018F0612. This re- tral feature overwhelmed by CH4. Transmission spec- search was carried out at the Jet Propulsion Laboratory, troscopy of the temperate giant planets around G/K California Institute of Technology, under a contract with stars will likely provide the sensitivity to detect CH4, the National Aeronautics and Space Administration.

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