Nitrogen as a Tracer of Giant Planet Formation. II. Comprehensive Study of Nitrogen Photochemistry and Implications for Observing NH₃ and HCN in Transmission and Emission Spectra

Here, we numerically investigate atmospheric chemical compositions using a publicly available photochemical kinetics code, VULCAN (Tsai et al. 2017, 2021b). The code computes the steady-state vertical distributions of chemical compositions by solving the transport equations given by

$$\begin{eqnarray}&&\displaystyle \frac{\partial {n}_{i}}{\partial t}={{ \mathcal P }}_{i}-{{ \mathcal L }}_{i}-\displaystyle \frac{\partial {{\rm{\Phi }}}_{i}}{\partial z},\end{eqnarray} \tag{ 5 }$$

where z is the altitude, n_i is the number density of species i, ${{ \mathcal P }}_{i}$ and ${{ \mathcal L }}_{i}$ are their production and loss rates, and ϕ_i is the vertical flux due to eddy and molecular diffusion. While several theoretical studies investigated the eddy diffusion coefficient K_zz on exoplanets using global circulation models (Parmentier et al. 2013; Charnay et al. 2015; Zhang & Showman 2018a, 2018b; Komacek et al. 2019; Menou 2019, 2022; Tan 2022), it remains poorly constrained from observations (see Kawashima & Min 2021). Thus, we test a broad range of eddy diffusion coefficients, K_zz = 10⁵, 10⁸, and 10¹¹ cm² s⁻¹, for the sensitivity tests. We assume a zero flux condition for both upper and lower boundaries. We set the depth of the lower boundary so that thermochemical equilibrium is maintained there (typically 1000 bar, depending on the thermal state of the deep atmosphere and K_zz). We adopt the C–H–N–O chemistry network implemented in VULCAN as a default. We assume the solar photospheric elemental abundances of Asplund et al. (2021) for fiducial simulations. To explore a range of parameter space for planetary properties shown in Figure 1, we extract the surface gravity and intrinsic temperature from the thermal evolution tracks of Fortney et al. (2007) ³ for several representative planetary masses and ages, as summarized in Table 1. Then, we compute the atmospheric P–T profiles using the "EGP" radiative-convective equilibrium model extensively used in previous studies ⁴ (e.g., McKay et al. 1989; Marley & McKay 1999; Fortney et al. 2005, 2007, 2008; Morley et al. 2012; Marley & Robinson 2015; Thorngren et al. 2019; Gao et al. 2020; Paper I) for various planetary equilibrium temperatures. Our fiducial simulations assume the solar spectrum (Gueymard 2018), where we set the orbital distance so that the planetary equilibrium temperature (for zero Bond albedo with full heat redistribution) coincides with a specified value. We test the effects of different stellar spectra in Section 5.2. We neglect the condensation of gas molecules since the planets studied in this paper are too warm to cause condensation of NH₃ and HCN (see the top panel of Figure 2).

We first explore how the NH₃ and HCN abundances vary with various planetary properties. Figure 3 shows the vertical distributions of NH₃ and HCN across equilibrium temperature, planetary mass, age, and eddy diffusion coefficient. In general, the NH₃ abundance is nearly constant in the middle atmosphere owing to vertical mixing, while it decreases with increasing altitudes in the upper atmosphere due to photodissociation. This general trend is in agreement with previous studies (e.g., Line et al. 2011; Moses et al. 2011; Miller-Ricci Kempton et al. 2012; Kawashima & Ikoma 2018). As predicted in Section 2, the quenched NH₃ abundances in middle atmospheres are nearly independent of the equilibrium temperature at T_eq ≲ 800 K. For T_eq ≳ 1000 K, the NH₃ abundance gradually decreases with decreasing pressure at P ∼ 1–100 bar because of the efficient thermochemical conversion to N₂ due to high temperatures. This trend is consistent with previous studies of hot Jupiters (Moses et al. 2011).

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The ratio of the quenched NH₃ to bulk nitrogen abundance depends on planetary mass and age. The gray bold lines in Figure 3 denote the bulk nitrogen abundance f_N. For Jupiter-mass planets (M_p = 1M_J) at 1 Gyr age (top left panel of Figure 3), the quenched NH₃ abundance is lower than the bulk nitrogen abundance by a factor of ∼2. The depletion factor even reaches a factor of ∼10 for an age of ∼0.1 Gyr (top right panel of Figure 3). On the other hand, the NH₃ abundance is almost equal to the bulk nitrogen abundances for Neptune-mass planets (M_p = 0.11M_J) at 1 Gyr (bottom left panel of Figure 3). These results are consistent with our prediction made in the previous section (Figure 1). Thus, higher planetary mass and younger age do act to deplete the quenched NH₃ as compared to the bulk nitrogen abundance.

It is worth noting that our semianalytical prediction of the quenched NH₃ abundance (Equation (1)) matches the numerical results quite well. The green bold lines in Figure 3 show the NH₃ abundance given by Equation (1), which coincides with the quenched NH₃ abundance below the NH₃ photodissociation base. Thus, even if the planetary mass and age fall into the regime where NH₃ depletion is expected, one may still be able to use our semi-analytic diagnostic model (Equation (4)) to give a first-order estimate on the bulk nitrogen abundance from the NH₃ abundance.

Of course, photochemistry may substantially deplete the observable NH₃ abundances at low pressure. As seen in the results for an eddy diffusion coefficient of K_zz = 10⁸ cm² s⁻¹ (upper panels and lower left panel of Figure 3), the NH₃ abundance drops off at P ≲ 10⁻³–10⁻⁴ bar through photodissociation. This pressure level is significantly deeper than the pressure level where many other chemical species experience photodissociation, say ∼10⁻⁵–10⁻⁶ bar. This difference is because NH₃ is fragile to UV photons to relatively longer wavelengths. To demonstrate this, Figure 4 shows the photospheric pressure level at UV wavelengths. While UV photons at ≲190 nm are mostly absorbed by other chemical species, such as H₂O, at ∼10⁻⁵–10⁻⁶ bar, near-UV (NUV) photons at 190–220 nm penetrate to deeper atmospheres because of negligible photolysis cross sections of other molecules. Those NUV photons largely act to deplete NH₃ at ∼10⁻³ bar, which explains why NH₃ is vulnerable to photochemistry at relatively higher pressures. We refer readers to Hu (2021) for further discussion on the depletion of NH₃ through photodissociation in middle atmosphere regions. We note that our simulations do not account for the presence of aerosols, such as photochemical hazes, while they may act to prevent UV photons from penetrating deep atmospheres, as discussed in Section 5.1.

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The strength of eddy diffusion affects where the photochemical depletion of NH₃ takes place. The left and right bottom panels of Figure 3 show the results for M_p = 0.11M_J and 1 Gyr but for K_zz = 10⁸ and K_zz = 10¹¹ cm² s⁻¹. Higher K_zz results in the quenched NH₃ abundance continuing to higher altitudes, as the fast eddy diffusion can more easily compensate against the NH₃ loss by photodissociation (see also Hu 2021). On the other hand, different values of K_zz have negligible impacts on the quenched abundance of NH₃, in agreement with previous studies (Zahnle & Marley 2014; Fortney et al. 2020).

Once the photolysis of NH₃ sets in, most of NH₃ is converted to HCN in the upper atmosphere for the equilibrium temperature of T_eq = 400–1400 K. In Figure 3, one can notice that HCN abundances at upper atmospheres, say P ≲ 10⁻³–10⁻⁴ bar, are approximately the same as the NH₃ abundances below the photodissociation base. This result indicates that the photodissociated NH₃ is almost completely converted to HCN. Thus, one might be able to evaluate the bulk nitrogen abundance from the measurement of HCN abundance even if photodissociation significantly depletes NH₃ at pressure levels probed by observations. If the abundance profiles of NH₃ and HCN were constrained simultaneously, it would provide complementary information to infer the bulk nitrogen abundance.

Although the detailed analysis of atmospheric chemistry is beyond the scope of this paper, we here briefly introduce HCN synthesis processes. HCN can be produced through photodissociation of NH₃ under the presence of CH₄. For example, Moses et al. (2011) and Line et al. (2011) identified the following channel of HCN production:

$$\begin{eqnarray*}&&\begin{array}{l}\ {\mathrm{CH}}_{4}+{\rm{H}}\longrightarrow {\mathrm{CH}}_{3}+{{\rm{H}}}_{2}\\ \ {\mathrm{NH}}_{3}+h\nu \longrightarrow {\mathrm{NH}}_{2}+{\rm{H}}\\ \ {\mathrm{NH}}_{2}+{\rm{H}}\longrightarrow \ \mathrm{NH}+{{\rm{H}}}_{2}\\ \ \mathrm{NH}+{\rm{H}}\ \longrightarrow {\rm{N}}+{{\rm{H}}}_{2}\\ \ {\rm{N}}+{\mathrm{CH}}_{3}\longrightarrow {{\rm{H}}}_{2}\mathrm{CN}+{\rm{H}}\\ \ {{\rm{H}}}_{2}\mathrm{CN}+{\rm{H}}\longrightarrow \mathrm{HCN}+{{\rm{H}}}_{2}\\ \overline{\ \ \ \ \ \ \ \ \mathrm{Net}:\,\ {\mathrm{NH}}_{3}+{\mathrm{CH}}_{4}\longrightarrow \ \mathrm{HCN}+3{{\rm{H}}}_{2}\ \ \ \ \ \ \ }.\end{array}\end{eqnarray*}$$

HCN synthesis initiated from NH₃ photodissociation requires CH₃ produced through the reaction of CH₄ with H, where H can be provided by the photodissociation of NH₃. In addition to the above channel through H₂CN, HCN can also directly form from N and CH₃ as (Kawashima & Ikoma 2018; Hobbs et al. 2019)

$$\begin{eqnarray*}&&\ {\rm{N}}+{\mathrm{CH}}_{3}\longrightarrow {{\rm{H}}}_{2}+\mathrm{HCN}.\end{eqnarray*}$$

On the other hand, for temperate to cold planets, Hu (2021) identified the following channels without bypassing NH:

$$\begin{eqnarray*}\begin{array}{rcl}\ {\mathrm{NH}}_{2}+{\mathrm{CH}}_{3} & \longrightarrow & \ {\mathrm{CH}}_{5}{\rm{N}}\\ \ {\mathrm{CH}}_{5}{\rm{N}}\ +h\nu & \longrightarrow & \mathrm{HCN}+2{{\rm{H}}}_{2},\end{array}\end{eqnarray*}$$

though CH₅N photodissociation does not actually directly yield HCN but yields CH₃NH that subsequently yield CH₂NH and HCN via reaction with atomic H and photodissociation (see Section 3.2 of Moses et al. 2010). As seen in those examples, the major reaction pathway of HCN production may depend on the specific photochemical model used. HCN is destroyed either by the reaction of HCN + H → CN + H₂ or photodissociation of HCN + h ν → CN + H, but CN quickly reacts with H₂ to reproduce HCN again (Moses et al. 2011). In our calculations, the H₂CN + H channel dominates over the N + CH₃ channel. The relative importance of the CH₅N channel in warm exoplanets remains unclear since the default chemical network of the VULCAN does not involve reactions around CH₅N (see Tsai et al. 2021b). Nevertheless, we predict that the addition of the CH₅N channel would barely affect our results in terms of HCN vertical distributions. This is because the HCN production rate is eventually limited by the upward flux of NH₃ in the limit of fast HCN synthesis, and the complete conversion of NH₃ to HCN in Figure 3 implies that the HCN synthesis is already limited by the upward NH₃ flux owing to fast chemical conversion.

Figure 5 summarizes NH₃ abundances at P = 1 and 100 mbar, which mimics the pressure levels probed by transmission and emission spectra, respectively, for various planetary masses, age, and K_zz. Overall, NH₃ abundances are nearly invariant with T_eq at temperate to warm exoplanets, which confirms the finding of Fortney et al. (2020). Beyond a certain equilibrium temperature, photodissociation depletes NH₃ from the pressure levels of interest. The threshold equilibrium temperature depends on the eddy diffusion coefficient: T_eq ∼ 1200 K for K_zz = 10¹¹ cm² s⁻¹, T_eq ∼ 800 K for K_zz = 10⁸ cm² s⁻¹, and T_eq ∼ 400 K for K_zz = 10⁵ cm² s⁻¹. Since NH₃ found at pressure levels higher than 100 mbar is more stable to photodissociation, emission spectroscopy would have the advantage of observing quenched NH₃ that is less affected by photodissociation.

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We have assumed solar elemental ratios of the atmosphere thus far; however, exoplanets potentially have considerable diversity in atmospheric elemental ratios. For example, the atmospheric nitrogen-to-oxygen ratio (N/O) can have both super-stellar and sub-stellar N/O, depending on the formation location and whether disk solids or gas dominates the atmospheric composition (e.g., Piso et al. 2016; Cridland et al. 2020; Ohno & Ueda 2021; Turrini et al. 2021; Notsu et al. 2022; Paper I). Recent retrieval studies have reported subsolar H₂O abundances in hot Jupiter atmospheres from low-resolution (Pinhas et al. 2019; Welbanks et al. 2019) and high-resolution spectroscopy (Pelletier et al. 2021), which may be attributed to a high atmospheric C/O. Several studies also suggested high metallicity atmospheres on sub-Neptunes, such as GJ 1214b (e.g., Fortney et al. 2013; Morley et al. 2015; Gao & Benneke 2018; Ohno & Okuzumi 2018; Ohno et al. 2020; Christie et al. 2022; Gao et al. 2023; Kempton et al. 2023) and GJ 436b (Morley et al. 2017), and exo-Saturns, such as WASP-39b (Wakeford et al. 2018; Ahrer et al. 2023; Alderson et al. 2023; Feinstein et al. 2023; JWST Transiting Exoplanet Community Early Release Science Team et al. 2023; Rustamkulov et al. 2023; Tsai et al. 2023), WASP-117b (Carone et al. 2021), and HD 149026 b (Bean et al. 2023).

Here we investigate how these different atmospheric compositions affect the NH₃ and HCN vertical distributions. We test different N/O, C/O, and bulk atmospheric metallicities. We recompute P–T profiles for different C/O and atmospheric metallicities, as such changes lead to important alternations in the P–T profile. However, for different N/Os, we adopt the same P–T profiles as used in the previous section, as a different N/O barely affects the abundances of other O- and C-bearing species, such as H₂O, as long as the oxygen-to-hydrogen ratio (O/H) and carbon-to-hydrogen ratio (C/H) are the same (Hobbs et al. 2019). When we change N/O or C/O, we fix O/H to the solar value and change N/H or C/H to achieve the assumed N/O or C/O. Note that the atmospheric composition and P–T profile can noticeably depend on individual C/Hs, O/Hs, and N/Hs even if C/O and N/O are the same (Drummond et al. 2019). We have fixed O/H here because we anticipate that it would be relatively easy to constrain O/H from observations, as the abundance of H₂O, a main atmospheric opacity source, is approximately proportional to O/H. We assume a Jupiter-mass planet at the age of 1 Gyr for simulations of different N/Os and C/Os, while we assume a lower planet mass of 0.11 M_J at the age of 1 Gyr for simulations of high atmospheric metallicity.

The quenched NH₃ abundance is sensitive to but is not strictly proportional to the atmospheric N/O (N/H in other words). The top two panels of Figure 6 show the vertical distributions of NH₃ and HCN abundances for N/O = 0.1× and 10× solar values. The quenched NH₃ abundance is approximately 10⁻⁵ and 2 × 10⁻⁴ for N/O = 0.1× and 10× solar values, respectively, for equilibrium temperature ≲800 K. Recalling that the quenched NH₃ abundance is ∼5 × 10⁻⁵ for the solar value of N/O (see the top left top of Figure 3), the NH₃ abundance only varies by an order of magnitude across the two decades of N/O. This relatively weak dependence on N/O is due to N₂ dominating over NH₃ in the deep atmospheres for a Jupiter mass planet at 1 Gyr, as suggested by the discrepancy between NH₃ and bulk N abundances in Figures 3 and 6. Since this situation corresponds to ${ \mathcal K }\ll 1$, Equation (1) indicates ${f}_{{\mathrm{NH}}_{3}}\propto {f}_{{\rm{N}}}\sqrt{{ \mathcal K }}\propto {f}_{{\rm{N}}}^{1/2}$, which explains the dependence seen in Figure 6. Thus, when N₂ likely dominates over NH₃ in the deep atmosphere, one would need precise measurements of NH₃ to well constrain the bulk nitrogen abundance. The relative importance of NH₃ and N₂ in the deep atmospheres could be inferred from the second term of Equation (4) by inserting a retrieved NH₃ abundance into ${f}_{{\mathrm{NH}}_{3}}$.

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The higher C/O only has minor effects on nitrogen chemistry. The bottom left panel of Figure 6 shows the results for C/O = 1.1. The NH₃ profile is largely similar to that of the solar C/O (top left panel of Figure 3). This is because an equilibrium NH₃ abundance and thus the quenched NH₃ abundance are insensitive to C/O (see Figure 6 of Moses et al. 2013a). The HCN profile in the upper atmosphere also becomes similar to that for solar C/O, as the HCN is initiated from the NH₃ photodissociation for the temperature range of our interest. However, a higher C/O acts to increase the HCN abundance at middle to deep hot atmospheres, as the thermochemistry leads to an increased HCN abundance for high C/O.

Higher atmospheric metallicity leads to more N₂ dominant atmospheres owing to two combined effects: preference of N₂ as compared to NH₃ in thermochemical equilibrium and hot deep interior due to enhanced atmospheric opacity. The bottom right panel of Figure 6 shows the results for 100× solar metallicity. The quenched NH₃ abundance is ∼2 × 10⁻⁴, which is approximately two orders of magnitude lower than the actual bulk nitrogen abundance. This large discrepancy is due to the fact that the high atmospheric metallicity yields hotter deep interiors. We show the P–T profiles of solar composition and 100 solar metallicity atmospheres in Figure 2. The figure demonstrates that the atmospheres with 100× solar metallicity yield deep adiabatic profiles much hotter than those of solar composition atmospheres, which acts to increase N₂/NH₃ ratio in the deep atmosphere. Furthermore, N₂, a metal-metal species, is also strongly favored compared to NH₃ as the metallicity increases, at a given P and T (Lodders & Fegley 2002; Moses et al. 2013a). Therefore, the quenched NH₃ at P ∼ 1–100 bar starts to be depleted through thermochemical conversion at a threshold temperature of T_eq ∼ 800 K, which is cooler than that found in solar composition atmospheres (T_eq ∼ 1200 K).

High atmospheric metallicity also impacts the HCN abundances in the upper atmosphere. While the HCN abundances at upper atmospheres are nearly the same as the quenched NH₃ abundances for solar composition atmospheres (Figure 3), for 100× solar metallicity the HCN abundances are much lower than the quenched NH₃ abundances at T_eq ≳ 600 K. This finding owes to the depletion of CH₄ in the high metallicity atmospheres. The bottom panel of Figure 2 shows the vertical distributions of CH₄ for solar composition and 100× solar metallicity atmospheres. We can see that, at T_eq ≳ 600 K, the high metallicity atmosphere yields much lower CH₄ abundances than those for solar composition atmospheres at P ∼ 10⁻³–10⁻⁴ bar, where the HCN production takes place. The CH₄ depletion is due to the preference for CO over CH₄ at higher metallicity, as well as the hotter temperature of the higher metallicity atmospheres. Because HCN production requires the presence of CH₄ as discussed earlier, the CH₄ depletion results in the HCN depletion at high metallicity atmospheres.

We next turn to the study of the observational feasibility of NH₃ and HCN in exoplanet transmission spectroscopy. We use the publicly available code CHIMERA (Line et al. 2013) to generate synthetic transmission spectra. We customize CHIMERA so that the molecular abundances of H₂O, CH₄, CO, CO₂, NH₃, N₂, HCN, and C₂H₂, C₂H₆ are extracted from the results of VULCAN. We assume thermochemical equilibrium for the remaining chemical species. We assume Jupiter-mass planets with 10 bar reference radii of 1.21, 1.11, and 1.04R_J at 0.1, 1, and 10 Gyr, respectively. These radii correspond to the surface gravities of 16.90, 19, 96, and 22.71 m s⁻², assumed in our photochemical calculations (see Table 1). To compute transit depths, we assume a solar radius for all spectral calculations.

The magnitudes of NH₃ and HCN features depend on the planetary equilibrium temperatures. The top left panel of Figure 7 shows the transmission spectra for different T_eq values. In general, NH₃ leaves relatively strong spectral features at 1.2, 1.5, 2.0, 3.0, and 11 μm, while HCN leaves features only at 14 μm. The NH₃ features at near-infrared wavelength are in agreement with MacDonald & Madhusudhan (2017a), whereas several unique features beyond 2 μm suggested by MacDonald & Madhusudhan (2017a) are barely seen in our spectra. This is because we mainly focus on warm exoplanets in which the spectral features of CH₄ tend to obscure the NH₃ spectral features. In our spectra relevant to hot Jupiters (T_eq = 1200 and 1400 K), the NH₃ depletion through thermochemical conversion and photodissociation significantly weakens the NH₃ feature, as compared to MacDonald & Madhusudhan (2017a) who fixed the NH₃ abundance regardless of planetary equilibrium temperature.

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We also conduct the same analysis for HCN; however, HCN features are almost absent in our synthetic spectra. HCN features are weak in our models because HCN is present only at low pressures (≲10⁻³ bar) as HCN forms through photodissociation of NH₃ at P ∼ 10⁻³–10⁻⁴ bar. The magnitudes of HCN features at 3.1 and 14 μm, though weak, gradually increase with increasing equilibrium temperature, as the enhanced stellar UV photons cause the HCN production at slightly higher pressures. In our model, the 3.1 μm feature is at most ∼20 ppm, while the 14 μm feature could be larger than 50 ppm.

The NH₃ and HCN features also modestly depend on the planet's age. The top right panel of Figure 7 shows the transmission spectra of Jupiter-mass planets with T_eq = 800 K and K_zz = 10⁸ cm² s⁻¹ for different system ages. As discussed in Section 3.2, NH₃ and HCN abundances are lower at younger planets because of hotter interiors and deep atmospheres (Fortney et al. 2020). Thus, the NH₃ and HCN features tend to be weaker for younger planets. On the other hand, younger planets have lower surface gravity and larger atmospheric scale height. Because the large scale height enhances the amplitudes of spectral features and partly compensates for the effect of decreased abundances of NH₃ and HCN, the magnitudes of spectral features only moderately depend on system age.

We note that, of course, the actual strength of NH₃ and HCN features depends on the planetary gravity. The bottom right panel of Figure 7 shows the spectra for the planetary mass of 1 and 0.11M_J, corresponding to the surface gravity of 19.96 and 3.47 m s⁻² at 1 Gyr age (see Table 1). The 0.11M_J mass planet shows much larger spectral features, including NH₃ and HCN features. This is mostly because the spectral features of the transmission spectrum are scaled by atmospheric scale height (e.g., Kreidberg 2018). In fact, the two spectra agree well with each other once we rescale the 1M_J planet spectrum by multiplying a factor of 19.969/3.475, the ratio of the surface gravities (dashed lines). The different gravities still alter the spectral shapes at certain wavelengths owing to differences in atmospheric composition, such as the CO₂ absorption feature at 4.3 μm.

The magnitudes of NH₃ and HCN features also depend on the eddy diffusion coefficient. The left panel of Figure 8 shows the transmission spectra for different K_zz values. The NH₃ features become prominent as K_zz increases, as a higher K_zz pushes the depth of the photodissociation to lower pressures. On the other hand, the HCN features have a non-monotonic dependence on K_zz. The HCN features become weak at high K_zz because HCN production, which is driven by NH₃ photodissociation, takes place at much higher altitudes than that probed by the transmission spectrum. The features also become weak at very low K_zz, as thermochemistry tends to convert NH₃ to N₂ in the middle atmospheres before NH₃ is converted to HCN. Thus, interestingly, there is a sweet spot value of K_zz that maximizes the HCN features.

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Atmospheric metallicity also has a strong impact on the NH₃ and HCN feature strengths. The right panel shows the spectra for the atmospheric metallicities of 1×, 10×, and 100× the solar value. The NH₃ and HCN features become weaker as the metallicity becomes higher. This is because the NH₃ abundance remains roughly the same as metallicity increases owing to the conversion of N into N₂ at deep atmospheres (see Paper I, Sections 2 and 3.3) whereas other molecular abundances, such as H₂O, increase with increasing metallicity. As a result, NH₃ features tend to be embedded into the absorption features of other molecules. Meanwhile, unless the planet is as cool as T_eq ≲ 400 K, higher atmospheric metallicity leads to a lower abundance of CH₄, which results in the depletion of HCN (Section 3.3, see also Figure 2). Thus, observations of NH₃ and HCN are more challenging for higher metallicity atmospheres.

We investigate the observational feasibility of NH₃ and HCN in emission spectroscopy as well. As in the previous section, we use the CHIMERA to compute synthetic emission spectra for hypothetical Jupiter-mass planets around a Sun-like star, where the stellar spectrum is taken from the PHOENIX grid (Husser et al. 2013) for stellar effective temperature of T_eff = 5780 K, metallicity of [M/H] = 0, and gravity of $\mathrm{log}(g)=4.43$.

The NH₃ features in the emission spectra are maximized at warm exoplanets with T_eq ∼ 600–1000 K, similar to transmission spectroscopy. Figure 9 shows the emission spectra for various equilibrium temperatures. The emission spectra always exhibit the strongest NH₃ feature around 11 μm followed by the feature around ∼6 μm. The features at longer wavelengths are more noticeable because of the more favorable planet-to-star flux contrast. Since the planetary emitting flux is intrinsically weaker at cooler planets, as seen in the T_eq = 400 K case, the cooler planets have weaker NH₃ features if we assume the same stellar properties. On the other hand, hotter planets emit more flux but have a lower NH₃ abundance owing to thermal conversion, which also results in weaker NH₃ features as seen in the cases of T_eq = 1200 and 1400 K.

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The system age moderately affects NH₃ and HCN features in emission spectra. The upper three right panels of Figure 9 show the spectrum of a Jupiter-mass planet with T_eq = 800 K at 0.1, 1, and 10 Gyr. The planet at 0.1 Gyr has a relatively weak NH₃ feature because its hot deep atmospheres convert NH₃ into N₂ efficiently. On the other hand, the planetary emission itself becomes stronger at younger ages owing to the hot deep atmosphere.

The strength of the NH₃ feature also depends on the eddy diffusion coefficient. The left columns of Figure 10 show how the strength of NH₃ and HCN features vary with K_zz for a 1 Gyr old Jupiter-mass planet with T_eq = 800 K. The spectral shape is nearly the same between K_zz = 10¹¹ and 10⁸ cm² s⁻¹. This is because the quenched NH₃ abundance is insensitive to K_zz (Saumon et al. 2006; Zahnle & Marley 2014; Fortney et al. 2020; Paper I), and emission spectra probe the pressure level below the NH₃ photodissociation base at K_zz = 10⁸ cm² s⁻¹. Thus, the further elevation of the photodissociation base by high K_zz no longer affects the strength of the NH₃ feature. NH₃ features become weaker at a very low value of K_zz = 10⁸ cm² s⁻¹ because thermochemistry converts NH₃ to N₂ at the pressure level probed by emission spectra.

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Atmospheric metallicity substantially affects the strength of NH₃ and HCN features. The right columns of Figure 10 show the emission spectra at 1×, 10×, and 100× solar metallicity. The NH₃ and HCN feature becomes weaker at the higher atmospheric metallicity owing to the thermochemical conversion of NH₃ into N₂ at deep atmospheres, which results in the depletion of NH₃ and HCN at upper atmospheres. This trend is the same as that seen in the transmission spectroscopy. However, while the high metallicity weakens the entire spectral features for the transmission spectrum, the high metallicity instead enhances planetary emission by warming the atmosphere.

As in the transmission spectra, HCN features are relatively weak compared to NH₃ features. Only the feature around 14 μm is noticeable. The relatively weak HCN feature can be attributed to the vertical distribution of HCN. The emission spectrum probes deeper in the atmosphere than the transmission spectrum, while HCN is mainly produced by photochemistry in the upper atmosphere. This spatial separation between the HCN production region and the observationally sensitive region results in the relatively weak HCN features in the emission spectrum.

We quantify the observational feasibility of NH₃ by examining the difference in spectrum with NH₃ and without nitrogen species (i.e., NH₃ and HCN). For transmission spectra, we define the strength of NH₃ features as

$$\begin{eqnarray}{\rm{\Delta }}{\left(\displaystyle \frac{{R}_{{\rm{p}}}}{{R}_{{\rm{s}}}}\right)}_{{\mathrm{NH}}_{3}}^{2}={\left(\displaystyle \frac{{R}_{{\rm{p}}}}{{R}_{{\rm{s}}}}\right)}_{{\rm{w}}/\,{\mathrm{NH}}_{3}}^{2}-{\left(\displaystyle \frac{{R}_{{\rm{p}}}}{{R}_{{\rm{s}}}}\right)}_{{\rm{w}}/{\rm{o}}\,{\mathrm{NH}}_{3}\& \mathrm{HCN}}^{2}.\end{eqnarray} \tag{ 6 }$$

This approach is similar to MacDonald & Madhusudhan (2017a). For emission spectra, the strength is defined as

$$\begin{eqnarray}{\rm{\Delta }}{\left(\displaystyle \frac{{F}_{{\rm{p}}}}{{F}_{{\rm{s}}}}\right)}_{{\mathrm{NH}}_{3}}={\left(\displaystyle \frac{{F}_{{\rm{p}}}}{{F}_{{\rm{s}}}}\right)}_{{\rm{w}}/{\rm{o}}\,{\mathrm{NH}}_{3}\& \mathrm{HCN}}-{\left(\displaystyle \frac{{F}_{{\rm{p}}}}{{F}_{{\rm{s}}}}\right)}_{{\rm{w}}/\,{\mathrm{NH}}_{3}}.\end{eqnarray} \tag{ 7 }$$

We compute the above metric at a wavelength for various planetary equilibrium temperatures assuming Jupiter-mass planets around a Sun-like star at 1 Gyr age, with a solar composition atmosphere and K_zz = 10⁸ cm² s⁻¹. We note that the actual feature strength depends on stellar and planetary properties; for example, the feature strengths of the transmission spectrum are enhanced for smaller stars and/or lower gravity planets with larger scale heights. Our objective here is to explore the optimum range of wavelength and planetary equilibrium temperature for detecting NH₃ under the same system conditions. The same analysis is also carried out for HCN.

The left column of Figure 11 shows the NH₃ and HCN feature strengths of the transmission spectrum as a function of wavelength and equilibrium temperature. In the transmission spectra, NH₃ leaves relatively strong spectral features at 1.5, 2.0, and 11.0 μm. These features could be relatively strong, at an amplitude of >50 ppm (black contours), at equilibrium temperatures from ∼400–1000 K. Since the observational noise floor was anticipated to be 20–50 ppm (Greene et al. 2016), the result suggests that NH₃ could be identified in the near-infrared with JWST. The unique NH₃ feature at 11.0 μm, accessible to JWST-MIRI, would be particularly useful to identify NH₃, as the feature is present in an opacity window of H₂O and CH₄ and atmospheric clouds/hazes tend to be optically thin at longer wavelengths. In general, warm (∼400–1000 K) exoplanets are optimum targets for detecting NH₃ because hot planets tend to experience NH₃ depletion by both thermochemistry and photochemistry whereas cold planets suffer from weak spectral features owing to small atmospheric scale heights.

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Although the NH₃ feature strength of the transmission spectra is at most ∼50 ppm for Jupiter-mass planets around a Sun-like star, the emission spectrum could show much larger NH₃ features for the same conditions. The right column of Figure 11 shows the NH₃ and HCN feature strength for emission spectra. In emission, NH₃ leaves a moderately strong feature at ∼6 μm and a very prominent feature at ∼11 μm. In particular, the 11 μm feature strength exceeds 300 ppm at T_eq ∼ 400–1200 K, meaning that the NH₃ feature is more than 6 times larger than the noise floor of JWST-MIRI anticipated by Greene et al. (2016). Although the observational noise tends to be large at such a long wavelength owing to the decreased number of stellar photons, given the prominence of feature and expectation for low cloud and haze opacity, emission spectroscopy by JWST-MIRI would offer a viable window to search for NH₃ in a wide range of the equilibrium temperatures through the 11 μm feature.

Our model predicts that HCN features are very weak at a wide range of wavelengths and equilibrium temperatures. In both transmission and emission spectra, the HCN feature strength is smaller than 50 ppm over the entire T_eq range explored by this study (250–1400 K), except for the feature around 14 μm whose feature strength could be as large as 50 ppm for transmission and 300 ppm for emission spectra. Thus, the observation by JWST-MIRI may still be able to find a hint of the HCN feature in addition to the NH₃ feature. On the other hand, if future observations detect prominent HCN features at <10 μm, it potentially indicates that the atmospheric composition is significantly different from the solar composition assumed in these figures. For example, a very high C/O (C/O ≫ 1) increases HCN abundance by orders of magnitude (Moses et al. 2013b; Hobbs et al. 2022), which may yield noticeable HCN features at short wavelengths.

We have assumed clear atmospheres in this study; however, recent studies suggested that warm exoplanets are universally veiled by photochemical hazes (e.g., Crossfield & Kreidberg 2017; Gao et al. 2020; Dymont et al. 2022). Photochemical hazes can affect our results in multiple ways, including flattening spectral features that limit the observability of atmospheric molecules (e.g., Fortney 2005; Morley et al. 2013; Lavvas & Koskinen 2017; Kawashima & Ikoma 2018, 2019; Adams et al. 2019; Lavvas et al. 2019; Gao & Zhang 2020; Ohno & Kawashima 2020; Ohno & Tanaka 2021; Steinrueck et al. 2021, 2023; Arfaux & Lavvas 2022).

An additional intriguing effect is that hazes alter the energy balance and P–T profiles significantly (Morley et al. 2015; Lavvas & Arfaux 2021; Arfaux & Lavvas 2022; Steinrueck et al. 2023). For example, Molaverdikhani et al. (2020) suggested that (though they focused on radiative feedback of mineral clouds) thick clouds may cause hot deep atmospheres and deplete NH₃. The consequence of radiative feedback of photochemical haze is not trivial. The hazes heat upper atmospheres by absorbing stellar flux (Morley et al. 2015; Lavvas & Arfaux 2021), which may deplete NH₃ via thermochemical conversion. On the other hand, the hazes cool lower atmospheres by blocking stellar light from reaching the deeper atmosphere (Morley et al. 2015), which may act to maintain the quenched NH₃ abundance by suppressing the thermochemical conversion of NH₃ to N₂.

Hazes also shield atmospheres from stellar UV photons and may alter photochemistry. Sagan & Chyba (1997) and Wolf & Toon (2010) suggested that photochemical hazes could shield NH₃ from solar UV photons in the Archean Earth, which might help to maintain warm climates. If similar processes work at warm exoplanets, hazes may help to stabilize NH₃ against photodissociation. Overall haze effects depend on particle properties, such as particle size and shape, which are controlled by microphysical processes. We will comprehensively investigate the overall impacts of photochemical hazes on atmospheric structure and chemistry in future work.

While we have assumed the solar spectrum for the photochemical modeling, different stellar spectra could affect the results, especially for the photochemical depletion of NH₃. Indeed, Hu (2021) studied photochemistry in three temperature and cold exoplanets, K2-18b, PH2 b, and Kepler-167 e, and found that photodissociation of NH₃ is insignificant on planets around M stars as compared to those around G/K stars (see also Baeyens et al. 2022 for the effects of stellar spectral type in pseudo-2D photochemical simulations). This was attributed to the low UV flux of M-type stars at 200–230 nm that mainly causes the photodissociation of NH₃ (Hu 2021, see also Section 3.2). Figure 12 shows the stellar spectra of G-, K-, and M-type stars, where we use a solar spectrum of Gueymard (2018) as an analog of a G-type star, the spectrum of HD 40307 (T_eff* = 4867 K, R_* = 0.716R_⊙, Stassun et al. 2019) as an analog of a K-type star, and GJ 1214 as an analog of an M-type star (T_eff* = 3250 K, R_* = 0.215R_⊙, Cloutier et al. 2021). The latter two spectra are measured by the MUSCLES Treasury Survey ⁵ (France et al. 2016; Loyd et al. 2016; Youngblood et al. 2016). The cooler the star is, the weaker the UV flux from 200–230 nm is, which potentially lessens NH₃ depletion by photodissociation.

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To investigate the effects of stellar spectral type, we perform additional photochemical calculations for G-, K-, and M-type stars shown in the top panel of Figure 12. To isolate the effects of stellar spectral type on photochemistry, we use the same P–T profile of a Jupiter-mass planet with T_eq = 600 K at 1 Gyr (for the effects of stellar spectral type on P–T profiles, see Mollière et al. 2015; Fortney et al. 2020). We also adjust the orbital distance d so that the stellar flux on the top of the atmosphere is consistent with the assumed equilibrium temperature, as

$$\begin{eqnarray}&&d=\displaystyle \frac{1}{2}{R}_{* }{\left(\displaystyle \frac{{T}_{\mathrm{eff}* }}{{T}_{\mathrm{eq}}}\right)}^{2}.\end{eqnarray} \tag{ 8 }$$

We confirm that NH₃ could be more stable against photodissociation at cooler stars. The bottom panel of Figure 12 shows the vertical distributions of NH₃ and HCN on the planet around G-, K-, and M-type stars. As expected, NH₃ retains the quenched abundance until ∼10⁻⁵ bar for K- and M-type stars, which is approximately an order of magnitude lower than the pressure level where photodissociation takes place for G-type stars. Thus, we suggest that warm planets around K-type and M-type stars are ideal targets for detecting NH₃, as the photodissociation of NH₃ would be relatively insignificant.

Thus far, there have been three exoplanets for which NH₃ absorption was reported: the canonical transiting hot Jupiter HD 209458b (T_eq = 1484 K, Giacobbe et al. 2021) and warm Jupiters WASP-80b (T_eq = 817 K, Carleo et al. 2022) and WASP-69b (T_eq = 963 K, Guilluy et al. 2022), the latter two planets fall in the temperature regime where NH₃ features are expected to be relatively large (see Section 4). All of the above detections were accomplished by high-resolution transmission spectroscopy. For HD 209458 b, MacDonald & Madhusudhan (2017b) also reported the detection of NH₃ from low-resolution transmission spectroscopy. Giacobbe et al. (2021) detect NH₃ by cross correlating the observations with synthetic spectra assuming a vertically constant NH₃ abundance of 1.3 × 10⁻⁴, while MacDonald & Madhusudhan (2017b) constrained the NH₃ abundance to 10⁻⁸–2.7 × 10⁻⁶. Our simulations of a Jupiter-mass planet at 1 Gyr yield NH₃ abundances of ∼10⁻⁶ at the pressure level of interest for T_eq = 1400 K (Figure 3), which appears to be consistent with the constraint by MacDonald & Madhusudhan (2017b). However, we need a more careful analysis for planet-specific comparisons, as the eddy diffusion coefficient K_zz and intrinsic temperature T_int could differ from planet to planet. This is beyond the scope of this study. Since the quenched NH₃ abundance is sensitive to the intrinsic temperature, the potential detection of NH₃ may provide observational tests on the suggested hot deep interiors of hot Jupiters (Thorngren et al. 2019; Fortney et al. 2020).

While we have predicted that warm exoplanets are favorable targets for searching for NH₃, no previous studies with low-resolution spectroscopy have reported the detection of NH₃ for warm exoplanets. This could be due to the prevalence of clouds and hazes in warm exoplanetary atmospheres that mute the absorption features of gaseous molecules (e.g., Knutson et al. 2014; Kreidberg et al. 2014, 2018, 2022; Wakeford et al. 2017; Chachan et al. 2019, 2020; Libby-Roberts et al. 2020; Mikal-Evans et al. 2021; Alam et al. 2022, see Dymont et al. 2022 for a recent compilation). Since cloud and haze opacity tends to decrease with increasing wavelength, future observations at longer wavelengths would have better chances to detect NH₃, such as through the detection of the 11 μm feature. Another possible cause of the nondetection of NH₃ could be deep atmospheres being much hotter than those predicted by thermal evolution models for non-synchronized exoplanets. For example, Benneke et al. (2019) reported the nondetection of NH₃ on warm sub-Neptune GJ 3470b, while the planet is known to have a nonzero eccentricity of e ∼ 0.1 (Kosiarek et al. 2019). Such nonzero eccentricity may yield hot deep atmospheres through tidal heating and affect upper atmospheric compositions (Agúndez et al. 2014b; Fortney et al. 2020).

One of the interesting possibilities for the lack of NH₃ detection is that many warm exoplanets may have atmospheric compositions considerably different from solar compositions. For example, if warm exoplanets typically have high metallicity atmospheres, the detection of NH₃ becomes more challenging, as shown in Section 4. The prevalence of high metallicity atmospheres may be compatible with the mass–metallicity relation of warm Jupiters (Thorngren et al. 2016), planet formation models (e.g., Fortney et al. 2013; Venturini et al. 2016; Cridland et al. 2020), and several atmospheric observations of giant exoplanets (Wakeford et al. 2018; Carone et al. 2021;​​​​​ Ahrer et al. 2023; Alderson et al. 2023; Bean et al. 2023; Feinstein et al. 2023; JWST Transiting Exoplanet Community Early Release Science Team et al. 2023; Rustamkulov et al. 2023; Tsai et al. 2023). A planet may also have a subsolar N/O if the solid accretion inside the N₂ snowline determines the atmospheric composition (see, e.g., Figure 1 of Paper I), which would also lower the NH₃ abundance as compared that for solar N/O with the same atmospheric metallicity.

While we have assumed vertically constant K_zz so far, in reality, the eddy diffusion coefficient likely has a vertical variation (e.g., Zhang & Showman 2018a). The vertically varying K_zz potentially affects our results at some points; for example, it may promote thermochemical conversion of NH₃ to N₂ in deep atmospheres because of low K_zz, as seen in Moses et al. (2021). We can test the effect of vertically variable K_zz by assuming K_zz = K_{zz,1 bar}(P/1 bar)^−0.5. Following Moses et al. (2021), we also set K_zz = 10¹⁰ cm² s⁻¹ at P > 100 bar and the maximum value of K_zz = 10¹¹ cm² s⁻¹. Figure 13 shows the photochemical calculation results for various values of K_{zz,1 bar}. The vertical variable K_zz tends to facilitate the thermochemical conversion of NH₃ to N₂ owing to the weak vertical mixing in the deep atmosphere, while it mitigates the NH₃ photodissociation thanks to the strong mixing in the upper atmosphere. The HCN abundance in the upper atmosphere reflects the quenched NH₃ abundance as in the constant K_zz case, while HCN abundance at the lower atmosphere could be higher compared to constant K_zz cases because downward diffusive transport becomes slower as the pressure increases. The vertical variation of K_zz and its strength have remained poorly constrained by observations (Kawashima & Min 2021). Future observations of disequilibrium species more sensitive to the quench point than NH₃ is, such as CO, would help to probe K_zz in deep atmospheres (e.g., Miles et al. 2020; Mukherjee et al. 2022).

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Our study has relied on a 1D framework, whereas real exoplanetary atmospheres are in 3D and may show strong temperature contrasts between daysides and nightsides (e.g., Perez-Becker & Showman 2013; Komacek & Showman 2016); however, we do not anticipate that this is a major drawback in this case. Several studies have investigated how horizontal temperature variations and horizontal winds affect the chemistry of exoplanetary atmospheres. These include 3D GCMs (Cooper & Showman 2006; Drummond et al. 2018a, 2018b, 2020; Mendonca et al. 2018), equatorial 2D models (Tsai et al. 2021a), and pseudo-2D models that rotate a 1D model along the equator (Agúndez et al. 2012, 2014a; Baeyens et al. 2021, 2022; Moses et al. 2021). According to the pseudo-2D works by Moses et al. (2021) and Baeyens et al. (2022), the NH₃ abundance is almost invariant with longitudes at warm exoplanets with T_eq ≲ 1000 K, except for the pressure level of ≲10⁻³–10⁻⁴ bar where the photodissociation takes place. Drummond et al. (2020) performed 3D global circulation simulations on hot Jupiters HD 189733b and HD 209458b using a 3D GCM that implements a full kinetic chemistry based on the reduced chemical network of Venot et al. (2019) and showed that NH₃ abundance is vertically and longitudinally uniform in both planets, though they did not include photochemistry. This longitudinal independence could be attributed to the long thermochemical conversion timescale of NH₃, >10¹⁵ s at 1000 K (see Figure 4 of Tsai et al. 2018), which is much longer than typical horizontal transport timescales. In the deep atmosphere where the chemical quenching takes place, on the other hand, the atmospheric P–T profile is invariant with longitude because of the long radiative timescale. Thus, we anticipate that the NH₃ spatial distribution in real atmospheres is reasonably approximated by the 1D framework, especially for warm exoplanets that are optimum for detecting NH₃.

In Paper I and this study, we have focused on NH₃ and HCN since N₂, the remaining main N reservoir, in general, has negligibly low opacity in visible and infrared wavelengths. However, N₂ actually has moderate opacity at extremely hot temperatures, say >4000 K. High-resolution spectroscopy might still have a chance to detect N₂ if it abundantly exists in a hot thermosphere. In the context of terrestrial exoplanets with N₂-dominated atmospheres, Schwieterman et al. (2015) suggested that N₂ can be detected from the absorption feature of ${({{\rm{N}}}_{2})}_{2}$ dimer produced by N₂–N₂ collisions, though it unlikely affects the observable spectra of giant planets with much lower N₂ abundances. N₂–H₂ collision-induced absorption (CIA) opacity might still have some impacts; however, quantitative assessment is difficult as of yet owing to the limited valid range of wavelength and temperature for the available CIA absorption coefficient (Karman et al. 2019).