The Peculiar Atmospheric Chemistry of KELT-9b

In Figures 2 and 4, we see that the abundance of CO remains remarkably constant across a broad range of temperatures (2000–4500 K), C/O values, and for pressures of 0.01–0.1 bar. It is not only the dominant carbon carrier by several orders of magnitude in the mixing ratio (its nearest competitor is CO₂), but it is the dominant molecule alongside water at low temperatures and C/O values.

In Figure 3, we further investigate the role of CO as a metallicity diagnostic. At temperatures of 2000–3000 K, almost all of the available carbon or oxygen is locked up in CO and the ratio of the CO number density to the total amount of either atomic C or O is very close to unity, depending on the value of C/O. This correspondence starts to break down at 4000 K and hotter, as CO dissociates into its constituents. Measuring CO alone would not constrain C/H or O/H directly, because C/O is a priori unknown. Additional molecules such as water are needed to set constraints on C/O being smaller or larger than unity and therefore to fully utilize CO as a metallicity diagnostic. In Figure 3, we also keep the ratios of the elemental abundances fixed, but increase the elemental abundances themselves by the same factor. For temperatures of 2000–3000 K and up to about 100× the solar metallicity, CO is a good tracer of the metallicity. By contrast, CO₂ is absent at these temperatures unless the metallicity approaches 1000–10,000 times the solar value and the temperature is 2000 K or lower. We consider these conditions to be unlikely for the atmosphere of KELT-9b. We predict CO, rather than CO₂ (e.g., Moses et al. 2013), to play the role of the metallicity diagnostic.

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In emission, the abundance of water holds steady until about 3000 K or higher, beyond which it starts to dissociate (Figure 2). A less intuitive outcome is that, because of the lower pressure probed in transmission, the drop in the water abundance is much steeper across temperature. In fact, at solar metallicity, it drops by more than 6 orders of magnitude between 2000–4500 K. Such a sensitivity to temperature implies that water may be used as a thermometer in the transmission spectrum of KELT-9b. Used in tandem with carbon monoxide, the elemental abundances of carbon and oxygen may be robustly determined. The atmosphere of KELT-9b becomes a tightly constrained chemical system.

A caveat is that water may also become scarce when C/O approaches unity (Kuchner & Seager 2005; Madhusudhan 2012), as shown in Figure 4. However, when C/O ≳ 1, we expect acetylene, methane, and hydrogen cyanide to become important. These species are spectroscopically active in the infrared range of wavelengths and should be detectable under these conditions. At these high temperatures, graphite formation (Moses et al. 2013) is unimportant, which would in principle allow C/O > 1 in the gas phase.

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A prediction of having a very hot atmosphere is that the neutral species of atomic metals becomes prominent. At solar metallicity, magnesium and iron have mixing ratios ∼10⁻⁴ in both emission and transmission from 2000–3500 K, dropping to ∼10⁻⁵ in transmission (with a slower drop in emission). Above 3000 K in transmission, atomic oxygen attains mixing ratios of ∼10⁻⁴. Aluminum, nickel, and sodium have mixing ratios as high as ∼10⁻⁶. All of these properties imply that it is possible to directly constrain the heavy-metal content of the atmosphere of KELT-9b. We will make predictions for detecting iron via ground-based, high-resolution spectroscopy in Section 4.

Another prediction is that free electrons have mixing ratios as high as ∼10⁻⁴ (Figure 2). For temperatures from 2000–4500 K, the mixing ratio of free electrons is comparable to or greater than that of hydrogen anions (H⁻). However, Thomson scattering has a somewhat small, wavelength-independent cross-section of σ_T ≈ 6.65 × 10⁻²⁵ cm². The cross-section associated with hydrogen anions (${\sigma }_{{{\rm{H}}}^{-}}$) has a bound-free component up to 1.6419 μm, the photo-detachment threshold, and a free–free component that extends into the mid-infrared range of wavelengths (John 1988). Figure 1 of Arcangeli et al. (2018) illustrates this graphically, where we see that ${\sigma }_{{{\rm{H}}}^{-}}\sim {10}^{-17}\mbox{--}{10}^{-16}$ cm². We conclude that Thomson scattering is a negligible effect compared to the extinction of light by H⁻.

To investigate the predicted prominence of spectral lines associated with neutral and singly ionized iron, we now simulate ground-based, resolution ∼100,000 observations of them. This technique has previously been established and consists of cross-correlating the observed system (star plus exoplanet) spectrum with a template of the atom or molecule being sought (Snellen et al. 2010; Brogi et al. 2012). To construct this template, we use the spectroscopic line list of Fe and Fe⁺ from the Vienna Atomic Line Database (Ryabchikova et al. 2015). We compute opacities from this line list using standard methods (e.g., Grimm & Heng 2015; Heng 2017). To generate transmission spectra, we use the analytical formula of Heng & Kitzmann (2017). For illustration, we assume a constant opacity of 0.01 cm² g⁻¹ to mimic a spectral continuum, a reference pressure of 0.1 bar at the white-light radius measured by Gaudi et al. (2017), a transit chord (terminator) temperature of 3000 K, and volume mixing ratios of 5 × 10⁻⁵ and 10⁻⁷ for Fe and Fe⁺, respectively.

Figure 5 shows our theoretical transmission spectra containing Fe and Fe⁺ versus Fe⁺ only in the visible range of wavelengths. At the expected temperatures of KELT-9b, the energy levels of Fe are preferentially populated compared to Fe⁺. It is therefore unsurprising that Fe is dominant over Fe⁺ as an opacity source. We expect the star to be deficient in Fe lines, because calculations assuming collisional ionization equilibrium have shown that the abundance of Fe drops rapidly as the temperature exceeds 10,000 K; the abundance of Fe⁺ becomes dominant only at these temperatures (Kaastra et al. 2008).

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In Figure 5, we also show a simulated transit observation of KELT-9b with the HARPS-N spectrograph located at the 3.6-meter TNG telescope at La Palma, which has a spectral resolution of about 110,000. Due to the brightness of KELT-9, HARPS-N is expected to provide a signal-to-noise ratio (S/N) of at least 100 in the stellar continuum at 500 nm after a single exposure of 200 s. The transit duration is 3 hr, implying that 54 observations may be obtained in-transit, resulting in a combined S/N of 735 at 500 nm. Here, our PHOENIX model for KELT-9 (Husser et al. 2013) is convolved with the line-spread function to match the rotational velocity broadening ($v\sin i=111.4$ km s⁻¹), because we are interested in resolving individual spectral lines. We also multiplied it with a SkyCalc model from ESO (Noll et al. 2012; Jones et al. 2013) of the telluric transmission spectrum across the wavelength range accessible by HARPS-N (387–691 nm). Our prediction is that iron can be observed at high S/N after observing a single transit with a high-resolution spectrograph on a 4-meter-class telescope, e.g., with HARPS-N or CARMENES.

Ultraviolet transit spectroscopy using HST is now an established technique (e.g., Ehrenreich et al. 2015). It has been used to detect both atomic hydrogen and metals (e.g., Vidal-Madjar et al. 2004). Besides the semi-forbidden lines, there is a zoo of near-ultraviolet resonant lines associated with neutral and singly ionized metal atoms, e.g., see Tables 9.3 and 9.4 of Draine (2011). These include the Fe i doublet at 0.37 and 0.39 μm, a set of Ni i lines from 0.34–0.35 μm, a set of Ti i lines from 0.33–0.52 μm, the C i triplet at 0.17 μm, the O i triplet at 0.13 μm, and a Mg i line at 0.29 μm.

Our predictions may be decisively tested by JWST via measurements of the transmission spectrum, dayside emission spectrum, and nightside emission spectrum. Such a program will conceivably fit within a small JWST proposal (≤25 hr). Detecting CO and H₂O jointly will set constraints on the temperatures, C/O, and metallicity.

The CHEOPS bandpass covers 0.33–1.1 μm (Broeg et al. 2013). For hot Jupiters with equilibrium temperatures ≲1300 K, a CHEOPS secondary eclipse translates directly into a measurement of the geometric albedo (Seager 2010). For somewhat hotter temperatures, the secondary eclipse measurement samples a combination of reflected light and thermal emission that depends on the dayside–nightside heat redistribution efficiency (Heng & Demory 2013). The dayside of KELT-9b is so hot that its blackbody peak wavelength is about 0.65 μm, which is in the middle of the CHEOPS bandpass (Figure 6). Similar to HST, CHEOPS will reside in low-Earth orbit, meaning Earth crossings of the South Atlantic Anomaly will prevent continuous monitoring in any direction. KELT-9 is visible to CHEOPS for ≈2.5 months per year and observations can be obtained at an observing efficiency between 50% and 70% (with the upper limit being the maximum obtainable), yielding about 35 occultations annually.

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The stellar effective temperature is 10,150 K, while for the planetary equilibrium temperature we assume no redistribution (f' = 2/3 in Equation (3.9) of Seager 2010) and a Bond albedo of 0.1 (geometric albedo of 0.067 assuming isotropic scattering). Both the star and exoplanet are assumed to emit as blackbodies, and we integrate their fluxes in the CHEOPS bandpass, which is shown in Figure 6. Using Equations (3.40) and (3.49) in Seager (2010), we compute the secondary eclipse depths due to thermal emission and reflected light, respectively. For KELT-9b, these are 427.9 parts per million (ppm) and 45.6 ppm, which gives 473.5 ppm in total. The thermal emission dominates reflected light by a factor of more than 9, implying that CHEOPS secondary eclipses are unambiguously sampling the thermal emission from KELT-9b.

To compute the precision attained with a single secondary eclipse of KELT-9b, we use the CHEOPS exposure time calculator (ETC). As input, we use the properties of the KELT-9 star (Gaudi et al. 2017). The exposure time was set to 1 s. Stellar granulation noise was excluded from the calculation as the star does not have a convective envelope. With these inputs, we estimate a precision of about 23 ppm for a single secondary eclipse (Figure 6). This translates into an S/N of ≈21, equivalent to better than a 5% precision in the thermal emission flux. The ability to obtain multiple secondary eclipses without data stacking means that we can quantify the climate variability of KELT-9b, for which only an upper limit was previously set on HD 189733b using Spitzer data (Agol et al. 2010).

One may use the secondary eclipse measurements to perform eclipse mapping (de Wit et al. 2012; Majeau et al. 2012). The eclipse mapping technique is sensitive to the brightness temperature contrast on the planet's dayside. Assuming a hotter region on the planet photosphere with a brightness temperature 1500 K larger than that of the continuum would yield a 30 ppm amplitude signal in both occultation ingress and egress in the CHEOPS bandpass. We estimate that a photometric precision of 15 ppm over 2 minutes is required to achieve a 4σ detection of the ingress/egress features. We expect CHEOPS to achieve a precision of about 100 ppm over 2 minutes, which would require about 45 occultations to retrieve an optical eclipse map of that planet. These observations bear two caveats. First, the impact parameter of b = 0.17 (Gaudi et al. 2017) will negatively impact our ability to constrain the latitudinal location of the hot spot. Second, the level of stellar activity on short timescales (∼minutes) probed at visible wavelengths will be critical to assess the feasibility of these observations.

In the current study, we have explored the atmospheric chemistry of ultra-hot Jupiters for which KELT-9b is an archetype. In contrast to other studies (Arcangeli et al. 2018; Kreidberg et al. 2018; Lothringer et al. 2018; Mansfield et al. 2018; Parmentier et al. 2018), we do not assume chemical equilibrium in our calculations, but instead perform photochemical kinetic calculations, which explicitly quantify the effects of atmospheric mixing and photochemistry. We then further explore the atmospheric chemistry using chemical equilibrium calculations that include a set of metals. Our findings include the following.

• 1.  
  Photochemistry, rather than atmospheric mixing, is the main driver for disequilibrium chemistry at low pressures. Nevertheless, at pressures probed by optical and infrared spectroscopy at low resolution, chemical equilibrium is a reasonable approximation.
• 2.  
  When analyzed in tandem, the abundances of carbon monoxide and water allows one to completely solve for C/H, O/H, and temperature, provided that chemical equilibrium is assumed.
• 3.  
  Metals in their atomic form are predicted to be observable. In particular, atomic iron should be seen via a forest of optical and near-infrared lines using high-resolution ground-based spectrographs such as HARPS-N and CARMENES.

While we have argued that horizontal mixing does not significantly introduce chemical disequilibrium in ultra-hot Jupiters, a more rigorous investigation would involve running 3D GCMs of KELT-9b-like exoplanets that include a treatment of disequilibrium chemistry (rather than assuming chemical equilibrium) and a varying specific heat capacity (due to the co-existence of atomic and molecular hydrogen in the same atmosphere). Existing work in the published literature already hint that results from hot Jupiter GCMs (executed at lower temperatures than that for KELT-9b) may not carry over straightforwardly. For example, Showman et al. (2013) studied the transition between moderate and intense stellar insolation using GCMs. To lowest order, the zonal wind speeds are driven by the dayside–nightside temperature contrast, which is unknown for KELT-9b. A higher dayside–nightside temperature contrast should lead to faster winds, but this cannot increase without bound (Fromang et al. 2016). Under moderate stellar insolation, the usual flow pattern of a zonal jet appears (see Heng & Showman 2015 for a review). Under intense stellar insolation, a combination of the damping of planetary-scale waves and frictional drag inhibit zonal jet formation and dayside-to-nightside flow. It remains an open question if the atmospheric flow of ultra-hot Jupiters occupy yet another regime and if these flows are capable of significantly driving the atmosphere away from chemical equilibrium. Future work needs to elucidate the flow behavior and its influence on the chemistry of KELT-9b-like exoplanets in 3D.