Detectable molecular features above hydrocarbon haze via transmission spectroscopy with JWST: Case studies of GJ 1214b-, GJ 436b-, HD 97658b-, and Kepler-51b-like planets

TL;DR

This study explores how JWST can detect molecular features in exoplanet atmospheres with hydrocarbon haze, using simulations of four specific planets to assess the visibility of absorption features despite haze effects.

Contribution

The paper demonstrates that JWST can detect molecular absorption features in hazy exoplanet atmospheres, especially at longer wavelengths, through detailed simulations of four case study planets.

Findings

Hazy, hydrogen-rich super-Earths can show detectable CH4 features at 3.3 μm.

Extremely low gravity planets like Kepler-51b have large haze particles causing flat spectra.

HST's muted features do not rule out strong JWST-detectable features at longer wavelengths.

Abstract

Some of the exoplanets so far observed show featureless or flat transmission spectra, possibly indicating the existence of clouds and/or haze in their atmospheres. Thanks to its large aperture size and broad wavelength coverage, JWST is expected to enable detailed investigation of exoplanet atmospheres, which could provide important constraints on the atmospheric composition obscured by clouds/haze. Here, we use four warm ($\lesssim 1000$ K) planets suitable for atmospheric characterization via transmission spectroscopy, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples to explore molecular absorption features detectable by JWST even in the existence of hydrocarbon haze in the atmospheres. We simulate photochemistry, the growth of hydrocarbon haze particles, and transmission spectra for the atmospheres of these four planets. Among the planetary parameters considered, super-Earths with hazy, relatively hydrogen-rich atmospheres are mostly expected to produce detectable molecular absorption features such as a quite prominent $\mathrm{CH_4}$ feature at 3.3 ${\rm \mu}$m even for the extreme case of the most efficient production of photochemical haze. For a planet that has extremely low gravity, such as Kepler-51b, haze particles grow significantly large in the upper atmosphere due to the small sedimentation velocity, resulting in the featureless or flat transmission spectrum in a wide wavelength range. This investigation shows that the transmission spectra with muted features measured by HST in most cases do not preclude strong features at the longer wavelengths accessible by JWST.

Tables

Table 1. Table 1: Model parameters and their values used in the simulations

Parameter	Description	Value	Reference
Common parameters
$K_{zz}$	Eddy diffusion coefficient	$1.00\times {10}^7$ ${\mathrm{cm}}^2$ $s^{-1}$
$s_1$	Monomer radius	$1.00\times {10}^{-3}$ $\mu$m
${\rho }_p$	Particle internal density	$1.00$ g ${\mathrm{cm}}^{-3}$
GJ 1214b
$R_s$	Host star radius	0.201 $R_{\odot }$	Anglada-Escudé et al. (2013)
$M_p$	Planet mass	$6.26$ $M_{\oplus }$	Anglada-Escudé et al. (2013)
$R_{1000}$ bar	1000-bar radius	2.07 $R_{\oplus }$
$a$	Semi-major axis	0.0148 AU	Anglada-Escudé et al. (2013)
$d$	Distance	14.6 pc	Youngblood et al. (2016)
$T_{\mathrm{int}}$	Intrinsic temperature	$120$ K
$T_{\mathrm{irr}}$	Irradiation temperature	$790$ K
$k_v$	Averaged opacity in the optical	${10}^{-4.1}$ ${\mathrm{cm}}^2$ $g^{-1}$
$k_{\mathrm{th}}$	Averaged opacity in the infrared	${10}^{-2.7}$ ${\mathrm{cm}}^2$ $g^{-1}$
GJ 436b
$R_s$	Host star radius	0.464 $R_{\odot }$	Torres et al. (2008)
$M_p$	Planet mass	$23.2$ $M_{\oplus }$	Torres et al. (2008)
$R_{1000}$ bar	1000-bar radius	3.758 $R_{\oplus }$
$a$	Semi-major axis	0.02872 AU	Torres et al. (2008)
$d$	Distance	10.1 pc	Youngblood et al. (2016)
$T_{\mathrm{int}}$	Intrinsic temperature	$170$ K
$T_{\mathrm{irr}}$	Irradiation temperature	$860$ K
$k_v$	Averaged opacity in the optical	${10}^{-3.6}$ ${\mathrm{cm}}^2$ $g^{-1}$
$k_{\mathrm{th}}$	Averaged opacity in the infrared	${10}^{-2.3}$ ${\mathrm{cm}}^2$ $g^{-1}$
HD 97658b
$R_s$	Host star radius	0.703 $R_{\odot }$	Dragomir et al. (2013)
$M_p$	Planet mass	$7.86$ $M_{\oplus }$	Dragomir et al. (2013)
$R_{1000}$ bar	1000-bar radius	1.943 $R_{\oplus }$
$a$	Semi-major axis	0.0796 AU	Dragomir et al. (2013)
$d$	Distance	21.1 pc	Youngblood et al. (2016)
$T_{\mathrm{int}}$	Intrinsic temperature	$120$ K
$T_{\mathrm{irr}}$	Irradiation temperature	$1037$ K
$k_v$	Averaged opacity in the optical	${10}^{-4.1}$ ${\mathrm{cm}}^2$ $g^{-1}$
$k_{\mathrm{th}}$	Averaged opacity in the infrared	${10}^{-2.7}$ ${\mathrm{cm}}^2$ $g^{-1}$
Kepler-51b
$R_s$	Host star radius	0.940 $R_{\odot }$	NASA Exoplanet Archiveaahttps://exoplanetarchive.ipac.caltech.edu
$M_p$	Planet mass	$2.1$ $M_{\oplus }$	Masuda (2014)
$R_{1000}$ bar	1000-bar radius	1.8 $R_{\oplus }$bbWe use the value of 2.3 $R_{\oplus }$ for the clear atmosphere case
$a$	Semi-major axis	0.2514 AU	Masuda (2014)
$T_{\mathrm{int}}$	Intrinsic temperature	$120$ K
$T_{\mathrm{irr}}$	Irradiation temperature	$793$ K
$k_v$	Averaged opacity in the optical	${10}^{-4.1}$ ${\mathrm{cm}}^2$ $g^{-1}$
$k_{\mathrm{th}}$	Averaged opacity in the infrared	${10}^{-2.7}$ ${\mathrm{cm}}^2$ $g^{-1}$

Table 2. Table 2: Detectable absorption features by JWST

Planet Type	Molecules	Wavelength [$\mu$m]
GJ 1214b	$H_{2}O$	1.4, 1.8, 1.9, 2.6, 2.7, 5.0, 5.2, 6.5, 6.6, 7.2
	${\mathrm{CH}}_4$	1.7, 2.3, 3.2, 3.3, 3.4, 3.6, 7.4, 7.7, 8.2, 8.3
	${\mathrm{NH}}_3$	3.0, 6.2, 8.9-11.8
	HCN	3.0
	${\mathrm{CO}}_2$	4.2
GJ 436b	${\mathrm{CH}}_4$	2.3, 3.3, 7.7
	${\mathrm{NH}}_3$	10.4, 10.7
HD 97658b	-	-
Kepler-51b	$H_{2}O$	2.6, 2.7, 5.2
	${\mathrm{CO}}_2$	4.3
	$\mathrm{CO}$	4.6

Full text

planets and satellites: atmospheres — planets and satellites: composition — planets and satellites: individual (GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b)

††journal: ApJL

1 Introduction

Transmission spectra of close-in exoplanets observed so far are somewhat diverse (Sing et al., 2016). There are some studies that explored such diversity by examining the correlation between the observed amplitude of absorption features and the planetary properties (Stevenson, 2016; Heng, 2016; Crossfield & Kreidberg, 2017). They all reached the conclusion that molecular absorption features are less pronounced in transmission spectra for lower equilibrium temperature although other planetary properties may affect such a correlation.

One explanation for this correlation is existence of photochemically-produced hydrocarbon haze obscuring the molecular features in the atmospheres of cooler planets (Zahnle et al., 2009; Miller-Ricci Kempton et al., 2012; Morley et al., 2013, 2015), because its primary source $\mathrm{CH_{4}}$ exists only at such low temperatures ($\lesssim 1000$ K) (e.g., Burrows & Sharp, 1999).

Among stars hosting currently observable warm ($\lesssim 1000$ K) low-mass planets, GJ 1214, GJ 436, and HD 97658 are the only three host stars whose UV emission spectra have been observed (France et al., 2016; Youngblood et al., 2016; Loyd et al., 2016). Also, high-precision transmission spectra for their planets were observed with HST (e.g., Kreidberg et al., 2014; Knutson et al., 2014a, b). They all show flat or featureless transmission spectra between 1.1 and 1.7 $\rm\mu m$, possibly indicating the existence of haze in the atmospheres. Since the knowledge of host-star’s UV spectrum is essential for the modeling of hydrocarbon haze (e.g., Kawashima & Ikoma, 2018, 2019), the above three planets serve as the most promising targets to understand the nature of haze in exoplanet atmospheres. In addition, Kepler-51b is attracting attention as a favorable target for atmospheric characterization via transmission spectroscopy due to its extremely low density and large atmospheric scale height (Masuda, 2014). In terms of haze science, this planet is also an interesting target because the sedimentation velocity of the particles in the atmosphere is expected to be quite low due to its low gravity, which allows particle growth in the upper atmosphere and mute features in the transmission spectrum. Recently, Wang & Dai (2019) investigated the effect of dusty outflows for Kepler-51b and 51d and showed that the existence of small dust of a fixed size at high altitudes could flatten the transmission spectra.

Currently, the number of exoplanets suitable for atmospheric characterization is still small due to the lack of bright targets and sufficient observational precision. Fortunately, TESS (Ricker et al., 2014) is expected to detect a great number of transiting exoplanets around nearby stars bright enough for atmospheric characterization. Also, JWST (Gardner et al., 2006) will enable high-precision transmission spectroscopy thanks to its large diameter, and also enable the spectroscopy at longer wavelengths than HST with its suite of spectroscopy instruments up to 12 $\mu$m, with photometry up to 28.5 $\mu$m (Beichman et al., 2014).

In this Letter, we use the above four favorable planets, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples and explore molecular absorption features detectable by JWST in the existence of hydrocarbon haze in their atmospheres. Planets similar in size to GJ 1214b and HD 97658b have been shown to be abundant (Fulton & Petigura, 2018), indicating more planets in this size range will be found by TESS and will be the primary targets for atmospheric characterization by JWST (Louie et al., 2018). We describe the models in §2, and show the results in §3. We discuss several effects to be examined in §4 and conclude this Letter in §5

2 Method

We model transmission spectra of an atmosphere with hydrocarbon haze using the photochemical, particle growth, and transmission spectrum models of Kawashima & Ikoma (2018) as follows: We first perform photochemical calculations to derive the steady-state, distribution of gaseous species. Our reaction rate list is the reduced vesion of Hu et al. (2012) and we include the reverse reactions in the same way as Hu & Seager (2014). Then we assume that the production rate of haze monomers at each altitude as the sum of the photodissociation rates of the major hydrocarbons in our photochemical model, $\mathrm{CH_{4}}$, $\mathrm{HCN}$, and $\mathrm{C_{2}H_{2}}$, as an upper limit for the monomer production rate since this approach effectively assumes 100% conversion efficiency from the photodissociation of these hydrocarbons to haze monomers. With this assumption, we derive the steady-state distribution of haze particles by the particle growth calculations. Finally, we model transmission spectra of the atmospheres with the obtained distributions of haze particles and gaseous species. For the details of each of the three models, see Kawashima & Ikoma (2018).

As for the UV spectra of the host stars GJ 1214, GJ 436, and HD 97658, we use the data constructed by the MUSCLES Treasury Survey (France et al., 2016; Youngblood et al., 2016; Loyd et al., 2016). As for Kepler-51 whose UV spectrum has not been observed, because of its similar properties to the Sun, we use the solar spectrum from Segura et al. (2003)111http://vpl.astro.washington.edu/spectra/stellar/other_stars.htm.

The setting for the atmospheres is as follows. We assume that the elemental abudance ratios of the atmospheric gas are the solar system ones, which we take from Table 2 of Lodders (2003). For the temperature-pressure profile, we use the analytical formula of Eq. (29) of Guillot (2010). We choose the values of the parameters, namely, the intrinsic temperature $T_{\mathrm{int}}$, irradiation temperature $T_{\mathrm{irr}}$, averaged opacity in the optical $k_{\mathrm{v}}$ and that in the infrared $k_{\mathrm{th}}$, so as to match the temperature-pressure profiles from Miller-Ricci & Fortney (2010) (the version with the solar metallicity and efficient dayside-to-nightside heat redistribution) for GJ 1214b and from Lewis et al. (2010) (their solar-metallicity version) for GJ 436b. As for HD 97658b and Kepler-51b, we adopt the same parameter values as the case of GJ 1214b except for $T_{\mathrm{irr}}$, which we calculate with Eq. (1) of Guillot (2010). We adopt the lower-boundary pressure of 1000 bar for photochemical calculation, while 10 bar in particle growth and transmission spectrum calculations.

For the calculations of photochemistry and particle growth, we choose the values of the reference radius equivalent to 1000 bar so as to roughly match the observed transit radii for a clear solar-composition atmosphere. Only for Kepler-51b, we use different values of the 1000-bar radius for two cases of the hazy and clear atmospheres. This is because with the same 1000-bar radius as in the clear atmosphere case, we would obtain too large transit radii for the hazy atmosphere to be consistent with the observed depth due to its extremely low gravity. When calculating the transmission spectra, we find the appropriate value of 10-bar radius that minimizes the reduced $\chi^{2}$ value in comparison between the theoretical and observed transit depths. We consider the observed transmission spectra of Kreidberg et al. (2014), Knutson et al. (2014a), Knutson et al. (2014b) for GJ 1214b, GJ 436b, and HD 97658b, respectively, and the observed radius of Kepler-51b from Masuda (2014). For the calculation of theoretical transit depth for each observed data point, we consider the transmission curve of the filter used in the observation, taking those data from the SVO Filter Profile Service222http://svo2.cab.inta-csic.es/theory/fps/ (Rodrigo et al., 2012; Rodrigo & Solano, 2013).

The parameters and their values we use are listed in Table 1.

3 Results

Figure 1 shows the transmission spectrum models for atmospheres with and without haze for the cases of GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b. We calculate the deviation in transit depth caused by $nH_{\mathrm{ref}}$ at a reference pressure level, $R_{\mathrm{ref}}$, as $2nR_{\mathrm{ref}}H_{\mathrm{ref}}/R_{s}^{2}$ (Brown, 2001), where $H_{\mathrm{ref}}$ is the atmospheric scale height at $R_{\mathrm{ref}}$. The reference pressures are taken to be $10^{-4}$ bar for GJ 1214b, GJ 436b, and HD 97658b, and $10^{-6}$ bar for Kepler-51b, which roughly correspond to the pressure-levels of the transit radii. Note that the transmission spectrum models for clear atmospheres are also calculated with the distribution of gaseous species from photochemical calculations.

A number of spectral features are produced by molecules above the optically-thick photochemical haze. These features are generally $\lesssim 2$ atmospheric scale heights for GJ 1214b- and GJ 436b-like planets, and $\lesssim 1$ for HD 97658b-like planets, while $\lesssim 6$ for the cases of clear atmospheres. As photodissociation is the driver for haze formation, this finding is general for exoplanets having solar composition atmospheres under similar levels of UV irradiation.

Considering a precision of $\sim$25 ppm expected to be achieved by JWST (Beichman et al., 2014) and a spectral resolution of $R=100$, we find detectable absorption features with the upper-limit production rate of haze monomers for each planet as listed in Table 2.

Some molecular absorption features will be detectable for a planet like GJ 1214b, due to lower incoming UV flux, namely lower monomer production rate, and larger planet-to-star radius ratio. For the planet GJ 1214b itself, however, the 1.4 $\mathrm{\mu}$m $\mathrm{H_{2}O}$ feature was not detected by Kreidberg et al. (2014) at the precision of $\sim 25$ ppm. While Morley et al. (2015) demonstrated that their haze formation efficiency parameters of $\gtrsim 10$% could match the observed flatness of Kreidberg et al. (2014) for 50 $\times$ Solar atmosphere, by considering particle growth, we have confirmed that our 1, 10, 100, 1000 $\times$ Solar atmospheres all fail to become as flat as the observation even adopting the maximum monomer production rates (Kawashima & Ikoma, 2019), possibly indicating extremely high metallicity, and/or aggregate haze particles (Adams et al., 2019), and/or coexistence of haze and other aerosols (see also discussion in §4). The message here is that a GJ 1214b-like planet having solar composition atmospheres and similar UV environment will be particularly suitable for future atmospheric characterization. For the case of HD 97658b, all the features in the wavelength range are undetectable due to the higher incoming UV flux, namely higher monomer production rate, and smaller planet-to-star radius ratio.

Among the detectable molecules, it is promising that several features of $\mathrm{CH_{4}}$, which is a key indicator of haze formation, remains detectable even in the existence of haze for GJ 1214b- and GJ 436b-like planets, especially for its 3.3 $\mathrm{\mu}$m feature. Note that this strong 3.3 $\mathrm{\mu}$m $\mathrm{CH_{4}}$ feature has been detected in the solar occultation spectrum of cooler celestial bodies in our solar system such as Saturn (Dalba et al., 2015) and Titan (Robinson et al., 2014). In the spectrum for Kepler-51b, the CH4 features are invisible, because $\mathrm{CH_{4}}$ is photodissociated and virtually absent above a thick haze layer at the low pressures of $\sim 10^{-6}$ bar.

In the case of Kepler-51b, the transmission spectrum model for the atmosphere with haze is quite featureless due to the existence of large haze particles in the upper atmosphere, unlike in the other three cases. However, distinct absorption features of $\mathrm{CO_{2}}$ and CO are detectable due to their larger abundances in the upper atmosphere. This comes from its extremely low gravity, which makes an optical depth for a given pressure much larger and thus both the photodissociation rate of $\mathrm{CH_{4}}$ and resultant production flux of atomic carbon much smaller. This very small production flux of $\mathrm{C}$ allows effective conversion of C into $\mathrm{CO}$/$\mathrm{CO_{2}}$ by reaction between $\mathrm{H_{2}O}$, while $\mathrm{C}$ remains abundant and $\mathrm{CO}$/$\mathrm{CO_{2}}$ less abundant for the other planet cases.

In Figure 2, we plot the calculated vertical profiles of haze properties for the typical super-Earth gravity case of (a) HD 97658b and the extremely low gravity case of (b) Kepler-51b. In the case of HD 97658b, in the upper atmosphere ($\lesssim$ 10*-6* bar), particles grow little because sedimentation occurs faster than collisional growth. Collisional growth occurs significantly from the pressure level of $\sim 10^{-6}$ bar on and results in haze particles with the average radius of $\sim 3-4$ $\mu$m at the lower boundary of 10 bar. On the other hand, in the case of Kepler-51b, it is demonstrated that haze particles grow much larger in the upper atmosphere ($\sim 0.1$ $\mu$m at $\sim 10^{-6}$ bar) and results in the particles of as large as $\sim 100$ $\mu$m at 10 bar. This is because particles can become large via collisional growth even in the upper atmosphere, instead of falling downward rapidly, due to the small sedimentation velocity from low gravity. Note that although the monomer production rate for Kepler-51b is $\sim 2$ times higher than that for HD 97658b, the effect of the extremely low gravity turns out to make a much greater contribution to such a difference between those two spectra than that of high monomer production rate. Trends of vertical profiles for GJ 1214b and GJ 436b are similar to that of HD 97658b but with slightly smaller haze mass density because of the smaller monomer production rates (see Kawashima & Ikoma, 2018, for the dependence on monomer production rate).

4 Discussion

In this study, we have assumed maximum production rate of haze monomers in order to explore the detectable features at the worst case for solar composition atmospheres. As for the eddy diffusion coefficient, the molecular absorption features become more prominent for the larger value because of the efficient downward transport of haze particles, while remaining similar for the smaller value (Kawashima & Ikoma, 2019).

In order to briefly assess the effect of metallicity and C/O ratio, in Figure 3, we show the transmission spectrum models for the cases of different metallicity and C/O ratio for GJ 1214b. One realizes that more absorption features become detectable for the case of 100 $\times$ Solar atmosphere because of the smaller monomer production rate due to an enhanced photon-shielding effect by other molecules, while some features at relatively long wavelengths become undetectable due to smaller atmospheric scale height (Kawashima & Ikoma, 2019). On the other hand, the effect of the C/O ratio is relatively small and among the detectable features for the solar composition atmosphere, $\mathrm{H_{2}O}$ features at 1.8, 5.0, 5.2, and 7.2 $\mu$m, $\mathrm{CO_{2}}$ features at 4.2 $\mu$m, and $\mathrm{NH_{3}}$ features at 6.2 $\mu$m become undetectable due to the slightly higher monomer production rate (Kawashima & Ikoma, 2019).

Besides hydrocarbon haze, the existence of other aerosols can mute spectral features in transmission: condensation clouds such as KCl, ZnS, $\mathrm{K_{2}SO_{4}}$, ZnO, and graphite clouds in the temperature range of interest in this study ($\lesssim 1000$ K) (Miller-Ricci Kempton et al., 2012; Morley et al., 2013; Mbarek & Kempton, 2016; Ohno & Okuzumi, 2018; Gao & Benneke, 2018; Ormel & Min, 2019) and photochemical haze made of sulfur species (Hu et al., 2013; Zahnle et al., 2016; Gao et al., 2017).

In outflowing atmospheres, while having little effect on the profiles of pressure and density, the velocity of the outward flow may affect the sedimentation of small particles. The sedimentation velocity of haze particles are much faster than the outward velocity, which we estimate with the isothermal Parker solution (Parker, 1958) for simplicity, for all the cases except Kepler-51b, whereas we have confirmed that in the case of Kepler-51b, the sedimentation velocity of the volume-averaged-size particles are smaller than the outward velocity for the region of the pressures lower than $1.3\times 10^{-7}$ bar. However, since the dominant monomer production region is below this pressure-level, the flow would have little impact on our results. The detailed consideration of this effect is beyond the scope of this study.

Also, as for extended atmospheres like Kepler-51b’s, the effect of the tidal potential may affect the hydrostatic structure of the atmosphere. By using Eq. (12) of Erkaev et al. (2007), we have confirmed that the gravitational potential at the optically thick radius at $1.0\times 10^{-6}$ bar, which is 9% of its Hill radius, would decrease to 86% due to the tidal potential and thus do not have significant impact on our results.

5 Conclusions

In this study, we have used four warm ($\lesssim 1000$ K) planets suitable for atmospheric characterization via transmission spectroscopy, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples and explored molecular absorption features detectable by JWST even in the existence of hydrocarbon haze in their atmospheres. Using the models of Kawashima & Ikoma (2018), we have simulated photochemistry, the growth of hydrocarbon haze particles, and transmission spectra for the atmospheres of these four planets.

We have found that among the planetary parameters considered, super-Earths with hazy, relatively hydrogen-rich atmospheres are mostly expected to produce detectable molecular absorption features such as a quite prominent $\mathrm{CH_{4}}$ feature at 3.3 ${\rm\mu}$m even for the extreme case of the most efficient production of photochemical haze. The sizes of those features correspond to $1\sim 2$ atmospheric scale heights; while they are substantially smaller than a haze-free atmosphere, those features would be detectable with at precision expected for JWST. Especially, planets with higher gravity, lower UV irradiation, and higher temperature are more suitable (Kawashima & Ikoma, 2019). Slight disagreement between our synthetic spectrum and very flat one observed for GJ 1214b, however, implies the importance of additional confounding effects.

We have also demonstrated that in the case of extremely low gravity planet, Kepler-51b, haze particles grow significantly large in the upper atmosphere due to the small sedimentation velocity, resulting in the featureless or flat transmission spectrum in a wide wavelength range.

In summary, various molecular absorption features are expected to be detectable for relatively hydrogen-rich atmospheres even in the existence of hydrocarbon haze with JWST, given its high precision and long-wavelength capabilities. We thus suggest that the transmission spectra with muted features measured by HST in most cases do not preclude strong features at the longer wavelengths accessible by JWST.

We thank the anonymous referee for his/her careful reading and constructive comments, which helped us improve this letter greatly. The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Y.K. thanks the travel support of JPL’s Science Visitor and Colloquium Program. Y.K. is supported by the Grant-in-Aid for JSPS Fellow (JSPS KAKENHI No.15J08463), Leading Graduate Course for Frontiers of Mathematical Sciences and Physics, Grant-in-Aid for Scientific Research (A) (JSPS KAKENHI No.15H02065), and the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement 776403. R.H. is supported by NASA Grant No. 80NM0018F0612. M.I. is supported by JSPS KAKENHI No. 18H05439 and Core-to-Core Program International Network of Planetary Sciences. This work has made use of the MUSCLES Treasury Survey High-Level Science Products (doi:10.17909/T9DG6F) and the SVO Filter Profile Service (http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO through grant AyA2014-55216.