Dim Prospects for Transmission Spectra of Ocean Earths around M Stars

The GCM outputs that we use for this work were simulated by Kopparapu et al. (2017). Briefly, Kopparapu et al. (2017) use a modified version of the Community Atmosphere Model (CAM) version 4 (Neale et al. 2010), called ExoCAM,^{9 ,10} that is suitable for studies of exoplanet habitability. More details about the updates made to ExoCAM are given in Wolf (2017), Haqq-Misra et al. (2018), and Wolf et al. (2019). Kopparapu et al. (2017) explored 39 different configurations of an ocean-covered Earth-sized planet synchronously rotating around a late-M to mid-K star (T_eff from 2600 to 4500 K) in the HZ. The simulated planets experience a range of varying incident fluxes from their host stars. The effective temperature, luminosity, period, and mass of the star are defined a priori, while the stellar radius is calculated using the Stefan–Boltzmann law (L = 4πσR²T⁴) for consistency. The planets in every simulation share a radius and mass of 1 R_⊕ and 1 M_⊕. They are fixed to be entirely covered with a 50 m slab of ocean without any ocean heat transport. Their atmospheres assume a surface pressure of 1 bar, like the Earth, and include just H₂O and N₂ (CO₂ is removed for simplicity because the original study was focused on water vapor and cloud processes near the inner edge of the HZ; see Section 3.1). Both liquid and ice water clouds are prognostically calculated in the model based on the local atmospheric conditions in each grid cell. Clouds are treated as Mie scatterers with the radii of liquid cloud droplets assumed to be 14 μm in all atmospheric layers. Ice clouds have effective radii of ice crystals ranging from a few tenths to a few hundred microns based on a temperature-dependent parameterization.

3D climate simulations were run until either they reached thermal equilibrium (i.e., the net absorbed stellar flux equals the outgoing longwave flux, and the global mean temperature has stabilized) or until a runaway greenhouse was triggered via a critical energy imbalance due to overwhelming thermal water vapor opacities (Goldblatt et al. 2013). The last converged solutions (i.e., climatologically stable) were taken as the inner edge of the HZ (Kopparapu et al. 2017). Note that a fully realized runaway greenhouse would evaporate the entirety of the oceans into its atmospheres, leading to surface temperatures of ∼1600 K (Goldblatt et al. 2013). However, such a climate is beyond the operational bounds of the GCM, which becomes numerically unstable when global mean surface temperatures approach ∼400 K. For these cases, Kopparapu et al. (2017) took the 3D model results from the last several orbits before the numerical instability occurred. Thus, the "runaway" cases represent a snapshot of planets that are undergoing a runaway greenhouse process, and are therefore in a transient state. With respect to observable phenomena, these incipient runaway states are perhaps best considered as a sampling of hot, moist, and optically thick atmospheres (e.g., Goldblatt 2015).

The results of Kopparapu et al. (2017) also indicate that some planets reach moist greenhouse states (>10⁻³ H₂O mixing ratio at 1 mbar) with relatively habitable surface temperatures (∼280 K) due to enhanced stratospheric water vapor driven by the general circulation of slow rotators. Note that Fujii et al. (2017) arrived at a similar result, arguing that increased near-IR absorption also contributed to elevated stratospheric water vapor mixing ratios. A list of the simulations implemented by Kopparapu et al. (2017) and their stellar–planetary characteristics can be found in Table 1.

Table 1.  Parameters for the Different Simulated Cases Run by Kopparapu et al. (2017)

Teff (K)	Stellar Radius (R⊙)	Incident Flux (W m−2)	Period (days)	Surface Temperature (K)	H2O Mixing Ratio (at 1 mbar)
2600	0.110	1200	4.51	264.75	$7.71\times {10}^{-7}$
		1250	4.37	275.71	3.13 × 10−6
		1300	4.25	284.97	1.18 × 10−5
		1350	4.13	300.86	6.94 × 10−5
		1375	4.07	342.45	(runaway)
		1400	4.02	361.82	(runaway)
3000	0.158	1300	8.83	257.96	4.14 × 10−5
		1400	8.35	265.97	2.12 × 10−4
		1500	7.93	270.23	2.57 × 10−4
		1550	7.74	275.59	5.14 × 10−4
		1575	7.65	280.47	6.39 × 10−4
		1600	7.56	377.81	(runaway)
3300	0.302	1400	22.13	254.39	3.41 × 10−5
		1600	20.02	266.71	1.24 × 10−4
		1650	19.57	275.67	5.55 × 10−4
		1700	19.13	293.98	7.60 × 10−3 (water loss)
		1750	18.72	362.18	(runaway)
		1800	18.33	324.41	(runaway)
3700	0.505	1500	44.33	253.25	2.19 × 10−5
		1600	42.24	259.25	7.85 × 10−5
		1800	38.66	282.10	2.89 × 10−3 (water loss)
		1900	37.13	308.93	2.82 × 10−2
		1950	36.41	333.18	(runaway)
		2000	35.73	353.44	(runaway)
4000	0.618	1600	65.79	253.13	1.76 × 10−5
		1800	60.23	266.87	3.61 × 10−4
		1900	57.83	279.24	1.48 × 10−3
		2000	55.65	301.08	1.64 × 10−2 (water loss)
		2050	54.63	329.98	(runaway)
		2100	53.65	330.68	(runaway)
		2200	51.81	348.21	(runaway)
4500	0.716	1800	100.20	253.21	2.97 × 10−6
		2000	92.59	262.92	7.04 × 10−5
		2200	86.20	281.23	1.41 × 10−3 (water loss)
		2250	84.76	291.63	7.41 × 10−3
		2300	83.37	303.64	1.79 × 10−2
		2350	82.04	337.93	(runaway)
		2400	80.75	352.77	(runaway)
		2500	78.32	351.58	(runaway)

Note. Stellar radius is included as calculated using the Stefan–Boltzmann law, along with the global surface temperature of the planet. The final column denotes the amount of water vapor available at the original model top, and also marks the incipient runaway cases.

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We do not model the effects of stellar UV activity and the corresponding photochemistry in this work. Recently, Chen et al. (2018) and Afrin Badhan et al. (2019) discussed the effects of changes in stellar activity on the atmospheric chemistry of HZ planets around M dwarfs in the context of biosignatures. In particular, Afrin Badhan et al. (2019) use the same GCM simulations as we do (from Kopparapu et al. 2017) to assess the impact of varying UV activity on the detectability of water vapor features in the transmission spectrum. We will discuss our results in the context of Afrin Badhan et al. (2019) in Section 4.

The model top for the GCMs conducted by Kopparapu et al. (2017) lies at 1 mbar. This model top reaches up to about Earth's stratopause, and captures the important processes for regulation of a planet's large-scale energy balance and thus its climate. However, a greater vertical extent is often needed for simulating transmission spectra (see Section 2.2) in order to fully capture the radiative interactions that occur during a transit event. For terrestrial climates of approximately Earth temperatures and below, a 1 mbar model top still can yield adequate results for transmission spectra. However, for warm water-rich planets (>300 K) a 1 mbar model becomes increasingly insufficient for properly capturing transmission spectra because the opacity of the atmosphere increases and pushes transit depths to lower atmospheric pressures. Therefore, before calculating transmission spectra, the GCM model columns must be artificially extended to as high as 1 μbar. Otherwise, in these hot climates the cloud layers can be pushed beyond the GCM model top, and their information can become skewed or lost entirely. Information about clouds that may exist in these low-pressure regimes, however, is essential for understanding the warm atmospheres of planets undergoing a runaway state and their transmission spectra. We explore several different assumptions for approximating the clouds in the extended layers of the atmospheric profiles, detailed in Section 2.3. We demonstrate that for hot aquaplanet spectroscopy it is crucial to understand cloud processes in these lower-pressure regimes.

In order to create synthesized spectra from our GCM outputs, we use the Planetary Spectrum Generator (PSG), a radiative transfer tool publicly available online at https://psg.gsfc.nasa.gov/ (Villanueva et al. 2018). PSG combines line-by-line modeling with a robust scattering model for aerosols in order to calculate planetary spectra both efficiently and precisely. Drawing upon repositories of spectral line data for various molecular species, multiple scattering models, and the latest radiative transfer methods, PSG can yield radiance values across a broad range of wavelengths. PSG also includes a realistic noise simulator, discussed in Section 3.5. To create each spectrum, we input basic parameters of the star and planet, along with vertical profiles of the planetary atmosphere. These profiles include temperature, pressure, altitude, mass mixing ratios and particle sizes for liquid and ice clouds, and volume mixing ratios for H₂O and N₂ gas—all outputs from the original GCM model combined with our upper-layer approximations (see Section 2.3). PSG treats the ice clouds as complex scatterers, and the optical properties for both the ice and liquid water clouds are derived from the HITRAN 2016 database (Massie & Hervig 2013). In order to produce a realistic representation of the planet's atmosphere as viewed through transmission spectroscopy, we use PSG to calculate a spectrum at every interval of 4° in latitude across the terminator of the planet (the terminator is the only part of the planet that is accessible through transmission spectroscopy). We then average the spectra over all latitude intervals, with equal weighting for each interval, to produce the final spectrum for the planet.

As we discussed further in Section 2.1, it is necessary to extend the layers of the atmospheric profiles created by the GCM up to 1 μbar. The non-runaway planets are unaffected by additional layers because their cloud deck lies well below the original model top, as seen in the profiles displayed in Figure 1. However, as Figure 1 shows, for the incipient runaway cases, both the water and ice clouds accumulate at the model top (1 mbar), indicating that there are not enough layers in the GCM model profiles to properly capture the altitude and vertical extent of the cloud decks. Note that ice clouds are particularly problematic because they form at low temperatures and thus occur higher in the atmosphere than liquid water clouds. We must therefore artificially add sufficient layers so that the model can reach 1 μbar, necessary for properly capturing the dynamic range of the transit spectra. To test how sensitive our spectra are to these low-pressure regions, we add the extra layers in three different ways:

• 1.  
  Iso. Extend the upper layers by keeping all variables (temperature, H₂O and N₂ volume mixing ratios, liquid and ice cloud mass mixing ratios) constant, starting from the last viable point of the original model. Note that the top layer of GCMs can be unreliable due to artificial diffusion added to damp spurious wave reflection off the model top.
• 2.  
  Zero. Extend the upper layers by keeping the temperature, H₂O, and N₂ volume mixing ratios as isovalues, but setting the liquid and ice cloud mass mixing ratios to zero.
• 3.  
  Intermediate. Find the pressure at which the liquid and ice cloud mass mixing ratios reach half of its maximum abundance of liquid and ice cloud mass mixing rations, determined from the original profile. This is treated as the bottom of the cloud deck. Ensure that the vertical extent of the cloud deck, starting from the bottom, reaches 1 decade (dec) in pressure. If the cloud deck in the original profile does not span 1 dec, we extend it until it does by setting the abundances as isovalues of the last viable point, and then we set the remaining layers to zero once the 1 dec requirement is reached.

The first two methods represent the limits of possible cloud abundances, while the intermediate profiles represent our best approximation based on our understanding of cloud profiles from our non-runaway cases as well as data on terrestrial planets in the solar system. We include the unlikely extreme cases so we can constrain the impact of the highly uncertain low-pressure cloud regime from 1 mbar to 1 μbar on the resulting spectra. For the intermediate method, we have reason to assume a 1 dec vertical extent for the cloud decks, because some incipient runaway cases that do have a complete cloud deck below the model top span 1 dec of pressure. In addition, this is consistent with the extent of the cloud deck observed on Earth and Venus (Bézard & de Bergh 2007; Taylor et al. 2018). We remind the reader that these approximations only make a difference for the planets in the incipient runaway regime. In Figure 1, one can see the profiles including the added layers using the three different methods listed above. For all of the above treatments of the model top, we keep the temperature constant because we make no temperature-dependent changes in the clouds or in the molecular abundance of water in the upper atmospheres. In general, transmission spectroscopy is insensitive to the shape of the pressure–temperature profile at these heights, so we deem it unimportant to determine a realistic mesospheric temperature profile. In addition, for all of the above methods, we first remove the lowest-pressure values of the original model to avoid any instabilities posed by the GCM while approaching the model top.

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Our ultimate goal for this study is to determine the observability of ocean Earths using transmission spectra with our current and future technological capabilities and limitations. As we discuss in Section 3.1, the four major water vapor signatures in the infrared are the features at 1.4 μm, 1.8 μm, 2.7 μm, and 6 μm. All of these features are within the bandpasses of current and next-generation instrumentation dedicated to atmospheric characterization of exoplanets. The JWST, estimated to launch in 2021 March, will have spectral capability ranging from 0.6 to 28 μm with its Near-Infrared Spectrograph (NIRSpec), Near-Infrared Camera, and Mid-Infrared Instrument (MIRI), though it will most likely be limited to less than 12 μm for transmission spectroscopy (Beichman et al. 2014). JWST would therefore be able to provide spectral coverage over all four of the primary water features in the planetary spectrum outlined in Figure 2.

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In addition to JWST, there are several concepts for flagship space telescope missions being examined for consideration by the upcoming Decadal Survey that will include spectroscopic capabilities for exoplanet characterization. If selected, LUVOIR would have capabilities for grism spectroscopy from 0.2 to 2.5 μm courtesy of the High-Definition Imager (HDI) instrument (The LUVOIR Team 2019). As such, LUVOIR would be able to observe the 1.4 and 1.8 μm features seen in Figure 2. There are currently two mission architectures for LUVOIR, one with a 15 m mirror (LUVOIR Architecture A) and one with an ∼8 m mirror (LUVOIR Architecture B). We include both designs in our study. Another proposed mission concept, OST, is currently designed to cover a wavelength range from 2.8 to 20 μm using a specially designed instrument for transit spectroscopy called the Mid-Infrared Imager, Spectrometer, Coronagraph (MISC) Transit Spectrometer (Meixner et al. 2019). OST would therefore have access to the large 6 μm spectral feature of water vapor. Each water vapor feature in the spectrum that we show in Figure 2 can thus be characterized by one or more upcoming/proposed telescopes (JWST, LUVOIR-A, LUVOIR-B, and OST). We note that it is not possible for both LUVOIR and OST to be selected. If either is chosen, the expected launch date would be in the mid-2030s.

In Figure 2, we present a single case study of the PSG-synthesized spectrum for an ocean Earth receiving an incident flux of 1650 W m⁻² from a star with an effective temperature of 3300 K. As can be seen in Table 1, this is a non-runaway case, and thus the spectrum in Figure 2 is independent of the treatment of the model top as described in Section 2.3. We choose to discuss this GCM-modeled planet–star pair because Kopparapu et al. (2017) highlighted the spectral features for this specific case, as a representative example of a transmission spectrum for the same GCM results used here. As we will see in Section 3.2, the absorption features present in this spectrum are general for all pairs modeled by Kopparapu et al. (2017), because the planetary atmosphere constituents are the same. In the synthesized spectrum, there are four major water vapor signatures in the infrared: those at 1.4 μm, 1.8 μm, 2.7 μm, and 6 μm, with the latter two being the most prominent. The small feature at 4.15 μm visible for the 2600 K lower-flux cases is an N₂–N₂ collision-induced absorption feature, which was examined in detail by Schwieterman et al. (2015). No features caused by other molecules are present, because the GCMs of Kopparapu et al. (2017) only include H₂O and N₂ in the atmospheres of the planets. The bulk of our analysis will focus on the water vapor features because they are indicators of potential habitability.

Kopparapu et al. (2017) reported that the depth of H₂O spectral features would be observable due to the circulation of clouds around the substellar point for slow and synchronously rotating planets. For the specific scenario of an ocean Earth experiencing 1650 W m⁻² of flux from a 3300 K star, their spectrum simulated using the SMART radiative transfer model (Meadows & Crisp 1996; Crisp 1997) estimated a depth of ∼15 ppm for the 6 μm feature. However, we correct this previous optimistic value by implementing three changes. We first recalculate the radius of the star. The radius that Kopparapu et al. (2017) used to simulate spectra was not consistent with the star's temperature. We adjust the radius from 0.137 R_⊙ to 0.301 R_⊙ using the Stefan–Boltzmann law. This correction vastly reduces the average signal of the 6 μm H₂O feature by ∼10 ppm. The second correction relates to the averaging scheme. Whereas Kopparapu et al. (2017) first averaged the profiles of the GCM results along the terminator to derive a single averaged profile and created a single simulated spectrum from this, we use the profile at each 4° interval of latitude for a separate radiative transfer calculation, and then average all of the resulting spectra. This correction affects the spectral depth by adding ∼1 ppm to the average depth of the 6 μm H₂O feature. Finally, we include the abundance of ice clouds from the model, which brings the average depth of the 6 μm H₂O spectral feature down to ∼2 ppm (see Figure 2). We note that these corrections affect the prospects for observability for these planets, but not the actual GCM results. We will continue to explore the spectra of the other planet–star pairs modeled by Kopparapu et al. (2017) before we predict how capable these telescopes will be of characterizing the atmospheres of these ocean-covered Earths.

Using PSG, we synthesize the transmission spectra for all 39 planet–star pairs modeled by Kopparapu et al. (2017) (see Table 1). The simulated spectroscopy results are displayed in Figures 3 and 4, in altitude and parts per million, respectively. Figure 3 is divided into subgraphs based on the temperature of the host star; we only show temperatures of 2600, 3300, and 4500 K for simplicity. Each subgraph has three panels displaying the spectra using the iso profiles, the zero profiles, and the intermediate profiles, with multiple spectra in each panel for the varying incident flux the planet receives. In Figure 3, the continuum (the relatively flat base of the spectrum where no spectral lines are present) represents how high the atmosphere's cloud deck lies above the planetary surface in kilometers. Therefore, the features visible in the presented spectra are solely due to the light from the star interacting with the molecules in the atmospheric layers above the cloud deck. Molecules below the cloud deck are inaccessible through transmission spectroscopy because the cloud deck is optically thick. Within any panel representing stellar temperature in Figure 3, the cloud decks of the planets experiencing higher incident flux occur at higher altitudes than those of the planets with lower fluxes. This is consistent with expectations, since for planets with a higher surface temperature the level at which the atmosphere has cooled enough to allow water to condense moves upward.

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Figure 3 also highlights that across all the sampled stellar temperatures, the spectra for the incipient runaway planets are highly dependent upon the nature of the upper atmospheric cloud decks. The features for the incipient runaway planets (typically the top one or two plotted lines in each panel, see Table 1) shrink and the continuum rises as the assumed cloudiness increases from zero profile to iso profile. This is consistent with what we expect from the treatment of the model top seen in Figure 1. For the zero-profile case, many of the ice cloud profiles do not reach 1 dec of vertical extent, explaining the clarity with which we see the features (reminiscent of Figure 2). For the intermediate and iso profiles, the spectral features for the incipient runaway planets are either diminutive or completely flat. In the temperature regimes explored here (planet surface temperatures up to ∼400 K), the upper atmosphere should remain cold enough to condense clouds, providing significant challenges for transit spectroscopy. Of course, other atmospheric constituents, not included in our model at present, could modify the stratospheric temperature profile through either cooling (e.g., CO₂) or heating (e.g., O₃, absorbing aerosols), resulting in changes to the expected cloud profiles. While low-top GCMs are generally sufficient for understanding the climate generalities of warm moist planets, they are not yet sufficient for interpreting future transmission spectra from these worlds. An understanding of high-altitude (low-pressure) cloud and aerosol formation and persistence will be critical for interpreting observations of hot moist planets.

Figure 4 divides the spectra into panels for various stellar temperatures just based on the intermediate profiles. Figure 4 shows in general that the planets orbiting cooler stars have much stronger spectral features than those orbiting hotter stars (up to ∼30 ppm compared to less than 1 ppm). The depths of spectral features for the planets orbiting 3700, 4000, and 4500 K stars are less than 1 ppm and too small to be observed by JWST. This relation is in fact the inverse of what was anticipated by Kopparapu et al. (2017). Because the planets are synchronously rotating, the orbital period (equal to the rotation period), stellar mass, stellar luminosity, and incident flux on the planet are inextricably related through Kepler's third law (see Equation (3) in Kopparapu et al. 2016). As a result, the planets orbiting within the HZ of low-mass and low-luminosity stars (such as the 2600 and 3000 K stars) in general rotate faster (or have shorter orbital periods) than those orbiting the hotter dwarf stars. Kopparapu et al. (2017) predicted that the slower-rotating planets (planets around 4000 and 4500 K stars) would have relatively larger spectral features than their faster-rotating counterparts because slowly rotating planets have elevated water vapor in their stratospheres at any given temperature due to the nature of their general circulation. However, we find in fact that the severe reduction in planet-to-star size ratio for warmer stars far outweighs the increase in stratospheric water vapor.

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Changes to the atmospheric circulation also contribute to the deeper spectral features observed for the planets orbiting stars with lower effective temperatures. In Figure 5, we show the mixing ratios of ice water clouds and liquid water clouds at the terminator for temperate planets around 2600, 3300, and 4500 K stars. The cloud abundances shown are the average of the east and west terminators. As discussed in Haqq-Misra et al. (2018) and elsewhere, as the planetary rotation rate increases, the atmospheric circulation transitions to different regimes. Circulation regimes have a substantial effect on the horizontal extent and location of clouds (Kopparapu et al. 2017) and also on their vertical extent. Relatively slowly rotating planets feature deep upwelling around the substellar point, resulting in thick, symmetric substellar clouds that reach high altitudes. However, as the planetary rotation rate increases, Coriolis forces support strengthened zonal flows, which cap upwelling motions in the atmosphere and shear the substellar clouds downstream. Thus, considering (approximately) identical mean surface temperatures, the cloud decks (both ice and liquid water) form progressively lower in the atmosphere as planetary rotation rate increases, as is seen in Figure 5. This is one contributing reason why the spectral features for the 2600 K stars in particular have a lower continuum height and are much deeper than those found for their counterparts with higher stellar temperatures. To highlight this effect, we display in Figure 6 a comparison between spectra generated with clouds and without, for a selection of our models with corresponding surface temperatures.

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In general, as Figure 4 shows, even with significant stratospheric water vapor, obtaining transmission spectra of water-rich Earth-sized planets synchronously rotating around mid-K and early-M dwarf stars is exceedingly difficult. The planets orbiting the smallest star—the star with an effective temperature of 2600 K—have the most prominent spectral signals due to a combination of a high planet-to-star size ratio and cloud asymmetry.

In order to understand the relationship describing the different feature depths detailed in Section 3.2 and Figure 3, we directly measure and compare the effective increase in planetary radius for each water vapor feature (1.4, 1.8, 2.7, and 6 μm) for all 39 available spectra. For each feature of each spectrum, we subtract the average value for the continuum from the average increase in planetary radius calculated within the spectral feature. We call this value ΔR, or the change in the apparent radius of the planet (in kilometers) across a specific wavelength range. ΔR is simply the depth, or the strength, of a spectral feature.

Figure 7 plots each simulated planet's ΔR value against its global surface temperature. Each panel in Figure 7 represents a different water vapor feature. For the incipient runaway cases, we plot results for the intermediate assumption for the model top; we mark these cases separately since they are strongly dependent on these assumptions. Figure 7 shows that for the higher-temperature host stars (3700, 4000, 4500 K), the feature depths generally increase with surface temperature until they reach an incipient runaway state, since the scale height H = kT/mg is proportional to the temperature. However, when the runaway state begins, the lowest layers of the atmosphere become more and more opaque due to clouds, raising the continuum and decreasing the depth of each line. This is consistent with Fujii et al. (2017), who report an increase in feature depth as the incident flux increases.

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Figure 7 shows that, in general, the transition between non-runaway and runaway regimes occurs when the planet experiences globally averaged surface temperatures above ∼310 K. We can use the orbital parameters for simulated planets at this transition boundary to calculate an empirical relationship relating orbital semimajor axis to stellar temperature, in order to categorize discovered ocean Earths orbiting M stars into these two states:

$$\begin{eqnarray}\begin{array}{rcl}{a}_{\mathrm{transition}} & = & -6.852\times {10}^{-11}{T}^{3}+7.720\times {10}^{-7}{T}^{2}\\ & & -\,2.664\times {10}^{-03}T+2.934\end{array}\end{eqnarray} \tag{ 1 }$$

in which the variable a_transition is the semimajor axis of the planet in astronomical units and T is the stellar temperature in kelvin. If a < a_transition, then the planet should be expected to be in a runaway greenhouse state.

Figure 8 shows the ΔR value of the 4 μm N₂–N₂ collision-induced absorption (CIA) feature against global surface temperature. It is clear that only the planets orbiting the 2600 K stars have noticeable dimer features. This is due to the dramatic difference in height of the cloud decks between the planets orbiting the 2600 K star and the planets orbiting higher-temperature stars, as seen in Figure 4; the spectral feature achieves significant depth only when the cloud-based continuum is lower than 30 km, as see in Figure 3. The maximum depth of the spectral feature for the 3000 K models is ∼3 ppm, similar to results of Schwieterman et al. (2015) for a similar stellar type. However, for even cooler stars, the effective continuum occurs at even lower altitudes, and the lowest-flux models produce a signal up to 11 ppm. The impact of clouds on the intensity of CIAs is so strong because their opacity scales quadratically with pressure. They are only prominent at high pressures (low altitudes), and their intensity quickly drops as clouds mask those high pressures. At pressures above 1 bar, the feature saturates at the core, and only the weaker peripheral features contribute to the overall contrast, so the overall intensity of the dimer remains practically unchanged when the surface pressure is increased beyond 1 bar. As clouds mask the lower pressures, the intensity of the N₂ dimer drops substantially, becoming undetectable at pressures lower than 10 mbar (>30 km) as shown in Figure 3.

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We can utilize our calculations for the depth of H₂O spectral features to calculate how long it would take for future telescopes to detect water vapor on an ocean planet orbiting within the HZs of observable cool dwarf stars. To do this, we compile a target list of observable cool dwarfs from the TIC, since the TESS mission will largely dictate the available database of transiting exoplanet systems with terrestrial planets that the exoplanetary community will work with for the next few decades.

TESS will observe 200,000 preselected stars at a cadence of two minutes and take full-frame images of all pixels every 30 minutes (Ricker et al. 2014). Although TESS will observe an area 40 times larger than Kepler did, flux contamination will be more problematic for TESS because its pixels are 25 times larger (Stassun et al. 2019). Due to this flux contamination, in combination with the inherent dimness of cool stars, it is unclear how many Earth-size planets TESS will discover around stars in our stellar temperature range of 2600 K < T_eff < 4500 K. However, even if TESS is not able to obtain sufficient sensitivity to detect small planets, augmentation through current and future ground-based and space-based observations may be able to achieve higher-quality light curves and detect additional planets.

One problem that the TIC may pose to our work is that dwarf stars may be misidentified as subgiants. It is estimated that as many as 50% of stars labeled as "dwarfs" in the previous TIC version 7 were actually subgiants (Stassun et al. 2019). However, thanks to the parallax measurements and photometry from the Gaia second data release, stellar radii in the TIC were revised in version 8, which greatly diminished the impact of this misidentification (Stassun et al. 2019). This degeneracy will not affect our calculations, but merely reclassify some stellar targets in our target list as irrelevant (as seen in Kane 2018, for example). By using Gaia DR2 as the base, the number of stars in TIC version 8 that have estimated radii and effective temperatures increased by factors of 2 and 20, respectively. These catalog improvements work to our advantage when it comes to selecting relevant stars.

From the TIC version 8, the latest version at the time of publication, we select stars in the temperature range 2600 K < T_eff < 4500 K. We then make additional cuts on our subset of stellar targets in order to maximize exposure time. We only consider stars with R < 0.5 R_⊙ in order to optimize the planet–star signal. In addition, we only select stars with K_mag brighter than 11. We choose this magnitude threshold so that we can maximize the photon flux of our stars to decrease our photon-noise limit, while still including ultracool dwarfs with small stellar radii similar to TRAPPIST-1 (K_mag = 10.3, Gillon et al. 2017), the current benchmark for ultracool transiting systems. The combination of these three criteria results in a subset of 52,412 cool stars from the TIC.

With some exceptions, most of the stars we are interested in for this study are in the Cool Dwarf Catalog (CDC), a sub-catalog curated specially for the TIC (Muirhead et al. 2018). This list includes cool dwarf targets with V − J > 2.7 and ${T}_{\mathrm{eff}}\lesssim 4000\,{\rm{K}}$. Muirhead et al. (2018) determine effective temperatures for the cool dwarfs in their catalog by implementing the color–T_eff relations found in Mann et al. (2015, 2016). However, Muirhead et al. (2018) do not apply this relation to stars with ${T}_{\mathrm{eff}}\lesssim 2700\,{\rm{K}}$ because the calibration sample used in Mann et al. (2015) does not include stars in this low-temperature regime. Therefore certain stars in the CDC do not have an assigned temperature, and thus did not survive our initial cut in stellar effective temperature of $2600\,{\rm{K}}\lt {T}_{\mathrm{eff}}\lt 4500\,{\rm{K}}$. Because M dwarfs in this low-temperature regime (such as TRAPPIST-1) are of great interest to the community, we estimate the stellar temperatures for these stars ourselves using the discontinuous T_eff–radius relation from Rabus et al. (2019). Rabus et al. (2019) use high-precision interferometry measurements of M dwarfs to derive two separate empirical relations between T_eff and radius for stars with masses M < 0.23 M_⊙ and M ≥ 0.23 M_⊙ respectively. For stars without T_eff but with R < 0.5 R_⊙ and K_mag < 11, we implement these relations to estimate effective temperatures. For stars with effective temperatures that lack radii but are marked as dwarfs in the TIC and have K_mag < 11, we implement the reverse of these relations to estimate radii. We only retain the stars with calculated radii of R < 0.5 R_⊙. These calculations add 9101 new stars to our original data set, bringing our total target list of M dwarfs up to 61,513 stars suitable for exposure time calculations (see Section 3.5). In our attached target list file, we flag which relation, if any, is used to calculate temperature or radius.

We then proceed to calculate exposure times for an ocean Earth orbiting around each star, as observed by either JWST, LUVOIR, or OST. One of the primary goals of the current era of transiting planet detection is to find targets for spectroscopic follow-up by the JWST; however, we expand this scope to include all current concepts for flagship space telescopes with spectroscopy capabilities in the next decades (LUVOIR and OST, as detailed in Section 2.4). This list of exposure times for 61,513 stars will essentially be a ranking of which stars, if they had an ocean Earth, would be most amenable to a detection of water vapor by these observatories.

To determine the detectability of an Earth-sized aquaplanet around one of the M stars in our target list, we compute how many hours it would take for each future observatory to detect a specific water vapor feature covered by the observatory's bandpass (Section 2.4). For this calculation, we must assume a ΔR using Figure 7. We make an optimistic choice by choosing the maximum ΔR that a planet around a particular host star achieves before entering an incipient runaway state. For example, if a target star has an effective temperature of 2700 K, we assume that the planet reaches a ΔR of 8.3 km for the 6 μm feature, as seen in Figure 7 for the 2600 K host star. Calculating exposure times for an incipient runaway planet will require a more robust treatment of the cloud properties for these planets, and is suggested as future work in Section 4.

We calculate the signal-to-noise ratio S/N for the exposure time T_exp using the following equation:

$$\begin{eqnarray}&&{\rm{S}}/{\rm{N}}=\displaystyle \frac{{\rm{\Delta }}\delta \times {S}_{t}\sqrt{{T}_{\exp }}}{{N}_{t}\sqrt{2}}\end{eqnarray} \tag{ 2 }$$

where S_t is the photon count rate per unit time of the star, N_t is the noise calculated per unit time, and Δδ is the feature depth in ppm (S/N is set to 5 as our discretionary standard for detection).

T_exp depends on Δδ, which we can approximate using ΔR as introduced in Section 3.3. To convert ΔR, the planet's water vapor feature depth in kilometers, to Δδ (the same variable in ppm), we use

$$\begin{eqnarray}&&{\rm{\Delta }}\delta =\displaystyle \frac{{({R}_{p}+{\rm{\Delta }}R)}^{2}-{R}_{p}}{{R}_{\star }^{2}}.\end{eqnarray} \tag{ 3 }$$

Our method for calculating the minimum exposure time necessary for a certain telescope to detect a designated water feature for a specific target star is as follows. We assign to each target star a model match based on its stellar effective temperature. For example, any target stars with effective temperatures between 2850 and 3150 K are assigned to use the simulation results for the planet at 1575 W m⁻² around a 3000 K star (as stated above, we choose this flux because it is the flux at which the highest ΔR is reached before reaching an incipient runaway state). Once we have a model match for the target star, we take the corresponding model's spectrum in kilometers (as seen in Figure 3) and convert it from units of kilometers to ppm using the target star's radius from the TIC and Equation (3).

We use PSG's instrument simulation module to simulate the signal and noise (both in photons) that a specific telescope will collect if observing a star of the brightness, size, and temperature of the target star. PSG uses the spectral radiance of the source, along with telescope and detector properties, to compute the integrated flux and an associated noise contribution (S_t and N_t). PSG's noise simulator incorporates background sky sources, photon noise from the source, and optical parameters of the telescope's instruments.

We list the detector parameters we use with PSG for each telescope in Table 2. For simplicity, we only use the instrument parameters for a single instrument on each observatory—otherwise, determining the optimal observing strategy for each of our 61,513 target stars would be prohibitively difficult, and would also make direct comparisons between individual targets more complex. In particular, we assume the parameters for the NIRSpec Prism instrument mode for JWST because it has access to most of the features (the 1.4, 1.8, and 2.7 μm water vapor features). We do not calculate exposure times for the 6 μm feature using the MIRI instrument because JWST is expected to be more sensitive in the near-infrared (0.8–5.0 μm). We do not investigate in detail the effect of issues related to higher read-out noise for brighter targets, because this will only affect a small number of stars in our sub-catalog. In addition, we are aware that the stated brightness limit for the Prism using the Bright Object Time-Series Spectroscopy mode is J ≲ 10 (Beichman et al. 2014); however, the overall noise budget is dominated by photon noise or a noise floor, and therefore exposure time calculations assuming the NIRSpec Prism parameters will be roughly equivalent to what we would find for other higher-resolution modes for the JWST NIR instruments. The only exception would be the brightest targets in our target list, which may not be observable using any NIR instrument modes on JWST, but again we leave these in the target list for completeness.

Table 2.  List of Observatory and Instrument Parameters Adopted for Exposure Time Calculations

	JWST	LUVOIR-A	LUVOIR-B	OST
Instrument	NIRSpec Prism	HDI	HDI	MISC-TRA
Wavelength	0.7–5.0 μm	0.2–2.2 μm	0.2–2.2 μm	2.8–20 μm
Collecting diameter (m)	5.64	14.05	7.46	5.64
Resolution (R)	100	100	100	100
Read noisea (e−)	16.8	2.0	2.0	⋯
Dark ratea (e− s−1)	0.005	0.001	0.001	⋯
Sensitivityb $({\rm{W}}\,{{\rm{Hz}}}^{-1/2})$	⋯	⋯	⋯	2 × 10−20
Total throughput	0.4	0.1–0.342c	0.1–0.342c	0.191–0.410c
Emissivity	0.1	0.1	0.1	0.1
Temperature (K)	50	270	270	4.5

Notes. The values for JWST were taken from current documentation for the observatory, while the values for LUVOIR and OST were taken from the concept study reports.

^aCCD. ^bNEP (noise equivalent power detector model). ^cWavelength-dependent function.

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We calculate exposure time T_exp using Equation (2), assuming a required S/N of 5 for a detection. However, instead of simply subtracting the continuum from the maximum depth of the water feature, we optimize the bandwidth of the feature in order to obtain Δδ. Starting with a small wavelength extent around the highest point, we compute the average depth of the feature within the extent and subtract it from the continuum. We then use this Δδ to calculate the exposure time with Equation (2). We then increase the wavelength extent surrounding the feature incrementally and repeat, until we find the optimal Δδ value that yields the minimum exposure time possible for a specific combination of telescope, water vapor feature, and target star.

The above calculation methodology assumes that there is no absolute noise floor imposed on the observations. The noise floor introduced by a telescope is a crucial factor to consider (Greene et al. 2016; Fauchez et al. 2019), especially with the low spectral depths seen in Figure 4. We recalculate exposure times with a noise floor of 1, 3, and 5 ppm. Note that for each such calculation, we still assume an S/N of 5, or a 5σ detection. To incorporate the noise floor at every wavelength extent in the optimization scheme, we also calculate T_floor, or the maximum exposure time that a telescope can observe for before the photon noise reaches the noise floor; at this point, any signal from the star is drowned out. T_floor is computed using the following equation:

$$\begin{eqnarray}&&{T}_{{\rm{floor}}}=\displaystyle \frac{2{N}_{t}^{2}}{{N}_{{\rm{ppm}}}^{2}{S}_{t}^{2}}\end{eqnarray} \tag{ 4 }$$

where N_ppm is the noise floor (1 ⨯ 10⁻⁶, 3 ⨯ 10⁻⁶, or 5 ⨯ 10⁻⁶). If T_floor is less than T_exp, then detection of the feature in that bandwidth is not possible due to the noise floor. At each wavelength extent, we calculate both T_exp and T_floor, and find the maximum wavelength range for which T_exp is less than T_floor (if at all).

We present the results from our exposure time calculations in Figure 9, which compares the computed exposure times of JWST, LUVOIR-A, LUVOIR-B, and OST using the assigned feature of each telescope that yields the shortest exposure times. As stated in Section 3.5, we do not exclude any targets based on brightness and saturation limits, since we want to compare the same target list across observatories and avoid delving too deeply into the subtleties of observing limitations. Although JWST can characterize three of the water vapor features using the NIRSpec Prism mode (2.7, 1.4, 1.8 μm), it is the 2.7 μm feature that provides a detection in the shortest exposure time. On the other hand, LUVOIR-A and -B can see both the 1.4 and 1.8 μm features, and the best feature for which these telescopes require shorter exposure times to achieve an S/N of 5 depends on the temperature of the star. For this reason, for LUVOIR-A and LUVOIR-B in the first panel of Figure 9, we only consider the shortest exposure time for each star regardless of which feature yields it. As detailed in Section 2.4, OST can only observe the 6 μm H₂O feature. Each histogram in Figure 9 is binned by factors of 10 in exposure time; for example, the first bin includes stars that would require an exposure time of between 100 and 1000 hr. It is clear from the first panel in Figure 9 that the majority of the stars in our target list have infeasible exposure times, with the average for JWST being of the order of 10⁵ hr.

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Each panel in Figure 9 contains a different consideration of noise floor. Assuming no noise floor (0 ppm) with the method described in Section 3.5, LUVOIR-A and JWST could characterize the most stars in the regime of shorter exposure time; we list the number of stars that each telescope could observe in under 1000 hr and under 300 hr assuming no noise floor in Table 3. When accounting for a 1 ppm noise floor, the number of stars whose planetary spectra do not get drowned out by the noise floor decreases drastically. For LUVOIR-A and -B, only exposure times using the 1.8 μm feature survive the noise floor. When implementing a 3 ppm noise floor, the number of stars both LUVOIR-A and -B can characterize reaches zero, since the depth of the 1.8 μm feature never rises above 15 ppm for any star. Only JWST and OST could detect the spectra of a handful of planets. Finally, we test a 5 ppm noise floor, in which no telescope can characterize the spectrum of a planet around any of our selected TESS stars. The numbers of stars that survive different considerations of noise floor for each telescope are shown in Table 3.

Returning to Equation (2), we note that since ΔR and R_p are constant for each calculation, and ${N}_{t}\approx \sqrt{{S}_{t}}$,

$$\begin{eqnarray}&&T\propto \displaystyle \frac{{R}_{\star }^{4}}{{S}_{t}}.\end{eqnarray} \tag{ 5 }$$

In other words, stars with smaller radii and brighter magnitudes (i.e., more photons) yield the shortest exposure times. It is these types of stars that will prove to be the best targets for characterizing ocean Earths. The explicit ranking of our stellar targets based on shortest exposure times is included as a supplementary digital file to the paper. The top 20 stars with the best S/N per hour of exposure time are shown in Table 4 along with their stellar parameters; many of these stars would require a very low noise floor or would saturate all of the JWST NIR instruments, but we include them as our list of the most ideal targets if instrument/observatory capabilities allow it. The 26 stars that remain detectable with a 3 ppm noise floor are listed in Table 5. These are all relatively dim stars, and therefore should all be observable by JWST as well as future observatories.

Table 4.  Ranked List of the Targets from the TESS Input Catalog with the Best Prospects for Detecting Water Vapor, Assuming Photon-limited Performance and No Brightness or Other Limits for the Observatory

	Identifier	Flaga	Kmag	Radius (R⊙)	Temp. (K)
1	G 58-18A	RML	8.7	0.129	2699
2	Proxima Centauri	RM	4.384	0.153719	3000b
3	Barnard's Star	TRML	4.524	0.193525	3259
4	2MASS J08262921+0424089	RML	10.211	0.124	2666
5	Wolf 359	RM	6.084	0.135286	2741
6	G 99-10B	TRML	10.901	0.132256	2880
7	2MASS J03293895+4441055	RML	10.048	0.124	2666
8	LSPM J1016+3925	RML	10.005	0.149	2832
9	G 208-45	TRML	7.387	0.142116	2865
10	YZ Ceti	RM	6.42	0.167787	2957
11	GJ 1061	TRML	6.61	0.155739	2905
12	LP 938-71c	RM	10.069	0.115627	2610
13	Ross 154	TRML	5.37	0.210477	3261
14	G 51-15	TRML	7.26	0.124013	2814
15	2MASS J04173685-2419503	RML	8.864	0.159	2898
16	Teegarden's Star	TRML	7.585	0.118649	2790
17	2MASS J15402966-2613422	RM	10.73	0.113881	2598
18	HD 173740	RM	5.0	0.278799	3213
19	HD 153026B	RML	5.614	0.218	3291
20	Ross 128	TRML	5.654	0.209628	3163

Notes. The stellar parameters are taken from the TIC when available, and calculated using relations from Rabus et al. (2019) when values are missing from the TIC. It is clear that the smallest stars are the best targets, along with several of the nearest and brightest mid-M stars.

^aTRML $\equiv$ TIC lists stellar temperature, radius, mass, and luminosity. ^bThe radius–temperature relation from Rabus et al. (2019) underestimates temperature for Proxima Centauri. We override the temperature with 3000 K, an approximation from Boyajian et al. (2012). ^cBrown dwarf.

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Table 5.  List of the Targets from the TESS Input Catalog that are Detectable with a 3 ppm Noise Floor Using JWST, Ranked by Lowest Exposure Time

	Identifier	JWST (hr)	Flaga	Kmag	Radius (R⊙)	Temp. (K)
1	2MASS J15402966-2613422	111.181	RM	10.73	0.113881	2598
2	2MASS J04133542+3127111	132.096	RML	10.748	0.113	2593
3	LP 938-71b	153.572	RM	10.069	0.115627	2610
4	Teegarden's Star	307.744	TRML	7.585	0.118649	2790
5	LSR J0539+4038	347.351	RM	10.044	0.11641	2615
6	VB 10	360.890	RM	8.765	0.113185	2594
7	TRAPPIST-1	528.936	RM	10.296	0.114827	2605
8	LSPM J2044+1517	909.158	RM	10.061	0.111911	2585
9	LP 760-3	1801.495	RML	9.843	0.121	2646
10	LP 98-79	1901.540	RM	9.788	0.115487	2609
11	2MASS J23312174-2749500	2083.498	RM	10.651	0.111914	2585
12	2MASS J04195212+4233304	2270.569	RM	9.9	0.11416	2600
13	LP 135-272	3038.508	RM	10.922	0.113564	2596
14	2MASS J07140394+3702459b	3351.862	RM	10.838	0.11384	2598
15	LP 326-21	3534.983	RM	10.616	0.116388	2615
16	LP 335-12	3688.572	TRML	10.005	0.121203	2722
17	2MASS J14230252+5146303	4145.738	TRML	10.95	0.116383	2758
18	LP 535-12	4196.176	TRML	10.693	0.11867	2792
19	LP 441-34	4297.327	RM	10.919	0.119315	2635
20	2MASS J21272531+5553150	4767.612	RM	10.913	0.117323	2621
21	LP 412-31	5102.946	TRML	10.639	0.115117	2766
22	2MASS J15242475+2925318b	7866.570	TRML	10.155	0.121363	2755
23	2MASS J17415439+0940537	8594.149	TRML	10.968	0.11895	2802
24	2MASS J00251602+5422547	9710.488	TRML	10.819	0.11805	2772
25	LP 485-17b	11638.093	TRML	10.756	0.119322	2772
26	LP 423-14	14252.130	TRML	10.942	0.121019	2768

Notes. The stellar parameters are taken from the TIC when available, and calculated using relations from Rabus et al. (2019) when values are missing from the TIC. Note that many of these stars do not have temperatures in the TIC. Only the smallest, coolest stars remain detectable, but all should be observable with one or more of the JWST NIR instruments.

^aTRML $\equiv$ TIC lists stellar temperature, radius, mass, and luminosity. ^bBrown dwarf.

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To unpack the trends in exposure time, we present Figure 10, where we plot each target star's exposure time for JWST—with no noise floor—against its magnitude and temperature. This figure shows that in general the stars with the lowest, most realistic exposure times are the brighter and cooler ones. This agrees with the relation provided by Equation (5). The lower the stellar temperature, the smaller the stellar radius, leading to a shorter exposure time. The higher the K_mag, the dimmer the star, the longer the exposure time. The starred points in Figure 10 represent stars that we already know to have a terrestrial planet in the HZ. We only label stars with planets with R < 1.5 R_⊕ that are at incident fluxes comparable to those in Kopparapu et al. (2017), listed in Table 1. Note that we do not mark LHS 1140b, due to its recent radius correction using Gaia DR2 data (Kane 2018). Figure 10 also marks the 26 stars that survive the 3 ppm noise floor. Note that these stars do not necessarily correlate to lower exposure times. These stars are the coolest, with effective temperatures ∼2600 K. As shown in Figure 4, only planets orbiting stars with T_eff < 2600 K would reach spectral features with a depth of ≥15–20 ppm. However, as shown in Table 2, no Earth-sized aquaplanet around any of our target stars would be detectable using any telescope if we can only achieve a noise floor of 5 ppm. This is because not even the planets orbiting the 2600 K stars in Figure 4 reach 25 ppm, the minimum feature depth required to still be visible with a 5σ detection and a 5 ppm noise floor. We analyze the implications of the noise floor and each telescope's prospects for realistic characterization in Section 4.

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A large number of studies investigate Earth-like planets in the HZ; here, we constrain our discussion to previous work done on aquaplanets in particular or using 3D GCMs for modeling water-rich worlds. Our most important result, that clouds produce the dominant impact on transit spectral characterization for slow and synchronous rotating planets, compares well with other GCM studies. For example, Komacek et al. (2020) have used ExoCam to simulate planets synchronously rotating around M dwarfs with effective temperatures of 2600 K. They study the impact that clouds have on the detection of water vapor spectral features for planets with various rotation periods, surface pressures, planetary radii, and surface radii. The maximum depth of water vapor features for any of their simulated planets around a star with T_eff = 2600 K is 20 ppm, consistent with our results for planets orbiting stars of the same temperature. Komacek et al. (2020) also predict that for an Earth-sized planet with a rotation period of 4.11 days around a 2600 K star (similar to our planet with an incident flux of 1350 W m⁻² around a 2600 K star), it would take JWST NIRSpec/Prism ∼320 transits to detect its water features, without a noise floor. This is comparable to our calculation of ∼254 hr for a JWST characterization of a similar planet around TRAPPIST-1, without a noise floor (Section 4.2). In addition, Pidhorodetska et al. (2020) have simulated TRAPPIST-1e observations by LUVOIR, HabEx, and OST, and have shown that water features are almost completely flattened by clouds, leading to no possible detections by these future observatories. This demonstrates that larger aperture sizes and/or better instrument precision offered by these telescopes cannot compensate for the weakness of the transmission spectroscopy technique used to probe tropospheric water.

Furthermore, Fujii et al. (2017) used the ROCKE-3D GCM to study the processes that control the water vapor mixing ratio in the upper atmosphere of synchronously rotating terrestrial planets with ocean-covered surfaces. In particular, they examine the variance in the water vapor mixing ratio for stellar effective temperatures between 3100 and 5800 K, producing synthetic transmission spectra based on GCM outputs in order to evaluate the detectability of H₂O signatures. They find that an increase in water vapor mixing ratios in the upper atmosphere leads to an increase in the H₂O absorption depth by a factor of a few, making the effective altitude of the H₂O absorption features as high as 15 km when clouds are included. The star they use to illustrate this result is GJ 876, which has T_eff = 3129 K and a period of 22 days at a flux of 1 S_⊕ (from their Table 2). Its mass is listed as 0.37  M_⊕ and its radius as 0.3761  R_⊕ (from their Table 1). To compare with our results, the closest simulations we can choose are the intermediate cases for the planet receiving 1400 Wm⁻² flux from a star with T_eff = 3300 K (period = 22 days, mass = 0.249 M_⊕, radius = 0.3 R_⊕, flux = 1.029 S_⊕). Using these planets for comparison, both of our studies generally agree that the effective absorption of water vapor is small. For the 2.7 μm feature, Fujii et al. (2017) find a depth of ∼2 ppm with clouds, or ∼15 km (see their Figure 8), while we report a depth of ∼1 ppm or ∼2.5 km (the disparity in the km value is reconciled when the different radii of GJ 876 and our planet orbiting a T_eff = 3300 K star are accounted for). Likewise, both studies find that clouds raise the baseline continuum, with the strength of the increase in the baseline proportional to the incident flux, and find differences in cloud properties between fast rotators (non-synchronous as well as ultracool dwarfs) and planets that rotate more slowly and synchronously around mid-M dwarfs.

While our study focuses on the climate and detectability aspects of the results from Kopparapu et al. (2017), photochemistry also plays a major role. M dwarfs possess strong UV activity, which may effectively photolyze stratospheric H₂O. A study involving transmission spectroscopy of a terrestrial planet orbiting an M star was conducted by Lincowski et al. (2018), who used a 1D photochemical model to simulate a modern Earth-like atmosphere on TRAPPIST-1e. Their results also show that H₂O lines are very shallow and their detection with JWST will be extremely challenging. TRAPPIST-1e has an orbital period of 6.1 days and orbits in the HZ of a 2550 K star. Its incident flux is colder than any of those simulated by Kopparapu et al. (2017) with a flux of 0.6 S_⊕ as opposed to the 0.88 S_⊕ simulated planet (2600 K, 1200 W m⁻²). For a model of TRAPPIST-1e with a surface pressure of 1 bar (80% N₂ and 20% O₂), Lincowski et al. (2018) show that the 2.7 μm H₂O feature has a depth of ∼10 ppm (see their Figure 3). In comparison, our synthesized spectrum for the 2600 K planet receiving 1200 W m⁻² has a 2.7 μm H₂O feature depth of ∼15 ppm. Given the difference in incident fluxes, a deeper spectral feature than Lincowski et al. (2018) would not be unexpected. However, comparisons are difficult due to the circulation differences between a 1D model and a 3D GCM as well as the inclusion of photochemistry by Lincowski et al. (2018). Fauchez et al. (2019) also examined TRAPPIST-1e using a full 3D GCM (LMD-G, Wordsworth et al. 2011) combined with the Atmos photochemical model, and examined various atmospheric compositions (modern Earth, Archean Earth, and CO₂-dominated atmospheres). For their model of modern Earth (the closest to our ocean Earth) and including clouds, they show a feature depth of ∼5 ppm for the 6 μm H₂O feature (the 2.7 μm feature disappears due to the addition of CO₂). Extrapolating from the trends seen in Figure 7 for the 2600 K star, and given that TRAPPIST-1e receives less insolation from its host star than our lowest-flux scenario, it follows that Fauchez et al. (2019) also report a feature depth that is smaller than ours, because our simulated planets lie in the inner HZ. This difference from our simulations could also be due to different convection schemes between ExoCAM and LMD-G leading to less stratospheric water in the latter case (Wolf & Toon 2015; Fauchez et al. 2019), or to photochemistry—near the top of the atmosphere, UV radiation massively photodissociates H₂O, drastically reducing its concentration. As a result, the H₂O absorption is very small, producing depths of only a few ppm. We leave it up to future studies to compare the various GCM models with similar photochemistry schemes to produce a more accurate comparison.

Afrin Badhan et al. (2019) also employed a 1D photochemical model with varied stellar UV to assess whether H₂O destruction driven by high stellar UV would affect its detectability in transmission spectroscopy, based on the results from Kopparapu et al. (2017). They find that as long as the atmosphere is well mixed up to 1 mbar, UV activity appears to not impact detectability of H₂O in the transmission spectrum. However, if the H₂O is not well mixed in the atmosphere (as in our simulations), photodissociation of H₂O can drastically reduce its concentration in the upper atmosphere and therefore weaken the H₂O spectral signature in transit even further (Fauchez et al. 2019). The strength of the spectral features that Afrin Badhan et al. (2019) present is similar to that of Kopparapu et al. (2017), with a peak strength of ∼15 ppm for the 3300 K star with clouds considered, compared to ∼2 ppm from our results (see Figure 4 in their paper and Figure 2 in ours). The reason for this is that Afrin Badhan et al. (2019) use a stellar radius of 0.137 R_⊙ following Kopparapu et al. (2017), which is quite small and inconsistent with the luminosity and temperature of this particular star. This overestimates the strength of the transit spectral features. While this is the dominant effect that reduces the strength of the features, other effects such as the use of a gray cloud model and the non-inclusion of liquid and ice data from the outputs of the GCM run likely also contribute to the differences.

The high cloud decks (especially for ice clouds) shown in Figure 1 that drown out water vapor features in the upper atmospheres of these warm, wet planets are responsible for the bleak observability prospects outlined in Section 3.6. In terms of the best exposure times, the 2.7 μm feature is the most observable based on the specific atmosphere we have outlined in this work. As stated in Section 3.6, when we run exposure time calculations for the three near-infrared features using JWST, the 2.7 μm feature is consistently characterized in the shortest exposure time. This spectral feature benefits from having both a large depth and a proximity to the peak of the blackbody spectrum for M stars. Meanwhile, both the 1.4 and 1.8 μm features are comparably smaller in depth, while the 6 μm feature resides too far out in the mid-infrared range to collect enough photons from the illuminating stellar source. However, the atmospheres modeled in this work are limited in compositional complexity, and do not include CO₂, which is expected to be very common in the atmospheres of rocky exoplanets. If CO₂ were included in the GCM simulations, we would expect those spectral lines to overlap or completely cover the 2.7 μm water vapor feature, making it difficult or impossible to detect (Fauchez et al. 2019). For this reason, the remaining features may be more realistic as observing targets.

However, when we compare each telescope's overall effectiveness in characterizing H₂O, instrument and telescope parameters clearly become important factors. Ignoring the noise floor, LUVOIR-A, although observing a smaller feature (1.8 μm), almost always has shorter exposure times than JWST at the 2.7 μm feature, due to its enormous mirror (effective diameter of 14.05 m, see Table 2). If the wavelength range and photon-noise sensitivity for LUVOIR-A extended farther into the infrared, we fully expect that the combination of the mirror size and access to the 2.7 μm feature would be the best match for minimizing exposure times for these particular planets. OST is less optimal than JWST because although they share the same mirror diameter and similar depths for available spectral features, OST only has access to the 6 μm feature, where not enough stellar photons are collected. Thus, for the same stars, JWST always requires a shorter exposure time to characterize the 2.7 μm water feature than OST does for the 6 μm feature. For 58% of our stellar targets, OST has shorter exposure times with its 6 μm feature than LUVOIR-B does with its 1.8 μm feature, implying that in this case the benefit of having a larger feature slightly outweighs the benefit of having a larger telescope.

Of course, the most realistic aspect of observing these atmospheres that cannot be ignored is the noise floor introduced by the telescope in its environment. Estimates for the JWST noise floor are in the range of 10–20 ppm for the NIR instruments to 50 ppm for MIRI (Greene et al. 2016). When we introduce a 5 ppm noise floor into the exposure times as detailed in Section 3.5, we find that no ocean Earth around any of our stellar targets is detectable using any telescope. Unlike JWST and OST, LUVOIR-A and -B are unable to detect any feature with a 3 ppm noise floor. With a 5σ detection and a 3 ppm noise floor, a feature depth of at least 15 ppm is required for detection. LUVOIR-A and -B only have access to the 1.4 and 1.8 μm features, which never reach a transit depth beyond 10 ppm (see Figure 4). Only 26 stars survive to 3 ppm that can be detectable by JWST; all are very cool and small. This is because, as seen in Figure 4, only the planets orbiting the 2600 K star have relatively large features because of their uniquely low cloud deck and smaller radii. Only eight of these stars that survive a 3 ppm noise floor also have exposure times less than 1000 hr (see Table 5). However, these exposure times are generally longer than they would be without a noise floor, because the noise floor sometimes shrinks the observable bandwidth of the feature. For example, a notable star that remains detectable at 3 ppm is TRAPPIST-1. Without considering the noise floor, TRAPPIST-1 would have an exposure time of ∼254 hr, but with a 3 ppm noise floor, the exposure time rises to ∼528 hr. Still, this is less than 1000 hr, so if JWST somehow were able to push its noise floor down to 3 ppm, the characterization of TRAPPIST-1 planets would be feasible if they had atmospheres similar to those modeled here—but considering that TRAPPIST-1e only transits once every six days with a transit duration of approximately 1 hr, it would take ∼8.7 yr of constant transit monitoring before a sufficient S/N would be achieved.

If the community aims for curating better databases for cooler and smaller stars, while pushing for technological advancements in detector capabilities to limit noise floors, then perhaps one day these water vapor features will be detectable through transmission spectroscopy. Should that time come, the exposure times calculated in this work essentially act as a priority list of TESS stars most amenable to characterization. As we discover more terrestrial planets in the HZs of cool stars, this list can assist the community in making valuable decisions on which rocky planets are worth pursuing through characterization.

Although the prospects for observing water vapor features on ocean-covered worlds using our next-generation telescopes are not promising, there are still other methods that can characterize the atmospheres of rocky exoplanets. Contrary to transmission spectroscopy, for which the starlight is transmitted through the terminator of the planet, reflection and thermal emission spectroscopy would probe the full disk of the planet. Unlike in transmission spectra where clouds clearly hinder spectral characterization, the radiative effect of clouds may give detectable signals in emission and reflection that yield useful information (Yang et al. 2014; Wolf et al. 2019). In addition, reflection and thermal emission spectroscopy are not affected by atmospheric refraction, and can probe the lowest level of the atmosphere where most of the water resides. Cloudy areas of planet may be discernible from clear-sky areas, where reflected and emitted radiation can originate from the planet's surface and present a different spectral profile. However, future direct imaging missions such as LUVOIR or HabEX would be limited by the inner working angle of their instrument, preventing the observation of HZ planets orbiting very close to their host star, such as those modeled in this work. Furthermore, reflected and emitted radiation from a planet may change as a function of orbital phase. This may be particularly relevant for tidally locked planets around M dwarf stars, where permanent day and permanent night sides exist, and can create significant longitudinal gradients in the temperature, cloud, and outgoing radiation fields. Such phase-dependent information can be used to characterize terrestrial planet climates (Haqq-Misra et al. 2018; Kreidberg et al. 2019; Wolf et al. 2019).

To further understand the detectability of terrestrial planets in the HZs of M stars, we recommend running GCM simulations with more complex atmospheres. Different molecular species, such as CO₂, O₂, and O₃, should be included, not only to represent a more realistic planet but also to see how exposure times are affected by these different compositions. CO₂ may cool the stratosphere while absorption by O₃ or aerosols may create inversion layers; these effects could potentially make these planetary atmospheres easier to detect. Note that Fauchez et al. (2019) have shown that CO₂ could be the best proxy to detect an atmosphere on terrestrial HZ planets due to its strong absorption at 4.3 μm. The detectability of this feature is weakly affected by the presence of clouds because enough CO₂ remains above the cloud deck to saturate this feature and still produce a strong, detectable signal. The presence of species with lower molecular weight, such as H₂, could also increase the scale height, therefore increasing the depths of the water vapor features. Future 3D modeling studies should also use prognostic atmospheric chemistry modules in order to self-consistently predict the atmospheric composition while including a rich set of gas species (Chen et al. 2018, 2019). In addition, further understanding cloud behavior in the upper atmospheres of incipient runaway planets could potentially lead to shorter exposure times. For example, if the ice cloud decks in actuality span less than 1 dec in pressure, it is possible that the feature depths may grow to be equal to or even greater than those in the non-runaway states (as seen in the "zero" treatment of the model top for Figure 3, although we do not expect this to be realistic).

This study also demonstrates that understanding cloud processes in the upper atmosphere is crucial for understanding transmission spectra of hot and moist exoplanets. In particular, on warm planets the cloud condensation level moves upward in the atmosphere and to lower pressures (Leconte et al. 2013; Wolf & Toon 2015; Kopparapu et al. 2017). This becomes problematic for many exoplanet GCMs, which generally have model tops no higher than ∼0.1 mbar, and cloud parameterizations that are benchmarked to tropospheric conditions on Earth. Only very recently have GCMs with a high model top begun to be used for studying mesospheric and lower thermospheric processes in Earth-like exoplanet atmospheres (Chen et al. 2019). Still, successfully incorporating higher model tops is only part of the challenge facing the next generation of 3D climate models. Cloud microphysical parameterizations in GCMs remain rudimentary, but the formation, persistence, and radiative properties of clouds are highly sensitive to the size, shape, and evolution of cloud particles. Microphysical calculations that self-consistently predict particle size distributions in clouds may affect both the overall climate and the resultant transmission spectra. We recommend that future GCM studies of exoplanets work toward increasing the minimum pressure of the model top, and including more sophisticated cloud microphysical schemes.