Observing Isotopologue Bands in Terrestrial Exoplanet Atmospheres with the James Webb Space Telescope: Implications for Identifying Past Atmospheric and Ocean Loss

In the near future, terrestrial exoplanets around small M dwarf stars will be observed by the James Webb Space Telescope (JWST) and extremely large ground-based telescopes (Cowan et al. 2015; Quanz et al. 2015; Snellen et al. 2015; Greene et al. 2016; Lovis et al. 2017; Morley et al. 2017; Lincowski et al. 2018). A number of nearby transiting targets have been discovered, including the seven-planet TRAPPIST-1 system (Gillon et al. 2016, 2017; Luger et al. 2017), which provides a plausible opportunity for studying the liquid water habitable zone (HZ) and planetary evolution in a single system. However, the atmospheres of these planets will likely be heavily evolved from their primordial composition, due to the long, superluminous pre-main-sequence evolution (Baraffe et al. 2015) and life-long stellar activity (Tarter et al. 2007) of their M dwarf host stars.

The superluminous pre-main-sequence phase of M dwarf stars may drive significant loss of a planet's surface water and atmosphere, and potentially produce large quantities of atmospheric oxygen. This superluminous phase could last for up to one billion years for the smallest stars (Baraffe et al. 2015). During this time, ocean-bearing planets that formed in what is presently the HZ would have been subjected to fluxes up to 100 times the stellar irradiation of the main sequence. This would cause a runaway greenhouse environment and severe hydrodynamic escape (Luger & Barnes 2015), which occurs when heating by extreme UV absorption induces an escape flow (e.g., Hunten et al. 1987). During this period, the TRAPPIST-1 planets could have lost up to 20 Earth oceans of water and generated thousands of bars of oxygen (see Bolmont et al. 2017; Lincowski et al. 2018; Wordsworth et al. 2018). This oxygen could remain in the atmosphere, but is more likely to be severely reduced by a number of planetary processes. These processes include oxidation of the surface, interaction with a magma ocean that reincorporates the O₂ into the mantle (Schaefer et al. 2016; Wordsworth et al. 2018), or loss of O₂ to space either via hydrodynamic escape early on or by a number of ongoing escape mechanisms (e.g., Hunten 1982; Lammer et al. 2007; Ribas et al. 2016; Airapetian et al. 2017; Dong et al. 2017; Garcia-Sage et al. 2017; Egan et al. 2019).

Any atmospheric oxygen left by these sequestration/loss processes could constitute a false-positive biosignature if the planet is being assessed for signs of life (Meadows 2017; Meadows et al. 2018b). Even with sequestration and loss processes, ocean loss may leave behind several bars of O₂ (Schaefer et al. 2016; Wordsworth et al. 2018), which could be potentially discriminated from the modest amounts generated by a photosynthetic biosphere via detection of O₂–O₂ collision-induced absorption (CIA) bands. The O₂–O₂ bands, particularly at 1.06 and 1.27 μm, are more prominent in massive O₂ atmospheres because the absorption cross section is proportional to the density of gas squared (Schwieterman et al. 2016; Lincowski et al. 2018; Meadows et al. 2018a). Detection of these bands alone does not prove that the planet lacks a surface ocean, only that large amounts of oxygen have been liberated, and this is likely from water vapor photolysis and subsequent hydrogen escape.

Evidence of past atmospheric escape and ocean loss may help test the concept of the HZ, that region around a star where liquid water could exist on the surface of an Earth-like planet (Kasting et al. 1993; Kopparapu et al. 2013). The inner edge of the habitable zone (IHZ) is conservatively defined by the moist greenhouse limit (where stratospheric H₂O exceeds 1000 ppm and so water vapor is easily lost to space), which lies close to Earth (0.99 au around a Sun-like star). However, an optimistic "recent Venus" limit can be defined under the assumption that Venus may have had surface water prior to approximately one billion years ago, before the last global resurfacing event, when the Sun was fainter (Solomon & Head 1991; Kasting et al. 1993). Additionally, there have been a number of modeling studies positing revised limits for the IHZ that depend on perturbations to some of the parameter assumptions, including planetary mass (Kopparapu et al. 2014) and rotation rates (e.g., Kopparapu et al. 2016). Because TRAPPIST-1d is between the recent Venus limit and the conservative inner edge as defined by Kopparapu et al. (2013), it is a valuable target for probing the position of the IHZ around M dwarf stars.

In a multiplanet system like TRAPPIST-1, evidence of past atmospheric escape from the inner planet(s) could inform the suitability for more difficult follow-up observations of an HZ target (e.g., TRAPPIST-1e). It is much easier to characterize the inner planets, due to the possibility of obtaining more transit observations and the larger scale heights afforded by the hotter atmospheres (Morley et al. 2017; Lincowski et al. 2018). The survival of an atmosphere inward of the IHZ could be an indicator for the atmospheric survival of the other planets. For example, if TRAPPIST-1b still has an atmosphere, then planets farther away—including those in the HZ—have a higher likelihood of also hosting an atmosphere. However, the presence of an atmosphere on an HZ planet does not guarantee the planet is habitable, as even HZ planets may have undergone complete ocean loss (Lincowski et al. 2018).

Another piece of evidence that can indicate a planetary environment lost its surface water, so is not likely to be habitable, is severe isotopic fractionation. Both Venus and Mars once likely had surface oceans (e.g., De Bergh et al. 1991; Wordsworth 2016), evidence for which includes isotopic fractionation in the observed atmospheric deuterium to hydrogen ratios (D/H) compared to the Vienna Standard Mean Ocean Water (VSMOW) for Earth. Compared to VSMOW, the atmosphere of Venus is enhanced by a factor of 120–140 (De Bergh et al. 1991; Matsui et al. 2012) and the atmosphere of Mars is enhanced by a factor of ∼4 (Owen et al. 1988; Villanueva et al. 2015; Encrenaz et al. 2018). These enhancements likely occurred from near-complete loss of their available water reservoirs (Hunten 1982; Owen et al. 1988), because any primordial reservoir would dilute fractionated gas and reduce the total observed fractionation. Note that Earth has the lowest D/H ratio among the solar system terrestrials—VSWOW has D/H ∼8 times the solar abundance (see Hagemann et al. 1970; Asplund et al. 2009). Measurements of large isotopic fractionations in the atmospheres of nearby exoplanets relative to their host stars would also likely represent departures from primordial compositions (Mollière & Snellen 2019).

Atmospheric water vapor observed in transmission is suggestive but not definitive proof of the presence of an ocean (see Earth, Venus; Lincowski et al. 2018; Meadows et al. 2018a). Unlike reflectance spectroscopy, transmission spectroscopy cannot detect surface absorption or reflectance features—additional observations would be needed to determine the likelihood of surface liquid water.

Atmospheric escape is the only known mechanism capable of the extreme mass-dependent fractionation observed in the D/H in our solar system (see the summary in Mollière & Snellen 2019 and references therein). Similarly, the fractionation of oxygen (¹⁸O/¹⁶O) during hydrodynamic or nonthermal escape of oxygen generated from photolysis of vaporized ocean water is another potential signature of past ocean loss. If the abiotic oxygen generated via ocean loss is not lost to space, but instead is dissolved into a magma ocean (Schaefer et al. 2016; Wordsworth et al. 2018) or oxidizes the surface, then only a comparably small level of fractionation would occur. Unlike atmospheric loss, adsorption by the surface sequesters heavier isotopes slightly more than lighter isotopes (e.g., Sharp 2017), and so it would impart a small fractionation signature opposing that of escape. Measuring the hydrogen and/or oxygen isotope fractionation for planets orbiting M dwarfs could provide additional evidence of past extreme ocean loss and atmospheric escape in systems very different from our own.

Because O₂ and its isotopologues are likely to be difficult to observe with JWST, isotopologues of CO₂ can be used as a more easily observed proxy for oxygen fractionation. Laboratory experiments (e.g., Shaheen et al. 2007) and numerical modeling (Liang et al. 2007) of CO₂ in the stratosphere of Earth have demonstrated rapid isotopic equilibrium (on the order of days) between CO₂ and O₂, indicating that fractionation in CO₂ can be efficiently induced if it coexists with heavily fractionated O₂. Because this process is UV-driven, it is likely to also occur efficiently in the atmospheres of planets orbiting M dwarfs.

Isotopic fractionation may therefore be a useful indicator for past ocean loss on terrestrial exoplanets and may help to observationally test the inner edge of the HZ. Here we assess how large isotopic fractionation could be observed spectroscopically in terrestrial exoplanet atmospheres with JWST. We focus primarily on the two TRAPPIST-1 planets most likely to produce the strongest transit signals, due to their large atmospheric scale heights and small semimajor axes: TRAPPIST-1b, which receives approximately twice the irradiation of Venus, and d, which lies between the conservative and optimistic IHZ limits. We also assess the more observationally challenging TRAPPIST-1e, an HZ candidate. The TRAPPIST-1 system is scheduled to be observed with JWST and is likely to produce a favorable signal that could be used to characterize evolved atmospheres (Morley et al. 2017; Lincowski et al. 2018). In Section 2, we summarize our models and methods; in Section 3, we show our results; in Section 4, we discuss the implications of our results for observations with JWST; and in Section 5, we summarize our findings.

To produce simulated transit transmission spectra (see, e.g., Robinson 2017 and references therein) with increased isotopic fractionation, we use a 1D line-by-line radiative transfer model and adjust the input line list isotopologue abundances. To assess simulated observations for JWST, we use an instrument noise model. We describe our models and inputs in the following subsections.

We adopt the following isotope geochemistry convention (e.g., Sharp 2017) to describe the isotopic fractionation of hydrogen (note this does not include the multiplier of 1000 typically used in isotope geochemistry, due to the extreme values we adopt here):

$$\begin{eqnarray}&&\delta {\rm{D}}=\displaystyle \frac{{\left({\rm{D}}/{\rm{H}}\right)}_{\mathrm{model}}}{{\left({\rm{D}}/{\rm{H}}\right)}_{\mathrm{VSMOW}}}-1,\end{eqnarray} \tag{ 1 }$$

and similarly, δ¹⁸O is the notation for changes in ¹⁸O/¹⁶O. "VSMOW" refers to the Vienna Standard Mean Ocean Water isotopic standard (Coplen 1995).

2.1. Radiative Transfer

2.2. Calculating Isotopologue Abundances

We determine the modified abundances for all isotopologues available for the molecules H₂O, CO₂, O₃, CO, and O₂ in the HITRAN2016 line lists by calculating the abundances for each isotopologue given the specified isotopic fractionation. For oxygen, we assume standard terrestrial linear mass fractionation, such that ${\delta }^{17}{\rm{O}}=0.5{\delta }^{18}{\rm{O}}$ (Sharp 2017), although around M dwarfs this may depend on the details of atmospheric escape for a given planet. We assume that enhancement of doubly fractionated molecules (e.g., D₂O) is stochastic, and therefore proportional to the production of the isotopic fractionation for each affected atom, which is generally a good assumption, especially at higher temperatures (Eiler 2007).

To compute isotopologue abundances for each molecule, we numerically solve for the multipliers (X) for the isotopologues of a given molecule to adjust its VSMOW abundances given in HITRAN. These multipliers are not wholly independent, because we assume each substitution is proportional to the abundance. For example, substitution of hydrogen for deuterium in H₂O, ${{\rm{H}}}_{2}^{17}{\rm{O}}$, or ${{\rm{H}}}_{2}^{18}{\rm{O}}$ is equally likely per molecule, in proportion to the abundance of hydrogen in each molecule. The multiplier is squared for doubly substituted isotopes, because it requires the probability that one atom is substituted and the other is also substituted. A generic notation may be written as

$$\begin{eqnarray}&&{X}_{{{\rm{A}}}_{m}{{\rm{B}}}_{n}}=\displaystyle \frac{{\left({x}_{{\rm{A}}}[{\rm{A}}]\right)}^{m}\cdot {\left({x}_{{\rm{B}}}[{\rm{B}}]\right)}^{n}}{{\left[{\rm{A}}\right]}^{m}\cdot {\left[{\rm{B}}\right]}^{n}},\end{eqnarray} \tag{ 2 }$$

where the square brackets (e.g., [A]) are the notation for abundance and the individual multipliers are (${x}_{{\rm{A}}}$) for a particular isotope A. This equation reduces to

$$\begin{eqnarray}&&{X}_{{{\rm{A}}}_{m}{{\rm{B}}}_{n}}={x}_{{\rm{A}}}^{m}{x}_{{\rm{B}}}^{n}.\end{eqnarray} \tag{ 3 }$$

For our example of D₂O (also the example in box 1 of Eiler 2007), if x_D is the multiplier for the enhancement in deuterium, the abundance multiplier of D₂O is

$$\begin{eqnarray}&&{X}_{{{\rm{D}}}_{2}{\rm{O}}}=\displaystyle \frac{{\left({x}_{{\rm{D}}}[{\rm{D}}]\right)}^{2}\cdot {[}^{16}{\rm{O}}]}{{\left[{\rm{D}}\right]}^{2}\cdot {[}^{16}{\rm{O}}]}={x}_{{\rm{D}}}^{2}.\end{eqnarray} \tag{ 4 }$$

For a molecule with different isotopic substitutions, such as HD¹⁷O, the abundance adjustment would be

$$\begin{eqnarray}&&{X}_{{\mathrm{HD}}^{17}{\rm{O}}}={x}_{{\rm{H}}}{x}_{{\rm{D}}}(0.5{x}_{{}^{18}{\rm{O}}}),\end{eqnarray} \tag{ 5 }$$

where here we have set ${x}_{{}^{17}{\rm{O}}}=0.5{x}_{{}^{18}{\rm{O}}}$. The multipliers x are solved for simultaneously using a standard minimization code under the constraint that the total number of atoms of each isotope for a given family of molecules (e.g., H₂O and its isotopologues) satisfy the desired fractionation criterion (i.e., for δD = 100, that the ratio of abundances for deuterium across all isotopologues for a given molecule is 100 times greater than compared to VSMOW).

We assume that the line intensities (and absorption coefficients) of the adjusted isotopologues scale directly with their abundances, in accordance with the Boltzmann equation:

$$\begin{eqnarray}&&\displaystyle \frac{{n}_{\mathrm{iso}}}{{n}_{0}}=\displaystyle \frac{{g}_{\mathrm{iso}}}{{g}_{0}}{e}^{-({E}_{\mathrm{iso}}-{E}_{0})/{kT}},\end{eqnarray} \tag{ 6 }$$

where n is the number of molecules in a given energy state (directly proportional to the absorption coefficient), g represents the multiplicity of states (here, the abundance of molecules of a given isotopologue), E is the energy of each state, k is the Boltzmann constant, and T is the temperature.

2.3. JWST Instrument Simulator

2.4. Model Planetary Atmospheres and Stellar Inputs

2.5. Isotopic Fractionation

We present noiseless simulated transit transmission spectra at 1 cm⁻¹ resolution demonstrating the signal present due to different levels of extreme isotopic fractionation for δD up to 100 VSMOW (similar to Venus) and δ¹⁸O up to 100 VSMOW. These spectra are presented as "relative transit depth," given as (see Winn 2010; Lincowski et al. 2018)

$$\begin{eqnarray}&&\displaystyle \frac{{{dF}}_{a}}{F}=\displaystyle \frac{2{R}_{p}{R}_{a}}{{R}_{* }^{2}}+{\left(\displaystyle \frac{{R}_{a}}{{R}_{* }}\right)}^{2},\end{eqnarray} \tag{ 7 }$$

where F is the stellar flux, dF_a is the difference in stellar flux due to occultation by the atmosphere of the transiting planet, R_p is the planet solid-body radius, R_a is the atmospheric height from the surface of the planet, and R_* is the radius of the star. In this work, the relative transit signals discussed are generally relative to the transit signal calculated with the nominal VSMOW abundances. The spectra and data are available online using the VPL Spectral Explorer,⁵ or upon request. We assess the detectability of the isotopically enhanced features of these spectra propagated through the PandExo JWST instrument noise simulator (Batalha et al. 2017).

3.1. Isotopologue Abundances

3.2. Simulated Spectra

We assessed isotopic fractions of δD up to 100 times VSMOW for two outgassing, O₂-dominated atmospheres, and a (clear-sky) Venus-like, CO₂-dominated atmosphere, for TRAPPIST-1b, d, and e. We assessed δ¹⁸O up to 10 for these atmospheres, and up to 100 VSMOW for a completely desiccated O₂-dominated atmosphere. The justification for these values was discussed in Section 2.5, and these environments are listed in Table 1.

Noiseless simulated spectra are shown in Figures 1–2 for TRAPPIST-1b. The spectral region around 3–4 μm is rich for observing δD enhancements in HDO and δ¹⁸O enhancements in ¹⁸O¹²C¹⁶O. TRAPPIST-1b exhibits transit transmission signal strengths up to 79 ppm for δD in the reduced H₂O, O₂-dominated atmosphere with outgassing and 94 ppm for δ¹⁸O in the desiccated O₂-dominated atmosphere, compared to nominal spectra with VSMOW abundances. For comparison with b, in Figure 3 we show simulated spectra for TRAPPIST-1d and e for the O₂-dominated atmospheres with outgassing. The atmospheres of both planets have smaller absorption features, due to lower water vapor abundances and temperatures and due to the refraction of stellar photons. TRAPPIST-1e has very small isotopologue features here compared to VSMOW abundances, but this simulated, uninhabitable environment has a temperate climate and stratospheric water abundance similar to a potentially habitable planet, which makes it an important comparison case.

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The transit signals of isotopic fractionation in our individual atmospheres vary considerably and depend on the abundances of water vapor and CO₂ (Figure 1). In an O₂-dominated atmosphere with some water vapor still present due to outgassing, Venus-like fractionation of δD could be observable. With ∼500 ppm stratospheric H₂O (Figure 1, upper panel), the modeled TRAPPIST-1b atmosphere may exhibit a transit signal up to 74 ppm in the broad 3.7 μm HDO band. There are also weaker features due to HDO at 1.5 and 2.4 μm if HDO is sufficiently abundant. If fractionation in oxygen was also present, the ¹⁸O¹²C¹⁶O features between 3.0 and 4.1 μm would overlap with the 3.7 μm HDO band, though the bandwidths and shapes are different. The climate-photochemistry models of Lincowski et al. (2018) calculated lower water abundances in the stratosphere of this environment for TRAPPIST-1d (10–50 ppm) and e (∼1 ppm), and the transit signal for enhanced HDO is similarly smaller (55 and 11 ppm, respectively). These transit signals are also reduced, due to refraction for both planets and a much smaller scale height for e. With reduced stratospheric water vapor (to ∼1–5 ppm each for b and d), compared to VSMOW the spectra exhibited isotopologue transit signals of 79 and 29 ppm for b and d, respectively.

For a more severe case in a desiccated (water-free) O₂-dominated environment (Figure 2, upper panel), enhancements to δ¹⁸O in ¹⁸O¹²C¹⁶O are evident throughout the NIR (strongest at 1.7, 2.2, and 3–4 μm; labeled as ¹⁸OCO), exhibiting transit signals compared to VSMOW of up to 94 ppm for b and 72 ppm for d. With a signal of 29 ppm, this was the only TRAPPIST-1e atmosphere to exhibit a transit signal near 30 ppm compared to VSMOW (i.e., the putative noise floor for NIRSpec; Greene et al. 2016). There are also strong ¹⁸O¹²C¹⁶O isotopologue bands in these atmospheres at 6.0, 7.3, and 7.9 μm (not shown), though this spectral region is less favorable for JWST observations (Morley et al. 2017; Lustig-Yaeger et al. 2019).

For all three modeled planets (b, d, and e), Venus-like atmospheres are thoroughly dominated by CO₂, with minimal differences in spectral features, due primarily to ¹⁸O¹²C¹⁶O (less than 30 ppm) in the transit signal compared to VSMOW (see, e.g., Figure 2, lower panel). These differences were at the same wavelengths exhibited by the O₂ atmospheres. With CO₂ absorption saturating the NIR spectrum, HDO was not detectable in our Venus-like cases.

While HDO and ¹⁸O¹²C¹⁶O were the primary detectable isotopologues, many other bands were included in our spectral models, but were generally not present in the simulated transit transmission spectra, including the O₂ A band. No isotopologues containing ¹⁷O were distinctly present, due to its lower abundance compared to ¹⁸O. Isotopologue absorption by ¹²C¹⁸O at 2.4 μm is distinguishable in the completely desiccated atmosphere (see Figure 1), but not likely individually discernible with JWST.

3.3. Detectability Assessment

Lustig-Yaeger et al. (2019) conducted a comprehensive detectability study for JWST instruments using the suite of model spectra from Lincowski et al. (2018) and identified several useful instrument modes for these atmospheres. These optimal instrument modes were used here and are listed along the bottom of Figure 4, which provides a summary of the number of transits required to attain an expected signal-to-noise ratio ($\langle {\rm{S}}/{\rm{N}}\rangle$) of 5 compared to the transit spectra with nominal VSMOW abundances for each model atmosphere. The number of transits required for a different $\langle {\rm{S}}/{\rm{N}}\rangle$ can be calculated as

$$\begin{eqnarray}&&N^{\prime} =N{\left(\displaystyle \frac{\left\langle {\rm{S}}/{\rm{N}}\right\rangle ^{\prime} }{\left\langle {\rm{S}}/{\rm{N}}\right\rangle }\right)}^{2},\end{eqnarray} \tag{ 8 }$$

where N is the number of transits (here at $\langle {\rm{S}}/{\rm{N}}\rangle =5$) and N' is the number of transits to attain $\langle {\rm{S}}/{\rm{N}}\rangle ^{\prime}$.

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Except for our CO₂-dominated, Venus-like environments, Venus-like levels of fractionation of D/H consistent with past ocean loss for each TRAPPIST-1b and d atmosphere may be detectable with JWST (see, e.g., Figure 5). The completely desiccated, O₂-dominated atmospheres modeled for TRAPPIST-1b and d have ¹⁸O¹²C¹⁶O bands that are also accessible to JWST. Assuming volcanically outgassed species in the O₂-dominated atmospheres allows detection of HDO bands. Fractionation in oxygen, in addition to hydrogen, increases the detectability of isotopologue bands, due to complementary signal increases in both HDO and ¹⁸O¹²C¹⁶O bands. As in Lustig-Yaeger et al. (2019), we find that NIRSpec Prism SUB512 (512 × 512 subarray) with a partial saturation strategy (allowing partial saturation at the SED peak to provide higher signal at other wavelengths), with six groups per integration (Batalha et al. 2018), is generally the ideal instrument/mode for these detections. The NIRSpec G395H grism is nearly as good, or in some cases better, due to coverage of the 3–4 μm region containing broad HDO and ¹⁸O¹²C¹⁶O bands. Similarly, due to its wavelength coverage, NIRCam F322W2 is also an acceptable instrument for these detections.

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With lower levels of stratospheric water vapor similar to Venus and Earth in an O₂-dominated atmosphere (here, 1–5 ppm H₂O), a similar number of transits are required for TRAPPIST-1b compared to the nominal outgassing atmospheres of Lincowski et al. (2018). This is significantly worse for TRAPPIST-1d, which may be in part due to the higher refraction altitude exhibited by d.

The Venus-like atmosphere with Venus-like isotopic fractionation is likely very difficult to detect with JWST, even without aerosols. This is due to the small scale height and high opacity of a CO₂-dominated atmosphere, which confines the transmission to the upper stratosphere and strongly reduces the signal from H₂O and HDO. To detect a fractionation signal, such a Venus-like planet would also have to exhibit substantial fractionation in oxygen (unlike Venus itself), which could enhance the transit depths of the ¹⁸O¹²C¹⁶O bands. In a cooler atmosphere such as that of TRAPPIST-1d, the CO₂ bands are not as broadened, and the occupancy of the lower energy states of isotopologue bands is higher (Mollière & Snellen 2019), so detecting ¹⁸O¹²C¹⁶O in a Venus-like (albeit clear-sky) atmosphere of d would require fewer transits than b.

For TRAPPIST-1e, detecting isotopic fractionation in H₂O would be difficult, requiring more than 100 transits for all fractionation values, atmospheric environments, and instrument modes considered here. Fractionation in CO₂ oxygen isotopes in the desiccated O₂-dominated atmosphere may be possible, if such extreme fractionation is possible. The HDO and ¹⁸O¹²C¹⁶O features in the model atmospheres for TRAPPIST-1e are substantially masked by atmospheric refraction. The cooler temperatures and higher surface gravity compared to TRAPPIST-1b and d result in small scale heights, which conspire to produce shallow transmission depths.

We have shown that an enhancement of 100 in either δD (via water vapor) or δ¹⁸O (via CO₂), which would likely be due to extreme ocean or atmospheric loss, may be detectable with JWST for the inner planets of the TRAPPIST-1 system. Simulated spectra for our O₂-dominated atmospheres exhibit transit signals up to 79 ppm and 94 ppm for δD and δ¹⁸O, respectively, for TRAPPIST-1b (55 and 72 ppm, respectively, for d; 11 and 29 ppm, respectively, for e). With optimal use of NIRSpec Prism (Batalha et al. 2018), these signals could be detected at $\langle {\rm{S}}/{\rm{N}}\rangle =5$ in 11 and four transits respectively for b (25 and five for d). In the desiccated, O₂-dominated case with δD = 100 and δ¹⁸O = 10, the isotopic enhancement can be distinguished from the nominal Earth VSMOW abundances in as few as eight transits for b (13 for d). This is only a few more transits than the two transits required with NIRSpec Prism SUB512 n = 6 to detect an atmosphere by ruling out a featureless spectrum at $\langle {\rm{S}}/{\rm{N}}\rangle$ = 5 for b or d (Lustig-Yaeger et al. 2019). It is more difficult to observe a fractionation signature in the atmosphere of an HZ planet like TRAPPIST-1e; only extreme fractionation of oxygen is possibly detectable (in 28 transits), due to a smaller atmospheric scale height, lower levels of stratospheric water vapor, and the refraction of stellar rays through the atmosphere during transit (Bétrémieux & Kaltenegger 2013, 2014; Misra et al. 2014; Robinson 2017).

The strongest transit signal is due to rotational–vibrational bands in the NIR, 1–5 μm, consistent with JWST NIRSpec. Transit observations are dependent on the stellar photons for signal, and this is the spectral region with the most stellar photons from M dwarf stars. These rotational–vibrational transitions are subject to mass-dependent spectral shifts for the bands between 1 and 3 μm, because such transitions are inversely proportional to the reduced mass of the molecule. Asymmetric molecules such as HDO and ¹⁸O¹²C¹⁶O provide new degrees of freedom, by breaking molecule symmetries compared to H₂O and CO₂, which produce new absorption bands between 3 and 8 μm.

The severe fractionation considered in this work would not likely be caused by any other known fractionation mechanism, including the composition of the host star (e.g., Mollière & Snellen 2019, and references therein). Interpreting observed isotopic abundances in the atmospheres of an exoplanet must be considered in relation to the host star. However, nearby stars differ in D/H by less than a factor of ∼2 compared to the Sun (see Linsky et al. 2006; Asplund et al. 2009). The fractionation of isotopic abundances compared to the host star value would indicate that a planet evolved from primordial conditions, which could include a small effect due to formation. However, a large fractionation compared to the host star would likely indicate an evolved atmosphere, though at this time we cannot say which mechanism may be responsible.

The ability to observe isotopic fractionation in H₂O or CO₂ may help to more robustly identify worlds without surface oceans. Transmission spectroscopy cannot directly probe the surface composition of a planet, and water vapor observed in transmission is suggestive, but is not conclusive, proof that an ocean is present. Current planetary hydrogen loss (though also not conclusive evidence of a surface ocean) could be identified via UV measurements of Lyα (e.g., Jura 2004). The detection of O₂–O₂ CIA is indicative of a large inventory of oxygen that is most likely produced during the loss of oceans of water (Luger & Barnes 2015; Schwieterman et al. 2016). A large O₂ inventory does not preclude the possibility that a significant amount of surface water remains, especially for more volatile-rich worlds, which may include the TRAPPIST-1 planets. However, the identification of isotopic fractionation in H₂O and/or CO₂ in conjunction with the detection of O₂–O₂ would be strong evidence that the planet lost the bulk of its available water inventory, and that it is unlikely that surface water remains. This is because an extant inventory of surface water would dilute the isotopic fractionation signal.

Isotopic fractionation signals could therefore complement observations of O₂–O₂ for ocean-loss planets, and these two sets of observations may be attainable with JWST, at least for the inner planets of TRAPPIST-1. Lustig-Yaeger et al. (2019) found that O₂–O₂ features in O₂-dominated atmospheres may be detected in as few as 10 transits (for TRAPPIST-1b) in the outgassing case with the NIRSpec Prism SUB512 (n_groups = 6), equal to the 10 transits required to distinguish HDO bands compared to VSMOW. NIRSpec Prism is particularly useful because the extra wavelength coverage (0.6–5.3 μm) can provide simultaneous evidence of the O₂ abundance (via O₂–O₂ at 1.06 and 1.27 μm) and of isotopic fractionation of hydrogen in H₂O or oxygen in CO₂. Here we have shown that for a planet like TRAPPIST-1b, the number of transits required to identify these individual O₂–O₂ bands is sufficient to begin distinguishing isotopologues as well, without the additional observing time necessary to identify a large (abiotic) inventory of O₂.

Although our motivation for assessing atmospheric and ocean loss through measuring the D/H ratio was inspired by remote-sensing measurements of D/H in the atmosphere of Venus, it will not likely be possible to conduct these measurements in the atmospheres of Venus-like exoplanets using transit observations. Sulfuric acid aerosol formation truncates the atmospheric levels that can be probed in transmission, and the saturated CO₂ bands largely blanket the NIR–MIR spectra of CO₂-dominated atmospheres. The effective greenhouses cause high temperatures, which disfavor the occupation of isotopologue rovibrational energy states (Mollière & Snellen 2019).

Isotopologue observations may help constrain the location of the IHZ by providing evidence for whether water vapor detected in the atmosphere of a planet is consistent with ocean loss or with a primordial reservoir (i.e., surface water or outgassing). Because TRAPPIST-1d sits between the recent Venus and moist greenhouse limits, it is a valuable target for this observation. The observation of water vapor with no evidence of fractionation in the atmosphere of an IHZ planet like TRAPPIST-1d would support the recent Venus limit, though the lack of fractionation could also be due to outgassing fluxes or a high volatile inventory—i.e., it could be a water world in a permanent runaway greenhouse state, which would be indicated by a large abundance of stratospheric water vapor. Conversely, isotopic evidence of ocean loss would strongly support the moist greenhouse limit as the true inner edge. Robust observational evidence for the location of the IHZ would require a survey of multiple planets and multiple systems with high-fidelity observations to constrain both the H₂O abundances and D/H ratios.

It may be difficult to observe isotopologues in the atmospheres of planets within the HZ. We found that TRAPPIST-1e exhibited only small signals, and even in the optimistic assessment we conducted, which ignored any systematic noise floor, it would generally require greater than 100 transits to identify isotopologues at $\langle {\rm{S}}/{\rm{N}}\rangle =5$. This is likely to apply to HZ planets in general, due to the lower atmospheric temperatures (and resultant lower atmospheric scale height), additional refraction due to distance from the star, and lower stratospheric water vapor.

The fractionation we have modeled may not be attainable for all small planets that may have undergone ocean and atmospheric loss in and around the HZs of M dwarf stars. If a planet targeted for observation is more volatile-rich than Earth, the volatile inventory available to the atmosphere may never be lost, and as discussed above, would not impart a significant fractionation signature to the atmosphere. This may be the case for one or more of the TRAPPIST-1 planets, which may be more volatile-rich than Earth due to slightly lower nominal densities (Grimm et al. 2018) and dynamical evidence of possible migration (Luger et al. 2017). However, within the calculated error, these densities are still within the range of terrestrial values in a mass–radius relationship (Grimm et al. 2018).

An observation of oxygen fractionation in CO₂ could indicate extreme atmospheric loss but may be difficult to achieve. The fractional mass difference between ¹⁸O and ¹⁶O is small, and Venus does not exhibit fractionation in oxygen (Hoffman et al. 1980; Bezard et al. 1987; Iwagami et al. 2015). So, significant fractionation in oxygen may require atmospheric escape mechanisms unknown in our solar system, or operating over longer time periods or at higher fluxes than for the solar system planets. However, if it occurred, oxygen fractionation could be retained within CO₂ if oxygen loss occurred in the presence of CO₂. Without surface liquid water, surface weathering processes (i.e., carbonate-silicate weathering; Walker et al. 1981) would no longer draw outgassed CO₂ from the atmosphere. Because the oxygen in CO₂ would dilute the isotopic signal from oxygen loss, the remaining CO₂ inventory must be small compared to the remaining oxygen to prevent significant dilution of the oxygen isotope abundances.

In addition to the potential dilution of oxygen isotopic fractionation, atmospheres with large inventories of CO₂ would make it more difficult to observe any isotopic fractionation signal considered here. Unlike the other typical terrestrial bulk atmospheric gases O₂ and N₂, CO₂ exhibits significant absorption throughout the NIR–MIR, which masks weaker absorption lines, including isotopologues. Large quantities of water vapor can similarly interfere with observing other trace gases. While Earth-like abundances of CO₂ and H₂O may be the most favorable for distinguishing and characterizing important isotopologue bands, low CO₂ abundance may not be likely for a planet that experienced total ocean loss because the lack of liquid surface water would reduce surface weathering that draws outgassed CO₂ from the atmosphere.

Other factors not considered in this work can affect the possibility of detecting isotopic fractionation, such as surface pressure and clouds. Morley et al. (2017) showed that for atmospheres with a surface pressure of 1 bar and lower, the number of transits required to detect features increased with decreasing pressure. In Lincowski et al. (2018), the amplitudes of transit transmission features did not change significantly as a result of higher surface pressure at pressures higher than 10 bars. Clouds and hazes, which may form at high altitude, can significantly truncate transit transmission spectra, particularly hazes such as those in the atmosphere of Venus, which form at much higher altitude than water clouds (e.g., Lincowski et al. 2018). For Venus-like clouds in particular, H₂SO₄ has many absorption bands longward of 2.5 μm. These absorption bands are not the same as CO₂ or H₂O, but together with these gases and due to the high altitude of haze aerosols, the presence of H₂SO₄ aerosols can effectively eliminate primary detectable isotopologue features in the 2.8–4.3 μm range, between CO₂ bands. While TRAPPIST-1d and e may form aerosols, Lincowski et al. (2018) showed that, due to high atmospheric temperatures, the most likely condensates in these oxidized atmospheres, H₂O and H₂SO₄, would not condense in the atmosphere of a Venus-like TRAPPIST-1b. While other metal aerosols have been suggested for hotter exoplanets (such as sodium- and potassium-based condensates), these are not plausible for the temperature regimes considered here, as it would not be possible to evaporate them from the planetary surface (see Schaefer & Fegley 2009). Hydrogen-dominated atmospheres could support other types of aerosols, particularly if these planets reached higher temperatures (e.g., He et al. 2018), but the TRAPPIST-1 planets are not likely to have H-dominated atmospheres (de Wit et al. 2016, 2018; Moran et al. 2018), with the possible exception of TRAPPIST-1g (Moran et al. 2018), which we do not consider here. Consequently, TRAPPIST-1b is not likely to support the majority of hypothesized aerosols, and so is more likely to be clear sky than the other planets in the system.

Here TRAPPIST-1b, d, and e were used as sample planets to assess the possibility of detecting isotopologue bands in exo-terrestrial atmospheres. The results could be extended to other planets in the system, in light of the results of Morley et al. (2017), Lincowski et al. (2018), and Lustig-Yaeger et al. (2019), or to other systems. While TRAPPIST-1c is one of the inner planets with parameters similar to Venus, it is more difficult to observe features in the atmosphere of TRAPPIST-1c than b and d, due to the higher density of c. Given the results for TRAPPIST-1e, it is unlikely that isotopologue bands could be observed in the atmospheres of the outer planets, TRAPPIST-1f, g, and h. The results of this work could be used to assess the detectability of isotopologue bands in the atmospheres of other M dwarf targets of interest, both those currently known and those yet to be discovered by SPECULOOS (Delrez et al. 2018), TESS (Barclay et al. 2018), CHEOPS (Broeg et al. 2013; Benz et al. 2018), and PLATO (Rauer et al. 2014).

We have shown that isotopic fractionation signals inferred from HDO or ¹⁸O¹²C¹⁶O may be feasible to observe with JWST and may provide important clues to the evolutionary history of planets around M dwarfs. Measurements with ground-based high-resolution instruments may also be able to search for isotopic signatures for the very nearest M dwarf planets (Mollière & Snellen 2019). The values we have considered can guide observers considering different levels of fractionation. These levels could also be used to assess the possibility of detecting isotopic fractionation if future comprehensive modeling of atmospheric escape demonstrates at what level hydrogen or oxygen fractionation is possible, and serve as a testable hypothesis for fractionation, due to ocean loss. After first determining that a planet has an atmosphere (Lincowski et al. 2018; Lustig-Yaeger et al. 2019), the next important assessment of the planetary environment may be to search for signs of severe ocean loss. Isotopic measurements can contribute evidence for assessing the atmosphere and ocean loss of M dwarf planets, which will soon be observed with JWST. Although severe atmospheric escape is likely to afflict all small planets in or near M dwarf HZs, caveats against such fractionation occurring also exist. Observations of one or more inner planets in a multiple-planet system could be used to inform the suitability of more time-consuming follow-up observations of an HZ sibling.

We have shown that for a Venus-like isotopic fractionation of D/H, or a similar fractionation in ¹⁸O/¹⁶O, isotopologue bands may be observable and distinguished from Earth-like isotopic abundances with JWST in as few as 10 transits (δD = 100) or four transits (δ¹⁸O = 100) for a clear-sky atmosphere not dominated by CO₂. The large fractionation values considered here are meant to demonstrate the potential for detecting these bands and discriminating them from Earth-like abundances. These fractionation values would require an ocean-free surface and ocean loss at least as severe as that experienced by Venus. A detection of these bands in transit transmission spectra would be evidence of a lack of a surface ocean, and the extreme atmospheric loss and oxygen build-up that has been proposed by a number of authors. This would provide valuable constraints for atmospheric escape models, the location of the IHZ (whether recent Venus or moist greenhouse), and on the habitability of M dwarf planets. Researchers currently preparing JWST observing proposals, and those who will be conducting retrievals on future JWST observations, may want to consider different isotopic abundances in line lists used as inputs to retrieval pipelines. Further work modeling atmospheric escape that includes elemental isotopes is also warranted, to understand to what degree isotopic fractionation is theoretically possible in the atmospheres of planets orbiting M dwarfs. A thorough analysis of atmospheric escape should consider thermal and nonthermal escape, including photochemistry and vertical transport, life-long outgassing, and the possibility of deep surface reservoirs (i.e., water worlds).

We thank Rodrigo Luger and David Crisp for useful discussions that helped improve this paper. This work was performed as part of the NASA Astrobiology Institute's Virtual Planetary Laboratory, supported by the National Aeronautics and Space Administration through the NASA Astrobiology Institute under solicitation NNH12ZDA002C and Cooperative Agreement Number NNA13AA93A, and by the NASA Astrobiology Program under grant 80NSSC18K0829 as part of the Nexus for Exoplanet System Science (NExSS) research coordination network. A.P.L. acknowledges support from NASA Headquarters under the NASA Earth and Space Science Fellowship Program—grant 80NSSC17K0468. This work was facilitated though the use of the advanced computational, storage, and networking infrastructure provided by the Hyak supercomputer system at the University of Washington. We also thank the anonymous reviewer, whose thoughtful comments helped us greatly improve the manuscript.

Software: SMART (Meadows & Crisp 1996; Crisp 1997), LBLABC (Meadows & Crisp 1996), PandExo (Batalha et al. 2017), GNU Parallel (Tange 2011).