Prospects for water vapor detection in the atmospheres of temperate and arid rocky exoplanets around M-dwarf stars

Detection of water vapor in the atmosphere of temperate rocky exoplanets would be a major milestone on the path towards characterization of exoplanet habitability. Past modeling work has shown that cloud formation may prevent the detection of water vapor on Earth-like planets with surface oceans using the James Webb Space Telescope (JWST). Here we analyze the potential for atmospheric detection of H2O on a different class of targets: arid planets. Using transit spectrum simulations, we show that atmospheric H2O may be easier to be detected on arid planets with cold-trapped ice deposits on the surface, because such planets will not possess thick H2O cloud decks that limit the transit depth of spectral features. However, additional factors such as band overlap with CO2 and other gases, extinction by mineral dust, overlap of stellar and planetary H2O lines, and the ultimate noise floor obtainable by JWST still pose important challenges. For this reason, combination of space- and ground-based spectroscopic observations will be essential for reliable detection of H2O on rocky exoplanets in the future.


INTRODUCTION
Water vapor has now been detected in the atmospheres of many gas-giant exoplanets (Fortney et al. 2021), and in some cases abundance constraints have been derived from the transmission spectra (e.g., Madhusudhan et al. 2014; Barstow et al. 2017;Pinhas et al. 2019). An important goal for future large ground-and space-based telescopes is to detect water vapor molecules in the secondary atmospheres of rocky exoplanets. In particular, detection of Earth-like water vapor levels on rocky planets orbiting within the habitable zones of their host stars would suggest the existence of a surface liquid water reservoir -a necessary condition for the survival of Earth-like life (Kasting et al. 1993;Kopparapu et al. 2013). Several recent studies have simulated the spectral features of Earth-like aqua-planets (with global surface entirely covered in oceans) around low-mass stars using three dimensional general circulation models (3D GCMs). These studies showed that ice cloud particles suspended in the upper atmosphere resulting from tropospheric deep convection and the large-scale circulation will mute H 2 O features in the transmission spectra of future space-based observations, e.g., the James Webb Space Telescope (JWST), likely rendering water vapor undetectable (Fauchez et al. 2019;Komacek et al. 2020;Pidhorodetska et al. 2020;Suissa et al. 2020).
However, the detectability of water vapor on rocky planets with limited surface water reservoirs (hereafter referred to as arid planets) has not yet been studied in detail. Many M-dwarf rocky planets may be water-poor as a result of their host stars' prolonged pre-main-sequence phase, which may cause extensive early water loss (Ramirez & Kaltenegger 2014;Luger & Barnes 2015;Tian & Ida 2015). Recent GCM studies have revealed multiple moist climate equilibrium states on such arid planets (e.g., Leconte et al. 2013;Ding & Wordsworth 2020. Figure 1 illustrates the multiple moist climate states as a result of the cold trapping competition between the substellar tropopause and the nightside surface, which was discussed in more detail in Ding & Wordsworth (2020) and Ding cycle on arid planets, the surface water reservoir can be either trapped by the substellar tropopause as a substellar oasis, or entirely evaporated into the atmosphere (Ding & Wordsworth 2020). The outcome depends on whether the incoming stellar radiation exceeds the runaway greenhouse threshold (1.2 ∼ 1.6F ⊕ for planets around mid-M dwarfs, where F ⊕ is the present-day Earth's incoming stellar flux, see Yang et al. 2014;Kopparapu et al. 2016 When the cold trap on the nightside surface dominates the hydrological cycle on arid planets, climate models predict that the surface water reservoir will be trapped on the nightside as ice caps. In this situation, the tropopause cold trap becomes ineffective and hence the atmospheric water vapor is in vapor-ice phase equilibrium with the surface ice layer and well-mixed in the atmosphere (Ding & Wordsworth 2020. This particular climate state with only nightside surface ice deposits and no dayside condensation clouds can exist under much higher stellar radiation beyond the runaway greenhouse threshold, because the extremely under-saturated dayside atmosphere behaves as an effective radiator fin (Pierrehumbert 1995;Abe et al. 2011;Zsom et al. 2013;Kodama et al. 2018;Ding & Wordsworth 2020) and the optically thin atmosphere redistributes heat inefficiently between the dayside and nightside (Leconte et al. 2013;Wordsworth 2015;Koll & Abbot 2016 (2015); Koll et al. (2019). A near-infrared (NIR) phase curve has been observed for LHS 3844b, a hotter rocky exoplanet receiving stellar flux of 70 F ⊕ . The symmetric shape and large amplitude of the phase curve rule out thick atmospheres (denser than 10 bar) on LHS 3844b (Kreidberg et al. 2019). Therefore, transit spectroscopic observations combined with thermal phase curve observations will be an ideal tool to characterize atmospheres and identify whether surface ice deposits can survive in cold-trap regions on temperate rocky exoplanets. The aim of this letter is to investigate the detectability of water vapor on planets in this climate state and compare with previously simulated results for habitable aqua-planets.

GCM setup
We simulate an Earth-sized synchronously rotating planet orbiting an M5V-type star with an effective temperature of 3060 K. We use the idealized GCM developed in Ding & Wordsworth (2019) to simulate climates on temperate arid exoplanets with nightside ice deposits. Our GCM uses a lineby-line approach to calculate radiative transfer, which maintains both flexibility and accuracy for simulating diverse planetary atmospheres. We assume the surface is bare rock with an albedo of 0.2.
The atmosphere is made of 1 bar N 2 and variable amounts of H 2 O. The effects of varying atmospheric composition beyond this idealized Earth-like case, and in particular the effects of adding CO 2 to the atmosphere, are discussed in subsequent sections. We run a series of simulations with various incoming stellar fluxes to determine the critical flux under which the initial H 2 O can condense on the nightside surface and form ice layers. For each given incoming stellar flux F , the model is integrated for 3000 days. The corresponding orbital period P of the planet is calculated self-consistently using Kepler's third law (Wordsworth 2015;Kopparapu et al. 2016;Haqq-Misra et al. 2018) as where L/L = 0.003 is the luminosity of the host star scaled by the luminosity of the Sun and M/M = 0.16 is the mass of the host star in solar mass units (Pecaut & Mamajek 2013).

Simulation of transmission spectra
We use the Planetary Spectrum Generator 2 (PSG, Villanueva et al. 2018) to simulate the transmission spectra of transiting planets with nightside ice deposits. In this study we make a conservative estimate by assuming that the planetary system is 15 parsec away, further than the confirmed nearby temperate rocky exoplanets mentioned earlier. The parameters of the host star and the simulated planet are the same as those used in the GCM simulation. We use PSG to simulate the near-infrared transmission spectra between 0.6 and 5.3 µm with a resolving power R = 50, which is relevant for the JWST Near-Infrared Spectrograph (NIRSpec)/PRISM instrument. We follow Louie et al. (2018) and Lustig-Yaeger et al. (2019) to estimate the total expected signal-to-noise ratio (S/N) as the quadrature sum of individual S/N from each spectral element when detecting water vapor features in the transmission spectra. We assume the out-of-transit observation time the same as the in-transit time and the noise level dominated by photon noise statistics. For detection of molecular features, we assume a signal-to-noise ratio of 5 is required. We first estimate the climate on temperate arid exoplanets with nightside ice deposits by performing a series of GCM simulations similar to the atmospheric collapse simulations in Wordsworth (2015).
We find that when the incoming stellar flux decreases to 6000 W m −2 (4.4F ⊕ , P = 3.86 days) water vapor starts to condense on the nightside surface for an atmosphere made of 1 bar N 2 with 10 ppmv ice layer is assumed to be 1 km thick and cover 10% of the global surface area. The climate state used to calculate the transmission spectrum in Figure 2 is marked by the white dot.
Next, we use PSG to explore how atmospheric N 2 and H 2 O inventories can affect the detectability of water vapor features in the transmission spectra by varying the surface partial pressure of N 2 from 0.02 bar to 2 bar and H 2 O from 0.1 Pa to 10 Pa. Here we simply assume the same orbital radius and period as used in Figure 2. This assumption has negligible effect on the transmission spectra calculation, but fixes the transit duration time and therefore the photon-noise statistics. The required number of transits to detect water vapor features is shown in Figure 3. The simulation results suggest water vapor features are observable in the transmission spectra, but only over a relatively narrow parameter range. For instance, in order to detect water vapor on a temperate arid planet with nightside ice deposits within less than 30 transits, the temperature of the nightside surface cold trap should be above 200 K if the background atmosphere is 1 bar N 2 .
For thinner background atmospheres, this required temperature is higher because collisions among air molecules are less frequent and higher H 2 O concentrations are therefore required to be detected.
On temperate arid planets, the surface temperature of the nightside cold trap depends on not only the incoming stellar flux but also many planetary parameters, such as planetary rotation rate and atmospheric composition (see also Section 4). Recent work has suggested that turbulent mixing near the nightside surface should be stronger than simulated by GCMs . So further studies combined with eddy-resolving models and large-scale GCMs are required to fully understand the nightside near surface conditions that are crucial for surface cold trapping.
An important factor determining the lifetime of surface ice deposits is atmospheric escape. In the parameter space we explore here, water vapor is the minor species in the atmosphere. In this circumstance, the atmospheric escape flux would most likely be limited by diffusion through the homopause. Here we estimate the lifetime of surface ice by using the diffusion-limited H 2 escape flux (measured by number of escape particles per unit surface area of the planet per unit time) following Abe et al. (2011) F where f str (H 2 ) is the mixing ratio of hydrogen in all forms at the homopause, T str ∼ 300 K is the homopause temperature, m N 2 and m H 2 are the particle mass of N 2 and H 2 , and b = 1.9 × 10 21 (T /300) 0.75 m −1 s −1 is the binary diffusion coefficient of H 2 in N 2 . If the diffusion species is H instead of H 2 above the homopause, the escape flux is increased by a factor of 2. Assuming the surface ice layer to be 1 km thick and cover 10% of the global surface area, we find the lifetime of the ice deposits for most parameters we consider here is greater than 1 Gyr. As a comparison, without the supply of water vapor from the surface ice deposits, the e-folding lifetime of atmospheric water vapor is shorter than 70 kyr. Combining the calculations of transmission spectra and surface ice lifetime, it is possible to detect water vapor features on temperate arid planets with nightside ice deposits when the background atmospheric pressure is above 0.05 bar and the nightside surface temperature is above 200 K.  Finally, it is worth noting that water vapor is not the only volatile species that can condense on the nightside on temperate rocky exoplanets. There are many other candidates given right conditions.
Another common condensing species is CO 2 . Wordsworth (2015) investigated the relation between the atmospheric CO 2 pressure and the critical incoming stellar flux to trigger nightside surface condensation (ranging from 0.2 F ⊕ to 3 F ⊕ ), focusing on slowly rotating planets around bright M-dwarfs.
Using our GCM, we similarly find that for a planet with 0.1 bar CO 2 atmosphere around a bright M-dwarf the critical incoming stellar flux that triggers the nightside surface condensation is ∼ 1 F ⊕ (Ding & Wordsworth 2019). When the host star is M5V-type, we find the critical flux increases to 4000 W m −2 (2.9 F ⊕ ). The corresponding orbital radius and period are 0.032 AU and 5.23 days, respectively. Then we use PSG to simulate the transmission spectrum of such a transiting planet, which is Mars-like with a CO 2 -dominated atmosphere but CO 2 ice deposits forming on the nightside rather than around the polar regions. The climate resembles the moist climate described in Figure 1c but with a condensing CO 2 atmosphere. We compare the result with the case of a dense 10 bar CO 2 atmosphere in Figure 4.
Both cases show stronger NIR absorption features than the 10 ppmv water vapor case in Figure 2 so that fewer transits are required to detect CO 2 features in the transmission spectra. Another major difference is that atmospheric refraction plays an important role in dense CO 2 atmospheres. For temperate planets with CO 2 -dominated atmosphere around M5V-type stars, PSG simulation results show that only the top 0.7 bar of atmosphere can be probed. This 0.7 bar layer mimics a surface (e.g., Hui & Seager 2002;Misra et al. 2014;Bétrémieux & Kaltenegger 2015) and raises the baseline of the transmission spectrum of the dense CO 2 atmosphere. So both cases have similar relative transit depths and can be further distinguished by observation of the thermal phase curve or eclipse photometry.

CONCLUSION AND DISCUSSIONS
Temperate rocky exoplanets inside the inner edge of conventional habitable zone can store substantial amount of remaining water ice on the nightside surface if the atmosphere is optically thin in the thermal infrared and redistributes heat inefficiently. Our simulation results suggest that strong water vapor features in transmission spectra of those climate systems can potentially be detected for surface pressures higher than 0.05 bar and nightside surface temperature higher than 200 K. NIR transit spectroscopy combined with thermal phase curve or eclipse photometry by JWST will be an ideal tool to identify the climate state of temperate rocky exoplanets covered by remnant ice deposits on the nightside. Phase curve observation has been proved to be very effective to distinguish whether the atmosphere is optically thin or thick on a hot rocky exoplanet, LHS 3844b (Kreidberg et al. 2019).
If water vapor was detected in the transit transmission spectrum of a temperate rocky exoplanet with an optically thin atmosphere, it is very likely that the water vapor would be in phase equilibrium with remnant nightside ice deposits, because the lifetime of water vapor in such atmosphere is usually shorter than 0.1 Myr without a surface supply.
There are several important factors that could complicate the analysis presented here. First, our assumption of an atmosphere only made of N 2 and H 2 O is very simplified. In reality, other gaseous species in the atmosphere are expected, such as CO 2 , O 2 , O 3 , H 2 , CO and CH 4 , depending on the redox evolution of the planet and other effects. These gases can provide additional thermal infrared opacity and raise the surface temperature on the nightside. If the IR opacity is not high enough to trigger a runaway greenhouse effect and sublimate the entire nightside ice layer, the existence of these gases in fact increases the atmospheric water vapor concentration and makes water vapor more detectable. Among these gases, CO 2 is most important because its absorption bands overlap with H 2 O at 1.8 µm and 2.7 µm. If only the 1.4 µm absorption band is used for the water vapor detection calculation in Figure 2, then at least 80 transits would be required.
Mineral dust is another complicating factor. Dust could be lifted by convective plumes around the substellar area on arid planets (Boutle et al. 2020). Dust particles transported by the large-scale circulation to the night hemisphere can increase the thermal infrared opacity and warm the nightside surface. Near the terminator, dust particles suspended in the atmosphere can obscure the water vapor features in transmission spectra, in a similar way to ice clouds on aqua-planets. Understanding the impacts of mineral dust on the climates of temperate rocky exoplanets with nightside ice deposits will require climate modeling that incorporates dust cycles. Stellar models suggest the spectra of M-dwarfs are likely to be enriched in water absorption lines, especially for late M-dwarfs (Deming & Sheppard 2017;Reiners et al. 2018). Deming & Sheppard (2017) showed including the overlap of stellar M-dwarf and planetary water lines at high spectral resolution can reduce the modeled transmission transit depth by ∼ 10%, referred to as spectral resolution-linked bias (RLB) in their study of TRAPPIST-1b. This RLB effect is not taken into account in the PSG simulation, which uses pre-computed correlated-k tables to calculate radiative transfer for resolving powers less than 5000 (Villanueva et al. 2018). The importance of water line overlaps between the spectra of temperate arid exoplanets and mid M-dwarfs should be evaluated by future line-by-line analyses.
Finally, the noise floor induced by the telescope in its environment is a key factor when detecting molecular absorption features in transmission spectra, especially with low spectral depths (Greene et al. 2016;Suissa et al. 2020). All calculations in this paper impose no absolute noise floor on observations. In our simulations, the absorption feature at 2.7 µm is most observable (Figure 2b) and stronger than those in simulations for habitable aqua-planets around the same type of stars. But a noise floor as low as 3 ppm is still required otherwise the photon noise will reach the noise floor and any signal from the star is drown out. If the noise floor in the near-infrared is in the range of 10-20 ppm, as estimated by Greene et al. (2016), none of the simulation results for temperate planets around M5V-type stars in Figure 3 can be detectable and only temperate planets with nightside ice deposits around late M-dwarfs might be detectable with JWST. As a result, synergies between future spacebased spectroscopy and ground-based spectroscopy (such as the Extremely Large Telescope (ELT) using cross-correlation techniques), building on past successes for hot Jupiters (e.g., Brogi et al. 2017;Brogi & Line 2019), may be essential in order to overcome these difficulties associated with absorption band overlap with CO 2 and the noise floor.
We thank the referee for thoughtful comments that improved the manuscript. R.W. acknowledges funding support from NASA/VPL grant UWSC10439. The GCM simulations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University.