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Short period exoplanets on circular orbits are thought to be tidally locked into synchronous rotation. If tidally locked, these planets must possess permanent day- and nightsides, with extreme irradiation on the dayside and none on the nightside. However, so far the tidal locking hypothesis for exoplanets is supported by little to no empirical evidence. Previous work showed that the super-Earth LHS 3844b likely has no atmosphere, which makes it ideal for constraining the planet's rotation. Here we revisit the Spitzer phase curve of LHS 3844b with a thermal model of an atmosphere-less planet and analyze the impact of non-synchronous rotation, eccentricity, tidal dissipation, and surface composition. Based on the lack of observed strong tidal heating we rule out rapid non-synchronous rotation (including a Mercury-like 3:2 spin-orbit resonance) and constrain the planet's eccentricity to less than 0.001 (more circular than Io's orbit). In addition, LHS 3844b's phase curve implies that the planet either still experiences weak tidal heating via a small-but-nonzero eccentricity (requiring an undetected orbital companion), or that its surface has been darkened by space weathering; of these two scenarios we consider space weathering more likely. Our results thus support the hypothesis that short period rocky exoplanets are tidally locked, and further show that space weathering can significantly modify the surfaces of atmosphere-less exoplanets., Comment: Accepted

The first JWST observations of TRAPPIST-1 c showed a secondary eclipse depth of 421+/-94 ppm at 15 um, which is consistent with a bare rock surface or a thin, O2-dominated, low CO2 atmosphere (Zieba et al. 2023). Here, we further explore potential atmospheres for TRAPPIST-1 c by comparing the observed secondary eclipse depth to synthetic spectra of a broader range of plausible environments. To self-consistently incorporate the impact of photochemistry and atmospheric composition on atmospheric thermal structure and predicted eclipse depth, we use a two-column climate model coupled to a photochemical model, and simulate O2-dominated, Venus-like, and steam atmospheres. We find that a broader suite of plausible atmospheric compositions are also consistent with the data. For lower pressure atmospheres (0.1 bar), our O2-CO2 atmospheres produce eclipse depths within 1$\sigma$ of the data, consistent with the modeling results of Zieba et al. (2023). However, for higher-pressure atmospheres, our models produce different temperature-pressure profiles and are less pessimistic, with 1-10 bar O2, 100 ppm CO2 models within 2.0-2.2$\sigma$ of the measured secondary eclipse depth, and up to 0.5% CO2 within 2.9$\sigma$. Venus-like atmospheres are still unlikely. For thin O2 atmospheres of 0.1 bar with a low abundance of CO2 ($\sim$100 ppm), up to 10% water vapor can be present and still provide an eclipse depth within 1$\sigma$ of the data. We compared the TRAPPIST-1 c data to modeled steam atmospheres of $\leq$ 3 bar, which are 1.7-1.8$\sigma$ from the data and not conclusively ruled out. More data will be required to discriminate between possible atmospheres, or to more definitively support the bare rock hypothesis., Comment: 15 pages, accepted to APJL

Seven rocky planets orbit the nearby dwarf star TRAPPIST-1, providing a unique opportunity to search for atmospheres on small planets outside the Solar System (Gillon et al., 2017). Thanks to the recent launch of JWST, possible atmospheric constituents such as carbon dioxide (CO2) are now detectable (Morley et al., 2017, Lincowski et al., 2018}. Recent JWST observations of the innermost planet TRAPPIST-1 b showed that it is most probably a bare rock without any CO2 in its atmosphere (Greene et al., 2023). Here we report the detection of thermal emission from the dayside of TRAPPIST-1 c with the Mid-Infrared Instrument (MIRI) on JWST at 15 micron. We measure a planet-to-star flux ratio of fp/fs = 421 +/- 94 parts per million (ppm) which corresponds to an inferred dayside brightness temperature of 380 +/- 31 K. This high dayside temperature disfavours a thick, CO2-rich atmosphere on the planet. The data rule out cloud-free O2/CO2 mixtures with surface pressures ranging from 10 bar (with 10 ppm CO2) to 0.1 bar (pure CO2). A Venus-analogue atmosphere with sulfuric acid clouds is also disfavoured at 2.6 sigma confidence. Thinner atmospheres or bare-rock surfaces are consistent with our measured planet-to-star flux ratio. The absence of a thick, CO2-rich atmosphere on TRAPPIST-1 c suggests a relatively volatile-poor formation history, with less than 9.5 +7.5 -2.3 Earth oceans of water. If all planets in the system formed in the same way, this would indicate a limited reservoir of volatiles for the potentially habitable planets in the system., Comment: Published in Nature on June 19th. 2023, 10 figures, 4 tables

About 2.5 billion years ago, microbes learned to harness plentiful Solar energy to reduce CO$_2$ with H$_2$O, extracting energy and producing O$_2$ as waste. O$_2$ production from this metabolic process was so vigorous that it saturated its photochemical sinks, permitting it to reach "runaway" conditions and rapidly accumulate in the atmosphere despite its reactivity. Here we argue that O$_2$ may not be unique: diverse gases produced by life may experience a "runaway" effect similar to O$_2$. This runaway occurs because the ability of an atmosphere to photochemically cleanse itself of trace gases is generally finite. If produced at rates exceeding this finite limit, even reactive gases can rapidly accumulate to high concentrations and become potentially detectable. Planets orbiting smaller, cooler stars, such as the M dwarfs that are the prime targets for the James Webb Space Telescope (JWST), are especially favorable for runaway due to their lower UV emission compared to higher-mass stars. As an illustrative case study, we show that on a habitable exoplanet with an H$_2$-N$_2$ atmosphere and net surface production of NH$_3$ orbiting an M dwarf (the "Cold Haber World" scenario, Seager et al. 2013ab), the reactive biogenic gas NH$_3$ can enter runaway, whereupon an increase in surface production flux of 1 order of magnitude can increase NH$_3$ concentrations by 3 orders of magnitude and render it detectable with JWST in just 2 transits. Our work on this and other gases suggests that diverse signs of life on exoplanets may be readily detectable at biochemically plausible production rates., Comment: In review at ApJ. Comments & feedback welcome. Code available by request via GitHub

The relationship between outgoing longwave radiation (OLR) and the surface temperature has a major influence on Earth's climate sensitivity. Studies often assume that this relationship is approximately linear, but it is unclear whether the approximation always holds. Here we show that, on seasonal timescales, clear-sky OLR is a multivalued function of local surface temperature. In many places, the OLR-temperature relationship is better approximated by a loop than a line and we quantify the resulting “OLR loopiness”, that is, how much clear-sky OLR varies between different seasons with the same surface temperature. Based on offline radiative calculations, in the tropics OLR loops are mainly caused by seasonal variations in relative humidity that are out of phase with surface temperature; in the extratropics, OLR loops are mainly due to variations in lapse rates. Our work provides a mechanism through which Earth's climate feedback can differ between seasonal and long-term time scales.

The spectroscopic characterization of terrestrial exoplanets will be made possible for the first time with JWST. One challenge to characterizing such planets is that it is not known a priori whether they possess optically thick atmospheres or even any atmospheres altogether. But this challenge also presents an opportunity - the potential to detect the surface of an extrasolar world. This study explores the feasibility of characterizing the atmosphere and surface of a terrestrial exoplanet with JWST, taking LHS 3844b as a test case because it is the highest signal-to-noise rocky thermal emission target among planets that are cool enough to have non-molten surfaces. We model the planetary emission, including the spectral signal of both atmosphere and surface, and we explore all scenarios that are consistent with the existing Spitzer 4.5 $\mu$m measurement of LHS 3844b from Kreidberg et al. (2019). In summary, we find a range of plausible surfaces and atmospheres that are within 3 $\sigma$ of the observation - less reflective metal-rich, iron oxidized and basaltic compositions are allowed, and atmospheres are restricted to a maximum thickness of 1 bar, if near-infrared absorbers at $\gtrsim$ 100 ppm are included. We further make predictions on the observability of surfaces and atmospheres, perform a Bayesian retrieval analysis on simulated JWST data and find that a small number, ~3, of eclipse observations should suffice to differentiate between surface and atmospheric features. However, the surface signal may make it harder to place precise constraints on the abundance of atmospheric species and may even falsely induce a weak H$_2$O detection., Comment: 33 pages, 20 figures

About 2.5 billion years ago, microbes learned to harness plentiful solar energy to reduce CO$_2$ with H$_2$O, extracting energy and producing O$_2$ as waste. O$_2$ production from this metabolic process was so vigorous that it saturated its photochemical sinks, permitting it to reach "runaway" conditions and rapidly accumulate in the atmosphere despite its reactivity. Here we argue that O$_2$ may not be unique: diverse gases produced by life may experience a "runaway" effect similar to O$_2$. This runaway occurs because the ability of an atmosphere to photochemically cleanse itself of trace gases is generally finite. If produced at rates exceeding this finite limit, even reactive gases can rapidly accumulate to high concentrations and become potentially detectable. Planets orbiting smaller, cooler stars, such as the M dwarfs that are the prime targets for the James Webb Space Telescope (JWST), are especially favorable for runaway due to their lower UV emission compared to higher-mass stars. As an illustrative case study, we show that on a habitable exoplanet with an H$_2$-N$_2$ atmosphere and net surface production of NH$_3$ orbiting an M dwarf (the "Cold Haber World" scenario), the reactive biogenic gas NH$_3$ can enter runaway, whereupon an increase in the surface production flux of one order of magnitude can increase NH$_3$ concentrations by three orders of magnitude and render it detectable by JWST in just two transits. Our work on this and other gases suggests that diverse signs of life on exoplanets may be readily detectable at biochemically plausible production rates., Comment: In press at ApJ (2022). Code available via GitHub; see Acknowledgements section for details and URLs. Comments & feedback welcome

All rights reserved. Satellite measurements and radiative calculations show that Earth's outgoing longwave radiation (OLR) is an essentially linear function of surface temperature over a wide range of temperatures (≳60 K). Linearity implies that radiative forcing has the same impact in warmer as in colder climates and is thus of fundamental importance for understanding past and future climate change. Although the evidence for a nearly linear relation was first pointed out more than 50 y ago, it is still unclear why this relation is valid and when it breaks down. Here we present a simple semianalytical model that explains Earth's linear OLR as an emergent property of an atmosphere whose greenhouse effect is dominated by a condensable gas. Linearity arises from a competition between the surface's increasing thermal emission and the narrowing of spectral window regions with warming and breaks down at high temperatures once continuum absorption cuts off spectral windows. Our model provides a way of understanding the longwave contribution to Earth's climate sensitivity and suggests that extrasolar planets with other condensable greenhouse gases could have climate dynamics similar to Earth's. ©2018 National Academy of Sciences., NSF (Grant no. AGS-1623218), James McDonnell Foundation Postdoctoral fellowship

Robustly modeling the inner edge of the habitable zone is essential for determining the most promising potentially habitable exoplanets for atmospheric characterization. Global climate models (GCMs) have become the standard tool for calculating this boundary, but divergent results have emerged among the various GCMs. In this study, we perform an inter-comparison of standard GCMs used in the field on a rapidly rotating planet receiving a G-star spectral energy distribution and on a tidally locked planet receiving an M-star spectral energy distribution. Experiments both with and without clouds are examined. We find relatively small difference (within 8 K) in global-mean surface temperature simulation among the models in the G-star case with clouds. In contrast, the global-mean surface temperature simulation in the M-star case is highly divergent (20-30 K). Moreover, even differences in the simulated surface temperature when clouds are turned off are significant. These differences are caused by differences in cloud simulation and/or radiative transfer, as well as complex interactions between atmospheric dynamics and these two processes. For example we find that an increase in atmospheric absorption of shortwave radiation can lead to higher relative humidity at high altitudes globally and, therefore, a significant decrease in planetary radiation emitted to space. This study emphasizes the importance of basing conclusions about planetary climate on simulations from a variety of GCMs and motivates the eventual comparison of GCM results with terrestrial exoplanet observations to improve their performance., Comment: 34 pages, 17 figures

Young terrestrial planets can capture or outgas hydrogen-rich atmospheres with tens to hundreds of bars of H2, which persist for 100 Myrs or longer. Although the earliest habitable conditions on Earth and terrestrial exoplanets could thus arise while the atmosphere is still dominated by H2, the climatic effects of H2 remain poorly understood. Previous work showed that H2 induces strong greenhouse warming at the outer edge of the habitable zone. Here we use a 1D radiative-convective model to show that H2 also leads to strong warming near the inner edge of the habitable zone. Unlike H2's greenhouse warming at the outer edge, however, its effect near the inner edge is driven by thermodynamics: H2's large thermal scale height allows the atmosphere to store more water vapor than either a pure-H2O atmosphere or an atmosphere with a heavy background gas, such as N2 or CO2, thereby amplifying the greenhouse effect of H2O. Using idealized grey calculations, we then present a general argument for how different background gases affect the inner edge of the habitable zone. H2 stands out for its ability to induce novel "Souffle" climates, which further support its warming effect. Our results show that if the earliest conditions on a planet near the inner edge of the habitable zone were H2-rich, they were likely also hot: 1 bar of H2 is sufficient to raise surface temperatures above 340 K, and 50 bar of H2 are sufficient to raise surface temperatures above 450 K., Comment: Accepted at Astrophysical Journal

Atmospheric heat redistribution shapes the remote appearance of rocky exoplanets but there is currently no easy way to predict a planet's heat redistribution from its physical properties. This paper proposes an analytical scaling theory for the heat redistribution on tidally-locked rocky exoplanets. The main parameters of the scaling are a planet's equilibrium temperature, surface pressure, and broadband longwave optical thickness. The scaling compares favorably against idealized general circulation model simulations of TRAPPIST-1b, GJ1132b, and LHS 3844b. For these planets heat redistribution generally becomes efficient, and a planet's observable thermal phase curve and secondary eclipse start to deviate significantly from that of a bare rock, once surface pressure exceeds O(1) bar. The scaling additionally points to planetary scenarios for which heat transport can be notably more or less efficient, such as H2 and CO atmospheres or hot lava ocean worlds. The results thus bridge the gap between theory and imminent observations with the James Webb Space Telescope. They can also be used to parameterize the effect of 3D atmospheric dynamics in 1D models, thereby improving the self-consistency of such models., Comment: Published in ApJ. Note minor changes in scaling since v1. Also see these three companion papers: Mansfield et al (2019) "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo"; Malik et al (2019) "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", Koll et al (2019) "Identifying Candidate Atmospheres on Rocky M dwarf Planets via Eclipse Photometry"

The upcoming launch of the James Webb Space Telescope (JWST) means that we will soon have the capability to characterize the atmospheres of rocky exoplanets. However, it is still unknown whether such planets orbiting close to M dwarf stars can retain their atmospheres, or whether high-energy irradiation from the star will strip the gaseous envelopes from these objects. We present a new method to detect an atmosphere on a synchronously rotating rocky exoplanet around a K/M dwarf, by using thermal emission during secondary eclipse to infer a high dayside albedo that could only be explained by bright clouds. Based on calculations for plausible surface conditions, we conclude that a high albedo could be unambiguously interpreted as a signal of an atmosphere for planets with substellar temperatures of $T_{sub}=$ 410-1250 K. This range corresponds to equilibrium temperatures of $T_{eq}=$ 300-880 K. We compare the inferred albedos of eight possible planet surface compositions to cloud albedo calculations. We determine that a layer of clouds with optical depths greater than $\tau=0.5$-$7$, would have high enough albedos to be distinguishable from a bare rock surface. This method of detecting an atmosphere on a rocky planet is complementary to existing methods for detecting atmospheres, because it provides a way to detect atmospheres with pressures below 1 bar (e.g. Mars), which are too tenuous to transport significant heat but thick enough to host high-albedo clouds., Comment: Accepted to ApJ. Also see these three companion papers: 1. Koll et al (accepted to ApJ), "Identifying Candidate Atmospheres on Rocky M Dwarf Planets Via Eclipse Photometry", 2. Malik et al (accepted to ApJ), "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", and 3. Koll (accepted to ApJ) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

Most rocky planets in the galaxy orbit a cool host star, and there is large uncertainty among theoretical models whether these planets can retain an atmosphere. The James Webb Space Telescope (JWST) might be able to settle this question empirically, but most proposals for doing so require large observational effort because they are based on spectroscopy. Here we show that infrared photometry of secondary eclipses could quickly identify "candidate" atmospheres, by searching for rocky planets with atmospheres thick enough that atmospheric heat transport noticeably reduces their dayside thermal emission compared to that of a bare rock. For a planet amenable to atmospheric follow-up, we find that JWST should be able to confidently detect the heat redistribution signal of an O(1) bar atmosphere with one to two eclipses. One to two eclipses is generally much less than the effort needed to infer an atmosphere via transmission or emission spectroscopy. Candidate atmospheres can be further validated via follow-up spectroscopy or phase curves. In addition, because this technique is fast it could enable a first atmospheric survey of rocky exoplanets with JWST. We estimate that the TESS mission will find ~100 planets that are too hot to be habitable but that can be quickly probed via eclipse photometry. Knowing whether hot, rocky planets around M dwarfs have atmospheres is important not only for understanding the evolution of uninhabitable worlds: if atmospheres are common on hot planets, then cooler, potentially habitable planets around M dwarfs are also likely to have atmospheres., Comment: Submitted to ApJ. Also see these three companion papers: 1. Mansfield et al (submitted), "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo", 2. Malik et al (submitted), "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", and 3. Koll (submitted) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

We study the red-optical photometry of the ultra-hot Jupiter WASP-121 b as observed by the Transiting Exoplanet Survey Satellite (TESS) and model its atmosphere through a radiative transfer simulation. Given its short orbital period of $\sim1.275$ days, inflated state and bright host star, WASP-121 b is exceptionally favorable for detailed atmospheric characterization. Towards this purpose, we use \texttt{allesfitter} to characterize its full red-optical phase curve, including the planetary phase modulation and the secondary eclipse. We measure the day and nightside brightness temperatures in the TESS passband as $3012\substack{+40 \\ -42}$ K and $2022\substack{+254 \\ -602}$ K, respectively, and do not find a statistically significant phase shift between the brightest and substellar points. This is consistent with an inefficient heat recirculation on the planet. We then perform an atmospheric retrieval analysis to infer the dayside atmospheric properties of WASP-121 b such as its bulk composition, albedo and heat recirculation. We confirm the temperature inversion in the atmosphere and suggest H$^-$, TiO and VO as potential causes of the inversion, absorbing heat at optical wavelengths at low pressures. Future HST and JWST observations of WASP-121 b will benefit from its first full phase curve measured by TESS., Comment: accepted for publication in The Astronomical Journal

The James Webb Space Telescope (JWST) will open up the possibility of comprehensively measuring the emission spectra of rocky exoplanets orbiting M dwarfs to detect and characterize their atmospheres. In preparation for this opportunity, we present model atmospheres for three M-dwarf planets particularly amenable to secondary eclipse spectroscopy -- TRAPPIST-1b, GJ 1132b, and LHS 3844b. Using three limiting cases of candidate atmospheric compositions (pure H2O, pure CO2 and solar abundances) we calculate temperature-pressure profiles and emission and reflection spectra in radiative-convective equilibrium, including the effects of a solid surface. We find that the atmospheric radiative transfer is significantly influenced by the cool M-star irradiation; H2O and CO2 absorption bands in the near-infrared are strong enough to absorb a sizeable fraction of the incoming stellar light at low pressures, which leads to temperature inversions in the upper atmosphere. The non-gray band structure of gaseous opacities in the infrared is hereby an important factor. Opacity windows are muted at higher atmospheric temperatures, so we expect temperature inversions to be common only for sufficiently cool planets. We also find that pure CO2 atmospheres exhibit lower overall temperatures and stronger reflection spectra compared to models of the other two compositions. We estimate that for GJ 1132b and LHS 3844b we should be able to distinguish between different atmospheric compositions with JWST. The emission lines from the predicted temperature inversions are currently hard to measure, but high resolution spectroscopy with future Extremely Large Telescopes may be able to detect them., Comment: published in ApJ. Also see these three companion papers: 1. Mansfield et al. 2019 (ApJ, 886, 2), "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo", 2. Koll et al. 2019 (ApJ, 886, 2), "Identifying candidate atmospheres on rocky M dwarf planets via eclipse photometry", 3. Koll (submitted) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

Most known terrestrial planets orbit small stars with radii less than 60% that of the Sun. Theoretical models predict that these planets are more vulnerable to atmospheric loss than their counterparts orbiting Sun-like stars. To determine whether a thick atmosphere has survived on a small planet, one approach is to search for signatures of atmospheric heat redistribution in its thermal phase curve. Previous phase curve observations of the super-Earth 55 Cancri e (1.9 Earth radii) showed that its peak brightness is offset from the substellar point $-$ possibly indicative of atmospheric circulation. Here we report a phase curve measurement for the smaller, cooler planet LHS 3844b, a 1.3 Earth radius world in an 11-hour orbit around a small, nearby star. The observed phase variation is symmetric and has a large amplitude, implying a dayside brightness temperature of $1040\pm40$ kelvin and a nightside temperature consistent with zero kelvin (at one standard deviation). Thick atmospheres with surface pressures above 10 bar are ruled out by the data (at three standard deviations), and less-massive atmospheres are unstable to erosion by stellar wind. The data are well fitted by a bare rock model with a low Bond albedo (lower than 0.2 at two standard deviations). These results support theoretical predictions that hot terrestrial planets orbiting small stars may not retain substantial atmospheres., Comment: Published in Nature on Aug 19, 2019. Co-authors Koll, Morley and Hu contributed equally to this manuscript

Recent studies have shown that ocean dynamics can have a significant warming effect on the permanent night sides of 1 to 1 tidally locked terrestrial exoplanets with Earth-like atmospheres and oceans in the middle of the habitable zone. However, the impact of ocean dynamics on the habitable zone's boundaries (inner edge and outer edge) is still unknown and represents a major gap in our understanding of this type of planets. Here we use a coupled atmosphere-ocean global climate model to show that planetary heat transport from the day to night side is dominated by the ocean at lower stellar fluxes and by the atmosphere near the inner edge of the habitable zone. This decrease in oceanic heat transport (OHT) at high stellar fluxes is mainly due to weakening of surface wind stress and a decrease in surface shortwave energy deposition. We further show that ocean dynamics have almost no effect on the observational thermal phase curves of planets near the inner edge of the habitable zone. For planets in the habitable zone's middle range, ocean dynamics moves the hottest spot on the surface eastward from the substellar point. These results suggest that future studies of the inner edge may devote computational resources to atmosphere-only processes such as clouds and radiation. For studies of the middle range and outer edge of the habitable zone, however, fully coupled ocean-atmosphere modeling will be necessary. Note that due to computational resource limitations, only one rotation period (60 Earth days) has been systematically examined in this study; future work varying rotation period as well as other parameters such as atmospheric mass and composition is required., Comment: 34 pages, 13 figures, and 1 table

Most rocky planets in the galaxy orbit a cool host star, and there is large uncertainty among theoretical models whether these planets can retain an atmosphere. The James Webb Space Telescope (JWST) might be able to settle this question empirically, but most proposals for doing so require large observational effort because they are based on spectroscopy. Here we show that infrared photometry of secondary eclipses could quickly identify "candidate" atmospheres, by searching for rocky planets with atmospheres thick enough that atmospheric heat transport noticeably reduces their dayside thermal emission compared to that of a bare rock. For a planet amenable to atmospheric follow-up, we find that JWST should be able to confidently detect the heat redistribution signal of an O(1) bar atmosphere with one to two eclipses. One to two eclipses is generally much less than the effort needed to infer an atmosphere via transmission or emission spectroscopy. Candidate atmospheres can be further validated via follow-up spectroscopy or phase curves. In addition, because this technique is fast it could enable a first atmospheric survey of rocky exoplanets with JWST. We estimate that the TESS mission will find ~100 planets that are too hot to be habitable but that can be quickly probed via eclipse photometry. Knowing whether hot, rocky planets around M dwarfs have atmospheres is important not only for understanding the evolution of uninhabitable worlds: if atmospheres are common on hot planets, then cooler, potentially habitable planets around M dwarfs are also likely to have atmospheres., Comment: Submitted to ApJ. Also see these three companion papers: 1. Mansfield et al (submitted), "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo", 2. Malik et al (submitted), "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", and 3. Koll (submitted) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

Recent studies have shown that ocean dynamics can have a significant warming effect on the permanent night sides of 1 to 1 tidally locked terrestrial exoplanets with Earth-like atmospheres and oceans in the middle of the habitable zone. However, the impact of ocean dynamics on the habitable zone's boundaries (inner edge and outer edge) is still unknown and represents a major gap in our understanding of this type of planets. Here we use a coupled atmosphere-ocean global climate model to show that planetary heat transport from the day to night side is dominated by the ocean at lower stellar fluxes and by the atmosphere near the inner edge of the habitable zone. This decrease in oceanic heat transport (OHT) at high stellar fluxes is mainly due to weakening of surface wind stress and a decrease in surface shortwave energy deposition. We further show that ocean dynamics have almost no effect on the observational thermal phase curves of planets near the inner edge of the habitable zone. For planets in the habitable zone's middle range, ocean dynamics moves the hottest spot on the surface eastward from the substellar point. These results suggest that future studies of the inner edge may devote computational resources to atmosphere-only processes such as clouds and radiation. For studies of the middle range and outer edge of the habitable zone, however, fully coupled ocean-atmosphere modeling will be necessary. Note that due to computational resource limitations, only one rotation period (60 Earth days) has been systematically examined in this study; future work varying rotation period as well as other parameters such as atmospheric mass and composition is required., Comment: 34 pages, 13 figures, and 1 table

Robustly modeling the inner edge of the habitable zone is essential for determining the most promising potentially habitable exoplanets for atmospheric characterization. Global climate models (GCMs) have become the standard tool for calculating this boundary, but divergent results have emerged among the various GCMs. In this study, we perform an inter-comparison of standard GCMs used in the field on a rapidly rotating planet receiving a G-star spectral energy distribution and on a tidally locked planet receiving an M-star spectral energy distribution. Experiments both with and without clouds are examined. We find relatively small difference (within 8 K) in global-mean surface temperature simulation among the models in the G-star case with clouds. In contrast, the global-mean surface temperature simulation in the M-star case is highly divergent (20-30 K). Moreover, even differences in the simulated surface temperature when clouds are turned off are significant. These differences are caused by differences in cloud simulation and/or radiative transfer, as well as complex interactions between atmospheric dynamics and these two processes. For example we find that an increase in atmospheric absorption of shortwave radiation can lead to higher relative humidity at high altitudes globally and, therefore, a significant decrease in planetary radiation emitted to space. This study emphasizes the importance of basing conclusions about planetary climate on simulations from a variety of GCMs and motivates the eventual comparison of GCM results with terrestrial exoplanet observations to improve their performance., Comment: 34 pages, 17 figures

We study the red-optical photometry of the ultra-hot Jupiter WASP-121 b as observed by the Transiting Exoplanet Survey Satellite (TESS) and model its atmosphere through a radiative transfer simulation. Given its short orbital period of $\sim1.275$ days, inflated state and bright host star, WASP-121 b is exceptionally favorable for detailed atmospheric characterization. Towards this purpose, we use \texttt{allesfitter} to characterize its full red-optical phase curve, including the planetary phase modulation and the secondary eclipse. We measure the day and nightside brightness temperatures in the TESS passband as $3012\substack{+40 \\ -42}$ K and $2022\substack{+254 \\ -602}$ K, respectively, and do not find a statistically significant phase shift between the brightest and substellar points. This is consistent with an inefficient heat recirculation on the planet. We then perform an atmospheric retrieval analysis to infer the dayside atmospheric properties of WASP-121 b such as its bulk composition, albedo and heat recirculation. We confirm the temperature inversion in the atmosphere and suggest H$^-$, TiO and VO as potential causes of the inversion, absorbing heat at optical wavelengths at low pressures. Future HST and JWST observations of WASP-121 b will benefit from its first full phase curve measured by TESS., Comment: accepted for publication in The Astronomical Journal

Most known terrestrial planets orbit small stars with radii less than 60% that of the Sun. Theoretical models predict that these planets are more vulnerable to atmospheric loss than their counterparts orbiting Sun-like stars. To determine whether a thick atmosphere has survived on a small planet, one approach is to search for signatures of atmospheric heat redistribution in its thermal phase curve. Previous phase curve observations of the super-Earth 55 Cancri e (1.9 Earth radii) showed that its peak brightness is offset from the substellar point $-$ possibly indicative of atmospheric circulation. Here we report a phase curve measurement for the smaller, cooler planet LHS 3844b, a 1.3 Earth radius world in an 11-hour orbit around a small, nearby star. The observed phase variation is symmetric and has a large amplitude, implying a dayside brightness temperature of $1040\pm40$ kelvin and a nightside temperature consistent with zero kelvin (at one standard deviation). Thick atmospheres with surface pressures above 10 bar are ruled out by the data (at three standard deviations), and less-massive atmospheres are unstable to erosion by stellar wind. The data are well fitted by a bare rock model with a low Bond albedo (lower than 0.2 at two standard deviations). These results support theoretical predictions that hot terrestrial planets orbiting small stars may not retain substantial atmospheres., Comment: Published in Nature on Aug 19, 2019. Co-authors Koll, Morley and Hu contributed equally to this manuscript

Atmospheric heat redistribution shapes the remote appearance of rocky exoplanets but there is currently no easy way to predict a planet's heat redistribution from its physical properties. This paper proposes an analytical scaling theory for the heat redistribution on tidally-locked rocky exoplanets. The main parameters of the scaling are a planet's equilibrium temperature, surface pressure, and broadband longwave optical thickness. The scaling compares favorably against idealized general circulation model simulations of TRAPPIST-1b, GJ1132b, and LHS 3844b. For these planets heat redistribution generally becomes efficient, and a planet's observable thermal phase curve and secondary eclipse start to deviate significantly from that of a bare rock, once surface pressure exceeds O(1) bar. The scaling additionally points to planetary scenarios for which heat transport can be notably more or less efficient, such as H2 and CO atmospheres or hot lava ocean worlds. The results thus bridge the gap between theory and imminent observations with the James Webb Space Telescope. They can also be used to parameterize the effect of 3D atmospheric dynamics in 1D models, thereby improving the self-consistency of such models., Comment: Published in ApJ. Note minor changes in scaling since v1. Also see these three companion papers: Mansfield et al (2019) "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo"; Malik et al (2019) "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", Koll et al (2019) "Identifying Candidate Atmospheres on Rocky M dwarf Planets via Eclipse Photometry"

Young terrestrial planets can capture or outgas hydrogen-rich atmospheres with tens to hundreds of bars of H2, which persist for 100 Myrs or longer. Although the earliest habitable conditions on Earth and terrestrial exoplanets could thus arise while the atmosphere is still dominated by H2, the climatic effects of H2 remain poorly understood. Previous work showed that H2 induces strong greenhouse warming at the outer edge of the habitable zone. Here we use a 1D radiative-convective model to show that H2 also leads to strong warming near the inner edge of the habitable zone. Unlike H2's greenhouse warming at the outer edge, however, its effect near the inner edge is driven by thermodynamics: H2's large thermal scale height allows the atmosphere to store more water vapor than either a pure-H2O atmosphere or an atmosphere with a heavy background gas, such as N2 or CO2, thereby amplifying the greenhouse effect of H2O. Using idealized grey calculations, we then present a general argument for how different background gases affect the inner edge of the habitable zone. H2 stands out for its ability to induce novel "Souffle" climates, which further support its warming effect. Our results show that if the earliest conditions on a planet near the inner edge of the habitable zone were H2-rich, they were likely also hot: 1 bar of H2 is sufficient to raise surface temperatures above 340 K, and 50 bar of H2 are sufficient to raise surface temperatures above 450 K., Comment: Accepted at Astrophysical Journal

The upcoming launch of the James Webb Space Telescope (JWST) means that we will soon have the capability to characterize the atmospheres of rocky exoplanets. However, it is still unknown whether such planets orbiting close to M dwarf stars can retain their atmospheres, or whether high-energy irradiation from the star will strip the gaseous envelopes from these objects. We present a new method to detect an atmosphere on a synchronously rotating rocky exoplanet around a K/M dwarf, by using thermal emission during secondary eclipse to infer a high dayside albedo that could only be explained by bright clouds. Based on calculations for plausible surface conditions, we conclude that a high albedo could be unambiguously interpreted as a signal of an atmosphere for planets with substellar temperatures of $T_{sub}=$ 410-1250 K. This range corresponds to equilibrium temperatures of $T_{eq}=$ 300-880 K. We compare the inferred albedos of eight possible planet surface compositions to cloud albedo calculations. We determine that a layer of clouds with optical depths greater than $\tau=0.5$-$7$, would have high enough albedos to be distinguishable from a bare rock surface. This method of detecting an atmosphere on a rocky planet is complementary to existing methods for detecting atmospheres, because it provides a way to detect atmospheres with pressures below 1 bar (e.g. Mars), which are too tenuous to transport significant heat but thick enough to host high-albedo clouds., Comment: Accepted to ApJ. Also see these three companion papers: 1. Koll et al (accepted to ApJ), "Identifying Candidate Atmospheres on Rocky M Dwarf Planets Via Eclipse Photometry", 2. Malik et al (accepted to ApJ), "Analyzing Atmospheric Temperature Profiles and Spectra of M dwarf Rocky Planets", and 3. Koll (accepted to ApJ) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

The James Webb Space Telescope (JWST) will open up the possibility of comprehensively measuring the emission spectra of rocky exoplanets orbiting M dwarfs to detect and characterize their atmospheres. In preparation for this opportunity, we present model atmospheres for three M-dwarf planets particularly amenable to secondary eclipse spectroscopy -- TRAPPIST-1b, GJ 1132b, and LHS 3844b. Using three limiting cases of candidate atmospheric compositions (pure H2O, pure CO2 and solar abundances) we calculate temperature-pressure profiles and emission and reflection spectra in radiative-convective equilibrium, including the effects of a solid surface. We find that the atmospheric radiative transfer is significantly influenced by the cool M-star irradiation; H2O and CO2 absorption bands in the near-infrared are strong enough to absorb a sizeable fraction of the incoming stellar light at low pressures, which leads to temperature inversions in the upper atmosphere. The non-gray band structure of gaseous opacities in the infrared is hereby an important factor. Opacity windows are muted at higher atmospheric temperatures, so we expect temperature inversions to be common only for sufficiently cool planets. We also find that pure CO2 atmospheres exhibit lower overall temperatures and stronger reflection spectra compared to models of the other two compositions. We estimate that for GJ 1132b and LHS 3844b we should be able to distinguish between different atmospheric compositions with JWST. The emission lines from the predicted temperature inversions are currently hard to measure, but high resolution spectroscopy with future Extremely Large Telescopes may be able to detect them., Comment: published in ApJ. Also see these three companion papers: 1. Mansfield et al. 2019 (ApJ, 886, 2), "Identifying Atmospheres on Rocky Exoplanets Through Inferred High Albedo", 2. Koll et al. 2019 (ApJ, 886, 2), "Identifying candidate atmospheres on rocky M dwarf planets via eclipse photometry", 3. Koll (submitted) "A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets"

A key legacy of the recently launched the Transiting Exoplanet Survey Satellite (TESS) mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. The James Webb Space Telescope (JWST), although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as the Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL) require the discovery and confirmation of several hundred additional sub-Jovian size planets (Rp<10 R⊕) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Groundbased extremely large telescopes (ELTs) will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-tonoise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al., we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of ∼300 high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds.

An accurate estimate of the inner edge of the habitable zone is critical for determining which exoplanets are potentially habitable and for designing future telescopes to observe them. Here, we explore differences in estimating the inner edge among seven one-dimensional (1D) radiative transfer models: two line-by-line codes (SMART and LBLRTM) as well as five band codes (CAM3, CAM4_Wolf, LMDG, SBDART, and AM2) that are currently being used in global climate models. We compare radiative fluxes and spectra in clear-sky conditions around G- and M-stars, with fixed moist adiabatic profiles for surface temperatures from 250 to 360 K. We find that divergences among the models arise mainly from large uncertainties in water vapor absorption in the window region (10 um) and in the region between 0.2 and 1.5 um. Differences in outgoing longwave radiation increase with surface temperature and reach 10-20 Wm^-2; differences in shortwave reach up to 60 Wm^-2, especially at the surface and in the troposphere, and are larger for an M-dwarf spectrum than a solar spectrum. Differences between the two line-by-line models are significant, although smaller than among the band models. Our results imply that the uncertainty in estimating the insolation threshold of the inner edge (the runaway greenhouse limit) due only to clear-sky radiative transfer is ~10% of modern Earth's solar constant (i.e., ~34 Wm^-2 in global mean) among band models and ~3% between the two line-by-line models. These comparisons show that future work is needed focusing on improving water vapor absorption coefficients in both shortwave and longwave, as well as on increasing the resolution of stellar spectra in broadband models., Comment: 25 pages, 1 table, and 10 figures

A key legacy of the recently launched TESS mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. JWST, although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as ARIEL require the discovery and confirmation of several hundred additional sub-Jovian size planets (R_p < 10 R_Earth) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Ground-based ELTs will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-to-noise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al. (2015), we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of $\sim300$ high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds., Comment: accepted to PASP

An accurate estimate of the inner edge of the habitable zone is critical for determining which exoplanets are potentially habitable and for designing future telescopes to observe them. Here, we explore differences in estimating the inner edge among seven one-dimensional (1D) radiative transfer models: two line-by-line codes (SMART and LBLRTM) as well as five band codes (CAM3, CAM4_Wolf, LMDG, SBDART, and AM2) that are currently being used in global climate models. We compare radiative fluxes and spectra in clear-sky conditions around G- and M-stars, with fixed moist adiabatic profiles for surface temperatures from 250 to 360 K. We find that divergences among the models arise mainly from large uncertainties in water vapor absorption in the window region (10 um) and in the region between 0.2 and 1.5 um. Differences in outgoing longwave radiation increase with surface temperature and reach 10-20 Wm^-2; differences in shortwave reach up to 60 Wm^-2, especially at the surface and in the troposphere, and are larger for an M-dwarf spectrum than a solar spectrum. Differences between the two line-by-line models are significant, although smaller than among the band models. Our results imply that the uncertainty in estimating the insolation threshold of the inner edge (the runaway greenhouse limit) due only to clear-sky radiative transfer is ~10% of modern Earth's solar constant (i.e., ~34 Wm^-2 in global mean) among band models and ~3% between the two line-by-line models. These comparisons show that future work is needed focusing on improving water vapor absorption coefficients in both shortwave and longwave, as well as on increasing the resolution of stellar spectra in broadband models., Comment: 25 pages, 1 table, and 10 figures

A key legacy of the recently launched TESS mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. JWST, although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as ARIEL require the discovery and confirmation of several hundred additional sub-Jovian size planets (R_p < 10 R_Earth) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Ground-based ELTs will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-to-noise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al. (2015), we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of $\sim300$ high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds., Comment: accepted to PASP

A key legacy of the recently launched the Transiting Exoplanet Survey Satellite (TESS) mission will be to provide the astronomical community with many of the best transiting exoplanet targets for atmospheric characterization. However, time is of the essence to take full advantage of this opportunity. The James Webb Space Telescope (JWST), although delayed, will still complete its nominal five year mission on a timeline that motivates rapid identification, confirmation, and mass measurement of the top atmospheric characterization targets from TESS. Beyond JWST, future dedicated missions for atmospheric studies such as the Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL) require the discovery and confirmation of several hundred additional sub-Jovian size planets (R p < 10 R ⊕) orbiting bright stars, beyond those known today, to ensure a successful statistical census of exoplanet atmospheres. Ground-based extremely large telescopes (ELTs) will also contribute to surveying the atmospheres of the transiting planets discovered by TESS. Here we present a set of two straightforward analytic metrics, quantifying the expected signal-to-noise in transmission and thermal emission spectroscopy for a given planet, that will allow the top atmospheric characterization targets to be readily identified among the TESS planet candidates. Targets that meet our proposed threshold values for these metrics would be encouraged for rapid follow-up and confirmation via radial velocity mass measurements. Based on the catalog of simulated TESS detections by Sullivan et al., we determine appropriate cutoff values of the metrics, such that the TESS mission will ultimately yield a sample of ~300 high-quality atmospheric characterization targets across a range of planet size bins, extending down to Earth-size, potentially habitable worlds.

Because of their intense incident stellar irradiation and likely tidally locked spin states, hot Jupiters are expected to have wind speeds that approach or exceed the speed of sound. In this work we develop a theory to explain the magnitude of these winds. We model hot Jupiters as planetary heat engines and show that hot Jupiters are always less efficient than an ideal Carnot engine. Next, we demonstrate that our predicted wind speeds match those from three-dimensional numerical simulations over a broad range of parameters. Finally, we use our theory to evaluate how well different drag mechanisms can match the wind speeds observed with Doppler spectroscopy for HD 189733b and HD 209458b. We find that magnetic drag is potentially too weak to match the observations for HD 189733b, but is compatible with the observations for HD 209458b. In contrast, shear instabilities and/or shocks are compatible with both observations. Furthermore, the two mechanisms predict different wind speed trends for hotter and colder planets than currently observed. As a result, we propose that a wider range of Doppler observations could reveal multiple drag mechanisms at play across different hot Jupiters., Comment: Accepted at ApJ, 10 pages, 7 figures

Because of their intense incident stellar irradiation and likely tidally locked spin states, hot Jupiters are expected to have wind speeds that approach or exceed the speed of sound. In this work we develop a theory to explain the magnitude of these winds. We model hot Jupiters as planetary heat engines and show that hot Jupiters are always less efficient than an ideal Carnot engine. Next, we demonstrate that our predicted wind speeds match those from three-dimensional numerical simulations over a broad range of parameters. Finally, we use our theory to evaluate how well different drag mechanisms can match the wind speeds observed with Doppler spectroscopy for HD 189733b and HD 209458b. We find that magnetic drag is potentially too weak to match the observations for HD 189733b, but is compatible with the observations for HD 209458b. In contrast, shear instabilities and/or shocks are compatible with both observations. Furthermore, the two mechanisms predict different wind speed trends for hotter and colder planets than currently observed. As a result, we propose that a wider range of Doppler observations could reveal multiple drag mechanisms at play across different hot Jupiters., Comment: Accepted at ApJ, 10 pages, 7 figures

Next-generation space telescopes will observe the atmospheres of rocky planets orbiting nearby M-dwarfs. Understanding these observations will require well-developed theory in addition to numerical simulations. Here we present theoretical models for the temperature structure and atmospheric circulation of dry, tidally locked rocky exoplanets with grey radiative transfer and test them using a general circulation model (GCM). First, we develop a radiative-convective model that captures surface temperatures of slowly rotating and cool atmospheres. Second, we show that the atmospheric circulation acts as a global heat engine, which places strong constraints on large-scale wind speeds. Third, we develop a radiative-convective-subsiding model which extends our radiative-convective model to hot and thin atmospheres. We find that rocky planets develop large day-night temperature gradients at a ratio of wave-to-radiative timescales up to two orders of magnitude smaller than the value suggested by work on hot Jupiters. The small ratio is due to the heat engine inefficiency and asymmetry between updrafts and subsidence in convecting atmospheres. Fourth, we show using GCM simulations that rotation only has a strong effect on temperature structure if the atmosphere is hot or thin. Our models let us map out atmospheric scenarios for planets such as GJ 1132b and show how thermal phase curves could constrain them. Measuring phase curves of short-period planets will require similar amounts of time on the James Webb Space Telescope as detecting molecules via transit spectroscopy, so future observations should pursue both techniques., Comment: Accepted in ApJ

Next-generation space telescopes will observe the atmospheres of rocky planets orbiting nearby M-dwarfs. Understanding these observations will require well-developed theory in addition to numerical simulations. Here we present theoretical models for the temperature structure and atmospheric circulation of dry, tidally locked rocky exoplanets with grey radiative transfer and test them using a general circulation model (GCM). First, we develop a radiative-convective model that captures surface temperatures of slowly rotating and cool atmospheres. Second, we show that the atmospheric circulation acts as a global heat engine, which places strong constraints on large-scale wind speeds. Third, we develop a radiative-convective-subsiding model which extends our radiative-convective model to hot and thin atmospheres. We find that rocky planets develop large day-night temperature gradients at a ratio of wave-to-radiative timescales up to two orders of magnitude smaller than the value suggested by work on hot Jupiters. The small ratio is due to the heat engine inefficiency and asymmetry between updrafts and subsidence in convecting atmospheres. Fourth, we show using GCM simulations that rotation only has a strong effect on temperature structure if the atmosphere is hot or thin. Our models let us map out atmospheric scenarios for planets such as GJ 1132b and show how thermal phase curves could constrain them. Measuring phase curves of short-period planets will require similar amounts of time on the James Webb Space Telescope as detecting molecules via transit spectroscopy, so future observations should pursue both techniques., Comment: Accepted in ApJ

Next-generation space telescopes will allow us to characterize terrestrial exoplanets. To do so effectively it will be crucial to make use of all available data. We investigate which atmospheric properties can, and cannot, be inferred from the broadband thermal phase curve of a dry and tidally locked terrestrial planet. First, we use dimensional analysis to show that phase curves are controlled by six nondimensional parameters. Second, we use an idealized general circulation model (GCM) to explore the relative sensitivity of phase curves to these parameters. We find that the feature of phase curves most sensitive to atmospheric parameters is the peak-to-trough amplitude. Moreover, except for hot and rapidly rotating planets, the phase amplitude is primarily sensitive to only two nondimensional parameters: 1) the ratio of dynamical to radiative timescales, and 2) the longwave optical depth at the surface. As an application of this technique, we show how phase curve measurements can be combined with transit or emission spectroscopy to yield a new constraint for the surface pressure and atmospheric mass of terrestrial planets. We estimate that a single broadband phase curve, measured over half an orbit with the James Webb Space Telescope, could meaningfully constrain the atmospheric mass of a nearby super-Earth. Such constraints will be important for studying the atmospheric evolution of terrestrial exoplanets as well as characterizing the surface conditions on potentially habitable planets., Comment: Accepted for publication in ApJ

Next-generation space telescopes will allow us to characterize terrestrial exoplanets. To do so effectively it will be crucial to make use of all available data. We investigate which atmospheric properties can, and cannot, be inferred from the broadband thermal phase curve of a dry and tidally locked terrestrial planet. First, we use dimensional analysis to show that phase curves are controlled by six nondimensional parameters. Second, we use an idealized general circulation model (GCM) to explore the relative sensitivity of phase curves to these parameters. We find that the feature of phase curves most sensitive to atmospheric parameters is the peak-to-trough amplitude. Moreover, except for hot and rapidly rotating planets, the phase amplitude is primarily sensitive to only two nondimensional parameters: 1) the ratio of dynamical to radiative timescales, and 2) the longwave optical depth at the surface. As an application of this technique, we show how phase curve measurements can be combined with transit or emission spectroscopy to yield a new constraint for the surface pressure and atmospheric mass of terrestrial planets. We estimate that a single broadband phase curve, measured over half an orbit with the James Webb Space Telescope, could meaningfully constrain the atmospheric mass of a nearby super-Earth. Such constraints will be important for studying the atmospheric evolution of terrestrial exoplanets as well as characterizing the surface conditions on potentially habitable planets., Comment: Accepted for publication in ApJ