Linking the Climate and Thermal Phase Curve of 55 Cancri e
Authors:
Hammond et al
Abstract:
The thermal phase curve of 55 Cancri e is the first measurement of the temperature distribution of a tidally locked super-Earth, but raises a number of puzzling questions about the planet's climate. The phase curve has a high amplitude and peak offset, suggesting that it has a significant eastward hot-spot shift as well as a large day–night temperature contrast. We use a general circulation model to model potential climates, and investigate the relation between bulk atmospheric composition and the magnitude of these seemingly contradictory features. We confirm theoretical models of tidally locked circulation are consistent with our numerical model of 55 Cnc e, and rule out certain atmospheric compositions based on their thermodynamic properties. Our best-fitting atmosphere has a significant hot-spot shift and day–night contrast, although these are not as large as the observed phase curve. We discuss possible physical processes that could explain the observations, and show that night-side cloud formation from species such as SiO from a day-side magma ocean could potentially increase the phase curve amplitude and explain the observations. We conclude that the observations could be explained by an optically thick atmosphere with a low mean molecular weight, a surface pressure of several bars, and a strong eastward circulation, with night-side cloud formation a possible explanation for the difference between our model and the observations.
NIR-driven Moist Upper Atmospheres of Synchronously Rotating Temperate Terrestrial Exoplanets
Authors:
Fuji et al
Abstract:
H2O is a key molecule in characterizing atmospheres of temperate terrestrial planets, and observations of transmission spectra are expected to play a primary role in detecting its signatures in the near future. The detectability of H2O absorption features in transmission spectra depends on the abundance of water vapor in the upper part of the atmosphere. We study the three-dimensional distribution of atmospheric H2O for synchronously rotating Earth-sized aquaplanets using the general circulation model (GCM) ROCKE-3D, and examine the effects of total incident flux and stellar spectral type. We observe a more gentle increase of the water vapor mixing ratio in response to increased incident flux than one-dimensional models suggest, in qualitative agreement with the climate-stabilizing effect of clouds around the substellar point previously observed in GCMs applied to synchronously rotating planets. However, the water vapor mixing ratio in the upper atmosphere starts to increase while the surface temperature is still moderate. This is explained by the circulation in the upper atmosphere being driven by the radiative heating due to absorption by water vapor and cloud particles, causing efficient vertical transport of water vapor. Consistently, the water vapor mixing ratio is found to be well-correlated with the near-infrared portion of the incident flux. We also simulate transmission spectra based on the GCM outputs, and show that for the more highly irradiated planets, the H2O signatures may be strengthened by a factor of a few, loosening the observational demands for a H2O detection.
The Thermal Phase Curve Offset on Tidally and Nontidally Locked Exoplanets: A Shallow Water Model
Authors:
Penn et al
Abstract:
Using a shallow water model with time-dependent forcing, we show that the peak of an exoplanet thermal phase curve is, in general, offset from the secondary eclipse when the planet is rotating. That is, the planetary hot spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset are functions of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady state in the reference frame of the moving forcing. The model is an extension of the well-studied Matsuno–Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet's surface) exceeds that of the gravity waves, then the hot spot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wave speed of the system, the hottest point may lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics, as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve.
Connecting the dots III: Night side cooling and surface friction affect climates of tidally locked terrestrial planets
Authors:
Carone et al
Abstract:
We investigate how night side cooling and surface friction impact surface temperatures and large scale circulation for tidally locked Earth-like planets. For each scenario, we vary the orbital period between Prot = 1 − 100 days and capture changes in climate states. We find drastic changes in climate states for different surface friction scenarios. For very efficient surface friction (ts, fric = 0.1 days), the simulations for short rotation periods (Prot ≤ 10 days) show predominantly standing extra tropical Rossby waves. These waves lead to climate states with two high latitude westerly jets and unperturbed meridional direct circulation. In most other scenarios, simulations with short rotation periods exhibit instead dominance by standing tropical Rossby waves. Such climate states have a single equatorial westerly jet, which disrupts direct circulation. Experiments with weak surface friction (ts, fric = ~10 − 100 days) show decoupling between surface temperatures and circulation, which leads to strong cooling of the night side. The experiment with ts, fric = ~100 days assumes climate states with easterly flow (retrograde rotation) for medium and slow planetary rotations Prot = 12 − 100 days. We show that an increase of night side cooling efficiency by one order of magnitude compared to the nominal model leads to a cooling of the night side surface temperatures by 80-100 K. The day side surface temperatures only drop by 25 K at the same time. The increase in thermal forcing suppresses the formation of extra tropical Rossby waves on small planets (RP = 1REarth) in the short rotation period regime (Prot ≤ 10 days).
Temperature Structure and Atmospheric Circulation of Dry, Tidally Locked Rocky Exoplanets
Authors:
Koll et al
Abstract:
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.
Astronomers from KU Leuven, Belgium, have shown that the interaction between the surface and the atmosphere of an exoplanet has major consequences for the temperature on the planet. This temperature, in turn, is a crucial element in the quest for habitable planets outside our Solar System.
In the quest for habitable planets outside our Solar System - also known as exoplanets - astronomers are currently focusing on rocky planets that don't look like Earth. These planets orbit so-called M dwarfs - stars that are smaller than our Sun. In our universe, there are many more M dwarfs than there are sun-like stars, making it more likely that astronomers will discover the first habitable exoplanet around an M dwarf. Most planets orbiting these M dwarfs always face their star with the same side. As a result, they have permanent day and night sides. The day side is too hot to make life possible, while the night side is too cold.
Last year, KU Leuven researchers Ludmila Carone, Professor Rony Keppens, and Professor Leen Decin already showed that planets with permanent day sides may still be habitable depending on their 'air conditioning' system. Two out of three possible 'air conditioning' systems on these exoplanets use the cold air of the night side to cool down the day side. And with the right atmosphere and temperature, planets with permanent day and night sides are potentially habitable.
Whether the 'air conditioning' system is actually effective depends on the interaction between the surface of the planet and its atmosphere, Ludmila Carone's new study shows.
Carone: "We built hundreds of computer models to examine this interaction. In an ideal situation, the cool air is transported from the night to the day side. On the latter side, the air is gradually heated by the star. This hot air rises to the upper layers of the atmosphere, where it is transported to the night side of the planet again."
But this is not always the case: on the equator of many of these rocky planets, a strong air current in the upper layers of the atmosphere interferes with the circulation of hot air to the night side. The 'air conditioning' system stops working, and the planet becomes uninhabitable because the temperatures are too extreme.
Nonlinear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability
Author:
Barker
Abstract:
I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the nonlinear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin-orbit alignment on a similar timescale as the spin synchronisation. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability, and in producing the observed burstiness. These results are broadly consistent with the picture obtained using a local Cartesian model (where columnar vortices played the role of zonal flows). I also simulate the instability in a container that is rigid (but stress-free) rather than free, finding broad quantitative agreement. The dissipation resulting from the elliptical instability could explain why the shortest-period hot Jupiters tend to have circular orbits inside about 2-3 days, and predicts spin-synchronisation (and spin-orbit alignment) out to about 10-15 days. However, other mechanisms must be invoked to explain tidal circularisation for longer orbital periods.
The inner edge of the habitable zone for synchronously rotating planets around low-mass stars using general circulation models
Authors:
Kopparapu et al
Abstract:
Terrestrial planets at the inner edge of the habitable zone of late-K and M-dwarf stars are expected to be in synchronous rotation, as a consequence of strong tidal interactions with their host stars. Previous global climate model (GCM) studies have shown that, for slowly-rotating planets, strong convection at the substellar point can create optically thick water clouds, increasing the planetary albedo, and thus stabilizing the climate against a thermal runaway. However these studies did not use self-consistent orbital/rotational periods for synchronously rotating planets placed at different distances from the host star. Here we provide new estimates of the inner edge of the habitable zone for synchronously rotating terrestrial planets around late-K and M-dwarf stars using a 3-D Earth-analog GCM with self-consistent relationships between stellar metallicity, stellar effective temperature, and the planetary orbital/rotational period. We find that both atmospheric dynamics and the efficacy of the substellar cloud deck are sensitive to the precise rotation rate of the planet. Around mid-to-late M-dwarf stars with low metallicity, planetary rotation rates at the inner edge of the HZ become faster, and the inner edge of the habitable zone is farther away from the host stars than in previous GCM studies. For an Earth-sized planet, the dynamical regime of the substellar clouds begins to transition as the rotation rate approaches ~10 days. These faster rotation rates produce stronger zonal winds that encircle the planet and smear the substellar clouds around it, lowering the planetary albedo, and causing the onset of the water-vapor greenhouse climatic instability to occur at up to ~25% lower incident stellar fluxes than found in previous GCM studies. For mid-to-late M-dwarf stars with high metallicity and for mid-K to early-M stars, we agree with previous studies.
Forced libration of tidally synchronized planets and moons
Authors:
Makarov et al
Abstraction:
Tidal dissipation of kinetic energy, when it is strong enough, tends to synchronize the rotation of planets and moons with the mean orbital motion, or drive it into long-term stable spin-orbit resonances. As the orbital motion undergoes periodic acceleration due to a finite orbital eccentricity, the spin rate oscillates around the equilibrium mean value too, giving rise to the forced, or eccentricity-driven, librations. Both the shape and amplitude of forced librations of synchronous viscoelastic planets and moons are defined by a combination of two different types of perturbative torque, the tidal torque and the triaxial torque. Consequently, forced librations can be tidally dominated (e.g., Io and possibly Titan) or deformation-dominated (e.g., the Moon) depending on a set of orbital, rheological, and other physical parameters. With small eccentricities, for the former kind, the largest term in the libration angle can be minus cosine of the mean anomaly, whereas for the latter kind, it is minus sine of the mean anomaly. The shape and the amplitude of tidal forced librations determine the rate of orbital evolution of synchronous planets and moons, i.e., the rate of dissipative damping of semimajor axis and eccentricity. The known super-Earth exoplanets can exhibit both kinds of libration, or a mixture thereof, depending on, for example, the effective Maxwell time of their rigid mantles. Our approach can be extended to estimate the amplitudes of other libration harmonics, as well as the forced libration in non-synchronous spin-orbit resonances.
Connecting the dots II: Phase changes in the climate dynamics of tidally locked terrestrial exoplanets
Authors:
Carone et al
Abstract:
We investigate 3D atmosphere dynamics for tidally locked terrestrial planets with an Earth-like atmosphere and irradiation for different rotation periods (Prot=1−100 days) and planet sizes (RP=1−2REarth) with unprecedented fine detail. We could precisely identify three climate state transition regions that are associated with phase transitions in standing tropical and extra tropical Rossby waves.
We confirm that the climate on fast rotating planets may assume multiple states (Prot≤12 days for RP=2REarth). Our study is, however, the first to identify the type of planetary wave associated with different climate states: The first state is dominated by standing tropical Rossby waves with fast equatorial superrotation. The second state is dominated by standing extra tropical Rossby waves with high latitude westerly jets with slower wind speeds. For very fast rotations (Prot≤5~days for RP=2REarth), we find another climate state transition, where the standing tropical and extra tropical Rossby wave can both fit on the planet. Thus, a third state with a mixture of the two planetary waves becomes possible that exhibits three jets.
Different climate states may be observable, because the upper atmosphere's hot spot is eastward shifted with respect to the substellar point in the first state, westward shifted in the second state and the third state shows a longitudinal 'smearing' of the spot across the substellar point.
We show, furthermore, that the largest fast rotating planet in our study exhibits atmosphere features known from hot Jupiters like fast equatorial superrotation and a temperature chevron in the upper atmosphere.
Tidal synchronization of close-in satellites and exoplanets. II. Spin dynamics and extension to Mercury and exoplanets host stars
Author:
Ferraz-Mello
Abstract:
This paper deals with the application of the creep tide theory (Ferraz-Mello, CeMDA 116, 109, 2013) to the rotation of close-in satellites, Mercury, close-in exoplanets and their host stars. The solutions show two extreme cases: close-in giant gaseous planets, with fast relaxation (low viscosity) and satellites and Earth-like planets, with slow relaxation (high viscosity). The rotation of close-in gaseous planets follows the classical Darwinian pattern: it is tidally driven towards a stationary solution which is synchronized, but, if the orbit is elliptical, with a frequency larger than the orbital mean-motion. The rotation of rocky bodies, however, may be driven to several attractors whose frequencies are 1/2,1,3/2,2,5/2 ... times the mean-motion. The number of attractors increases with the viscosity of the body and with the orbital eccentricity. The classical example is Mercury, whose rotational period is 2/3 of the orbital period (3/2 attractor). The planet behaves as a molten body with a relaxation that allowed it to cross the 2/1 attractor without being trapped, but not to escape being trapped in the 3/2 one. In that case, the relaxation is estimated to lie in the interval 4.6 -- 27 x 10^{-9} s^{-1} (equivalent to a quality factor roughly constrained to the interval 5 less than Q less than 50). The stars have relaxation similar to the hot Jupiters and their rotation is also driven to the only stationary solution existing in these cases. However, solar-type stars may lose angular momentum due to stellar wind, braking the rotation and displacing the attractor towards larger periods. Old active host stars with big close-in companions generally have rotational periods larger than the orbital periods of the companions. The paper also includes the study of the energy dissipation and the evolution of the orbital eccentricity.
Insolation patterns on eccentric exoplanets
Author:
Dobrovolskis
Abstract:
Several studies have found that synchronously-rotating Earth-like planets in the habitable zones of M-dwarf stars should exhibit an “eyeball” climate pattern, with a pupil of open ocean facing the parent star, and ice everywhere else. Recent work on eccentric exoplanets by Wang et al. (Wang, Y., Tian, F., Hu, Y. [2014b] Astrophys. J. 791, L12) has extended this conclusion to the 2:1 spin–orbit resonance as well, where the planet rotates twice during one orbital period. However, Wang et al. also found that the 3:2 and 5:2 half-odd resonances produce a zonally-striped climate pattern with polar icecaps instead. Unfortunately, they used incorrect insolation functions for the 3:2 and 5:2 resonances whose long-term time averages are essentially independent of longitude.
This paper presents the correct insolation patterns for eccentric exoplanets with negligible obliquities in the 0:1, 1:2, 1:1, 3:2, 2:1, 5:2, 3:1, 7:2, and 4:1 spin–orbit resonances. I confirm that the mean insolation is distributed in an eyeball pattern for integer resonances; but for half-odd resonances, the mean insolation takes a “double-eyeball” pattern, identical over the “eastern” and “western” hemispheres. Presuming that liquids, ices, clouds, albedo, and thermal emission are similarly distributed, this has significant implications for the observation and interpretation of potentially habitable exoplanets.
Finally, whether a striped ball, eyeball, or double-eyeball pattern emerges, the possibility exists that long-term build-up of ice (or liquid) away from the hot spots may alter the planet’s inertia tensor and quadrupole moments enough to re-orient the planet, ultimately changing the distribution of liquid and ice.
Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars
Authors:
Leconte et al
Abstract:
Planets in the habitable zone of lower-mass stars are often assumed to be in a state of tidally synchronized rotation, which would considerably affect their putative habitability. Although thermal tides cause Venus to rotate retrogradely, simple scaling arguments tend to attribute this peculiarity to the massive Venusian atmosphere. Using a global climate model, we show that even a relatively thin atmosphere can drive terrestrial planets’ rotation away from synchronicity. We derive a more realistic atmospheric tide model that predicts four asynchronous equilibrium spin states, two being stable, when the amplitude of the thermal tide exceeds a threshold that is met for habitable Earth-like planets with a 1 bar atmosphere around stars more massive than ~0.5 – 0.7 M☉. Thus, many recently discovered terrestrial planets could exhibit asynchronous spin-orbit rotation, even with a thin atmosphere.
Deciphering thermal phase curves of dry, tidally locked terrestrial planets
Authors:
Koll et al
Abstract:
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.
Atmospheric heat redistribution and collapse on tidally locked rocky planets
Author:
Wordsworth
Abstract:
Atmospheric collapse is likely to be of fundamental importance to tidally locked rocky exoplanets but remains understudied. Here, general results on the heat transport and stability of tidally locked terrestrial-type atmospheres are reported. First, the problem is modeled with an idealized 3D general circulation model (GCM) with gray gas radiative transfer. It is shown that over a wide range of parameters the atmospheric boundary layer, rather than the large-scale circulation, is the key to understanding the planetary energy balance. Through a scaling analysis of the interhemispheric energy transfer, theoretical expressions for the day-night temperature difference and surface wind speed are created that reproduce the GCM results without tuning. Next, the GCM is used with correlated-k radiative transfer to study heat transport for two real gases (CO2 and CO). For CO2, empirical formulae for the collapse pressure as a function of planetary mass and stellar flux are produced, and critical pressures for atmospheric collapse at Earth's stellar flux are obtained that are around five times higher (0.14 bar) than previous gray gas estimates. These results provide constraints on atmospheric stability that will aid in future interpretation of observations and exoplanet habitability modeling.
Water Trapping on Tidally Locked Terrestrial Planets Requires Special Conditions
Authors:
Yang et al
Abstract:
Surface liquid water is essential for standard planetary habitability. Calculations of atmospheric circulation on tidally locked planets around M stars suggest that this peculiar orbital configuration lends itself to the trapping of large amounts of water in kilometers-thick ice on the night side, potentially removing all liquid water from the day side where photosynthesis is possible. We study this problem using a global climate model including coupled atmosphere, ocean, land, and sea-ice components as well as a continental ice sheet model driven by the climate model output. For a waterworld we find that surface winds transport sea ice toward the day side and the ocean carries heat toward the night side. As a result, night-side sea ice remains O(10 m) thick and night-side water trapping is insignificant. If a planet has large continents on its night side, they can grow ice sheets O(1000 m) thick if the geothermal heat flux is similar to Earth's or smaller. Planets with a water complement similar to Earth's would therefore experience a large decrease in sea level when plate tectonics drives their continents onto the night side, but would not experience complete day-side dessication. Only planets with a geothermal heat flux lower than Earth's, much of their surface covered by continents, and a surface water reservoir O(10 %) of Earth's would be susceptible to complete water trapping.
Connecting the dots: A versatile terrestrial planet benchmark for the atmospheres of tidally locked Super-Earths
Authors:
Carone et al
Abstract:
We develop a benchmark for quantifying sustained global dynamics in the atmospheres of tidally locked terrestrial planets using the MITgcm core as the basis of a dry 3D-GCM with simplified thermal forcing. Our forcing employs a Newtonian relaxation scheme based on a simple greenhouse model. Our model is of the same conceptional simplicity than the model of Held& Suarez1994 and is thus versatile and computationally fast. As a case study relevant for Super-Earths, we investigate a Gl581g-like planet with Earth-like atmosphere and irradiation, and present all details on the obtained thermodynamics for representative rotation periods of Prot=10 days and Prot=36.5 days. This provides proof of concept and identifies interesting dynamical features for the rotating regime 3 less than Period of rotation less than 100 days, which was shown by Edson et al. 2011 to be an intermediate regime between equatorial superrotation and divergence.
We confirm that the Prot=10 days case is more dominated by equatorial superrotation dynamics than the Prot=36.5 days case, which shows diminishing influence of standing Rossby-Kelvin waves and increasing influence of divergence at the top of the atmosphere. We argue that this relates to the increase in Rossby deformation radius, in agreement with previous studies using more complex models. However, we also pay attention to other features that are not or only in partial agreement with other studies, like, e.g., the number of circulation cells and strength, the role and extent of thermal inversion layers, and the details of heat transport.
Life on a tidally-locked planet
Authors:
Singal et al
Abstract:
A tidally-locked planet in its orbit around a star keeps the same face towards the star. This happens when the rotation period of the planet around its own axis becomes equal to its revolution period around the star. Many questions then arise. What gives rise to a tidal locking? Are there any tidally-locked planets somewhere? What will be the atmospheric system of a tidally-locked planet? Could life be sustained on a tidally-locked planet? What will be a sort of DAY in the life of a denizen of a tidally-locked planet? We dwell on these questions.
A LOW-ORDER MODEL OF WATER VAPOR, CLOUDS, AND THERMAL EMISSION FOR TIDALLY LOCKED TERRESTRIAL PLANETS
Authors:
Yang et al
Abstract:
In the spirit of minimal modeling of complex systems, we develop an idealized two-column model to investigate the climate of tidally locked terrestrial planets with Earth-like atmospheres in the habitable zone of M-dwarf stars. The model is able to approximate the fundamental features of the climate obtained from three-dimensional (3D) atmospheric general circulation model (GCM) simulations. One important reason for the two-column model's success is that it reproduces the high cloud albedo of the GCM simulations, which reduces the planet's temperature and delays the onset of a runaway greenhouse state. The two-column model also clearly illustrates a secondary mechanism for determining the climate: the nightside acts as a "radiator fin" through which infrared energy can be lost to space easily. This radiator fin is maintained by a temperature inversion and dry air on the nightside, and plays a similar role to the subtropics on modern Earth. Since one-dimensional radiative-convective models cannot capture the effects of the cloud albedo and radiator fin, they are systematically biased toward a narrower habitable zone. We also show that cloud parameters are the most important in the two-column model for determining the day-night thermal emission contrast, which decreases and eventually reverses as the stellar flux increases. This reversal is important because it could be detected by future extrasolar planet characterization missions, which would suggest that the planet has Earth-like water clouds and is potentially habitable.
