This paper describes the Habitable Energy balance model for eXoplaneT ObseRvations (HEXTOR), which is a model for calculating latitudinal temperature profiles on Earth and other rapidly rotating planets. HEXTOR includes a lookup table method for calculating the outgoing infrared radiative flux and planetary albedo, which provides improvements over other approaches at parameterizing radiative transfer in an energy balance model. Validation cases are presented for present-day Earth and other Earth-sized planets with aquaplanet and land planet conditions from 0 to 45 degrees obliquity. A tidally locked coordinate system is also implemented in the energy balance model, which enables calculation of the horizontal temperature profile for planets in synchronous rotation around low mass stars. This coordinate transformed model is applied to cases for TRAPPIST-1e as defined by the TRAPPIST Habitable Atmosphere Intercomparison protocol, which demonstrates better agreement with general circulation models compared to the latitudinal energy balance model. Advances in applying energy balance models to exoplanets can be made by using general circulation models as a benchmark for tuning as well as by conducting intercomparisions between energy balance models with different physical parameterizations.
A key factor in determining the potential habitability of synchronously rotating planets is the strength of the atmospheric boundary layer inversion between the dark side surface and the free atmosphere. Here we analyse data obtained from polar night measurements at the South Pole and Alert Canada, which are the closest analogues on Earth to conditions on the dark sides of synchronously rotating exoplanets without and with a maritime influence, respectively. On Earth, such inversions rarely exceed 30 K in strength, because of the effect of turbulent mixing induced by phenomena such as so-calle…
H$_2$O 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 H$_2$O 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 H$_2$O 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 …
We investigate the atmospheric dynamics of terrestrial planets in synchronous rotation within the habitable zone of low-mass stars using the Community Atmosphere Model (CAM). The surface temperature contrast between day and night hemispheres decreases with an increase in incident stellar flux, which is opposite the trend seen on gas giants. We define three dynamical regimes in terms of the equatorial Rossby deformation radius and the Rhines length. The slow rotation regime has a mean zonal circulation that spans from day to night side, with both the Rossby deformation radius and the Rhines len…
Earth-like planets within the liquid water habitable zone of M type stars may evolve into synchronous rotators. On these planets, the sub-stellar hemisphere experiences perpetual daylight while the opposing anti-stellar hemisphere experiences perpetual darkness. Because the night-side hemisphere has no direct source of energy, the air over this side of the planet is prone to freeze out and deposit on the surface, which could result in atmospheric collapse. However, general circulation models (GCMs) have shown that atmospheric dynamics can counteract this problem and provide sufficient energy t…
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 d…
Terrestrial-type exoplanets orbiting nearby red dwarf stars (M dwarfs) are the first potentially habitable exoplanets suitable for atmospheric characterization in the near future. Understanding the stability of water in cold-trap regions on such planets is critical because it directly impacts transmission spectroscopy observations, the global energy budget, and long-term surface water evolution. Here we diagnose the humidity distribution in idealized general circulation model (GCM) simulations of terrestrial-type exoplanets. We use the `tracer of last saturation' technique to study the saturat…
Terrestrial planets in the habitable zones (HZs) of low-mass stars and cool dwarfs have received significant scrutiny recently because their shorter orbital periods increase their chances of detection and characterization compared to planets around G-dwarfs. As these planets are likely tidal-locked, improved 3D numerical simulations of such planetary atmospheres are needed to guide target selection. Here we use a 3-D climate system model, updated with new water-vapor absorption coefficients derived from the HITRAN 2012 database, to study ocean covered planets at the inner edge of the HZ around…
Robust atmospheric and radiative transfer modeling will be required to properly interpret reflected light and thermal emission spectra of terrestrial exoplanets. This will help break observational degeneracies between the numerous atmospheric, planetary, and stellar factors that drive planetary climate. Here we simulate the climates of Earth-like worlds around the Sun with increasingly slow rotation periods, from Earth-like to fully Sun-synchronous, using the ROCKE-3D general circulation model. We then provide these results as input to the Spectral Planet Model (SPM), which employs the SMART r…
The recent detections of temperate terrestrial planets orbiting nearby stars and the promise of characterizing their atmospheres motivates a need to understand how the diversity of possible planetary parameters affects the climate of terrestrial planets. In this work, we investigate the atmospheric circulation and climate of terrestrial exoplanets orbiting both Sun-like and M-dwarf stars over a wide swath of possible planetary parameters, including the planetary rotation period, surface pressure, incident stellar flux, surface gravity, planetary radius, and cloud particle size. We do so using …
The pathways through which incoming energy is distributed between the surface and atmosphere has been analyzed for the Earth. However, the effect of the spectral energy distribution of a host star on the energy budget of an orbiting planet may be significant given the wavelength-dependent absorption properties of atmospheric CO2 and water vapor, and surface ice and snow. We have quantified the flow of energy on aqua planets orbiting M-, G-, and F-dwarf stars, using a 3D Global Climate Model with a static ocean. The atmosphere and surface of an M-dwarf planet receiving an instellation equal to …
The ice-albedo feedback on rapidly-rotating terrestrial planets in the habitable zone can lead to abrupt transitions (bifurcations) between a warm and a snowball (ice-covered) state, bistability between these states, and hysteresis in planetary climate. This is important for planetary habitability because snowball events may trigger rises in the complexity of life, but could also endanger complex life that already exists. Recent work has shown that planets tidally locked in synchronous rotation states will transition smoothly into the snowball state rather than experiencing bifurcations. Here …
We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos that grow rapidly experience radiogenic ingrowth of mantle $^{182}$W that is inconsistent with the measured terrestrial composition, unless much of the tungsten is removed by an impactor core that m…
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 c…
We model the assembly of planets from planetary embryos under the conditions suggested by various scenarios for the formation of the planetary system around the millisecond pulsar B1257+12. We find that the most likely models fall at the low angular momentum end of the proposed range. Models that invoke supernova fallback produce such disks, although we find that a solar composition disk produces a more likely evolution than one composed primarily of heavy elements. Furthermore, we find that dust sedimentation must occur rapidly as the disk cools, in order that the solid material be confined t…
Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals…
Pressure is a key parameter in the physics and chemistry of planet formation and evolution. Previous studies have erroneously assumed that internal pressures monotonically increase with the mass of a body. Using smoothed particle hydrodynamics and potential field method calculations, we demonstrate that the hot, rapidly-rotating bodies produced by giant impacts can have much lower internal pressures than cool, slowly-rotating planets of the same mass. Pressures subsequently increase due to thermal and rotational evolution of the body. Using the Moon-forming impact as an example, we show that t…
The terrestrial planets are believed to have formed by violent collisions of tens of lunar- to Mars-size protoplanets at time t<200 Myr after the protoplanetary gas disk dispersal (t_0). The solar system giant planets rapidly formed during the protoplanetary disk stage and, after t_0, radially migrated by interacting with outer disk planetesimals. An early (t<100 Myr) dynamical instability is thought to have occurred with Jupiter having gravitational encounters with a planetary-size body, jumping inward by ~0.2-0.5 au, and landing on its current, mildly eccentric orbit. Here we investigate how…
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 a…
The discovery of a large number of terrestrial exoplanets in the habitable zones of their stars, many of which are qualitatively different from Earth, has led to a growing need for fast and flexible 3D climate models, which could model such planets and explore multiple possible climate states and surface conditions. We respond to that need by creating ExoPlaSim, a modified version of the Planet Simulator (PlaSim) that is designed to be applicable to synchronously rotating terrestrial planets, planets orbiting stars with non-solar spectra, and planets with non-Earth-like surface pressures. In t…
Recent high-precision measurements of the isotopic composition of lunar rocks demonstrate that the bulk silicate Earth and the Moon show an unexpectedly high degree of similarity. This is inconsistent with one of the primary results of classic dynamical simulations of the widely accepted giant impact model for the formation of the Moon, namely that most of the mass of the Moon originates from the impactor, not Earth. Resolution of this discrepancy without changing the main premises of the giant impact model requires total isotopic homogenisation of Earth and impactor material after the impact …
Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of …
We study the evolution of debris created in the giant impacts expected during the final stages of terrestrial planet formation. The starting point is the debris created in a simulation of the Moon-forming impact. The dynamical evolution is followed for 10 Myr including the effects of Earth, Venus, Mars and Jupiter. The spatial distribution evolves from a clump in the first few months to an asymmetric ring for the first 10 kyr and finally becoming an axisymmetric ring by about 1 Myr after the impact. By 10 Myr after the impact 20% of the particles have been accreted onto Earth and 17% onto Venu…
We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial pla…
Understanding when global glaciations occur on Earth-like planets is a major challenge in climate evolution research. Most models of how greenhouse gases like CO2 evolve with time on terrestrial planets are deterministic, but the complex, nonlinear nature of Earth's climate history motivates study of non-deterministic climate models. Here a maximally simple stochastic model of CO2 evolution and climate on an Earth-like planet with an imperfect CO2 thermostat is investigated. It is shown that as stellar luminosity is increased in this model, the decrease in the average atmospheric CO concentrat…
We investigate the abiotic production of oxygen and its photochemical byproduct ozone through water vapor photolysis in moist atmospheres of temperate terrestrial exoplanets. The amount of water vapor available for photolysis in the middle atmosphere of a planet can be limited by an atmospheric cold-trap, the formation of which largely depends on the amount of non-condensable gases. We study this effect using a photochemical model coupled to a 1D radiative-convective equilibrium model in atmospheres with N2, CO2 and H2O as the main constituents. We find that in atmospheres with a low N2 invent…
We present simulations of atmospheres of Earth-like aquaplanets that are tidally locked to their star, that is, planets whose orbital period is equal to the rotation period about their spin axis, so that one side always faces the star and the other side is always dark. As extreme cases illustrating the effects of slow and rapid rotation, we consider planets with rotation periods equal to one current Earth year and one current Earth day. The dynamics responsible for the surface climate (e.g., winds, temperature, precipitation) and the general circulation of the atmosphere are discussed in light…
Spatial heterogeneity and temporal variability are general features in planetary weather and climate, due to the effects of planetary rotation, uneven stellar flux distribution, fluid motion instability, etc. In this study, we investigate the asymmetry and variability in the transmission spectra of 1:1 spin--orbit tidally locked (or called synchronously rotating) planets around low-mass stars. We find that for rapidly rotating planets, the transit atmospheric thickness on the evening terminator (east of the substellar region) is significantly larger than that of the morning terminator (west of…
Efforts to characterize extrasolar giant planet (EGP) atmospheres have so far emphasized planets within 0.05 AU of their stars. Despite this focus, known EGPs populate a continuum of orbital separations from canonical hot Jupiter values (0.03-0.05 AU) out to 1 AU and beyond. Unlike typical hot Jupiters, these more distant EGPs will not in general be synchronously rotating. In anticipation of observations of this population, we here present three-dimensional atmospheric circulation models exploring the dynamics that emerge over a broad range of rotation rates and incident stellar fluxes appropr…
We present a new method to probe atmospheric pressure on Earthlike planets using (O2-O2) dimers in the near-infrared. We also show that dimer features could be the most readily detectable biosignatures for Earthlike atmospheres, and may even be detectable in transit transmission with the James Webb Space Telescope (JWST). The absorption by dimers changes more rapidly with pressure and density than that of monomers, and can therefore provide additional information about atmospheric pressures. By comparing the absorption strengths of rotational and vibrational features to the absorption strength…
We present the discovery of TOI 540 b, a hot planet slightly smaller than Earth orbiting the low-mass star 2MASS J05051443-4756154. The planet has an orbital period of $P = 1.239149$ days ($\pm$ 170 ms) and a radius of $r = 0.903 \pm 0.052 R_{\rm Earth}$, and is likely terrestrial based on the observed mass-radius distribution of small exoplanets at similar insolations. The star is 14.008 pc away and we estimate its mass and radius to be $M = 0.159 \pm 0.014 M_{\rm Sun}$ and $R = 0.1895 \pm 0.0079 R_{\rm Sun}$, respectively. The star is distinctive in its very short rotational period of $P_{\r…
The detection and characterization of Earth-like planet is approaching rapidly thanks to radial velocity surveys (HARPS), transit searches (Corot, Kepler) and space observatories dedicated to their characterization are already in development phase (James Webb Space Telescope), large ground based telescopes (ELT, TNT, GMT), and dedicated space-based missions like Darwin, Terrestrial Planet Finder, New World Observer). In this paper we discuss how we can read a planets spectrum to assess its habitability and search for the signatures of a biosphere. Identifying signs of life implies understandin…
There is a long-standing debate regarding the origin of the terrestrial planets' water as well as the hydrated C-type asteroids. Here we show that the inner Solar System's water is a simple byproduct of the giant planets' formation. Giant planet cores accrete gas slowly until the conditions are met for a rapid phase of runaway growth. As a gas giant's mass rapidly increases, the orbits of nearby planetesimals are destabilized and gravitationally scattered in all directions. Under the action of aerodynamic gas drag, a fraction of scattered planetesimals are deposited onto stable orbits interior…
The increasing richness of exoplanet observations has motivated a variety of three-dimensional atmospheric circulation models of these planets. Under strongly irradiated conditions, models of tidally locked, short-period planets (both hot Jupiters and terrestrial planets) tend to exhibit a circulation dominated by a fast eastward, or "superrotating," jet stream at the equator. Under appropriate conditions, this phenomenon can cause the hottest regions to be displaced eastward from the substellar point by tens of degrees longitude. Such an offset has been observed on HD 189733b, supporting the …
Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics (ROCKE-3D) is a 3-Dimensional General Circulation Model (GCM) developed at the NASA Goddard Institute for Space Studies for the modeling of atmospheres of Solar System and exoplanetary terrestrial planets. Its parent model, known as ModelE2 (Schmidt et al. 2014), is used to simulate modern and 21st Century Earth and near-term paleo-Earth climates. ROCKE-3D is an ongoing effort to expand the capabilities of ModelE2 to handle a broader range of atmospheric conditions including higher and lower atmospheric…
We have numerically studied the thermal evolution of various-mass terrestrial planets in habitable zones, focusing on duration of dynamo activity to generate their intrinsic magnetic fields, which may be one of key factors in habitability on the planets. In particular, we are concerned with super-Earths, observations of which are rapidly developing. We calculated evolution of temperature distributions in planetary interior, using Vinet equations of state, Arrhenius-type formula for mantle viscosity, and the astrophysical mixing length theory for convective heat transfer modified for mantle con…
King’s College London（伦敦国王学院）；University of Central Florida（中佛罗里达大学）；University of Pittsburgh（匹兹堡大学）；Luxembourg Institute of Science and Technology（卢森堡科学技术研究院）；University of Oxford（牛津大学）；University of Bern（伯尔尼大学）；Google Cloud（谷歌云）；NASA Astrobiology Institute（美国国家航空航天局天体生物学研究所）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）
Over the past decade, the study of extrasolar planets has evolved rapidly from plain detection and identification to comprehensive categorization and characterization of exoplanet systems and their atmospheres. Atmospheric retrieval, the inverse modeling technique used to determine an exoplanetary atmosphere's temperature structure and composition from an observed spectrum, is both time-consuming and compute-intensive, requiring complex algorithms that compare thousands to millions of atmospheric models to the observational data to find the most probable values and associated uncertainties for…
A possible surface type that may form in the environments of M-dwarf planets is sodium chloride dihydrate, or "hydrohalite" (NaCl $\cdot$ 2H$_2$O), which can precipitate in bare sea ice at low temperatures. Unlike salt-free water ice, hydrohalite is highly reflective in the near-infrared, where M-dwarf stars emit strongly, making the effect of the interaction between hydrohalite and the M-dwarf SED necessary to quantify. We carried out the first exploration of the climatic effect of hydrohalite-induced salt-albedo feedback on extrasolar planets, using a three-dimensional global climate model. …
We use the Massachusetts Institute of Technology general circulation model (GCM) dynamical core, in conjunction with a Newtonian relaxation scheme that relaxes to a gray, analytical solution of the radiative transfer equation, to simulate a tidally locked, synchronously orbiting super-Earth exoplanet. This hypothetical exoplanet is simulated under the following main assumptions: (1) the size, mass, and orbital characteristics of GJ 1214b (Charbonneau et al., 2009), (2) a greenhouse-gas dominated atmosphere, (3), the gas properties of water vapor, and (4) a surface. We have performed a paramete…
We study the masses and radii of 65 exoplanets smaller than 4 Earth radii with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 Earth radii and identify a density maximum of 7.6 g/cc at 1.4 Earth radii. Planets with radii up to R = 1.5 Earth radii increase in density with increasing radius. Above 1.5 Earth radii, planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Including the solar system terrestrial planets with the exoplanets below…
About 4000 exoplanets have been confirmed since the year of 1992, and for most of the planets, the main parameters that can be measured are planetary radius and mass. Based on these two parameters, surface gravity can be estimated. In this work, we investigate the effects of varying radius and gravity on the climate of rapidly rotating terrestrial planets with assuming they have an ocean and Earth-like atmospheres (N$_2$, CO$_2$, and H$_2$O). Using a three-dimensional (3D) atmospheric general circulation model (GCM), we find that varying radius mainly influences the equator-to-pole surface tem…
Over the past several decades, thousands of planets have been discovered outside of our Solar System. These planets exhibit enormous diversity, and their large numbers provide a statistical opportunity to place our Solar System within the broader context of planetary structure, atmospheres, architectures, formation, and evolution. Meanwhile, the field of exoplanetary science is rapidly forging onward towards a goal of atmospheric characterization, inferring surface conditions and interiors, and assessing the potential for habitability. However, the interpretation of exoplanet data requires the…
The up to 150 day uninterrupted high-precision photometry of about 100000 stars - provided so far by the exoplanet channel of the CoRoT space telescope - gave a new perspective on the planet population of our galactic neighbourhood. The seven planets with very accurate parameters widen the range of known planet properties in almost any respect. Giant planets have been detected at low metallicity, rapidly rotating and active, spotted stars. CoRoT-3 populated the brown dwarf desert and closed the gap of measured physical properties between standard giant planets and very low mass stars. CoRoT ex…
As the powerhouse of our solar system, the Sun's electromagnetic planetary influences appear contradictory. On the one hand, the Sun for aeons emitted radiation which was "just right" for life to evolve in our terrestrial Goldilocks zone, even for such complex organisms as ourselves. On the other, in the dawn of Earth's existence the Sun was far dimmer than today, and yet evidence for early liquid water is written into geology. Now in middle age, the Sun should be a benign object of little interest to society or even astronomers. However, for physical reasons yet to be fully understood, it con…
