This paper is an extension of the work done by Pierens & Nelson (2008) in which they have investigated the behaviour of a two-planet system embedded in a protoplanetary disc. They have put a Jupiter mass gas giant on the internal orbit and a lower mass planet on the external one. We consider here a similar problem taking into account a gas giant with masses in the range of 0.5 to 1 Jupiter mass and a Super-Earth as the outermost planet. By changing disc parameters and planet masses we have succeeded in getting the convergent migration which allows for the possibility of their resonant locking. However, in the case in which the gas giant has the mass of Jupiter, before any mean motion first order commensurability could be achieved, the Super-Earth is caught in a trap when it is very close to the edge of the gap opened by the giant planet. This confirms the result obtained by Pierens & Nelson (2008) in their simulations. Additionally, we have found that, in a very thin disc, an apsidal resonance is observed in the system if the Super-Earth is captured in the trap. Moreover, the eccentricity of the small planet remains low, while that of the gas giant increases slightly due to the imbalance between Lindblad and corotational resonances. We have also studied analogous systems in which the gas giant is allowed to take Sub-Jupiter masses. In this case, after performing an extensive survey over all possible parameters, we have succeeded in getting the 1:2 mean motion resonant configuration only in a disc with low aspect ratio and low surface density. However, the resonance is maintained just for few thousand orbits. Thus, we conclude that for typical protoplanetary discs the mean motion commensurabilities are rare if the Super-Earth is located on the external orbit relative to the gas giant. (abridged)
Past studies have demonstrated that atmospheric escape by the core-powered mass-loss mechanism can explain a multitude of observations associated with the radius valley that separates the super-Earth and sub-Neptune planet populations. Complementing such studies, in this work, we present a shortlist of planets that could be losing their atmospheres today if their evolution is indeed primarily dictated by core-powered mass-loss. We use Bayesian inference analysis on our planet evolution and mass-loss model to estimate the posteriors of the parameters that encapsulate the current state of a give…
We explore whether close-in super-Earths were formed as rocky bodies that failed to grow fast enough to become the cores of gas giants before the natal protostellar disk dispersed. We model the failed cores' inward orbital migration in the low-mass or type I regime, to stopping points at distances where the tidal interaction with the protostellar disk applies zero net torque. The three kinds of migration traps considered are those due to the dead zone's outer edge, the ice line, and the transition from accretion to starlight as the disk's main heat source. As the disk disperses, the traps move…
We present an XMM-Newton X-ray observation of TRAPPIST-1, which is an ultracool dwarf star recently discovered to host three transiting and temperate Earth-sized planets. We find the star is a relatively strong and variable coronal X-ray source with an X-ray luminosity similar to that of the quiet Sun, despite its much lower bolometric luminosity. We find L_x/L_bol=2-4x10^-4, with the total XUV emission in the range L_xuv/L_bol=6-9x10^-4, and XUV irradiation of the planets that is many times stronger than experienced by the present-day Earth. Using a simple energy-limited model we show that th…
Three Earth-sized exoplanets were recently discovered close to the habitable zone of the nearby ultracool dwarf star TRAPPIST-1. The nature of these planets has yet to be determined, since their masses remain unmeasured and no observational constraint is available for the planetary population surrounding ultracool dwarfs, of which the TRAPPIST-1 planets are the first transiting example. Theoretical predictions span the entire atmospheric range from depleted to extended hydrogen-dominated atmospheres. Here, we report a space-based measurement of the combined transmission spectrum of the two inn…
Ultracool dwarfs (UCD; $T_{\rm eff}<\sim3000~$K) cool to settle on the main sequence after $\sim$1 Gyr. For brown dwarfs, this cooling never stops. Their habitable zone (HZ) thus sweeps inward at least during the first Gyr of their lives. Assuming they possess water, planets found in the HZ of UCDs have experienced a runaway greenhouse phase too hot for liquid water prior to entering the HZ. It has been proposed that such planets are desiccated by this hot early phase and enter the HZ as dry worlds. Here we model the water loss during this pre-HZ hot phase taking into account recent upper limi…
Nine transiting Earth-sized planets have recently been discovered around nearby late M dwarfs, including the TRAPPIST-1 planets and two planets discovered by the MEarth survey, GJ 1132b and LHS 1140b. These planets are the smallest known planets that may have atmospheres amenable to detection with JWST. We present model thermal emission and transmission spectra for each planet, varying composition and surface pressure of the atmosphere. We base elemental compositions on those of Earth, Titan, and Venus and calculate the molecular compositions assuming chemical equilibrium, which can strongly d…
With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, the correct treatment of tidal interactions is becoming necessary. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeed the result of tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets, which can then be responsible for volcanism and/or surface deformation. In the majority of studies to estimate the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology…
Planet traps are necessary to prevent forming planets from falling onto their host star by type I migration. Surface mass density and temperature gradient irregularities favor the apparition of traps and deserts. Such features are found at the dust sublimation lines and heat transition barriers. We study how planets may remain trapped or escape as they grow and as the disk evolves. We model the temporal viscous evolution of a protoplanetary disk by coupling its dynamics, thermodynamics, geometry and composition. The resulting mid-plane density and temperature profiles allow the modeling of the…
The Rossiter-McLaughlin effect is the principal method of determining the sky-projected spin--orbit angle ($β$) of transiting planets. Taking the example of the recently discovered TRAPPIST-1 system, we explore how ultracool dwarfs facilitate the measurement of the spin--orbit angle for Earth-sized planets by creating an effect that can be an order of magnitude more ample than the Doppler reflex motion caused by the planet if the star is undergoing rapid rotation. In TRAPPIST-1's case we expect the semi-amplitudes of the Rossiter-McLaughlin effect to be $40-50$ m/s for the known transiting pla…
Super Earths are the largest population of exoplanets and are seen to exhibit a rich diversity of compositions as inferred through their mean densities. Here we present a model that combines equilibrium chemistry in evolving disks with core accretion that tracks materials accreted onto planets during their formation. In doing so, we aim to explain why super Earths form so frequently and how they acquire such a diverse range of compositions. A key feature of our model is disk inhomogeneities, or planet traps, that act as barriers to rapid type-I migration. The traps we include are the dead zone…
The atmospheres of rocky exoplanets are close to being characterized by astronomical observations, in part due to the commissioning of the James Webb Space Telescope. These observations compel us to understand exoplanetary atmospheres, in the voyage to find habitable planets. With this aim, we investigate the effect that CO$_2$ partial pressure (pCO$_2$) has on exoplanets' climate variability, by analyzing results from ExoCAM model simulations of the tidally locked TRAPPIST-1e exoplanet, an Earth-like aqua-planet and Earth itself. First, we relate the differences between the planets to their e…
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 …
The TRAPPIST-1 system provides an exquisite laboratory for understanding exoplanetary atmospheres and interiors. Their mutual gravitational interactions leads to transit timing variations, from which Grimm et al. (2018) recently measured the planetary masses with precisions ranging from 5% to 12%. Using these masses and the <5% radius measurements on each planet, we apply the method described in Suissa et al. (2018) to infer the minimum and maximum CRF (core radius fraction) of each planet. Further, we modify the maximum limit to account for the fact that a light volatile envelope is excluded …
Limits on forming coreless terrestrial worlds in the TRAPPIST-1 system
SKLab-DeepMinE, MOEKLab-OBCE, School of Earth and Space Sciences, Peking University（北京大学地球与空间科学学院）；Research Institute of Extraterrestrial Material at PKU (RIEMPKU)（北京大学地外物质研究所）；Institute for Particle Physics and Astrophysics, ETH Zürich（苏黎世联邦理工学院粒子物理与天体物理研究所）
The recent discovery of three Earth-sized, potentially habitable planets around a nearby cool star, TRAPPIST-1, has provided three key targets for the upcoming James Webb Space Telescope (JWST). Depending on their atmospheric characteristics and precise orbit configurations, it is possible that any of the three planets may be in the liquid water habitable zone, meaning that they may be capable of supporting life. We find that present-day Earth levels of ozone, if present, would be detectable if JWST observes 60 transits for innermost planet 1b and 30 transits for 1c and 1d.
Seven temperate Earth-sized exoplanets readily amenable for atmospheric studies transit the nearby ultracool dwarf star TRAPPIST-1 (refs 1,2). Their atmospheric regime is unknown and could range from extended primordial hydrogen-dominated to depleted atmospheres (refs 3-6). Hydrogen in particular is a powerful greenhouse gas that may prevent the habitability of inner planets while enabling the habitability of outer ones (refs 6-8). An atmosphere largely dominated by hydrogen, if cloud-free, should yield prominent spectroscopic signatures in the near-infrared detectable during transits. Observa…
The recent discovery of the planetary system hosted by the ultracool dwarf star TRAPPIST-1 could open new perspectives into the investigation of planetary climates of Earth-sized exoplanets, their atmospheres and their possible habitability. In this paper, we use a simple climate-vegetation energy-balance model to study the climate of the seven TRAPPIST-1 planets and the climate dependence on the global albedo, on the fraction of vegetation that could cover their surfaces and on the different greenhouse conditions. The model allows us to investigate whether liquid water could be maintained on …
TRAPPIST-1 is a nearby 0.08 M M-star, which was recently found to harbor a planetary system of at least seven Earth-mass planets, all within 0.1 au. The configuration confounds theorists as the planets are not easily explained by either in situ or migration models. In this Paper we present a scenario for the formation and orbital architecture of the TRAPPIST-1 system. In our model, planet formation starts at the H2O iceline, where pebble-size particles -- whose origin is the outer disk -- concentrate to trigger streaming instabilities. After their formation, planetary embryos quickly mature by…
It is often assumed that the "Kepler dichotomy" -- the apparent excess of planetary systems with a single detected transiting planet in the Kepler catalog -- reflects an intrinsic bimodality in the mutual inclinations of planetary orbits. After conducting 600 simulations of planet formation followed by simulated Kepler observations, we instead propose that the apparent dichotomy reflects a divergence in the amount of migration and the separation of planetary semimajor axes into distinct "clusters". We find that our simulated high-mass systems migrate rapidly, bringing more planets into orbital…
The ultracool dwarf star TRAPPIST-1 hosts seven Earth-size transiting planets, some of which could harbour liquid water on their surfaces. UV observations are essential to measure their high-energy irradiation, and to search for photodissociated water escaping from their putative atmospheres. Our new observations of TRAPPIST-1 Ly-$α$ line during the transit of TRAPPIST-1c show an evolution of the star emission over three months, preventing us from assessing the presence of an extended hydrogen exosphere. Based on the current knowledge of the stellar irradiation, we investigated the likely hist…
The Trappist-1 system contains seven roughly Earth-sized planets locked in a multi-resonant orbital configuration, which has enabled precise measurements of the planets' masses and constrained their compositions. Here we use the system's fragile orbital structure to place robust upper limits on the planets' bombardment histories. We use N-body simulations to show how perturbations from additional objects can break the multi-resonant configuration by either triggering dynamical instability or simply removing the planets from resonance. The planets cannot have interacted with more than ${\sim 5\…
One of the most significant goals of modern science is establishing whether life exists around other suns. The most direct path towards its achievement is the detection and atmospheric characterization of terrestrial exoplanets with potentially habitable surface conditions. The nearest ultracool dwarfs (UCDs), i.e. very-low-mass stars and brown dwarfs with effective temperatures lower than 2700 K, represent a unique opportunity to reach this goal within the next decade. The potential of the transit method for detecting potentially habitable Earth-sized planets around these objects is drastical…
The rapid growth in the number of known exoplanets has revealed the existence of several distinct planetary populations in the observed mass-period diagram. Two of the most surprising are, (1) the concentration of gas giants around 1AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenari…
The TRAPPIST-1 system, consisting of an ultra-cool host star having seven known Earth-size planets will be a prime target for atmospheric characterization with JWST. However, the detectability of atmospheric molecular species may be severely impacted by the presence of clouds and/or hazes. In this work, we perform 3-D General Circulation Model (GCM) simulations with the LMD Generic model supplemented by 1-D photochemistry simulations at the terminator with the Atmos model to simulate several possible atmospheres for TRAPPIST-1e, 1f and 1g: 1) modern Earth, 2) Archean Earth, and 3) CO2-rich atm…
The James Webb Space Telescope (JWST) will provide an opportunity to investigate the atmospheres of potentially habitable planets. Aerosols, significantly mute molecular features in transit spectra because they prevent light from probing the deeper layers of the atmosphere. Earth occasionally has stratospheric/high tropospheric clouds at 15-20 km that could substantially limit the observable depth of the underlying atmosphere. We use solar occultations of Earth's atmosphere to create synthetic JWST transit spectra of Earth analogs orbiting dwarf stars. Unlike previous investigations, we consid…
We investigate the spin behavior of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyze the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rota…
Context. Findings by the Helios and STEREO mission have indicated the presence of a resonant circumsolar ring of dust associated with Venus. Attempts to model this phenomenon as an analogue to the resonant ring of Earth - as a result of migrating dust trapped in external mean-motion resonances (MMRs) - have so far been unable to reproduce the observed dust feature. Other theories of origin have recently been put forward. However, the reason for the low trapping efficiency of Venus's external MMRs remains unclear. Aims. Here we look into the nature of the dust trapping resonant phenomena that a…
Discoveries of terrestrial, Earth-sized exoplanets that lie within the habitable zone (HZ) of their host stars continue to occur at increasing rates. Transit spectroscopy can potentially enable the detection of molecular signatures from such worlds, providing an indication of the presence of an atmosphere and its chemical composition, including gases potentially indicative of a biosphere. Such planets around nearby M-dwarf stars - such as TRAPPIST-1 - provide relatively good signal, high signal/noise, and frequent transits for follow-up spectroscopy. However, even with these advantages, transi…
We present the highest resolution study to date of super-Earths migrating in inviscid and low-viscosity discs, motivated by the connection to laminar, wind-driven models of protoplanetary discs. Our models unveil the critical role of vortices in determining the migration behaviour for partial gap-opening planets. Vortices form in pressure maxima at gap edges, and prevent the disc-feedback stopping of migration for intermediate planets in low-viscosity and inviscid discs, contrary to the concept of the `inertial limit' or `disc feedback' halting predicted from analytical models. Vortices may al…
We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST and K2 transit time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets' densities may be described with a single rocky mass-radius relation which is depleted in i…
Using orbital integration and analytical arguments, we have found a new mechanism (an "eccentricity trap") to halt type I migration of planets near the inner edge of a protoplanetary disk. Because asymmetric eccentricity damping due to disk-planet interaction on the innermost planet at the disk edge plays a crucial role in the trap, this mechanism requires continuous eccentricity excitation and hence works for a resonantly interacting convoy of planets. This trap is so strong that the edge torque exerted on the innermost planet can completely halt type I migrations of many outer planets throug…
One focus of modern astronomy is to detect temperate terrestrial exoplanets well-suited for atmospheric characterisation. A milestone was recently achieved with the detection of three Earth-sized planets transiting (i.e. passing in front of) a star just 8% the mass of the Sun 12 parsecs away. Indeed, the transiting configuration of these planets with the Jupiter-like size of their host star - named TRAPPIST-1 - makes possible in-depth studies of their atmospheric properties with current and future astronomical facilities. Here we report the results of an intensive photometric monitoring campai…
In recent years we have been witnessing the discovery of one extrasolar gas giant after another. Now the time has come to detect more low-mass planets like Super-Earths and Earth-like objects. An interesting question to ask is: where should we look for them? We have explored here the possibility of finding Super-Earths in the close vicinity of gas giants, as a result of the early evolution of planetary systems. For this purpose, we have considered a young planetary system containing a Super-Earth and a gas giant, both embedded in a protoplanetary disc. We have shown that, if the Super-Earth is…
Upcoming telescopes such as the James Webb Space Telescope (JWST), or the Extremely Large Telescope (ELTs), may soon be able to characterize, through transmission, emission or reflection spectroscopy, the atmospheres of rocky exoplanets orbiting nearby M dwarfs. One of the most promising candidates is the late M dwarf system TRAPPIST-1 which has seven known transiting planets for which Transit Timing Variation (TTV) measurements suggest that they are terrestrial in nature, with a possible enrichment in volatiles. Among these seven planets, TRAPPIST-1e seems to be the most promising candidate t…
Overcoming type I migration and preventing low-mass planets from spiralling into the central star is a long-studied topic. It is well known that outward migration is possible in viscous-heated discs relatively close to the central star because the entropy gradient can be sufficiently steep that the positive corotation torque overcomes the negative Lindblad torque. Yet efficiently trapping planets in this region remains elusive. Here we study disc conditions that yield outward migration for low-mass planets under specific planet migration prescriptions. Using a steady-state disc model with a co…
We investigate the evolution of a system of two super-Earths with masses < 4 Earth masses embedded in a turbulent protoplanetary disk. The aim is to examine whether or not resonant trapping can occur and be maintained in presence of turbulence and how this depends on the amplitude of the stochastic density fluctuations in the disk. We have performed 2D numerical simulations using a grid-based hydrodynamical code in which turbulence is modelled as stochastic forcing. We assume that the outermost planet is initially located just outside the position of the 3:2 mean motion resonance (MMR) with th…
It is widely believed that the carbonate-silicate cycle is the main agent to trigger deglaciations by CO$_2$ greenhouse warming on Earth and on Earth-like planets when they get in frozen state. Here we use a 3D Global Climate Model to simulate the ability of frozen planets to escape from glaciation by accumulating enough gaseous CO$_2$. We find that Earth-like planets orbiting a Sun-like star may never be able to escape from glaciation if their orbital distance is greater than $\sim$ 1.27 AU (Flux $<$ 847 W m$^{-2}$ or 62$\%$ of the Solar constant), because CO$_2$ would condense at the poles f…
The nearby (d = 12 pc) M8 dwarf star TRAPPIST-1 (2MASS J23062928-0502285) hosts a compact system of at least seven exoplanets with sizes similar to Earth. Given its importance for testing planet formation and evolution theories, and for assessing the prospects for habitability among Earth-size exoplanets orbiting the most common type of star in the Galaxy, we present a comprehensive assessment of the age of this system. We collate empirical age constraints based on the color-absolute magnitude diagram, average density, lithium absorption, surface gravity features, metallicity, kinematics, rota…
In this paper the migration of a 10 Earth-mass planetary core is investigated at the outer boundary of the dead zone of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the FARGO code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion s…
The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star. At least seven planets similar to Earth in radius and in mass were previously found to transit this host star. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances li…
The majority of potentially habitable exoplanets detected orbit stars cooler than the Sun, and therefore are irradiated by a stellar spectrum peaking at longer wavelengths than that incident on Earth. Here, we present results from a set of simulations of tidally-locked terrestrial planets orbiting three different host stars to isolate the effect of the stellar spectra on the simulated climate. Specifically, we perform simulations based on TRAPPIST-1e, adopting an Earth-like atmosphere and using the UK Met Office Unified Model in an idealised 'aqua-planet' configuration. Whilst holding the plan…
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 …
