Recent observational results show that very low mass stars and brown dwarfs are able to host close-in rocky planets. Low-mass stars are the most abundant stars in the Galaxy and the formation efficiency of their planetary systems is relevant in the computation of a global probability of finding Earth-like planets inside habitable zones. Tidal forces and relativistic effects are relevant in the latest dynamical evolution of planets around low-mass stars and their effect on the planetary formation efficiency still needs to be addressed. Our goal is to evaluate the impact of tidal forces and relativistic effects on the formation of rocky planets around a star close to the substellar mass limit, in terms of the resulting planetary architectures and its distribution according to the corresponding evolving habitable zone. Thus, we performed a set of $N$-body simulations spanning the first 100~Myr of the evolution of two systems composed respectively by 224 embryos with a total mass 0.25M$_\oplus$ and 74 embryos with a total mass 3 M$_\oplus$ around a central object of 0.08~M$_\odot$. For these two scenarios, we compared the planetary architectures that result from simulations that are purely gravitational with those from simulations that include the early contraction and spin-up of the central object, the distortions and dissipation tidal terms and general relativistic effects. We found that including these effects allows the formation and survival of a close-in population located in the habitable zone of the system. This means that both effects are relevant during the formation of rocky planets and their early evolution around stars close to the substellar mass limit, in particular when low-mass planetary embryos are involved.
Our main goal is to study the formation of rocky planets and the first $100~\textrm{Myr}$ of their dynamical evolution around a star with mass $0.08 M_\odot$ close to the substellar mass limit. We developed two sets of $N$-body simulations assuming an embryo population affected by tidal and general relativistic effects refined by the inclusion of the spin-up and contraction of the central star, and immerse in a gas disk during the first 10 Myr. Each set of simulations incorporates a different prescription from literature to calculate the interaction between the gas-disk and the embryos: one wi…
We provide estimates of atmospheric pressure and surface composition on short-period rocky exoplanets with dayside magma pools and silicate vapor atmospheres. Atmospheric pressure tends toward vapor-pressure equilibrium with surface magma, and magma-surface composition is set by the competing effects of fractional vaporization and surface-interior exchange. We use basic models to show how surface-interior exchange is controlled by the planet's temperature, mass, and initial composition. We assume that mantle rock undergoes bulk melting to form the magma pool, and that winds flow radially away …
The determination of an exoplanet as rocky is critical for the assessment of planetary habitability. Observationally, the number of small-radius, transiting planets with accompanying mass measurements is insufficient for a robust determination of the transitional mass or radius. Theoretically, models predict that rocky planets can grow large enough to become gas giants when they reach ~10 Earth-masses, but the transitional mass remains unknown. Here I show how transit data, interpreted in the context of tidal theory, can reveal the critical radius that separates rocky and gaseous exoplanets. S…
Using an idealised general circulation model, we investigate the atmospheric circulation of Earth-like terrestrial planets in a variety of orbital configurations. We relax the common assumption of the planet being tidally-locked, and look at the role atmospheric dynamics can have in the observed thermal phase curve when the substellar point is non-stationary. In slowly rotating planets, a moving forcing can induce strong jets in the upper troposphere, both prograde and retrograde, sensitive to the speed and direction of the diurnal forcing. We find that, consistent with previous shallow water …
Massachusetts Institute of Technology（麻省理工学院）；Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理学与空间研究研究所）；California Institute of Technology（加州理工学院）
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 tr…
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 …
Observed Hot Jupiters exhibit a wide range of physical properties. For a given mass, many planets have inflated radii, while others are surprisingly compact and may harbor large central cores. Motivated by the observational sample, this paper considers possible effects from collisions of smaller rocky planets with gas giant planets. In this scenario, the Jovian planets migrate first and enter into (approximately) 4 day orbits, whereas rocky planets (mass = 0.1-20 that of Earth) migrate later and then encounter the gaseous giants. Previous work indicates that the collision rates are high for su…
Spitzer IRAC observations of 15 metal-polluted white dwarfs reveal infrared excesses in the spectral energy distributions of HE 0110-5630, GD 61, and HE 1349-2305. All three of these stars have helium-dominated atmospheres, and their infrared emissions are consistent with warm dust produced by the tidal destruction of (minor) planetary bodies. This study brings the number of metal-polluted, helium and hydrogen atmosphere white dwarfs surveyed with IRAC to 53 and 38 respectively. It also nearly doubles the number of metal-polluted helium-rich white dwarfs found to have closely orbiting dust by …
Cloud is critical for planetary climate and habitability, but it is also one of the most challenging parts of studying planets in and beyond the solar system. Here we use a cloud-resolving model (CRM) with high resolution (2 km) in a two-dimensional (2D) configuration to simulate the clouds and circulation on tidally locked aqua-planets. We find that the substellar area is covered by deep convective clouds, the nightside is dominated by low-level clouds, and these two are linked by a global-scale Walker circulation. We further find that a uniform surface warming causes the substellar cloud wid…
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…
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 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 is a function 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 f…
Solid body tides provide key information on the interior structure, evolution, and origin of the planetary bodies. Our Solar system harbours a very diverse population of planetary bodies, including those composed of rock, ice, gas, or a mixture of all. While a rich arsenal of geophysical methods has been developed over several years to infer knowledge about the interior of the Earth, the inventory of tools to investigate the interiors of other Solar-system bodies remains limited. With seismic data only available for the Earth, the Moon, and Mars, geodetic measurements, including the observatio…
The potential habitability of tidally locked planets orbiting M-dwarf stars has been widely investigated in recent work, typically with a non-dynamic ocean and without continents. On Earth, ocean dynamics are a primary means of heat and nutrient distribution. Continents are a critical source of nutrients, strongly influence ocean dynamics, and participate in climate regulation. In this work, we investigate how the size of a substellar land mass affects the oceans ability to transport heat and upwell nutrients on the tidally locked planet Proxima Centauri b using the ROCKE-3D coupled ocean-atmo…
Spitzer observations reveal the presence of warm debris from a tidally destroyed rocky and possibly icy planetary body orbiting the white dwarf GD 61. Ultraviolet and optical spectroscopy of the metal-contaminated stellar photosphere reveal traces of hydrogen, oxygen, magnesium, silicon, iron, and calcium. The nominal ratios of these elements indicate an excess of oxygen relative to that expected from rock-forming metal oxides, and thus it is possible that water was accreted together with the terrestrial-like debris. Iron is found to be deficient relative to magnesium and silicon, suggesting t…
Over large timescales, a terrestrial planet may be driven towards spin-orbit synchronous rotation by tidal forces. In this particular configuration, the planet exhibits permanent dayside and nightside, which may induce strong day-night temperature gradients. The nightside temperature depends on the efficiency of the day-night heat redistribution and determines the stability of the atmosphere against collapse. To better constrain the atmospheric stability, climate, and surface conditions of rocky planets located in the habitable zone of their host star, it is thus crucial to understand the comp…
The habitable zone (HZ) is the circumstellar region where a planet can sustain surface liquid water. Searching for terrestrial planets in the HZ of nearby stars is the stated goal of ongoing and planned extrasolar planet surveys. Previous estimates of the inner edge of the HZ were based on one-dimensional radiative-convective models. The most serious limitation of these models is the inability to predict cloud behavior. Here we use global climate models with sophisticated cloud schemes to show that due to a stabilizing cloud feedback, tidally locked planets can be habitable at twice the stella…
CoRoT-7 b is the first confirmed rocky exoplanet, but, with an orbital semi-major axis of 0.0172 AU, its origins may be unlike any rocky planet in our solar system. In this study, we consider the roles of tidal evolution and evaporative mass loss in CoRoT-7 b's history, which together have modified the planet's mass and orbit. If CoRoT-7 b has always been a rocky body, evaporation may have driven off almost half its original mass, but the mass loss may depend sensitively on the extent of tidal decay of its orbit. As tides caused CoRoT-7 b's orbit to decay, they brought the planet closer to its…
Plate tectonics is a geophysical process currently unique to Earth, has an important role in regulating the Earth's climate, and may be better understood by identifying rocky planets outside our solar system with tectonic activity. The key criterion for whether or not plate tectonics may occur on a terrestrial planet is if the stress on a planet's lithosphere from mantle convection may overcome the lithosphere's yield stress. Although many rocky exoplanets closely orbiting their host stars have been detected, all studies to date of plate tectonics on exoplanets have neglected tidal stresses in…
To date not a single-bona fide planet has been identified orbiting a single white dwarf. In fact we are ignorant about the final configuration of >95% of planetary systems. Theoretical models predict a gap in the final distribution of orbital periods, due to the opposite effects of stellar mass loss (planets pushed outwards) and tidal interactions (planets pushed inwards) during the RGB and the AGB stellar expansions. Over its five year primary mission, Gaia is expected to astrometrically detect the first (few tens of) WD massive planets/BDs giving first evidence that WD planets exist, at leas…
The first discovered interstellar object (ISO), `Oumuamua (1I/2017 U1) shows a dry and rocky surface, an unusually elongated short-to-long axis ratio $c/a \lesssim 1/6$, a low velocity relative to the local standard of rest ($\sim 10$ km s$^{-1}$), non-gravitational accelerations, and tumbles on a few hours timescale. The inferred number density ($\sim 3.5 \times 10^{13} - 2 \times 10^{15}$ pc$^{-3}$) for a population of asteroidal ISOs outnumbers cometary ISOs by $\geq 10^3$, in contrast to the much lower ratio ($\lesssim 10^{-2}$) of rocky/icy Kuiper belt objects. Although some scenarios can…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant planets, as a function of core size and mass. We demonstrate that in general …
Feedbacks that can destabilize the climates of synchronously-rotating rocky planets may arise on planets with strong day-night surface temperature contrasts. Earth-like habitable-zone (HZ) planets maintain stable surface liquid water over geological time. This requires equilibrium between the temperature-dependent rate of greenhouse-gas consumption by weathering,and greenhouse-gas resupply by other processes. Detected small-radius exoplanets, and anticipated M-dwarf HZ rocky planets, are expected to be tidally locked. We investigate two feedbacks that can destabilize climate on tidally-locked …
The transiting planet candidate KOI 1843.03 ($0.6 R_\oplus$ radius, 4.245 hour orbital period, $0.46 M_\odot$ host star) has the shortest orbital period of any planet yet discovered. Here we show, using the first three-dimensional interior structure simulations of ultra-short-period tidally distorted rocky exoplanets, that KOI 1843.03 may be shaped like an American football, elongated along the planet-star axis with an aspect ratio of up to 1.79. Furthermore, for KOI 1843.03 to have avoided tidal disruption (wherein the planet is pulled apart by the tidal gravity of its host star) on such a cl…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints are now obtained both in the Solar and exoplanetary systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this work, we compute separately the contributions of the potential dense rocky/icy core and of the convective fluid envelope of gaseous giant …
Rocky planets orbiting M-dwarf stars in the habitable zone tend to be driven to synchronous rotation by tidal dissipation, potentially causing difficulties for maintaining a habitable climate on the planet. However, the planet may be captured into asynchronous spin-orbit resonances, and this capture may be more likely if the planet has a sufficiently large intrinsic triaxial deformation. We derive the analytic expression for the maximum triaxiality of a rocky planet, with and without a liquid envelope, as a function of the planet's radius, density, rigidity and critical strain of fracture. The…
It has been established theoretically that atmospheric thermal tides on rocky planets can lead to significant modifications of rotational evolution, both close to synchronous rotation and at faster rotations if certain resonant conditions are met. Here it is demonstrated that the normally considered dissipative gravitational tidal evolution of rocky planet rotation could, in principle, be 'stalled' by thermal tide resonances for Earth-analog worlds in the liquid water orbital zone of stars more massive than ~0.3 Msolar. The possibility of feedback effects between a planetary biosphere and the …
We develop a description of tidal effects in astrophysical systems using effective field theory techniques. While our approach is equally capable of describing objects in the Newtonian regime (e.g. moons, rocky planets, main sequence stars, etc.) as well as relativistic objects (e.g. neutron stars and black holes), in this paper we focus special attention on the Newtonian regime. In this limit, we recover the dynamical equations for the "weak friction model" with additional corrections due to tidal and rotational deformations.
Aims. We investigate possible driving mechanisms of volcanic activity on rocky super-Earths with masses exceeding 3-4 Mearth. Due to high gravity and pressures in the mantles of these planets, melting in deep mantle layers can be suppressed, even if the energy releae due to tidal heating and radioactive decay is substantial. Here we investigate whether a newly identified heating mechanism, namely induction heating by the star's magnetic field, can drive volcanic activity on these planets due to its unique heating pattern in the very upper part of the mantle. In this region the pressure is not …
Multi-wavelength observations provide a complementary view of the formation of young directly-imaged planet-mass companions. We report the ALMA 1.3 mm and Magellan adaptive optics (MagAO) H-alpha, i', z', and Ys observations of the GQ Lup system, a classical T Tauri star with a 10-40 Mjup substellar companion at ~110 AU projected separation. We estimate the accretion rates for both components from the observed H-alpha fluxes. In our 0.05 arcsec resolution ALMA map, we resolve GQ Lup A's disk in dust continuum, but no signal is found from the companion. The disk is compact, with a radius of ~22…
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…
We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, ${\rm Im}[{\tilde k}_2(ω)]$, as a function of the forcing frequency $ω$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we…
Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints are now obtained both in the Solar and exoplanetary systems. Tidal dissipation in planets is intrinsically related to their internal structure. In particular, fluid and solid layers behave differently under tidal forcing. Therefore, their respective dissipation reservoirs have to be compared. In this letter, we compute separately the contributions of the potential dense rocky/icy core and the convective fluid envelope of gaseous giant p…
An Evolving Cosmic Shoreline and Sandbar Bounding the Rocky Airless Valley
Stanford University（斯坦福大学）；The University of Chicago（芝加哥大学）；University of California, San Diego（加州大学圣地亚哥分校）；University of Hawai‘i（夏威夷大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of Maryland, College Park（马里兰大学帕克分校）
It has been proposed recently that the first step in the formation of both rocky and gas giant planets is dust sedimentation into a solid core inside a gas clump (giant planet embryo). The clumps are then assumed to migrate closer to the star where their metal poor envelopes are sheared away by the tidal forces or by an irradiation-driven mass loss. We consider the implications of this hypothesis for natal rotation rates of both terrestrial and gas giant planets. It is found that both types of planets may rotate near their break up angular frequencies at birth. The direction of the spin should…
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 br…
We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semi-major axis. We perform the largest-yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances and semi-major axes between 3 AU and 150 AU. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as …
A Formation-Stage Bottleneck for Exomoons around Close-in Rocky Planets
Chengdu University of Technology（成都理工大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；University of Zurich（苏黎世大学）；Sun Yat-sen University（中山大学）；Institute of Geochemistry, Chinese Academy of Sciences（中国科学院地球化学研究所）
The standard picture of planet formation posits that giant gas planets are over-grown rocky planets massive enough to attract enormous gas atmospheres. It has been shown recently that the opposite point of view is physically plausible: the rocky terrestrial planets are former giant planet embryos dried of their gas "to the bone" by the influences of the parent star. Here we provide a brief overview of this "Tidal Downsizing" hypothesis in the context of the Solar System structure.
We use numerical simulations to measure the sensitivity of the tidal spin down rate of a homogeneous triaxial ellipsoid to its axis ratios by comparing the drift rate in orbital semi-major axis to that of a spherical body with the same mass, volume and simulated rheology. We use a mass-spring model approximating a viscoelastic body spinning around its shortest body axis, with spin aligned with orbital spin axis, and in circular orbit about a point mass. The torque or drift rate can be estimated from that predicted for a sphere with equivalent volume if multiplied by $0.5 (1 + b^4/a^4)(b/a)^{-4…
With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, the correct treatment of tidal interactions is becoming necessary. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeed the result of tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets, which can then be responsible for volcanism and/or surface deformation. In the majority of studies to estimate the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology…
The ideal exoplanets to search for life are those within a star's habitable zone. However, even within the habitable zone planets can still develop uninhabitable climate states. Sustaining a temperate climate over geologic ($\sim$Gyr) timescales requires a planet contain sufficient internal energy to power a planetary-scale carbon cycle. A major component of a rocky planet's energy budget is the heat produced by the decay of radioactive elements, especially $^{40}$K, $^{232}$Th, $^{235}$U and $^{238}$U. As the planet ages and these elements decay, this radiogenic energy source dwindles. Here w…
We present ALMA observations of the 2M1207 system, a young binary made of a brown dwarf with a planetary-mass companion at a projected separation of about 40 au. We detect emission from dust continuum at 0.89 mm and from the $J = 3 - 2$ rotational transition of CO from a very compact disk around the young brown dwarf. The small radius found for this brown dwarf disk may be due to truncation from the tidal interaction with the planetary-mass companion. Under the assumption of optically thin dust emission, we estimated a dust mass of 0.1 $M_{\oplus}$ for the 2M1207A disk, and a 3$σ$ upper limit …
Three planets with minimum masses less than 10 Earth masses orbit the star HD 40307, suggesting these planets may be rocky. However, with only radial velocity data, it is impossible to determine if these planets are rocky or gaseous. Here we exploit various dynamical features of the system in order to assess the physical properties of the planets. Observations allow for circular orbits, but a numerical integration shows that the eccentricities must be at least 0.0001. Also, planets b and c are so close to the star that tidal effects are significant. If planet b has tidal parameters similar to …
