Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.
The detection of lower mass planets now being reported via radial velocity and microlensing surveys suggests that they may be ubiquitous. If missions such as Kepler are able to confirm this, the detection and study of rocky planets via direct imaging with ground-based telescopes of apertures > 20 m is feasible in the thermal infrared. We discuss two cases for detecting rocky planets, the first via detection of molten Earths formed though an Earth-Moon like impact event, and the second via detection of planets around very nearby stars. These observations have the potential to give us a first lo…
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 …
Planets with sizes between those of Earth and Neptune divide into two populations: purely rocky bodies whose atmospheres contribute negligibly to their sizes, and larger gas-enveloped planets possessing voluminous and optically thick atmospheres. We show that whether a planet forms rocky or gas-enveloped depends on the solid surface density of its parent disk. Assembly times for rocky cores are sensitive to disk solid surface density. Lower surface densities spawn smaller planetary embryos; to assemble a core of given mass, smaller embryos require more mergers between bodies farther apart and …
The Kepler Mission, combined with ground based radial velocity (RV) follow-up and dynamical analyses of transit timing variations, has revolutionized the observational constraints on sub-Neptune-size planet compositions. The results of an extensive Kepler follow-up program including multiple Doppler measurements for 22 planet-hosting stars more than doubles the population of sub-Neptune-sized transiting planets that have RV mass constraints. This unprecedentedly large and homogeneous sample of planets with both mass and radius constraints opens the possibility of a statistical study of the und…
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…
Rocky planets both in and outside of our solar system are observed to have a range of core-mass fractions (CMFs). Imperfect collisions can preferentially strip mantle material from a planet, changing its CMF, and are therefore thought to be the most likely cause of this observed CMF variation. However, previous work that implements these collisions into N-body simulations of planet formation has struggled to reliably form high CMF super-Earths. In this work, we specify our initial conditions and simulation parameters to maximize the prevalence of high-energy, CMF-changing collisions in order t…
The observed population of Hot Jupiters displays a stunning variety of physical properties, including a wide range of densities and core sizes for a given planetary mass. Motivated by the observational sample, this paper studies the accretion of rocky planets by Hot Jupiters, after the Jovian planets have finished their principal migration epoch and become parked in $\sim4$-day orbits. In this scenario, rocky planets form later and then migrate inward due to torques from the remaining circumstellar disk, which also damps the orbital eccentricity. This mechanism thus represents one possible cha…
One of the most significant advances by NASA's ${\mathit Kepler}$ Mission was the discovery of an abundant new population of highly irradiated planets with sizes between the Earth and Neptune. Subsequent analysis showed that at ~1.5 Earth radii there is a transition from a population of predominantly rocky super-Earths to non-rocky sub-Neptunes, which must have substantial volatile envelopes. Determining the origin of these highly irradiated rocky planets will be critical to our understanding of low-mass planet formation and the frequency of potentially habitable Earth-like planets. These shor…
Exoplanets smaller than Neptune are common around red dwarf stars (M dwarfs), with those that transit their host star constituting the bulk of known temperate worlds amenable for atmospheric characterization. We analyze the masses and radii of all known small transiting planets around M dwarfs, identifying three populations: rocky, water-rich, and gas-rich. Our results are inconsistent with the previously known bimodal radius distribution arising from atmospheric loss of a hydrogen/helium envelope. Instead, we propose that a density gap separates rocky from water-rich exoplanets. Formation mod…
The formation of super-Earths, the most abundant planets in the Galaxy, remains elusive. These planets have masses that typically exceed that of the Earth by a factor of a few; appear to be predominantly rocky, although often surrounded by H/He atmospheres; and frequently occur in multiples. Moreover, planets that encircle the same star tend to have similar masses and radii, whereas those belonging to different systems exhibit remarkable overall diversity. Here, we advance a theoretical picture for rocky planet formation that satisfies the aforementioned constraints: building upon recent work …
Recent observations and analysis of low mass (<10$M_{\oplus}$), exoplanets have found that rocky planets only have radii up to 1.5-2$R_{\oplus}$. Two general hypotheses exist for the cause of the dichotomy between rocky and gas-enveloped planets (or possible water worlds): either low mass planets do not necessarily form thick atmospheres of a few wt. %, or the thick atmospheres on these planets easily escape driven by x-ray and extreme ultraviolet (XUV) emissions from young parent stars. Here we show that a cutoff between rocky and gas-enveloped planets due to hydrodynamic escape is most likel…
Nominally anhydrous minerals in rocky planet mantles can sequester oceans of water as a whole, giving a constraint on bulk water inventories. Here we predict mantle water capacities from the thermodynamically-limited solubility of water in their constituent minerals. We report the variability of mantle water capacity due to (i) host star refractory element abundances that set mineralogy, (ii) realistic mantle temperature scenarios, and (iii) planet mass. We find that planets large enough to stabilise perovskite almost unfailingly have a dry lower mantle, topped by a high-water-capacity transit…
The quest for atmospheric spectral signatures that may witness biological activity in exoplanets is focused on rocky planets. The best targets for future, challenging spectroscopic observations will be selected among potentially habitable planets. Surface habitability can be quantified and explored with climate and atmospheric models according to temperature-based criteria. The conceptual, modellistic, technological and interpretative complexity of the problem requires to develop flexible climate and atmospheric models suited for a comprehensive exploration of observationally unconstrained par…
An ice giant planet was recently reported orbiting white dwarf WD J0914+1914 at an approximate distance of 0.07 au. The striking non-detection of rocky pollutants in this white dwarf's photosphere contrasts with the observations of nearly every other known white dwarf planetary system. Here, I analyze the prospects for exterior extant rocky asteroids, boulders, cobbles and pebbles to radiatively drift inward past the planet due to the relatively high luminosity (0.1 L_Sun) of this particularly young (13 Myr) white dwarf. Pebbles and cobbles drift too slowly from Poynting-Robertson drag to bypa…
We present here the detection of a system of four low-mass planets around the bright (V=5.5) and close-by (6.5 pc) star HD219134. This is the first result of the Rocky Planet Search program with HARPS-N on the TNG in La Palma. The inner planet orbits the star in 3.0937 +/-0.0004 days, on a quasi-circular orbit with a semi-major axis of 0.0382 +/- 0.0003 AU. Spitzer observations allowed us to detect the transit of the planet in front of the star making HD219134b the nearest known transiting planet to date. From the amplitude of the radial-velocity variation (2.33 +/- 0.24 m/s) and observed dept…
Main sequence stars hosting extreme quantities of inner planetary system debris are likely experiencing transient dust production events. The nature of these events, if they can be unambiguously attributed to a single process, can potentially inform us on the formation and/or early evolution of rocky Earth-like planets. In this contribution I examine some of the dustiest main sequence stars known and three processes that may be capable of reproducing their observed properties. Through this activity I also make an estimate for the likelihood of an A-type star to have an asteroid belt-like plane…
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…
The thermal evolution of rocky planets on geological timescales (Gyr) depends on the heat input from the long-lived radiogenic elements potassium, thorium, and uranium. Concentrations of the latter two in rocky planet mantles are likely to vary by up to an order of magnitude between different planetary systems because Th and U, like other heavy r-process elements, are produced by rare stellar processes. Here we discuss the effects of these variations on the thermal evolution of an Earth-size planet, using a 1D parameterized convection model. Assuming Th and U abundances consistent with geochem…
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）
Progressive astronomical characterization of planet-forming disks and rocky exoplanets highlight the need for increasing interdisciplinary efforts to understand the birth and life cycle of terrestrial worlds in a unified picture. Here, we review major geophysical and geochemical processes that shape the evolution of rocky planets and their precursor planetesimals during planetary formation and early evolution, and how these map onto the astrophysical timeline and varying accretion environments of planetary growth. The evolution of the coupled core-mantle-atmosphere system of growing protoplane…
The bulk density of a planet, as measured by mass and radius, is a result of planet structure and composition. Relative proportions of iron core, rocky mantle, and gaseous envelopes are degenerate for a given density. This degeneracy is reduced for rocky planets without significant gaseous envelopes when the structure is assumed to be a differentiated iron core and rocky mantle, in which the core mass fraction (CMF) is a first-order description of a planet's bulk composition. A rocky planet's CMF may be derived both from bulk density and by assuming the planet reflects the host star's major ro…
The interior composition of exoplanets is not observable, limiting our direct knowledge of their structure, composition, and dynamics. Recently described observational trends suggest that rocky exoplanets, that is, planets without significant volatile envelopes, are likely limited to $<$1.5 Earth radii. We show that given this likely upper limit in the radii of purely-rocky super-Earth exoplanets, the maximum expected core-mantle boundary pressure and adiabatic temperature is relatively moderate, 630 GPa and 5000 K, while the maximum central core pressure varies between 1.5 and 2.5 TPa. We fur…
Evolution and Observable Properties of Rocky Planet Atmospheres
ETH Zurich（苏黎世联邦理工学院）；Freie Universität Berlin（柏林自由大学）；National Astronomical Observatory of Japan（日本国立天文台）；Institute of Science Tokyo（东京科学大学）；NASA Goddard Institute for Space Studies（美国宇航局戈达德太空研究所）；Uppsala University（乌普萨拉大学）；DLR, Institute of Space Research（德国航空航天中心空间研究所）；University of Tokyo（东京大学）；Institut des Sciences de la Terre d’Orléans,Université d’Orléans-CNRS-BRGM（奥尔良地球科学学院，奥尔良大学-法国国家科学研究中心-地质调查局）；Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）
Life on Earth emerged at the interface of the geosphere, hydrosphere and atmosphere. This setting serves as our basis for how biological systems originate on rocky planets. Often overlooked, however, is the fact that the chemical nature of a rocky planet is ultimately a product of galactic chemical evolution. Elemental abundances of the major rock-forming elements can be different for different stars and planets formed at different times in galactic history. These differences mean that we cannot expect small rocky exoplanets to be just like Earth. Furthermore, age of the system dictates starti…
Rocky planets are common around other stars, but their atmospheric properties remain largely unconstrained. Thanks to a wealth of recent planet discoveries and upcoming advances in observing capability, we are poised to characterize the atmospheres of dozens of rocky exoplanets in this decade. Theoretical understanding of rocky exoplanet atmospheres has advanced considerably in the last few years, yielding testable predictions of their evolution, chemistry, dynamics and even possible biosignatures. Here we review key progress in this field to date and discuss future objectives. Our major concl…
Most rocky planets in the galaxy orbit a cool host star, and there is large uncertainty among theoretical models whether these planets can retain an atmosphere. The James Webb Space Telescope (JWST) might be able to settle this question empirically, but most proposals for doing so require large observational effort because they are based on spectroscopy. Here we show that infrared photometry of secondary eclipses could quickly identify "candidate" atmospheres, by searching for rocky planets with atmospheres thick enough that atmospheric heat transport noticeably reduces their dayside thermal e…
Short-period exoplanets can have dayside surface temperatures surpassing 2000 K, hot enough to vaporize rock and drive a thermal wind. Small enough planets evaporate completely. We construct a radiative-hydrodynamic model of atmospheric escape from strongly irradiated, low-mass rocky planets, accounting for dust-gas energy exchange in the wind. Rocky planets with masses < 0.1 M_Earth (less than twice the mass of Mercury) and surface temperatures > 2000 K are found to disintegrate entirely in < 10 Gyr. When our model is applied to Kepler planet candidate KIC 12557548b --- which is believed to b…
Terrestrial planets, with silicate mantles and metallic cores, are likely to obtain water and carbon compounds during accretion. Here I examine the conditions that allow early formation of a surface water ocean (simultaneous with cooling to clement surface conditions), and the timeline of degassing the planetary interior into the atmosphere. The greatest fraction of a planet's initial volatile budget is degassed into the atmosphere during the end of magma ocean solidification, leaving only a small fraction of the original volatiles to be released into the atmosphere through later volcanism. Ro…
The existence of water in extrasolar planetary systems is of great interest as it constrains the potential for habitable planets and life. Here, we report the identification of a circumstellar disk that resulted from the destruction of a water-rich and rocky, extrasolar minor planet. The parent body formed and evolved around a star somewhat more massive than the Sun, and the debris now closely orbits the white dwarf remnant of the star. The stellar atmosphere is polluted with metals accreted from the disk, including oxygen in excess of that expected for oxide minerals, indicating the parent bo…
Volatile molecules containing hydrogen, carbon, and nitrogen are key components of planetary atmospheres. In the pebble accretion model for rocky planet formation, these volatile species are accreted during the main planetary formation phase. For this study, we modelled the partitioning of volatiles within a growing planet and the outgassing to the surface. The core stores more than 90\% of the hydrogen and carbon budgets of Earth for realistic values of the partition coefficients of H and C between metal and silicate melts. The magma oceans of Earth and Venus are sufficiently deep to undergo …
We reconsider the commonly held assumption that warm debris disks are tracers of terrestrial planet formation. The high occurrence rate inferred for Earth-mass planets around mature solar-type stars based on exoplanet surveys (roughly 20%) stands in stark contrast to the low incidence rate (less than 2-3%) of warm dusty debris around solar-type stars during the expected epoch of terrestrial planet assembly (roughly 10 Myr). If Earth-mass planets at AU distances are a common outcome of the planet formation process, this discrepancy suggests that rocky planet formation occurs more quickly and/or…
Magma oceans are a common result of the high degree of heating that occurs during planet formation. It is thought that almost all of the large rocky bodies in the Solar System went through at least one magma ocean phase. In this paper, we review some of the ways in which magma ocean models for the Earth, Moon, and Mars match present day observations of mantle reservoirs, internal structure, and primordial crusts, and then we present new calculations for the oxidation state of the mantle produced during the magma ocean phase. The crystallization of magma oceans likely leads to a massive mantle …
The composition of rocky exoplanets in the context of stars' composition provides important constraints to formation theories. In this study, we select a sample of exoplanets with mass and radius measurements with an uncertainty <25% and obtain their interior structure. We calculate compositional markers, ratios of iron to magnesium and silicon, as well as core-mass fractions (cmf) that fit the planetary parameters, and compare them to the stars'. We find four key results that successful planet formation theories need to predict: (1) In a population sense, the composition of rocky planets span…
The Kepler Mission has found thousands of planetary candidates with radii between 1 and 4 R$_\oplus$. These planets have no analogues in our own Solar System, providing an unprecedented opportunity to understand the range and distribution of planetary compositions allowed by planet formation and evolution. A precise mass measurement is usually required to constrain the possible composition of an individual super-Earth-sized planet, but these measurements are difficult and expensive to make for the majority of Kepler planet candidates. Fortunately, adopting a statistical approach helps us to ad…
As we begin to discover rocky planets in the habitable zone of nearby stars with missions like TESS and CHEOPS, we will need quick advancements on instrumentation and observational techniques that will enable us to answer key science questions, such as What are the atmospheric characteristics of habitable zone rocky planets? How common are Earth-like biosignatures in rocky planets?} How similar or dissimilar are those planets to Earth? Over the next decade we expect to have discovered several Earth-analog candidates, but we will not have the tools to study the atmospheres of all of them in det…
Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10000 K, implying significant redistribution of rocky core material in Jup…
We present a detailed chemical abundance analysis of 15 elements in the planet-hosting wide binary system HD80606 + HD80607 using Keck/HIRES spectra. As in our previous analysis of the planet-hosting wide binary HD20782 + HD20781, we presume that these two G5 dwarf stars formed together and therefore had identical primordial abundances. In this binary, HD80606 hosts an eccentric ($e\approx0.93$) giant planet at $\sim$0.5 AU, but HD80607 has no detected planets. If close-in giant planets on eccentric orbits are efficient at scattering rocky planetary material into their host stars, then HD80606…
This work aims at exploring the scaling relations among rocky exoplanets. With the assumption of internal gravity increasing linearly in the core, and staying constant in the mantle, and tested against numerical simulations, a simple model is constructed, applicable to rocky exoplanets of core mass fraction (CMF) $\in 0.1\sim0.4$ and mass $\in 0.1 \sim 10 M_{\oplus}$. Various scaling relations are derived: (1) core radius fraction $\rm CRF \approx \sqrt{CMF}$, (2) Typical interior pressure $P_{\text{typical}} \sim g_{\rm{s}}^2$ (surface gravity squared), (3) core formation energy $E_{\rm diff}…
To ascertain whether magnetic dynamos operate in rocky exoplanets more massive or hotter than the Earth, we developed a parametric model of a differentiated rocky planet and its thermal evolution. Our model reproduces the established properties of Earth's interior and magnetic field at the present time. When applied to Venus, assuming that planet lacks plate tectonics and has a dehydrated mantle with an elevated viscosity, the model shows that the dynamo shuts down or never operated. Our model predicts that at a fixed planet mass, dynamo history is sensitive to core size, but not to the initia…
The formation of satellites is thought to be a natural by-product of planet formation in our Solar System, and thus, moons of extrasolar planets (exomoons) may be abundant in extrasolar planetary systems, as well. Exomoons have yet to be discovered. However, moons larger than 0.1 Earth masses can be detected and characterized using current transit techniques. Here, we show that collisions between rocky planets with masses between a quarter to ten Earth masses can create impact-generated debris disks that could accrete into moons. Collisions between like-sized objects, at oblique impact angles,…
The study of origins of life on Earth and the search for life on other planets are closely linked. Prebiotic chemical scenarios can help prioritize planets as targets for the search for life as we know it and can provide informative priors to help us assess the likelihood that particular spectroscopic features are evidence of life. The prerequisites for origins scenarios themselves predict spectral signatures. The interplay between origins research and the search for extraterrestrial life must start with lab work guiding exploratory ventures in the solar system, and the discoveries in the sola…
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…
We use an end-to-end model of planet formation, thermodynamic evolution, and atmospheric escape to investigate how the statistical imprints of evaporation depend on the bulk composition of planetary cores (rocky vs. icy). We find that the population-wide imprints like the location of the "evaporation valley" in the distance-radius plane and the corresponding bimodal radius distribution clearly differ depending on the bulk composition of the cores. Comparison with the observed position of the valley (Fulton et al. 2017) suggests that close-in low-mass Kepler planets have a predominately Earth-l…
