Recent observations have found a valley in the size distribution of close-in super-Earths that is interpreted as a signpost that close-in super-Earths are mostly rocky in composition. However, new models predict that planetesimals should first form at the water ice line such that close-in planets are expected to have a significant water ice component. Here we investigate the water contents of super-Earths by studying the interplay between pebble accretion, planet migration and disc evolution. Planets' compositions are determined by their position relative to different condensation fronts (ice lines) throughout their growth. Migration plays a key role. Assuming that planetesimals start at or exterior to the water ice line ($r>r_{\rm H_2O}$), inward migration causes planets to leave the source region of icy pebbles and therefore to have lower final water contents than in discs with either outward migration or no migration. The water ice line itself moves inward as the disc evolves, and delivers water as it sweeps across planets that formed dry. The relative speed and direction of planet migration and inward drift of the water ice line is thus central in determining planets' water contents. If planet formation starts at the water ice line, this implies that hot close-in super-Earths (r<0.3 AU) with water contents of a few percent are a signpost of inward planet migration during the early gas phase. Hot super-Earths with larger water ice contents on the other hand, experienced outward migration at the water ice line and only migrated inwards after their formation was complete either because they become too massive to be contained in the region of outward migration or in chains of resonant planets. Measuring the water ice content of hot super-Earths may thus constrain their migration history.
We present a series of papers dedicated to modelling the accretion and differentiation of rocky planets that form by pebble accretion within the lifetime of the protoplanetary disc. In this first paper, we focus on how the accreted ice determines the distribution of iron between the mantle (oxidized FeO and FeO$_{1.5}$) and the core (metallic Fe and FeS). We find that an initial primitive composition of ice-rich material leads, upon heating by the decay of $^{26}$Al, to extensive water flow and the formation of clay minerals inside planetesimals. Metallic iron dissolves in liquid water and pre…
The Earth's ocean mass is only 2.3 x 10^{-4} of the whole planet mass. Even including water in the interior, it would be at most 10^{-3}-10^{-2}. Ancient Mars may have had a similar or slightly smaller water fraction. It is important to clarify the water delivery mechanism to rocky planets in habitable zones in exoplanetary systems, as well as that to the Earth and Mars. Here, we consider water delivery to planets by icy pebbles after the snowline inwardly passes the planetary orbits and derive the water mass fraction (f_{water}) of the final planet as a function of disk parameters and discuss…
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 …
Many habitable zone exoplanets are expected to form with water mass fractions higher than that of the Earth. For rocky exoplanets with 10-1000x Earth's H2O but without H2, we model the multi-Gyr evolution of ocean temperature and chemistry, taking into account C partitioning, high-pressure ice phases, and atmosphere-lithosphere exchange. Within our model, for Sun-like stars, we find that: (1)~the duration of habitable surface water is strongly affected by ocean chemistry; (2)~possible ocean pH spans a wide range; (3)~surprisingly, many waterworlds retain habitable surface water for >1 Gyr, and…
We study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim at computing the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler's size distribution. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection-diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation and sublimation at the water iceline are included. The disc evolut…
We present nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of Mars- to Earth-mass planetary embryos. The simulations extend from the surface of the embryos to a few vertical disk scale heights, with \rev{a spatial} dynamic range \rev{of} $\sim\! 1.4\times 10^5$. Our results confirm that "pebble"-sized particles are readily accreted, with accretion rates continuing to increase up to metre-size "boulders" for a 10\% MMSN surface density model. The gas mass flux in and out of the Hill sphere is consistent with the Hill rate, $ΣΩR_\mathrm{H}^2 = 4…
I examine the standard model of planet formation, including pebble accretion, using numerical simulations. Planetary embryos large enough to become giant planets do not form beyond the ice line within a typical disk lifetime unless icy pebbles stick at higher speeds than in experiments using rocky pebbles. Systems like the Solar System (small inner planets, giant outer planets) can form if (i) icy pebbles are stickier than rocky pebbles, and (ii) the planetesimal formation efficiency increases with pebble size, which prevents the formation of massive terrestrial planets. Growth beyond the ice …
We explore the heating and differentiation of rocky planets that grow by rapid pebble accretion. Our terrestrial planets grow outside of the ice line and initially accrete 28\% water ice by mass. The accretion of water stops after the protoplanet reaches a mass of $0.01\,M_{\rm E}$ where the gas envelope becomes hot enough to sublimate the ice and transport the vapour back to the protoplanetary disc by recycling flows. The energy released by the decay of $^{26}$Al melts the accreted ice to form clay (phyllosilicates), oxidized iron (FeO), and a water surface layer with ten times the mass of Ea…
It is important to clarify where and when rocky and icy planetesimals are formed in a viscously evolving disk. We wish to understand how local runaway pile-up of solids occurs inside or outside the snow line. We assume an icy pebble contains micron-sized silicate grains that are uniformly mixed with ice and are released during the ice sublimation. Using a local one-dimensional code, we solve the radial drift and the turbulent diffusion of solids and the water vapor, taking account of their sublimation/condensation around the snow line. We systematically investigate effects of back-reactions of…
The formation of super-Earths is strongly linked to the structure of the protoplanetary disc, which determines growth and migration. In the pebble accretion scenario, planets grow to the pebble isolation mass, at which the planet carves a small gap in the gas disc halting the pebble flux and thus its growth. The pebble isolation mass scales with the disc's aspect ratio, which directly depends on the disc structure. I compare the growth of super-Earths in viscously heated discs and discs purely heated by the central star with super-Earth observations. This allows two formation pathways of super…
Topography on a wet rocky exoplanet could raise land above its sea level. Although land elevation is the product of many complex processes, the large-scale topographic features on any geodynamically-active planet are the expression of the convecting mantle beneath the surface. This so-called "dynamic topography" exists regardless of a planet's tectonic regime or volcanism; its amplitude, with a few assumptions, can be estimated via numerical simulations of convection as a function of the mantle Rayleigh number. We develop new scaling relationships for dynamic topography on stagnant lid planets…
Volatile depletion in rocky planets as a chemical fingerprint of hybrid accretion
University of Copenhagen（哥本哈根大学）；ETH Zürich（苏黎世联邦理工学院）；University of Alabama（阿拉巴马大学）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；University of Arizona（亚利桑那大学）
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…
We investigate the effects of radiative energy transfer on a series of nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of an Earth-mass planetary embryo. We include heating due to the accretion of solids and the subsequent convective motions. Using a constant embryo surface temperature, we show that radiative energy transport results in a tendency to reduce the entropy in the primordial atmosphere, but this tendency is alleviated by an increase in the strength of convective energy transport, triggered by a correspondingly increased super-adiab…
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…
Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion
Center for Star and Planet Formation, Globe Institute, University of Copenhagen（哥本哈根大学全球研究所恒星与行星形成中心）；Division of Astrophysics, Department of Physics, Lund University（隆德大学物理系天体物理学部）；New Mexico State University, Department of Astronomy（新墨西哥大学天文学系）
Context: The formation of rocky planetesimals is a long-standing problem in planet formation theory. One of the possibilities is that it results from gravitational instability as a result of pile-up of small silicate dust particles released from sublimating icy pebbles that pass the snow line. Aims: We want to understand and quantify the role of the water snow line for the formation of rock-rich and ice-rich planetesimals. In this paper, we focus on the formation of rock-rich planetesimals. A companion paper examines the combined formation of both rock-rich and ice-rich planetesimals. Methods:…
Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose Stokes numbers approach unity. While fast, pebble accretion is also lossy. Gas drag brings pebbles to protocores but also sweeps them past; those particles with the largest accretion cross-sections also have the fastest radial drift speeds and are the most easily drained out of discs. We present a global model of planet formation by pebble accretion that keeps …
We investigate the pebble isolation mass for a planet on a fixed eccentric orbit in its protoplanetary disc by conducting a set of 2D hydrodynamical simulations including dust turbulent diffusion. A range of planet eccentricities up to $e=0.2$ is adopted. Our simulations also cover a range of $α-$turbulent viscosities, and for each pair $\{α,e\}$ the pebble isolation mass is estimated as the minimum planet mass in our simulations such that solids with a Stokes number $\gtrsim 0.05$ do not flow across the planet orbit and remain trapped around a pressure bump outside the planet gap. For $α<10^{…
Though ~10 Earth mass rocky/icy cores are commonly held as a prerequisite for the formation of gas giants, theoretical models still struggle to explain how these embryos can form within the lifetimes of gaseous circumstellar disks. In recent years, aerodynamic-aided accretion of "pebbles," objects ranging from centimeters to meters in size, has been suggested as a potential solution to this long-standing problem. While pebble accretion has been demonstrated to be extremely effective in local simulations that look at the detailed behavior of these pebbles in the vicinity of a single planetary e…
Two fundamentally different processes of rocky planet formation exist, but it is unclear which one built the terrestrial planets of the solar system. Either they formed by collisions among planetary embryos from the inner solar system, or by accreting sunward-drifting millimeter-sized 'pebbles' from the outer solar system. We show that the isotopic compositions of Earth and Mars are governed by two-component mixing among inner solar system materials, including material from the innermost disk unsampled by meteorites, whereas the contribution of outer solar system material is limited to a few p…
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Re…
Context: Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by accreting cm-to-m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This provides early enrichment to the planet's envelope, which changes the process of core growth. Aims: We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Methods: We…
Around the snow line, icy pebbles and silicate dust may locally pile-up and form icy and rocky planetesimals via streaming instability and/or gravitational instability. We perform 1D diffusion-advection simulations that include the back-reaction to radial drift and diffusion of icy pebbles and silicate dust, ice sublimation, release of silicate dust, and their recycling through recondensation and sticking onto pebbles outside the snow line. We use a realistic description of the scale height of silicate dust obtained from Ida et al. and that of pebbles including the effects of a Kelvin-Helmholt…
Chondrules in primitive meteorites likely formed by recrystallisation of dust aggregates that were flash-heated to nearly complete melting. Chondrules may represent the building blocks of rocky planetesimals and protoplanets in the inner regions of protoplanetary discs, but the source of ubiquitous thermal processing of their dust aggregate precursors remains elusive. Here we demonstrate that escape of positrons released in the decay of the short-lived radionuclide $^{26}$Al leads to a large-scale charging of dense pebble structures, resulting in neutralisation by lightning discharge and flash…
Standard accretion disk models suggest that the snow line in the solar nebula migrated interior to the Earth's orbit in a late stage of nebula evolution. In this late stage, a significant amount of ice could have been delivered to 1 AU from outer regions in the form of mm to dm-sized pebbles. This raises the question why the present Earth is so depleted of water (with the ocean mass being as small as 0.023% of the Earth mass). Here we quantify the amount of icy pebbles accreted by terrestrial embryos after the migration of the snow line assuming that no mechanism halts the pebble flow in outer…
We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs, in the (sub)stellar mass range between $0.01 \ M_{\odot}$ and $0.1 \ M_{\odot}$. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial masses of the protoplanets (largest bodies from the planetesimal size distributions), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary dis…
The existence of a Radius Valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between that of Earth and Neptune. The goal of this work is to provide insights into the existence of the Radius Valley from, first, a pure formation point of view, and second, a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift and fragmentation; and the evolution of the gaseous disc by viscous accretion and photoevaporat…
The most widely-studied mechanism of mass loss from extrasolar planets is photoevaporation via XUV ionization, primarily in the context of highly irradiated planets. However, the EUV dissociation of hydrogen molecules can also theoretically drive atmospheric evaporation on low-mass planets. For temperate planets such as the early Earth, impact erosion is expected to dominate in the traditional planetesimal accretion model, but it would be greatly reduced in pebble accretion scenarios, allowing other mass loss processes to be major contributors. We apply the same prescription for photoionizatio…
We show that condensation is an efficient particle growth mechanism, leading to growth beyond decimeter-sized pebbles close to an ice line in protoplanetary discs. As coagulation of dust particles is frustrated by bouncing and fragmentation, condensation could be a complementary, or even dominant, growth mode in the early stages of planet formation. Ice particles diffuse across the ice line and sublimate, and vapour diffusing back across the ice line recondenses onto already existing particles, causing them to grow. We develop a numerical model of the dynamical behaviour of ice particles close…
It is generally accepted that silicate-metal (`rocky') planet formation relies on coagulation from a mixture of sub-Mars sized planetary embryos and (smaller) planetesimals that dynamically emerge from the evolving circum-solar disc in the first few million years of our Solar System. Once the planets have, for the most part, assembled after a giant impact phase, they continue to be bombarded by a multitude of planetesimals left over from accretion. Here we place limits on the mass and evolution of these planetesimals based on constraints from the highly siderophile element (HSE) budget of the …
It is believed that satellites of giant planets form in circumplanetary disks. Many of the previous contributions assumed that their formation process proceeds similarly to rocky planet formation, via accretion of the satellite seeds, called satellitesimals. However, the satellitesimal formation itself poses a nontrivial problem as the dust evolution in the circumplanetary disk is heavily impacted by fast radial drift and thus dust growth to satellitesimals is hindered. To address this problem, we connected state-of-the-art hydrodynamical simulations of a circumplanetary disk around a Jupiter-…
Uranus and Neptune are ice giants with $\sim$ 15% atmospheres by mass, placing them in an intermediate category between rocky planets and gas giants. These atmospheres are too massive to have been primarily outgassed, yet they never underwent runaway gas accretion. The ice giants never reached critical core mass ($M_\text{crit}$) in a full gas disk, yet their cores are $\gtrsim M_\text{crit}$, suggesting that their envelopes were mainly accreted at the end of the disk lifetime. Pebble accretion calls into question traditional slow atmospheric growth during this phase. We show that the full-siz…
Planets intermediate in size between the Earth and Neptune, and orbiting closer to their host stars than Mercury does the Sun, are the most common type of planet revealed by exoplanet surveys over the last quarter century. Results from NASA's Kepler mission have revealed a bimodality in the radius distribution of these objects, with a relative underabundance of planets between 1.5 and 2.0 $R_{\oplus}$. This bimodality suggests that sub-Neptunes are mostly rocky planets that were born with primary atmospheres a few percent by mass accreted from the protoplanetary nebula. Planets above the radiu…
Protoplanetary discs form and evolve in a wide variety of stellar environments and are accordingly exposed to a wide range of ambient far ultraviolet (FUV) field strengths. Strong FUV fields are known to drive vigorous gaseous flows from the outer disc. In this paper we conduct the first systematic exploration of the evolution of the solid component of discs subject to external photoevaporation. We find that the main effect of photoevaporation is to reduce the reservoir of dust at large radii and this leads to more efficient subsequent depletion of the disc dust due to radial drift. Efficient …
