Super-Earths and mini-Neptunes exhibit great diversity in their compositional and orbital properties. Their bulk densities span a large range, from those dense enough to be purely rocky to those needing a substantial contribution from volatiles to their volumes. Their orbital configurations range from compact, circular multi-transiting systems like Kepler-11 to systems like our Solar System's terrestrial planets with wider spacings and modest but significant eccentricities and mutual inclinations. Here we investigate whether a continuum of formation conditions resulting from variation in the amount of solids available in the inner disk can account for the diversity of orbital and compositional properties observed for super Earths, including the apparent dichotomy between single transiting and multiple transiting system. We simulate in situ formation of super-Earths via giant impacts and compare to the observed Kepler sample. We find that intrinsic variations among disks in the amount of solids available for in situ formation can account for the orbital and compositional diversity observed among Kepler's transiting planets. Our simulations can account for the planets' distributions of orbital period ratios, transit duration ratios, and transit multiplicity; higher eccentricities for single than multi transiting planets; smaller eccentricities for larger planets; scatter in the mass-radius relation, including lower densities for planets with masses measured with TTVs than RVs; and similarity in planets' sizes and spacings within each system. Our findings support the theory that variation among super-Earth and mini-Neptune properties is primarily locked in by different in situ formation conditions, rather than arising stochastically through subsequent evolution.
Quantifying the energy budget of Earth in the first few million years following the Moon-forming giant impact is vital to understanding Earth's initial thermal state and the dynamics of lunar tidal evolution. After the impact, the body was substantially vaporized and rotating rapidly, very different from the planet we know today. The subsequent evolution of Earth's energy budget, as the body cooled and angular momentum was transferred during lunar tidal recession, has not been accurately calculated with all relevant energy components included. Here, we use giant impact simulations and planetar…
According to the generally accepted scenario, the last giant impact on the Earth formed the Moon and initiated the final phase of core formation by melting the Earth's mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 My) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is …
The Earth's Moon is thought to have formed by an impact between the Earth and an impactor around 4.5 billion years ago. This impact could have been so energetic that it could have mixed and homogenized the Earth's mantle. However, this view appears to be inconsistent with geochemical studies that suggest that the Earth's mantle was not mixed by the impact. Another plausible outcome is that this energetic impact melted the whole mantle, but the extent of mantle melting is not well understood even though it must have had a significant effect on the subsequent evolution of the Earth's interior an…
Close-in super-Earths, with radii R = 2-5 R_Earth and orbital periods P < 100 days, orbit more than half, and perhaps nearly all Sun-like stars in the universe. We use this omnipresent population to construct the minimum-mass extrasolar nebula (MMEN), the circumstellar disk of solar-composition solids and gas from which such planets formed, if they formed near their current locations and did not migrate. In a series of back-of-the-envelope calculations, we demonstrate how in-situ formation in the MMEN is fast, efficient, and can reproduce many of the observed properties of close-in super-Earth…
The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally …
According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto Earth and a Mars sized impactor. The initial structure of the disk significantly affects the Moon forming process, including the Moons mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here…
A large fraction of stars host one or multiple close-in super-Earth planets. There is an active debate about whether these planets formed in situ or at greater distances from the central star and migrated to their current position. It has been shown that part of their observed properties (e.g., eccentricity distribution) can be reproduced by N-body simulations of in situ formation starting with a population of protoplanets of high masses and neglecting the effects of the disk gas. We plan to reassess the in situ formation of close-in super-Earths through more complete simulations. We performed…
The Moon is believed to have formed in the aftermath of a giant impact between a planetary mass body and the proto-Earth. In a typical giant impact scenario, a disk of vapor, liquid, and solid debris forms around the proto-Earth and--after possibly decades of evolution--condenses to form the Moon. Using state-of-the-art numerical simulations, we investigate the dynamical effects of magnetic fields on the Moon-forming giant impact. We show that turbulence generated by the collision itself, shear in the boundary layer between the post-impact debris field and the proto-Earth, and turbulence in th…
Simulations of the moon-forming impact suggest that most of the lunar material derives from the impactor rather than the Earth. Measurements of lunar samples, however, reveal an oxygen isotope composition that is indistinguishable from terrestrial samples, and clearly distinct from meteorites coming from Mars and Vesta. Here we explore the possibility that the silicate Earth and impactor were compositionally distinct with respect to oxygen isotopes, and that the terrestrial magma ocean and lunar-forming material underwent turbulent mixing and equilibration in the energetic aftermath of the gia…
Motivated by recent discoveries of low-density super-Earths with short orbital periods, we have investigated in-situ accretion of H-He atmospheres on rocky bodies embedded in dissipating warm disks, by simulating quasi-static evolution of atmospheres that connect to the ambient disk. We have found that the atmospheric evolution has two distinctly different outcomes, depending on the rocky body's mass: While the atmospheres on massive rocky bodies undergo runaway disk-gas accretion, those on light rocky bodies undergo significant erosion during disk dispersal. In the atmospheric erosion, the he…
Kepler's observation shows that many of the detected planets are super-Earths. They are inside a range of critical masses overlapping the core masses (2-20 $M_{\bigoplus}$), which would trigger the runaway accretion and develop the gas giants. Thus, super-Earths/sub-Neptunes can be formed by restraining runaway growth of gaseous envelopes. We assess the effect of planetary rotation in delaying the mass growth. The centrifugal force, induced by spin, will offset a part of the gravitational force and deform the planet. Tracking the change in structure, we find that the temperature at the radiati…
The large number of exoplanets found to orbit their host stars in very close orbits have significantly advanced our understanding of the planetary formation process. It is now widely accepted that such short-period planets cannot have formed {\em in situ}, but rather must have migrated to their current orbits from a formation location much farther from their host star. In the late stages of planetary formation, once the gas in the proto-planetary disk has dissipated and migration has halted, gas-giants orbiting in the inner disk regions will excite planetesimals and planetary embryos, resultin…
We fit an isothermal oscillatory density model of Jupiter's protoplanetary disk to the present-day Galilean and other nearby satellites and we determine the radial scale length of the disk, the equation of state and the central density of the primordial gas, and the rotational state of the Jovian nebula. Although the radial density profile of Jupiter's disk was similar to that of the solar nebula, its rotational support against self-gravity was very low, a property that also guaranteed its long-term stability against self-gravity induced instabilities for millions of years.
The chemical compositions of Earth's core and mantle provide insight into the processes that led to their formation. N-body simulations, on the other hand, generally do not contain chemical information, and seek to only reproduce the masses and orbits of the terrestrial planets. These simulations can be grouped into four potentially viable scenarios of Solar System formation (Classical, Annulus, Grand Tack, and Early Instability) for which we compile a total of 433 N-body simulations. We relate the outputs of these simulations to the chemistry of Earth's core and mantle using a melt-scaling la…
From iodine-plutonium-xenon isotope systematics, we re-evaluate time constraints on the early evolution of the Earth-atmosphere system and, by inference, on the Moon-forming event. Two extinct radioactivites (129I, T1/2 = 15.6 Ma, and 244Pu, T1/2 = 80 Ma) have produced radiogenic 129Xe and fissiogenic 131-136Xe, respectively, within the Earth, which related isotope fingerprints are seen in the compositions of mantle and atmospheric Xe. Recent studies of Archean rocks suggest that xenon atoms have been lost from the Earth's atmosphere and isotopically fractionated during long periods of geologi…
Effects of Outer Giant Planets on In Situ Formation of Inner Super-Earths
The Pennsylvania State University（宾夕法尼亚州立大学）；The College of New Jersey（新泽西学院）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；Missouri State University（密苏里州立大学）
Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic composition show them to be highly similar. In contrast, the compositions of other solar system bodies are significantly different than the Earth and Moon. This poses a major challenge to the giant impact scenario since the Moon-forming impactor is then thought to al…
Recent high-precision measurements of the isotopic composition of lunar rocks demonstrate that the bulk silicate Earth and the Moon show an unexpectedly high degree of similarity. This is inconsistent with one of the primary results of classic dynamical simulations of the widely accepted giant impact model for the formation of the Moon, namely that most of the mass of the Moon originates from the impactor, not Earth. Resolution of this discrepancy without changing the main premises of the giant impact model requires total isotopic homogenisation of Earth and impactor material after the impact …
Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using $N$-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a 'seed-model' and an 'equal-mass-model'. The former has a more massive protoplanet placed among…
We examine the possibility that icy super-Earth mass planets, formed over long time scales (0.1--1~Gyr) at large distances ($\sim$ 200--1000~AU) from their host stars, will develop massive H-rich atmospheres. Within the interior of these planets, high pressure converts CH$_4$ into ethane, butane, or diamond and releases H$_2$. Using simplified models which capture the basic physics of the internal structure, we show that the physical properties of the atmosphere depend on the outflux of H$_2$ from the mantle. When this outflux is $\lesssim 10^{10}$ [molec cm$^{-2}$ s$^{-1}$], the outgassed atm…
In spite of substantial advancements in simulating planet formation, the planet Mercury's diminutive mass, isolated orbit, and the absence of planets with shorter orbital periods in the solar system continue to befuddle numerical accretion models. Recent studies have shown that, if massive embryos (or even giant planet cores) formed early in the innermost parts of the Sun's gaseous disk, they would have migrated outward. This migration may have reshaped the surface density profile of terrestrial planet-forming material and generated conditions favorable to the formation of Mercury-like planets…
We fit an isothermal oscillatory density model of Uranus' protoplanetary disk to the present-day major satellites and we determine the radial scale length of the disk, the equation of state and the central density of the primordial gas, and the rotational state of the Uranian nebula. This disk does not at all look like the Jovian disk that we modeled previously. Its rotation parameter that measures centrifugal support against self-gravity is a lot smaller ($β_0=0.00507$), as is the radial scale length (only 27.6 km) and the size of the disk (only 0.60 Gm). On the other hand, the central densit…
The formation of cold gas giants similar to Jupiter and Saturn in orbit and mass is a great challenge for planetesimal-driven core accretion models because the core growth rates far from the star are low. Here we model the growth and migration of single protoplanets that accrete planetesimals and gas. We integrated the core growth rate using fits in the literature to $N$-body simulations, which provide the efficiency of accreting the planetesimals that a protoplanet migrates through. We take into account three constraints from the solar system and from protoplanetary discs: (1) the masses of t…
The origin of Uranus and Neptune is still unknown. In particular, it has been challenging for planet formation models to form the planets in their current radial distances within the expected lifetime of the solar nebula. In this paper, we simulate the in-situ formation of Uranus and Neptune via pebble accretion and show that both planets can form within ~ 3 Myr at their current locations, and have final compositions that are consistent with the heavy-element to H-He ratios predicted by structure models. We find that Uranus and Neptune could have been formed at their current locations. In seve…
We fit an isothermal oscillatory density model to two ALMA/DSHARP-observed disks, AS 209 and HL Tau, in which planets have presumably already formed and they are orbiting within the observed seven dark gaps in each system. These large disks are roughly similar to our solar nebula, albeit they exhibit milder radial density profiles and they enjoy lower centrifugal support. We find power-law density profiles with index $k=0.0$ (radial densities $ρ(R) \propto R^{-1}$) and centrifugal support against self-gravity so small that it guarantees dynamical stability for millions of years of evolution. T…
It has been proposed that the observed systems of hot super-Earths formed in situ from high-mass disks. By fitting a disk profile to the entire population of Kepler planet candidates, Chiang & Laughlin (2013) constructed a "minimum-mass extrasolar nebula" with surface density profile Sigma r^-1.6. Here we use multiple-planet systems to show that it is inconsistent to assume a universal disk profile. Systems with 3-6 low-mass planets (or planet candidates) produce a diversity of minimum-mass disks with surface density profiles ranging from Sigma r^-3.2 to Sigma r^0.5 (5th-95th percentile). By s…
Recent studies have unequivocally proven the existence of clouds in super-Earth atmospheres (Kreidberg et al. 2014). Here we provide a theoretical context for the formation of super-Earth clouds by determining which condensates are likely to form under the assumption of chemical equilibrium. We study super-Earth atmospheres of diverse bulk composition, which are assumed to form by outgassing from a solid core of chondritic material, following Schaefer & Fegley (2010). The super-Earth atmospheres that we study arise from planetary cores made up of individual types of chondritic meteorites. They…
Hot Jupiters, giant extrasolar planets with orbital periods shorter than ~10 days, have long been thought to form at large radial distances, only to subsequently experience long-range inward migration. Here, we propose that in contrast with this picture, a substantial fraction of the hot Jupiter population formed in situ via the core accretion process. We show that under conditions appropriate to the inner regions of protoplanetary disks, rapid gas accretion can be initiated by Super-Earth type planets, comprising 10-20 Earth masses of refractory composition material. An in situ formation scen…
We fit an isothermal oscillatory density model to the disk of HD 163296 in which planets have presumably already formed and they are orbiting at least within the four observed dark gaps. This 156 AU large axisymmetric disk shows various physical properties comparable to those of AS 209, HL Tau, and TW Hya that we have modeled previously; but it compares best to AS 209. The disks of HD 163296 and AS 209 are comparable in size and they share similar values of the power-law index $k\approx 0$ (a radial density profile of the form $ρ(R)\propto R^{-1}$), the rotational parameter $β_0$ (to within a …
In recent years, ALMA has been able to observe large-scale substructures within protoplanetary disks. Comparison with the predictions from models of planet-disk interaction has indicated that most of these disk substructures can be explained by the presence of planets with the mass of Neptune or larger at orbital radii of $\approx 5 - 100$ au. Better resolution is needed to observe structures closer to the star, where terrestrial planets are expected to form, as well as structures opened by planets with masses lower than Neptune. We investigate the capabilities of a possible extension to ALMA …
The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage collisions have been limited by assuming that all collisions lead to perfect accretion, and many of these studies lack the large number of realizations needed to account for the chaotic nature of N-body systems. We improve on these limitations by performing 280 simulations of planet formation around a Sun-like star, half of which used an N-body algorithm that …
Super-Earths with orbital periods less than 100 days are extremely abundant around Sun-like stars. It is unlikely that these planets formed at their current locations. Rather, they likely formed at large distances from the star and subsequently migrated inward. Here we use N-body simulations to study the effect of super-Earths on the accretion of rocky planets. In our simulations, one or more super-Earths migrates inward through a disk of planetary embryos and planetesimals embedded in a gaseous disk. We tested a wide range of migration speeds and configurations. Fast-migrating super-Earths ($…
We first consider how the level of turbulence in a protoplanetary disk affects the formation locations for the observed close-in super-Earths in exosolar systems. We find that a protoplanetary disk that includes a dead zone (a region of low turbulence) has substantially more material in the inner parts of the disk, possibly allowing for in situ formation. For the dead zone to last the entire lifetime of the disk requires the active layer surface density to be sufficiently small, <100 g/cm^2. Migration through a dead zone may be very slow and thus super-Earth formation followed by migration tow…
The radius valley, a bifurcation in the size distribution of small, close-in exoplanets, is hypothesized to be a signature of planetary atmospheric loss. Such an evolutionary phenomenon should depend on the age of the star-planet system. In this work, we study the temporal evolution of the radius valley using two independent determinations of host star ages among the California-Kepler Survey (CKS) sample. We find evidence for a wide and nearly empty void of planets in the period-radius diagram at the youngest system ages ($\lesssim$2-3 Gyr) represented in the CKS sample. We show that the orbit…
Binary stars form from the same parent molecular cloud and thus have the same chemical composition. Forming planets take building material (solids) away from the surrounding protoplanetary disc. Assuming that the disc's accretion onto the star is the main process that clears the disc, the atmosphere of the star will show abundance reductions caused by the material accreted by the forming planet(s). If planets are only forming around one star of a binary system, the planet formation process can result in abundance differences in wide binary stars, if their natal protoplanetary discs do not inte…
Context.The Kepler mission has provided a large sample to statistically analyze the orbital properties of the super-Earth planets. We hypothesize that these planets formed early and consider the problem of matching planet formation theory to the current observations. Two scenarios, disk migration and in-situ formation, have been proposed to explain their origin. In the migration scenario planets migrate inward due to planet-disk interaction, whereas in the in-situ scenario planets assemble locally. Therefore, planets formed by migration are expected to end up in resonances, whereas those forme…
Water is crucial for the emergence and evolution of life on Earth. Recent studies of the water content in early forming planetary systems similar to our own show that water is an abundant and ubiquitous molecule, initially synthesized on the surfaces of tiny interstellar dust grains by the hydrogenation of frozen oxygen. Water then enters a cycle of sublimation/freezing throughout the successive phases of planetary system formation, namely, hot corinos and protoplanetary disks, eventually to be incorporated into planets, asteroids, and comets. The amount of heavy water measured on Earth and in…
We fit an isothermal oscillatory density model of Saturn's protoplanetary disk to the present-day major satellites and innermost rings D/C and we determine the radial scale length of the disk, the equation of state and the central density of the primordial gas, and the rotational state of the Saturnian nebula. This disk does not look like the Jovian and Uranian disks that we modeled previously. Its power-law index is extremely steep ($k=-4.5$) and its radial extent is very narrow ($ΔR\lesssim 0.9$ Gm), its rotation parameter that measures centrifugal support against self-gravity is somewhat la…
We simulate the hypothesised collision between the proto-Earth and a Mars-sized impactor that created the Moon. Amongst the resulting debris disk in some impacts, we find a self-gravitating clump of material. It is roughly the mass of the Moon, contains $\sim1\%$ iron like the Moon, and has its internal composition resolved for the first time. The clump contains mainly impactor material near its core but becomes increasingly enriched in proto-Earth material near its surface. A graduated composition has recently been measured in the oxygen isotope ratios of Apollo samples, suggesting incomplete…
Prediction of the effects of coronal mass ejections (CMEs) on Earth strongly depends on knowledge of the interplanetary magnetic field southward component, Bz. Predicting the strength and duration of Bz inside a CME with sufficient accuracy is currently impossible, which forms the so-called Bz problem. Here, we provide a proof-of-concept of a new method for predicting the CME arrival time, speed, Bz and the resulting Dst index at Earth based only on magnetic field data, measured in situ in the inner heliosphere (< 1AU). On 2012 June 12-16, three approximately Earthward-directed and interacting…
Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in Δ"17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average Δ"17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.
The riddle posed by super-Earths (1-4$R_\oplus$, 2-20$M_\oplus$) is that they are not Jupiters: their core masses are large enough to trigger runaway gas accretion, yet somehow super-Earths accreted atmospheres that weigh only a few percent of their total mass. We show that this puzzle is solved if super-Earths formed late, as the last vestiges of their parent gas disks were about to clear. This scenario would seem to present fine-tuning problems, but we show that there are none. Ambient gas densities can span many (up to 9) orders of magnitude, and super-Earths can still robustly emerge after…
Using N-body simulations with planet-disk interactions, we present a mechanism capable of forming compact systems of hot super Earths such as Kepler 11. Recent studies show that outward migration is common in the inner parts of radiative disks. However we show that two processes naturally tip the balance in favor of inward migration. First the corotation torque is too weak to generate outward migration for planetary embryos less massive than $4\mearth$. Second, system of multiple embryos generate sustained non-zero eccentricities that damp the corotation torque and again favor inward migration…
Recent high precision meteoritic data infers that Mars finished its accretion rapidly within 10 Myr of the beginning of the Solar system and had an accretion zone that did not entirely overlap with the Earth's. Here we present a detailed study of the accretion zone of planetary embryos from high resolution simulations of planetesimals in a disc. We found that all simulations with Jupiter and Saturn on their current eccentric orbits (EJS) result in a similar accretion zone between fast-forming Mars and Earth region embryos. Assuming more circular orbits for Jupiter and Saturn (CJS), on the othe…
We fit an isothermal oscillatory density model to the outer disk of TW Hya in which planets have presumably already formed and they are orbiting within four observed dark gaps. At first sight, this 52 AU small disk does not appear to be similar to our solar nebula; it shows several physical properties comparable to those in HL Tau (size $R_{\rm max}=102$ AU) and very few similarities to AS 209 ($R_{\rm max}=144$ AU). We find a power-law density profile with index $k=-0.2$ (radial densities $ρ(R) \propto R^{-1.2}$) and centrifugal support against self-gravity so small that it virtually guarante…
The Moon is generally thought to have formed from the debris ejected by the impact of a planet-sized object with the proto-Earth towards the end of planetary accretion. Modeling of the impact process predicts that the lunar material was disaggregated into a circumplanetary disk and that lunar accretion subsequently placed the Moon in a near equatorial orbit. Forward integration of the lunar orbit from this initial state predicts a modern inclination at least an order of magnitude smaller than the lunar value, a long-standing discrepancy known as the lunar inclination problem. Here we show that…
The first estimation of the energy cascade rate ${|ε_C|}$ of magnetosheath turbulence is obtained using the CLUSTER and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. ${|ε_C|}$ is found to be of the order of ${10{^{-13}} J.m^{3}.s^{-1}}$, at least two orders of magnitude larger than its value in the solar wind (order of ${10{^{-16}} J.m^{3}.s^{-1}}$ in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or magnetosonic-like fluctuations. Density fluctuations are shown to amplify t…
Modern terrestrial planet formation models are highly successful at consistently generating planets with masses and orbits analogous to those of Earth and Venus. In stark contrast to classic theoretical predictions and inferred demographics of multi-planet systems of rocky exoplanets, the mass (>10) and orbital period (>2) ratios between Venus and Earth and the neighboring Mercury and Mars are not common outcomes in numerically generated systems. While viable solutions to the small-Mars problem are abundant in the literature, Mercury's peculiar origin remains rather mysterious. In this paper, …
Kepler's observations show most of the exoplanets are super-Earths. The formation of super-Earth is generally related to the atmospheric mass loss that is crucial in the planetary structure and evolution. The shock driven by the giant impact will heat the planet, resulting in the atmosphere escape. We focus on whether self-gravity changes the efficiency of mass loss. Without self-gravity, if the impactor mass is comparable to the envelope mass, there is a significant mass-loss. The radiative-convective boundary will shift inward by self-gravity. As the temperature and envelope mass increase, t…
