The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets. We investigated the effects of the planetesimal-driven migration of Jupiter and Saturn, and the influence of their mutual 1:2 MMR crossing on terrestrial planet formation for the first time, by performing N-body simulations. These simulations considered distinct timescales of MMR crossing and planet migration. In total, 68 high-resolution simulation runs using 2000 disk planetesimals were performed, which was a significant improvement on previously published results. Even when the effects of the 1:2 MMR crossing and planet migration were included in the system, Venus and Earth analogs (considering both orbits and masses) successfully formed in several runs. In addition, we found that the orbits of planetesimals beyond a ~1.5-2 AU were dynamically depleted by the strengthened sweeping secular resonances associated with Jupiter's and Saturn's more eccentric orbits (relative to present-day) during planet migration. However, this depletion did not prevent the formation of massive Mars analogs (planets with more than 1.5 times Mars' mass). Although late MMR crossings (at t > 30 Myr) could remove such planets, Mars-like small mass planets survived on overly excited orbits (high e and/or i), or were completely lost in these systems. We conclude that the orbital migration and crossing of the mutual 1:2 MMR of Jupiter and Saturn are unlikely to provide suitable orbital conditions for the formation of solar system terrestrial planets. This suggests that to explain Mars' small mass and the absence of other planets between Mars and Jupiter, the outer asteroid belt must have suffered a severe depletion due to interactions with Jupiter/Saturn, or by an alternative mechanism (e.g., rogue super-Earths).
In this work, we extensively investigate the formation of near 4:2:1 mean motion resonances (MMRs) configuration by performing two sets of N-body simulations. We model the eccentricity damping, gas drag, type I and type II planetary migration of planetesimals, planetary embryos and giant planets in the first sets. For the simulations of giant planets with type II migration, the massive terrestrial planets, with a mass up to several Earth masses, are likely produced in the systems. We further show that by shepherding and/or scattering mechanisms through Jovian planet's type II migration, the te…
The formation and subsequent migration of gas giants could significantly affect the material mixing in the Solar System. In this study, we use N-body simulations to investigate how much water is transported into the region of the terrestrial planet formation during the growth and migration phases of Jupiter in the Grand Tack model. We found that Jupiter's growth was accompanied by significant mass transport, and that a substantial amount of water (about 10 times Earth's ocean mass for the initial planetesimal distribution based on the minimum-mass solar nebula) was transported into the terrest…
Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals…
Terrestrial planets are commonly observed to orbit M dwarfs with close-in trajectories. In this work, we extensively perform N-body simulations of planetesimal accretion with three models of in-situ, inward migration and reversed migration to explore terrestrial formation in tightly compact systems of M dwarfs. In the simulations, the solid disks are assumed to be 0.01\% of the masses of host stars and spread from 0.01 to 0.5 AU with the surface density profile scaling with $r^{-k}$ according to the observations. Our results show that in-situ scenario may produce $7.77^{+3.23}_{-3.77}$ terrest…
The Grand Tack model of terrestrial planet formation has emerged in recent years as the premier scenario used to account for several observed features of the inner solar system. It relies on early migration of the giant planets to gravitationally sculpt and mix the planetesimal disc down to ~1 AU, after which the terrestrial planets accrete from material left in a narrow circum-solar annulus. Here we have investigated how the model fares under a range of initial conditions and migration course-change (`tack') locations. We have run a large number of N-body simulations with a tack location of 1…
Recent three-dimensional magnetohydrodynamical simulations have identified a disk wind by which gas materials are lost from the surface of a protoplanetary disk, which can significantly alter the evolution of the inner disk and the formation of terrestrial planets. A simultaneous description of the realistic evolution of the gaseous and solid components in a disk may provide a clue for solving the problem of the mass concentration of the terrestrial planets in the solar system. We simulate the formation of terrestrial planets from planetary embryos in a disk that evolves via magnetorotational …
Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of …
The past decade has seen major progress in our understanding of terrestrial planet formation. Yet key questions remain. In this review we first address the growth of 100 km-scale planetesimals as a consequence of dust coagulation and concentration, with current models favoring the streaming instability. Planetesimals grow into Mars-sized (or larger) planetary embryos by a combination of pebble- and planetesimal accretion. Models for the final assembly of the inner Solar System must match constraints related to the terrestrial planets and asteroids including their orbital and compositional dist…
Context. Giant planets open gaps in their protoplanetary and subsequently suffer so-called type II migration. Schematically, planets are thought to be tightly locked within their surrounding disks, and forced to follow the viscous advection of gas onto the central star. This fundamental principle however has recently been questioned, as migrating planets were shown to decouple from the gas' radial drift. Aims. In this framework, we question whether the traditionally used linear scaling of migration rate of a giant planet with the disk's viscosity still holds. Additionally, we assess the role o…
Many features of the outer solar system are replicated in numerical simulations if the giant planets undergo an orbital instability that ejects one or more ice giants. During this instability, Jupiter and Saturn's orbits diverge, crossing their 2:1 mean motion resonance (MMR), and this resonance-crossing can excite the terrestrial planet orbits. Using a large ensemble of simulations of this giant planet instability, we directly model the evolution of the terrestrial planet orbits during this process, paying special attention to systems that reproduce the basic features of the outer planets. In…
We review the state of the field of terrestrial planet formation with the goal of understanding the formation of the inner Solar System and low-mass exoplanets. We review the dynamics and timescales of accretion from planetesimals to planetary embryos and from embryos to terrestrial planets. We discuss radial mixing and water delivery, planetary spins and the importance of parameters regarding the disk and embryo properties. Next, we connect accretion models to exoplanets. We first explain why the observed hot Super Earths probably formed by in situ accretion or inward migration. We show how t…
N-body Simulations of Terrestrial Planet Formation under the Influence of a Hot Jupiter
我们调查的多行星系统的形成中存在的热木星使用扩展N体模拟，同时进行半解析计算。我们的主要目标是使用高分辨率模拟从星子开始描述行星形成过程，并检查行星系的结构对输入参数的依赖性（例如，盘质量、盘粘度）。我们观察到，由寡头增长产生并经历I型迁移的原行星在加入热木星轨道外的共振行星链时停止迁移。共振链的形成几乎与我们的模型参数无关，因此是一个鲁棒的过程。在我们的模拟结束时，几个类地行星仍然在0.1天文单位左右。形成的行星质量不等;最大的行星占近区总质量的50%以上，这也较少依赖于参数。在本文之前的工作（Ogihara et al. 2013）中，我们发现了一种新的热木星诱导迁移的物理机制，称为挤出。如果热木星在圆盘上打开了一个很大的缺口（例如，由于低的圆盘粘性），挤出变得不那么有效，热木星仍然存在。我们还讨论了行星与盘之间的角动量转移。
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…
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
No planets exist inside the orbit of Mercury and the terrestrial planets of the solar system exhibit a localized configuration. According to thermal structure calculation of protoplanetary disks, a silicate condensation line (~ 1300 K) is located around 0.1 au from the Sun except for the early phase of disk evolution, and planetesimals could have formed inside the orbit of Mercury. A recent study of disk evolution that includes magnetically driven disk winds showed that the gas disk obtains a positive surface density slope inside ~ 1 au from the central star. In a region with positive midplane…
Our Solar system is almost entirely devoid of material interior to Mercury's orbit, in sharp contrast to the multiple Earth masses of material commonly residing within the analogous region of extrasolar planetary systems. Recent work has suggested that Jupiter's orbital migration early in the Solar system's history fragmented primordial planetary material within the inner Solar System. However, the reason for the absence of subsequent planet formation within 0.4AU remains unsolved. Here, we show that the up debris interior to Mercury's current orbit is susceptible to outward migration driven b…
The dynamics of the innermost Galilean satellites (Io, Europa and Ganymede) is characterised by a chain of mean motion resonances, called Laplace resonance, and by a strong tidal dissipation that causes wide variations of their semi-major axes over large timescales. The precise history of energy dissipation in the Jovian system is not known, but several theories have been proposed. Tidal resonance locking states that big outer moons can also migrate fast. If this is the case for Callisto, then it should have crossed the 2:1 mean motion resonance with Ganymede in the past, affecting the motion …
Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the existence of inclined terrestrial planets. We have performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under …
We report on five years of 3-5 micron photometry measurements obtained by warm Spitzer to track the dust debris emission in the terrestrial zone of HD 166191 in combination with simultaneous optical data. We show that the debris production in this young (~10 Myr) system increased significantly in early 2018 and reached a record high level (almost double by mid 2019) by the end of the Spitzer mission (early 2020), suggesting intense collisional activity in its terrestrial zone likely due to either initial assembling of terrestrial planets through giant impacts or dynamical shake-up from unseen …
Jupiter's core is generally assumed to have formed beyond the snow line. Here we consider an alternative scenario, that Jupiter's core may have accumulated in the innermost parts of the protoplanetary disk. A growing body of research suggests that small particles ("pebbles") continually drift inward through the disk. If a fraction of drifting pebbles is trapped at the inner edge of the disk a several Earth-mass core can quickly grow. Subsequently, the core may migrate outward beyond the snow line via planet-disk interactions. Of course, to reach the outer Solar System Jupiter's core must trave…
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 ($…
Water condensed as ice beyond the water snowline, the location in the Sun's natal gaseous disk where temperatures were below 170 K. As the disk evolved and cooled, the snowline moved inwards. A low temperature in the terrestrial planet-forming region is unlikely to be the origin of water on the planets, and the distinct isotopic compositions of planetary objects formed in the inner and outer disks suggest limited early mixing of inner and outer Solar System materials. Water in our terrestrial planets has rather been derived from H-bearing materials indigenous to the inner disk and delivered by…
Capture and escape from the 2:1 resonance between Ariel and Umbriel in a fast-migration scenario of the Uranian system
University of Pisa（比萨大学）；Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安东·范·列文虎克天文学研究所）；Université PSL, Sorbonne Université, Université de Lille（巴黎文理研究大学、索邦大学、里尔大学）
Water content and the internal evolution of terrestrial planets and icy bodies are closely linked. The distribution of water in planetary systems is controlled by the temperature structure in the protoplanetary disk and dynamics and migration of planetesimals and planetary embryos. This results in the formation of planetesimals and planetary embryos with a great variety of compositions, water contents and degrees of oxidation. The internal evolution and especially the formation time of planetesimals relative to the timescale of radiogenic heating by short-lived 26Al decay may govern the amount…
Combining isotopic constraints from meteorite data with dynamical models of planet formation proves to be advantageous in identifying the best model for terrestrial planet formation. Prior studies have shown that the probability of reproducing the distinct isotopic compositions of the Earth and Mars for both classical and Grand Tack models is very low. In the framework of the Grand Tack model, for Mars to be isotopically different from the Earth, it had to form under very specific conditions. Here, we subjected a fairly new and unexplored model--the depleted disc model--to the test. It presupp…
The process of planet conglomeration, which primarily unfolds in a geometrically thin disk of gas and dust, is often accompanied by dynamical excitation of the forming planets and planetesimals. The ensuing orbital crossing can lead to large-scale collisional fragmentation, populating the system with icy and rocky debris. In a gaseous nebula, such leftover solid matter tends to spiral down towards the host star due to aerodynamic drag. Along the way, the inward drifting debris can encounter planets and gravitationally couple to them via mean-motion resonances, sapping them of their orbital ene…
The importance of the dynamical corotation torque for the migration of low-mass planets -- 1D analytical prescriptions verified by 2D hydrodynamical simulations
Two phase, inward-then-outward migration of Jupiter and Saturn in the gaseous Solar Nebula
最近的研究表明，如果巨行星经历了向内然后向外的迁移，类地行星和小行星带可以重现（“大钉”; Walsh et al 2011）。向内迁移发生在木星打开一个缺口时，II型向内迁移。当土星到达质量间隙并与木星发生3：2共振时，行星会向外移动。其目的是测试Grand Tack模型的可行性，并研究木星和土星从10个地球质量的核心成长过程中的动态演变。我们已经进行了数值模拟，使用基于网格的流体动力学代码。我们大多数的模拟假设一个等温状态方程的磁盘，但一个子集使用完全辐射版本的代码。对于一个等温盘，木星和土星的两相迁移是非常强大的，并独立于这些行星的质量增长的历史，如果磁盘是足够冷。对于辐射盘，我们发现一些结果与两相迁移和其他更复杂的行为。我们构建了一个简单的，1-D模型的不断发展的粘性磁盘计算磁盘的辐射特性的演变：磁盘从辐射到等温从其最外层区域向内的时间过渡。我们表明，一个两相迁移是一个自然的结果，即使在有限的假设下，等温条件是必需的。因此，我们的模拟提供了强有力的支持，大塔克的情况。
Migration of planetesimals from the feeding zone of the terrestrial planets, which was divided into seven regions depending on the distance to the Sun, was simulated. The influence of gravity of all planets was taken into account. In some cases, the embryos of the terrestrial planets rather than the planets themselves were considered; their masses were assumed to be 0.1 or 0.3 of the current masses of the planets. The arrays of orbital elements of migrated planetesimals were used to calculate the probabilities of their collisions with the planets, the Moon, or their embryos. Based on our calcu…
观测到的系外行星都具有大质量（平均M sin i为1.65 MJ）和大范围的轨道偏心率（0 < e < 0.94）。由于行星被认为是在星周盘中形成的，因此行星形成的一个重要问题是确定气体盘是否会影响偏心行星的轨道，以及影响的程度。最近的研究已经探索了盘与偏心轨道上的类地行星之间的相互作用，以及盘与近圆轨道上的气体巨星之间的相互作用，但对盘与偏心气体巨星之间的相互作用知之甚少。这种情况可能是由于在盘仍然存在时的散射，或者可能是通过引力不稳定性形成的行星形成。我们填补了这一空白的偏心，大规模（间隙形成）行星盘使用流体动力学代码FARGO模拟。虽然行星的长期轨道演化取决于盘的性质，包括所使用的边界条件，但当行星被释放到盘中时，盘总是起到阻尼偏心的作用。这种偏心阻尼发生在40年的时间尺度上，比迁移时间尺度快15倍。
The solar system's terrestrial planets are thought to have accreted over millions of years out of a sea of smaller embryos and planetesimals. Because it is impossible to know the surface density profile for solids and size frequency distribution in the primordial solar nebula, distinguishing between the various proposed evolutionary schemes has been historically difficult. Nearly all previous simulations of terrestrial planet formation assume that Moon to Mars massed embryos formed throughout the inner solar system during the primordial gas-disk phase. However, validating this assumption throu…
Immediately after their formation, the terrestrial planets experienced intense impact bombardment by comets, leftover planetesimals from primary accretion, and asteroids. This temporal interval in solar system evolution, termed late accretion, thermally and chemically modified solid planetary surfaces and may have impeded the emergence of life on the Hadean Earth. The sources and tempo of late accretion are, however, vague. Here, we present a timeline that relates variably retentive radiometric ages from asteroidal meteorites, to new dynamical models of late accretion that invokes giant planet…
Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane. On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons. We show how a past crossing of the 5:1 mean motion…
