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Register a new userThe Feeding Zones of Terrestrial Planets and Insights into Moon Formation
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[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planets feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planets mass and its volatile inventory. Instead, we find that the feeding zone of any planet more massive than 0.1M_Earth is roughly proportional to the radial extent of the initial disk from which it formed: Delta a~0.25(a_max-a_min), where a_min and a_max are the inner and outer edge of the initial planetesimal disk. These wide stochastic feeding zones have significant consequences for the origin of the Moon, since the canonical scenario predicts the Moon should be primarily composed of material from Earths last major impactor (Theia), yet its isotopic composition is indistinguishable from Earth. In particular, we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs. Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk, we find a ~5% or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moons. In fact we predict that every planetary mass body should be expected to have a unique isotopic signature. In addition, we find paucities of massive Theia analogs and high velocity moon-forming collisions, two recently proposed explanations for the Moons isotopic composition. Our work suggests that there is still no scenario for the Moons origin that explains its isotopic composition with a high probability event.
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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 calculations, we drew conclusions on the process of accumulation of the terrestrial planets. The embryos of the terrestrial planets, the masses of which did not exceed a tenth of the current planetary masses, accumulated planetesimals mainly from the vicinity of their orbits. When planetesimals fell onto the embryos of the terrestrial planets from the feeding zone of Jupiter and Saturn, these embryos had not yet acquired the current masses of the planets, and the material of this zone (including water and volatiles) could be accumulated in the inner layers of the terrestrial planets. The inner layers of each of the terrestrial planets were mainly formed from the material located in the vicinity of the orbit of a certain planet. The outer layers of the Earth and Venus could accumulate the same material for these two planets from different parts of the feeding zone of the terrestrial planets. The Earth and Venus could acquire more than half of their masses in 5 Myr. A relatively rapid growth of the bulk of the Martian mass can be explained by the formation of Mars embryo (the mass of which is several times less than that of Mars) due to contraction of a rarefied condensation.
From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiters orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earths embryo, when its mass was smaller than the current mass of the Earth. While the Earths embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiters orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two-three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiters orbit could be less than that for the Earth by a factor not more than 20.
We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about $60% - 80%$. In each simulation, 3 - 4 terrestrial planets are formed inside Jupiter with masses of $0.15 - 3.6 M_{oplus}$. In the $0.5 - 4$ AU, when the eccentricities of planetesimals are excited, planetesimals are able to accrete material from wide radial direction. The plenty of water material of the terrestrial planet in the Habitable Zone may be transferred from the farther places by this mechanism. Accretion could also happen a few times between two major planets only if the outer planet has a moderate mass and the small terrestrial planet could survive at some resonances over time scale of $10^8$ yr. In one of our simulations, com-mensurability of the orbital periods of planets is very common. Moreover, a librating-circulating 3:2 configuration of mean motion resonance is found.
The core accretion theory of planet formation has at least two fundamental problems explaining the origins of Uranus and Neptune: (1) dynamical times in the trans-Saturnian solar nebula are so long that core growth can take > 15 Myr, and (2) the onset of runaway gas accretion that begins when cores reach 10 Earth masses necessitates a sudden gas accretion cutoff just as the ice giant cores reach critical mass. Both problems may be resolved by allowing the ice giants to migrate outward after their formation in solid-rich feeding zones with planetesimal surface densities well above the minimum-mass solar nebula. We present new simulations of the formation of Uranus and Neptune in the solid-rich disk of Dodson-Robinson et al. (2009) using the initial semimajor axis distribution of the Nice model (Gomes et al. 2005; Morbidelli et al. 2005; Tsiganis et al. 2005), with one ice giant forming at 12 AU and the other at 15 AU. The innermost ice giant reaches its present mass after 3.8-4.0 Myr and the outermost after 5.3-6 Myr, a considerable time decrease from previous one-dimensional simulations (e.g. Pollack et al. 1996). The core masses stay subcritical, eliminating the need for a sudden gas accretion cutoff. Our calculated carbon mass fractions of 22% are in excellent agreement with the ice giant interior models of Podolak et al. (1995) and Marley et al. (1995). Based on the requirement that the ice giant-forming planetesimals contain >10% mass fractions of methane ice, we can reject any solar system formation model that initially places Uranus and Neptune inside the orbit of Saturn. We also demonstrate that a large population of planetesimals must be present in both ice giant feeding zones throughout the lifetime of the gaseous nebula.
To reproduce the orbits and masses of the terrestrial planets (analogs) of the solar system, most studies scrutinize simulations for success as a batch. However, there is insufficient discussion in the literature on the likelihood of forming planet analogs simultaneously in the same system (analog system). To address this issue, we performed 540 N-body simulations of protoplanetary disks representative of typical models in the literature. We identified a total of 194 analog systems containing at least three analogs, but only 17 systems simultaneously contained analogs of the four terrestrial planets. From an analysis of our analog systems, we found that, compared to the real planets, truncated disks based on typical outcomes of the Grand Tack model produced analogs of Mercury and Mars that were too dynamically cold and located too close to the Venus and Earth analogs. Additionally, all the Mercury analogs were too massive, while most of the Mars analogs were more massive than Mars. Furthermore, the timing of the Moon-forming impact was too early in these systems, and the amount of additional mass accreted after the event was too great. Therefore, such truncated disks cannot explain the formation of the terrestrial planets. Our results suggest that forming the four terrestrial planets requires disks with the following properties: 1) Mass concentrated in narrow core regions between ~0.7-0.9 and ~1.0-1.2 au; 2) an inner region component starting at ~0.3-0.4 au; 3) a less massive component beginning at ~1.0-1.2 au; 4) embryos rather than planetesimals carrying most of the disk mass; and 5) Jupiter and Saturn placed on eccentric orbits.
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