An episode of dynamical instability is thought to have sculpted the orbital structure of the outer solar system. When modeling this instability, a key constraint comes from Jupiter's fifth eccentric mode (quantified by its amplitude M-55), which is an important driver of the solar system's secular evolution. Starting from commonly-assumed near-circular orbits, the present-day giant planets' architecture lies at the limit of numerically generated systems, and M-55 is rarely excited to its true value. Here we perform a dynamical analysis of a large batch of artificially triggered instabilities, and test a variety of configurations for the giant planets' primordial orbits. In addition to more standard setups, and motivated by the results of modern hydrodynamical simulations of the giant planets' evolution within the primordial gaseous disk, we consider the possibility that Jupiter and Saturn emerged from the nebular gas locked in 2:1 resonance with non-zero eccentricities. We show that, in such a scenario, the modern Jupiter-Saturn system represents a typical simulation outcome, and M-55 is commonly matched. Furthermore, we show that Uranus and Neptune's final orbits are determined by a combination of the mass in the primordial Kuiper belt and that of an ejected ice giant.

The absence of planets interior to Mercury continues to puzzle terrestrial-planet formation models, particularly when contrasted with the relatively high derived occurrence rates of short-period planets around Sun-like stars. Recent work proposed that the majority of systems hosting hot super-Earths attain their orbital architectures through an epoch of dynamical instability after forming in quasi-stable, tightly packed configurations. Isotopic evidence seems to suggest that the formation of objects in the super-Earth-mass regime is unlikely to have occurred in the solar system as the terrestrial-forming disk is thought to have been significantly mass deprived starting around 2 Myr after the formation of calcium-aluminum-rich inclusions-a consequence of either Jupiter's growth or an intrinsic disk feature. Nevertheless, terrestrial-planet formation models and high-resolution investigations of planetesimal dynamics in the gas-disk phase occasionally find that quasi-stable protoplanets with mass comparable to that of Mars emerge in the vicinity of Mercury's modern orbit. In this paper, we investigate whether it is possible for a primordial configuration of such objects to be cataclysmically destroyed in a manner that leaves Mercury behind as the sole survivor without disturbing the other terrestrial worlds. We use numerical simulations to show that this scenario is plausible. In many cases, the surviving Mercury analog experiences a series of erosive impacts, thereby boosting its Fe/Si ratio. A caveat of our proposed genesis scenario for Mercury is that Venus typically experiences at least one late giant impact.

The formation of gas-giant planets within the lifetime of a protoplanetary disk is challenging especially far from a star. A promising model for the rapid formation of giant-planet cores is pebble accretion in which gas drag during encounters leads to high accretion rates. Most models of pebble accretion consider disks with a monotonic, radial pressure profile. This causes a continuous inward flux of pebbles and inefficient growth. Here we examine planet formation in a disk with multiple, intrinsic pressure bumps. In the outer disk, pebbles become trapped near these bumps allowing rapid growth under suitable conditions. In the inner disk, pebble traps may not exist because the inward gas advection velocity is too high. Pebbles here are rapidly removed. In the outer disk, growth is very sensitive to the initial planet mass and the strength of turbulence. This is because turbulent density fluctuations raise planetary eccentricities, increasing the planet-pebble relative velocity. Planetary seeds above a distance-dependent critical mass grow to a Jupiter mass in 0.5-3 Myr out to at least 60 au in a 0.03 solar-mass disk. Smaller bodies remain near their initial mass, leading to a sharp dichotomy in growth outcomes. For turbulent alpha = 1e-4, the critical masses are 1e-4M (circle plus) and 1e-3M (circle plus) at 9 and 75 au, respectively. Pressure bumps in disks may explain the large mass difference between the giant planets and Kuiper Belt objects, and also the existence of wide-orbit planets in some systems.

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 multiplanet systems of rocky exoplanets, the mass (greater than or similar to 10) and orbital period (greater than or similar to 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, we investigate the possibility that Mercury formed in a mass-depleted, inner region of the terrestrial disk (a < 0.5 au). This regime is often ignored in terrestrial-planet formation models because of the high computational cost of resolving hundreds of short-period objects over similar to 100 Myr timescales. By testing multiple disk profiles and mass distributions, we identify several promising sets of initial conditions that lead to remarkably successful analog systems. In particular, our most successful simulations consider moderate total masses of Mercury-forming material (0.1-0.25 Earth masses). While larger initial masses tend to yield disproportionate Mercury analogs, smaller values often inhibit the planets' formation as the entire region of material is easily accreted by Venus. Additionally, we find that shallow surface density profiles and larger inventories of small planetesimals moderately improve the likelihood of adequately reproducing Mercury.

The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of dynamical instability. Several qualifies of the solar system have recently been interpreted as evidence of this event transpiring within the first similar to 100 Myr after the Sun's birth; around the same time as the final assembly of the inner planets. In a series of recent papers we argued that such an early instability could resolve several problems revealed in classic numerical studies of terrestrial planet formation; namely the small masses of Mars and the asteroid belt. In this paper, we revisit the early instability scenario with a large suite of simulations specifically designed to understand the degree to which Earth and Mars' formation are sensitive to the specific evolution of Jupiter and Saturn's orbits. By deriving our initial terrestrial disks directly from recent high-resolution simulations of planetesimal accretion, our results largely confirm our previous findings regarding the instability's efficiency of truncating the terrestrial disk outside of the Earth-forming region in simulations that best replicate the outer solar system. Moreover, our work validates the primordial 2:1 Jupiter-Saturn resonance within the early instability framework as a viable evolutionary path for the solar system. While our simulations elucidate the fragility of the terrestrial system during the epoch of giant planet migration, many realizations yield outstanding solar system analogs when scrutinized against a number of observational constraints. Finally, we highlight the inability of models to form adequate Mercury-analogs and the low eccentricities of Earth and Venus as the most significant outstanding problems for future numerical studies to resolve.

In a recent paper we proposed that the giant planets' primordial orbits may have been eccentric (e(J) similar to e(S) similar to 0.05), and used a suite of dynamical simulations to show outcomes of the giant planet instability that are consistent with their present-day orbits. In this follow-up investigation, we present more comprehensive simulations incorporating superior particle resolution, longer integration times, and eliminating our prior means of artificially forcing instabilities to occur at specified times by shifting a planets' position in its orbit. While we find that the residual phase of planetary migration only minimally alters the planets' ultimate eccentricities, our work uncovers several intriguing outcomes in realizations where Jupiter and Saturn are born with extremely large eccentricities (e(J) similar or equal to 0.10; e(S) similar or equal to 0.25). In successful simulations, the planets' orbits damp through interactions with the planetesimal disk prior to the instability, thus loosely replicating the initial conditions considered in our previous work. Our results therefore suggest an even wider range of plausible evolutionary pathways are capable of replicating Jupiter and Saturn's modern orbital architecture.

In spite of substantial advancements in simulating planet formation, the planet Mercury's diminutive mass and 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. Here we continue to develop this model with an updated suite of numerical simulations. We favor a scenario where Earth's and Venus's progenitor nuclei form closer to the Sun and subsequently sculpt the Mercury-forming region by migrating toward their modern orbits. This rapid formation of similar to 0.5 M (circle plus) cores at similar to 0.1-0.5 au is consistent with modern high-resolution simulations of planetesimal accretion. In successful realizations, Earth and Venus accrete mostly dry, enstatite chondrite-like material as they migrate, thus providing a simple explanation for the masses of all four terrestrial planets, the inferred isotopic differences between Earth and Mars, and Mercury's isolated orbit. Furthermore, our models predict that Venus's composition should be similar to the Earth's and possibly derived from a larger fraction of dry material. Conversely, Mercury analogs in our simulations attain a range of final compositions.