Observations support the hypothesis that gas disk gravitational instability might explain the formation of massive or wide-orbit gas giant exoplanets. The situation with regard to Jupiter-mass exoplanets orbiting within $\sim$ 20 au is more uncertain. Theoretical models yield divergent assessments often attributed to the numerical handling of the gas thermodynamics. Boss (2019) used the $β$ cooling approximation to calculate three dimensional hydrodynamical models of the evolution of disks with initial masses of 0.091 $M_\odot$ extending from 4 to 20 au around 1 $M_\odot$ protostars. The models considered a wide range (1 to 100) of $β$ cooling parameters and started from an initial minimum Toomre stability parameter of $Q_i = 2.7$ (gravitationally stable). The disks cooled down from initial outer disk temperatures of 180 K to as low as 40 K as a result of the $β$ cooling, leading to fragmentation into dense clumps, which were then replaced by virtual protoplanets (VPs) and evolved for up to $\sim$ 500 yr. The present models test the viability of replacing dense clumps with VPs by quadrupling the spatial resolution of the grid once dense clumps form, sidestepping in most cases VP insertion. After at least $\sim$ 200 yr of evolution, the new results compare favorably with those of Boss (2019): similar numbers of VPs and dense clumps form by the same time for the two approaches. The results imply that VP insertion can greatly speed disk instability calculations without sacrificing accuracy.
While collisional accumulation is nearly universally accepted as the formation mechanism of rock and ice worlds, the situation regarding gas giant planet formation is more nuanced. Gas accretion by solid cores formed by collisional accumulation is the generally favored mechanism, but observations increasingly suggest that gas disk gravitational instability might explain the formation of at least the massive or wide-orbit gas giant exoplanets. This paper continues a series aimed at refining three-dimensional (3D) hydrodynamical models of disk instabilities, where the handling of the gas thermod…
The Solar System's orbital structure is thought to have been sculpted by an episode of dynamical instability among the giant planets. However, the instability trigger and timing have not been clearly established. Hydrodynamical modeling has shown that while the Sun's gaseous protoplanetary disk was present the giant planets migrated into a compact orbital configuration in a chain of resonances. Here we use dynamical simulations to show that the giant planets' instability was likely triggered by the dispersal of the gaseous disk. As the disk evaporated from the inside-out, its inner edge swept …
The solar system's dynamical state can be explained by an orbital instability among the giant planets. A recent model has proposed that the giant planet instability happened during terrestrial planet formation. This scenario has been shown to match the inner solar system by stunting Mars' growth and preventing planet formation in the asteroid belt. Here we present a large sample of new simulations of the "Early Instability" scenario. We use an N-body integration scheme that accounts for collisional fragmentation, and also perform a large set of control simulations that do not include an early …
Many dynamical aspects of the solar system can be explained by the outer planets experiencing a period of orbital instability sometimes called the Nice Model. Though often correlated with a perceived delayed spike in the lunar cratering record known as the Late Heavy Bombardment (LHB), recent work suggests that this event may have occurred much earlier; perhaps during the epoch of terrestrial planet formation. While current simulations of terrestrial accretion can reproduce many observed qualities of the solar system, replicating the small mass of Mars requires modification to standard planet …
The fragility of the Uranian moons during the giant planet instability
Johns Hopkins APL（约翰斯·霍普金斯大学应用物理实验室）；Planetary Science Institute（行星科学研究所）；University of Oklahoma（俄克拉荷马大学）；Rice University（莱斯大学）；Southwest Research Institute（西南研究院）
Axisymmetric disks of high eccentricity, low mass bodies on near-Keplerian orbits are unstable to an out-of-plane buckling. This "inclination instability" exponentially grows the orbital inclinations, raises perihelia distances and clusters in argument of perihelion. Here we examine the instability in a massive primordial scattered disk including the orbit-averaged gravitational influence of the giant planets. We show that differential apsidal precession induced by the giant planets will suppress the inclination instability unless the primordial mass is $\gtrsim 20$ Earth masses. We also show …
The terrestrial planets are believed to have formed by violent collisions of tens of lunar- to Mars-size protoplanets at time t<200 Myr after the protoplanetary gas disk dispersal (t_0). The solar system giant planets rapidly formed during the protoplanetary disk stage and, after t_0, radially migrated by interacting with outer disk planetesimals. An early (t<100 Myr) dynamical instability is thought to have occurred with Jupiter having gravitational encounters with a planetary-size body, jumping inward by ~0.2-0.5 au, and landing on its current, mildly eccentric orbit. Here we investigate how…
Observational evidence suggests that gas disk instability may be responsible for the formation of at least some gas giant exoplanets, particularly massive or distant gas giants. With regard to close-in gas giants, Boss (2017) used the $β$ cooling approximation to calculate hydrodynamical models of inner gas disk instability, finding that provided disks with low values of the initial minimum Toomre stability parameter (i.e., $Q_i < 2$ inside 20 au) form, fragmentation into self-gravitating clumps could occur even for $β$ as high as 100 (i.e., extremely slow cooling). Those results implied that …
Spiral arm structures seen in scattered light observations of protoplanetary disks can potentially serve as signposts of planetary companions. They can also lend unique insights into disk masses, which are critical in setting the mass budget for planet formation but are difficult to determine directly. A surprisingly high fraction of disks that have been well-studied in scattered light have spiral arms of some kind (8/29), as do a high fraction (6/11) of well-studied Herbig intermediate mass stars (i.e., Herbig stars $> 1.5M_\odot$). Here we explore the origin of spiral arms in Herbig systems …
The large scale structure of the Solar System has been shaped by a transient dynamical instability that may have been triggered by the interaction of the giants planets with a massive primordial disk of icy debris. In this work, we investigate the conditions under which this primordial disk could have coalesced into planets using analytic and numerical calculations. In particular, we perform numerical simulations of the Solar System's early dynamical evolution that account for the viscous stirring and collisional damping within the disk. We demonstrate that if collisional damping would have be…
Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt
今天人们普遍认为，我们的太阳系经历了一个阶段，在此期间，巨行星的轨道变得非常不稳定。近年来，许多研究已经确定了这种事件的痕迹，并为这种事件的发生提供了合理的理由。然而，不稳定性的大小（就轨道变化而言）和时间（就气盘的扩散而言，是早是晚）仍然是一个公开的辩论。类地行星似乎设置了严格的约束：要么巨行星不稳定发生得很早，而类地行星仍在形成，要么木星和土星的轨道必须冲动地彼此分离，在半长轴上有足够大的“跳跃”（Brasser et al. 2009; Kaib and Chambers 2016），以使类地行星保持稳定。由于大的轨道跳跃是一个低概率事件，早期不稳定性假说似乎是有利的。然而，假设不稳定幅度不同，小行星带也会以不同的方式演化。这两个约束条件需要相互匹配，以使一个场景优于另一个场景。Morbidelli等人（2010年）考虑到小行星最初的动力学冷盘，得出结论认为，需要一个巨大的跳跃来重建当前的小行星带。在这里，我们确认了相同的结论，但考虑到小行星群已经在离心率方面受到强烈激发，例如在Grand Tack情景中产生的小行星群（Walsh等人，2011年）。由于小行星是在气体盘被移除后才存在的，与类地行星不同，无论不稳定性发生的早或晚，这种对巨行星跳跃宽度的限制都是有效的。因此，在这个阶段，假设早期不稳定性似乎没有提供任何优势，在概率重建的太阳系结构。
Celestial bodies with a mass of M ~ 10 M_Jup have been found orbiting nearby stars. It is unknown whether these objects formed like gas-giant planets through core accretion or like stars through gravitational instability. I show that objects with M <~ 4 M_Jup orbit metal-rich solar-type dwarf stars, a property associated with core accretion. Objects with M >~ 10 M_Jup do not share this property. This transition is coincident with a minimum in the occurrence rate of such objects, suggesting that the maximum mass of a celestial body formed through core accretion like a planet is less than 10 M_J…
Born as ice-rich planetesimals, cometary nuclei were gravitationally scattered onto their current orbits in the Kuiper Belt and the Oort Cloud during the giant planets' dynamical instability in the early stages of our Solar System's history. Here, we model the thermal evolution of planetesimals during and after the giant planet instability. We couple an adapted thermal evolution model to orbital trajectories provided by \textit{N}-body simulations to account for the planetesimals' orbital evolution, a parameter so far neglected by previous thermal evolution studies. Our simulations demonstrate…
Searches for young gas giant planets at wide separations have so far focused on techniques appropriate for compact (Jupiter sized) planets. Here we point out that protoplanets born through Gravitational Instability (GI) may remain in an initial pre-collapse phase for as long as the first $ 10^5-10^7$ years after formation. These objects are hundreds of times larger than Jupiter and their atmospheres are too cold ($T\sim$ tens of K) to emit in the NIR or H$α$ via accretion shocks. However, it is possible that their dust emission can be detected with ALMA, even around Class I and II protoplaneta…
Advances in computing power and numerical methodologies over the past several decades sparked a prolific output of dynamical investigations of the late stages of terrestrial planet formation. Among other peculiar inner solar system qualities, the ability of simulations to reproduce the small mass of Mars within the planets' geochemically inferred accretion timescale of <10 Myr after the appearance of calcium aluminum-rich inclusions (CAIs) is arguably considered the gold standard for judging evolutionary hypotheses. At present, a number of independent models are capable of consistently generat…
The dynamical structure of the Solar System can be explained by a period of orbital instability experienced by the giant planets. While a late instability was originally proposed to explain the Late Heavy Bombardment, recent work favors an early instability. We model the early dynamical evolution of the outer Solar System to self-consistently constrain the most likely timing of the instability. We first simulate the dynamical sculpting of the primordial outer planetesimal disk during the accretion of Uranus and Neptune from migrating planetary embryos during the gas disk phase, and determine t…
The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduces the effective adiabatic index $γ$ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at $γ=4/3$, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all $γ> 1$). When instabil…
We present a semi-analytical population synthesis model of protoplanetary clumps formed by disk instability at radial distances of 80 - 120 AU. Various clump density profiles, initial mass functions, protoplanetary disk models, stellar masses, and gap opening criteria are considered. When we use more realistic gap opening criteria, we find that gaps open only rarely which strongly affects clump survival rates and their physical properties (mass, radius and radial distance). The inferred surviving population is then shifted towards less massive clumps at smaller radial distances. We also find t…
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 M55), 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 M55 is rarely excited to its true value. Here we perform a dynamical analysis of a large batch of artificially triggered instabilities, an…
The non-resonant Kuiper belt objects (KBOs) between the 3:2 and 2:1 Neptunian mean motion resonances can be largely divided between a cold classical belt (CCB) and a hot classical belt (HCB). A notable difference between these two subpopulations is the prevalence of widely spaced, equal-mass binaries in the CCB and a much smaller but non-zero number in the HCB. The primary reason for this difference in binary rate remains unclear. Here using N-body simulations we examine whether close encounters with the giant planets during an early outer solar system instability may have disrupted primordial…
Exoplanet surveys have confirmed one of humanity's (and all teenagers') worst fears: we are weird. If our Solar System were observed with present-day Earth technology -- to put our system and exoplanets on the same footing -- Jupiter is the only planet that would be detectable. The statistics of exo-Jupiters indicate that the Solar System is unusual at the ~1% level among Sun-like stars (or ~0.1% among all stars). But why are we different? Successful formation models for both the Solar System and exoplanet systems rely on two key processes: orbital migration and dynamical instability. Systems …
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）
