When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are obtained as a function of planetesimals' eccentricity, inclination, planet's radius, and non-dimensional gas-drag parameters which can be expressed by several physical quantities such as the radius of planetesimals and the mass of the protoplanet. Assuming that the radial distribution of the gas density near the surface can be approximated by a power-law, we performed analytic calculation for the loss of planetesimals' kinetic energy due to gas drag, and confirmed agreement with numerical results. We confirmed that the above approximation of the power-law density distribution is reasonable for accretion rate of protoplanets with one to ten Earth-masses, unless the size of planetesimals is too small. We also calculated the accretion rates of planetesimals averaged over a Rayleigh distribution of eccentricities and inclinations, and derived a semi-analytical formula of accretion rates, which reproduces the numerical results very well. Using the obtained expression of the accretion rate, we examined the growth of protoplanets in nebular gas. We found that the effect of atmospheric gas drag can enhance the growth rate significantly, depending on the size of planetesimals.
Using self-consistent models of turbulent particle growth in an evolving protoplanetary nebula of solar composition we find that recently proposed local metallicity and Stokes number criteria necessary for the streaming instability to generate gravitationally bound particle overdensities are generally not approached anywhere in the disk during the first million years, an epoch in which meteoritic and observational evidence strongly suggests that the formation of the first planetesimals and perhaps giant planet core accretion is already occurring.
On the dynamics of planetesimals embedded in turbulent protoplanetary discs
原行星盘中的角动量输运和吸积通常被认为是由MHD湍流通过磁旋转不稳定性（MRI）驱动的。嵌入这些圆盘中的固体（尘埃颗粒、巨石、微行星和行星）的动力学可能受到湍流的强烈影响，因此行星系的形成路径部分取决于湍流的强度和空间分布。我们使用三维MHD模拟研究了嵌入湍流原行星盘中的半径在1米至10公里之间的微行星的动力学。微行星受到气体阻力和随机引力的作用，这是由于湍流盘造成的。在这项研究中，我们使用并比较了局部剪切箱模拟和全球模型的结果。这项工作的主要目的是检查：的增长，和可能的饱和度，嵌入式微行星的速度色散作为其大小和光盘参数的函数;微行星的径向迁移和扩散的速率;剪切盒和全球模拟结果一致的条件下。当使用尺寸为4 H x 16 H x 2 H的剪切盒（H为局部尺度高度）时，我们发现局部和全局模拟之间存在良好的一致性。由于螺旋密度波的激发和传播，所获得的密度波动的幅度对盒子的尺寸敏感。这影响了微行星所经历的随机强迫。[...]我们的模型表明，充分发展的MHD湍流在原行星盘将嵌入星子的破坏性影响。相对较低的湍流水平需要的星子吸积的传统模型的运作，这是一致的存在一个死区的原行星盘。
Nearly-axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We test this hypothesis by performing global 1-D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore dif…
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplaneta…
Modelling circumbinary protoplanetary disks II. Gas disk feedback on planetesimal dynamical and collisional evolution in the circumbinary systems Kepler-16 and 34
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…
In the standard model for giant planet formation, the planetary growth begins with accretion of solids followed by a buildup of a gaseous atmosphere as more solids are accreted, and finally, by rapid accretion of gas. The interaction of the solids with the gaseous envelope determines the subsequent planetary growth and the final internal structure. In this work we simulate the interaction of planetesimals with a growing giant planet (proto-Jupiter) and investigate how different treatments of the planetesimal-envelope interaction affect the heavy-element distribution, and the inferred core mass…
Planetesimal and Protoplanet Dynamics in a Turbulent Protoplanetary Disk: Ideal Stratified Disks
由于气体盘中磁旋转不稳定性驱动的密度波动的引力影响，微行星和原行星经历扩散径向迁移以及其他轨道性质的变化。对粒子轨道影响的大小可能对行星形成的情景产生重要影响。我们使用本地剪切盒近似来模拟一个理想的，等温的，磁化的气体盘与垂直密度分层，并同时演化的气体和宿主恒星的引力场下移动的许多无质量的粒子。我们测量的粒子轨道特性的演变，包括平均半径，偏心率，倾角，和速度色散，其依赖于磁盘的属性和粒子的初始条件。虽然结果收敛与分辨率为固定的盒子尺寸，我们发现的颗粒的湍流气体的重力的响应与水平的盒子大小，高达16个磁盘规模的高度。这种相关性表明，在解释涉及磁旋转湍流引力物理学的局部剪切盒模型时应谨慎。然而，基于启发式的论证，我们提出了L_h / R ~ O（1）准则，其中L_h是水平盒子的大小，R是到主星的距离，从而可能地解决这个难题。如果这一标准成立，我们仍然可以得出结论，磁旋转湍流似乎是无效的驱动扩散迁移或碰撞侵蚀在大多数情况下。
Studies of internal structure of gas giant planets suggest that their envelopes are enriched with heavier elements than hydrogen and helium relative to their central stars. Such enrichment likely occurred by solid accretion during late formation stages of gas giant planets in which gas accretion dominates protoplanetary growth. Some previous studies performed orbital integration of planetesimals around a growing protoplanet with the assumption of an uniform circumstellar disc to investigate how efficiently the protoplanet captures planetesimals. However, not only planetesimals but also disc ga…
On the accumulation of planetesimals near disc gaps created by protoplanets
我们已经进行了三维二维流体（气尘）流体动力学模型的拱盘嵌入原行星（3 - 333 M \oplu）和小固体（半径10厘米至10米）。我们发现，大质量行星（\gtrsim土星质量）在气体盘中打开足够深的间隙，使得间隙外缘的密度最大值可以非常有效地捕获米级固体。这允许固体在间隙的外边缘处积聚，因为固体从大半径螺旋向内到捕获区域。对于那些向内螺旋最快的物体，通常是米大小的巨石，这种积累过程发生得最快，而较小和较大的物体在圆盘的寿命内不会足够快地迁移以从该过程中受益。在木星质量的行星周围，我们发现可能会形成与几个地球质量一样大的固体物质的束缚团块，可能会在自引力下坍塌形成行星或微行星。这些结果与Lyra et al.（2009）一致，支持他们的发现，即第二代微行星或类地行星的形成可能是由高质量行星的存在引发的。
Planet formation around one component of a tight, eccentric binary system such as $γ$ Cephei (with semimajor axis around 20 AU) is theoretically challenging because of destructive high-velocity collisions between planetesimals. Despite this fragmentation barrier, planets are known to exist in such orbital configurations. Here we present a novel numerical framework for carrying out multi-annulus coagulation-fragmentation calculations of planetesimal growth, which fully accounts for the specifics of planetesimal dynamics in binaries, details of planetesimal collision outcomes, and the radial tra…
Aeolian-erosion is a destructive process which can erode small-size planetary objects through their interaction with a gaseous environment. Aeolian-erosion operates in a wide range of environments and under various conditions. Aeolian-erosion has been extensively explored in the context of geophysics in terrestrial planets. Here we show that aeolian-erosion of cobbles, boulders and small planetesimals in protoplanetary-discs can constitute a significant barrier for the early stages of planet formation. We use analytic calculations to show that under the conditions prevailing in protoplanetary-…
We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from…
Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a dead zone. In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism. We improve upon the previous study of the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. We performed 1D diffusion-advection simulations of drifting pebbles…
The first stages of planet formation take place in protoplanetary disks that are largely made up of gas. Understanding how the gas affects planetesimals in the protoplanetary disk is therefore essential. In this paper, we discuss whether or not gas flow can erode planetesimals. We estimate how much shear stress is exerted onto the planetesimal surface by the gas as a function of disk and planetesimal properties. To determine whether erosion can take place, we compare this with previous measurements of the critical stress that a pebble-pile planetesimal can withstand before erosion begins. If e…
Planetesimal Formation under Realistic Gas Dynamics: Dust Concentration in Turbulent and Windy Protoplanetary Disks
CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院行星科学重点实验室、紫金山天文台）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Astronomy, Tsinghua University（清华大学天文学系）
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
Planet formation begins with collisional growth of small planetesimals accumulating into larger ones. Such growth occurs while planetesimals are embedded in a gaseous protoplanetary disc. However, small-planetesimals experience collisions and gas-drag that lead to their destruction on short timescales, not allowing, or requiring fine tuned conditions for the efficient growth of $\sim$ metre-size objects. Here we show that $\sim10^{4}$ interstellar objects such as the recently detected 1I/2017-U1 ('Oumuamua) could have been captured, and become part of the young Solar System, together with up t…
We explore the growth of planetary embryos by planetesimal accretion up to and beyond the point where pebble accretion becomes efficient at the so-called Hill-transition mass. Both the transition mass and the characteristic mass of planetesimals formed by the streaming instability increase with increasing distance from the star. We developed a model for the growth of a large planetesimal (embryo) embedded in a population of smaller planetesimals formed in a filament by the streaming instability. The model includes in a self-consistent way the collisional mass growth of the embryo, the fragment…
Highly porous dust aggregates can break through the radial drift barrier, but previous studies assumed disks in their later stage, where the disks have a very small mass and low temperature. In contrast, dust coagulation should begin in the very early stage such as the disk formation stage because the growth timescale of dust is shorter than the disk formation timescale if there is no process to suppress the collisional growth of dust. We investigate the possibility of planetesimal formation via direct collisional growth in the very early stage of a protoplanetary disk. We show that, in the ve…
Protoplanets develop via collisions between planetesimals and planetary embryos in the final assembly stage of planet formation. The efficiency of the planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of embryos and planetesimals. In final assembly planet formation models, the gravitational interactions between planetesimals are usually neglected due to computational difficulties, namely, computations require fewer resources in this way. We investigated the effect of this simplification via modeling the planet formation efficiency in a circumste…
Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary first step to planetesimal formation. In laminar discs, dust settling is an efficient mechanism to raise the dust-to-gas ratio at the disc midplane. However, turbulence, if present, can stir and lift dust particles, which ultimately hinders planetesimal formation. In this work, we study dust settling in protoplanetary discs with hydrodynamic turbulence sustained by the vertical shear instability. We perform axisymmetric numerical simulations to investigate the effect of turbulence, particle size, and solid abundance o…
The formation of the first planetesimals and the final growth of planetary cores relies on the abundance of small pebbles. The efficiencies of both the streaming instability (SI) process, suggested to catalyze the early growth of planetesimals, and the pebble-accretion process, suggested to accelerate the growth of planetary cores, depend on the sizes of solids residing in the disk. In particular, these processes were found to be sensitive to size distribution of solids, and efficient planetesimal formation and growth through these channels require a limited pebble size distribution. Here we s…
We study how the interaction between the streaming instability and intrinsic gas-phase turbulence affects planetesimal formation via gravitational collapse in protoplanetary disks. Turbulence impedes the formation of particle clumps by acting as an effective turbulent diffusivity, but it can also promote planetesimal formation by concentrating solids, for example in zonal flows. We quantify the effect of turbulent diffusivity using numerical simulations of the streaming instability in small local domains, forced with velocity perturbations that establish approximately Kolmogorov-like turbulenc…
The streaming instability (SI) is one of the most promising candidates for triggering planetesimal formation by producing dense dust clumps that undergo gravitational collapse. Understanding how the SI operates in realistic protoplanetary disks (PPDs) is therefore crucial to assess the efficiency of planetesimal formation. Modern models of PPDs show that large-scale magnetic torques or winds can drive laminar gas accretion near the disk midplane. In a previous study, we identified a new linear dust-gas instability, the azimuthal drift SI (AdSI), applicable to such accreting disks and is powere…
We develop simple, physically motivated models for drag-induced dust-gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary disks. The models explain, based on the physics of gaseous epicyclic motion and dust-gas drag forces, the most important features of the streaming instability and its simple generalisation, the disk settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas-mass ratio surpasses one, the slow growth r…
