In the context of massive fragmenting protoplanetary discs, Boss (1998) suggested that grains can grow and sediment inside giant planet embryos formed at R ~ 5 AU away from the star. Several authors since then criticised the suggestion. Convection may prevent grain sedimentation, and the embryos cannot even form so close to the parent star as cooling is too inefficient at these distances. Here we reconsider the grain sedimentation process suggested by Boss (1998) but inside an embryo formed, as expected in the light of the cooling constraints, at R ~ 100 AU. Such embryos are much less dense and are also cooler. We make analytical estimates of the process and also perform simple spherically symmetric radiation hydrodynamics simulations to test these ideas. We find that convection in our models does not become important before a somewhat massive (~ an Earth mass, this is clarified in a followup paper) solid core is built. Turbulent mixing slows down dust sedimentation but is overwhelmed by grain sedimentation when the latter grow to a centimetres size. The minimum time required for dust sedimentation to occur is a few thousand years, and is a strong function of the embryo's mass, dust content and opacity. An approximate analytical criterion is given to delineate conditions in which a giant embryo contracts and heats up faster than dust can sediment. As Boss et al (2002), we argue that core formation through grain sedimentation inside the giant planet embryos may yield an unexplored route to form giant gas and giant ice planets. The present model also stands at the basis of paper III, where we study the possibility of forming terrestrial planet cores by tidal disruption and photoevaporation of the planetary envelope.
Recently, the gravitational instability (GI) model of giant planet and brown dwarf formation has been revisited and recast into what is often referred to as the "tidal downsizing" hypothesis. The fragmentation of self-gravitating protostellar discs into gravitationally bound embryos - with masses of a few to tens of Jupiter masses, at semi major axes above 30 - 40 au - is followed by grain sedimentation inside the embryo, radial migration towards the central star and tidal disruption of the embryo's upper layers. The properties of the resultant object depends sensitively on the timescales upon…
In this paper, we reexamine the possibility of shear-driven turbulence during sedimentation of dust grains in the protoplanetary disk. The shear-driven turbulence is expected to occur before the onset of the gravitational instability for MMSN model. While according to previous studies without taking account of growth of dust grains, with the larger abundance of dust grains, the gravitational instability is indicated to occur before shear-driven turbulence. In this paper, the case with dust growth is considered, and it is found that the Kelvin-Helmholtz instability tends to occur before the gra…
Giant planet embryos are believed to be spawned by gravitational instability in massive extended (R ~ 100 AU) protostellar discs. In a recent paper we have shown that dust can sediment inside the embryos, as argued earlier by Boss (1998) in a slightly different model. Here we study numerically the next stage of this process -- the formation of a solid core. If conditions are conducive to solid core formation, the centre of the gas cloud goes through the following sequence of phases: (i) becomes grain (and metal) rich; (ii) forms a terrestrial mass solid core via a rapid collapse driven by self…
We present a self-consistent model of a protoplanetary disk: 'ANDES' ('AccretioN disk with Dust Evolution and Sedimentation'). ANDES is based on a flexible and extendable modular structure that includes 1) a 1+1D frequency-dependent continuum radiative transfer module, 2) a module to calculate the chemical evolution using an extended gas-grain network with UV/X-ray-driven processes surface reactions, 3) a module to calculate the gas thermal energy balance, and 4) a 1+1D module that simulates dust grain evolution. For the first time, grain evolution and time-dependent molecular chemistry are in…
It has been proposed recently that the first step in the formation of both rocky and gas giant planets is dust sedimentation into a solid core inside a gas clump (giant planet embryo). The clumps are then assumed to migrate closer to the star where their metal poor envelopes are sheared away by the tidal forces or by an irradiation-driven mass loss. We consider the implications of this hypothesis for natal rotation rates of both terrestrial and gas giant planets. It is found that both types of planets may rotate near their break up angular frequencies at birth. The direction of the spin should…
Circumstellar discs are expected to be the nursery of planets. Grain growth within such discs is the first step in the planet formation process in the core-accretion gas-capture scenario. We aim at providing selected criteria on observational quantities derived from multi-wavelength imaging observations that allow to identify dust grain growth and settling. We define a wide-ranged parameter space of discs in various states of their evolution. Using a parametrised model set-up and radiative transfer techniques we compute multi-wavelength images of discs at different inclinations. Using millimet…
The basic structure of the solar system is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot e…
Just a Phase? Weakening Vertical Shear Instability Explains Class II Disk Morphologies: Simulations with dust coagulation, sedimentation, thermal relaxation, and backreaction
Flatiron Institute（平顿研究所）；Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Columbia University（哥伦比亚大学）；Stony Brook University（石溪大学）
We consider the observational signatures of giant impacts between planetary embryos. While the debris released in the impact remains in a clump for only a single orbit, there is a much longer lasting asymmetry caused by the fact that all debris must pass through the collision-point. The resulting asymmetry is stationary, it does not orbit the star. The debris is concentrated in a clump at the collision-point, with a more diffuse structure on the opposite side. The asymmetry lasts for typically around 1000 orbital periods of the progenitor, which can be several Myr at distances of ~50 AU. We de…
Depending on their sizes, dust grains store more or less charges, catalyse more or less chemical reactions, intercept more or less photons and stick more or less efficiently to form embryos of planets. Hence the need for an accurate treatment of dust coagulation and fragmentation in numerical modelling. However, existing algorithms for solving the coagulation equation are over-diffusive in the conditions of 3D simulations. We address this challenge by developing a high-order solver based on the Discontinuous Galerkin method. This algorithm conserves mass to machine precision and allows to comp…
We investigate dust growth due to settling in a 1D vertical column of a protoplanetary disk. It is known from the observed 10 micron feature in disk SEDs, that small micron-sized grains are present at the disk atmosphere throughout the lifetime of the disk. We hope to explain such questions as what process can keep the disk atmospheres dusty for the lifetime of the disk and how does the particle properties change as a function of height above the midplane. We use a Monte Carlo code to follow the mass and porosity evolution of the particles in time. The used collision model is based on laborato…
We investigate the critical core mass and the envelope growth timescale, assuming grain-free envelopes, to examine how small cores are allowed to form gas giants in the framework of the core accretion model. This is motivated by a theoretical dilemma concerning Jupiter formation: Modelings of Jupiter's interior suggest that it contains a small core of < 10 Earth mass, while many core accretion models of Jupiter formation require a large core of > 10 Earth mass to finish its formation by the time of disk dissipation. Reduction of opacity in the accreting envelope is known to hasten gas giant fo…
The growth of dust particles into planet embryos needs to circumvent the radial-drift barrier, i.e. the accretion of dust particles onto the central star by radial migration. The outcome of the dust radial migration is governed by simple criteria between the dust-to-gas ratio and the exponents p and q of the surface density and temperature power laws. The transfer of radiation provides an additional constraint between these quantities because the disc thermal structure is fixed by the dust spatial distribution. To assess which discs are primarily affected by the radial-drift barrier, we used t…
In laboratory experiments, we study the motion of levitated, sedimenting clouds of sub-mm grains at low ambient pressure and at high solid-to-gas ratios $ε$. The experiments show a collective behavior of particles, i.e. grains in clouds settle faster than an isolated grain. In collective particle clouds, the sedimentation velocity linearly depends on $ε$ and linearly depends on the particle closeness $C$. However, collective behavior only sets in at a critical value $ε_{\rm crit}$ which linearly increases with the experiment Stokes number St. For $\rm St <0.003 $ particles always behave collec…
Observations of protoplanetary disks provide information on planet formation and the reasons for the diversity of planetary systems. The key to understanding planet formation is the study of dust evolution from small grains to pebbles. Smaller grains are well-coupled to the gas dynamics, and their distribution is significantly extended above the disk midplane. Larger grains settle much faster and are efficiently formed only in the midplane. By combining near-infrared polarized light and millimeter observations, it is possible to constrain the spatial distribution of both the small and large gr…
One of the most challenging steps in planet formation theory is the one leading to the formation of planetesimals of kilometre size. A promising scenario involves the existence of vortices able to concentrate a large amount of dust and grains in their centres. Up to now this scenario has been studied mostly in 2D razor thin disks. A 3D study including, simultaneously, the formation and resulting dust concentration of the vortices with vertical settling, was still missing. The Rossby wave instability self-consistently forms 3D vortices, which have the unique quality of presenting a large scale …
We use SPH simulations with an approximate radiative cooling prescription to model evolution of a massive and large ($\sim 100$ AU) very young protoplanetary disc. We also model dust growth and gas-grain dynamics with a second fluid approach. It is found that the disc fragments onto a large number of $\sim 10$ Jupiter mass clumps that cool and contract slowly. Some of the clumps evolve onto eccentric orbits delivering them into the inner tens of AU, where they are disrupted by tidal forces from the star. Dust grows and sediments inside the clumps, displaying a very strong segregation, with the…
Dust emission mechanisms as one aspect of wind-driven particle motion on planetary surfaces are still poorly understood. The microphysics is important though as it determines dust sizes and morphologies which set sedimentation speeds and optical properties. We consider the effects of tribocharging in this context as grains in wind driven granular matter charge significantly. This leads to large electric fields above the granular bed. Airborne dielectric grains are polarized in these electric fields, which leads to attractive forces between grains. To simulate aggregation under these conditions…
Axisymmetric dust rings containing tens to hundreds of Earth masses of solids have been observed in protoplanetary discs with (sub-)millimetre imaging. Here, we investigate the growth of a planetary embryo in a massive (150M$_\oplus$) axisymmetric dust trap through dust and gas hydrodynamics simulations. When accounting for the accretion luminosity of the planetary embryo from pebble accretion, the thermal feedback on the surrounding gas leads to the formation of an anticyclonic vortex. Since the vortex forms at the location of the planet, this has significant consequences for the planet's gro…
Numerical simulations of pebble dynamics inside gas clumps formed by gravitational instability of protoplanetary discs are presented. We find that dust-mediated Rayleigh-Taylor instabilities transport pebbles inward rapidly via dense metal-rich "fingers". This speeds up sedimentation of small pebbles by up to two orders of magnitude and yet does not impede grain growth because grains of all sizes sediment at the same collective speed as long as Stokes number is less than unity. In simulations with a fixed pebble size, solid planetary cores form if pebble size exceeds a few cm. Pebble growth le…
Observations indicate that large, dust-laden protoplanetary discs are common. Some features, like gaps, rings and spirals, suggest they may host young planets, which can excite the orbits of nearby leftover planetesimals. Energetic collisions among these bodies can lead to the production of second-generation dust. Grains produced by collisions may have a dynamical behaviour different from that of first-generation, primordial dust out of which planetesimals and planets formed. We aim to study these differences for the HD 163296 system and determine whether dynamical signatures in the mixture of…
Giant planet formation in the core accretion (CA) paradigm is predicated by the formation of a core, assembled by the coagulation of grains and later by planetesimals within a protoplanetary disc. In contrast, in the disc instability paradigm, giant planet formation is believed to be independent of core formation: massive self-gravitating gas fragments cool radiatively and collapse as a whole. We show that giant planet formation in the disc instability model may be also enhanced by core formation for reasons physically very similar to the CA paradigm. In the model explored here, efficient grai…
[Abridged] Combining a time-dependent astrochemical model with a model of planet formation and migration, we compute the carbon-to-oxygen ratio (C/O) of a range of planetary embryos starting their formation in the inner solar system (1-3 AU). The volatile and ice abundance of relevant carbon and oxygen bearing molecular species are determined through a complex chemical kinetic code which includes both gas and grain surface chemistry. This is combined with a model for the abundance of the refractory dust grains to compute the total carbon and oxygen abundance in the protoplanetary disk availabl…
Depending on the stellar densities, protoplanetary discs in stellar clusters undergo background heating, disc truncation-driven by stellar encounter, and photo-evaporation. Disc truncation leads to reduced characteristic sizes and disc masses that eventually halts gas giant planet formation. We investigate how disc truncation impacts planet formation via pebble-based core accretion paradigm, where pebble sizes were derived from the full grain-size distribution within the disc lifetimes. We make the best-case assumption of one embryo and one stellar encounter per disc. Using planet population s…
This paper considers the dynamics of scattering of planetesimals or planetary embryos by a planet on a circumstellar orbit. We classify six regions in the planet's mass versus semimajor axis parameter space according to the dominant outcome for scattered objects: ejected, accreted, remaining, escaping, Oort Cloud, depleted Oort Cloud. We use these outcomes to consider which planetary system architectures maximise the observability of specific signatures, given that signatures should be detected first around systems with optimal architectures (if such systems exist in nature). Giant impact debr…
