We present 3D smoothed particle hydrodynamics simulations of the collapse of clumps formed through gravitational instability in the outer part of a protoplanetary disc. The initial conditions are taken directly from a global disc simulation, and a realistic equation of state is used to follow the clumps as they contract over several orders of magnitude in density, approaching the molecular hydrogen dissociation stage. The effects of clump rotation, asymmetries, and radiative cooling are studied. Rotation provides support against fast collapse, but non-axisymmetric modes develop and efficiently transport angular momentum outward, forming a circumplanetary disc. This transport helps the clump reach the dynamical collapse phase, resulting from molecular hydrogen dissociation, on a thousand-year timescale, which is smaller than timescales predicted by some previous spherical 1D collapse models. Extrapolation to the threshold of the runaway hydrogen dissociation indicates that the collapse timescales can be shorter than inward migration timescales, suggesting that clumps could survive tidal disruption and deliver a proto-gas giant to distances of even a few AU from the central star.
The streaming instability and Kelvin--Helmholtz instability are considered the two major sources causing clumping of dust particles and turbulence in the dust layer of a protoplanetary disk as long as we consider the dead zone where the magneto-rotational instability does not grow. Extensive numerical simulations have been carried out in order to elucidate the condition for the development of particle clumping caused by the streaming instability. In this paper, a set of two parameters suitable for classifying the numerical results is proposed. One is the Stokes number that has been employed in…
It is well known that massive protoplanetary disc are gravitationally unstable beyond tens of AU from their parent star. The eventual fate of the self-gravitating gas clumps born in the disc is currently not understood, although the range of uncertainty is well known. If clumps migrate inward rapidly, they are tidally disrupted, which may leave behind giant or terrestrial like planets. On the other hand, if clumps migrate less rapidly, they tend to accrete gas, becoming proto brown dwarfs or low mass companions to the parent star. Here we argue that radiative feedback of contracting clumps (pr…
Although it is fairly established that Gravitational Instability (GI) should occur in the early phases of the evolution of a protoplanetary disk, the fate of the clumps resulting from disk fragmentation and their role in planet formation is still unclear. In the present study we investigate semi-analytically their evolution following the contraction of a synthetic population of clumps with varied initial structure and orbits coupled with the surrounding disk and the central star. Our model is based on recently published state-of-the-art 3D collapse simulations of clumps with varied thermodynam…
Planetary systems form in gas-dust protoplanetary discs via the growth of solid bodies. In this paper, we show that the most intriguing stage of such growth --- namely, the transformation of 1-10 m boulders into kilometre-sized planetesimals --- can be explained by a mechanism of gravitational instability. The present work focused on the origin of self-gravitating clumps in which planetesimal formation could take place. Our computer simulations demonstrated that such clumps of gas and boulders formed due to the development of a two-phase instability. This instability revealed a so-called 'mutu…
In order to understand which mechanism is responsible for accretion in protoplanetary discs, a robust knowledge of the observed disc radius using gas tracers such as $^{12}$CO and other CO isotopologues is pivotal. Indeed, the two main theories proposed, viscous accretion and wind-driven accretion, predict different time evolution for the disc radii. In this Letter, we present an analytical solution for the evolution of the disc radii in viscously evolving protoplanetary discs using $^{12}$CO as a tracer, under the assumption that the $^{12}$CO radius is the radius where the surface density of…
In this paper, we investigate whether overdensity formation via streaming instability is consistent with recent multi-wavelength ALMA observations in the Lupus star forming region. We simulate the local action of streaming instability in 2D using the code ATHENA, and examine the radiative properties at mm wavelengths of the resulting clumpy dust distribution by focusing on two observable quantities: the optically thick fraction $ff$ (in ALMA band 6) and the spectral index $α$ (in bands 3-7). By comparing the simulated distribution in the $ff-α$ plane before and after the action of streaming in…
Based on the interstellar CO/H2 ratio, carbon monoxide-based censuses of protoplanetary disks in Lupus, sigma Orionis, and Chamaeleon I found no disks more massive than the minimum-mass solar nebula, which is inconsistent with the existence of exoplanets more massive than Jupiter. Observations and models are converging on the idea that ionization-driven chemistry depletes carbon monoxide in T-Tauri disks. Yet the extent of CO depletion depends on the incident flux of ionizing radiation, and some T-Tauri stars may have winds strong enough to shield their disks from cosmic rays. There is also a …
Spatial distribution and growth of dust in a clumpy protoplanetary disk subject to vigorous gravitational instability and fragmentation is studied numerically with sub-au resolution using the FEOSAD code. Hydrodynamics equations describing the evolution of self-gravitating and viscous protoplanetary disks in the thin-disk limit were modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a variable maximum radius. The conversion of small to grown dust, dust growth, friction of dust with gas, and dust self-gravity were also considered. We found th…
We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results to those …
The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong pa…
Protoplanetary disks form through angular momentum conservation in collapsing dense cores. In this work, we perform the first simulations with a maximal resolution down to the astronomical unit (au) of protoplanetary disk formation, through the collapse of 1000 solar mass clumps, treating self-consistently both non-ideal magnetohydrodynamics with ambipolar diffusion as well as radiative transfer in the flux-limited diffusion approximation including stellar feedback. Using the adaptive mesh-refinement code RAMSES, we investigate the influence of the magnetic field on the disks properties with t…
The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on…
We show results from the radiation hydrodynamics (RHD) simulations of tidal disruption of a star on a parabolic orbit by a supermassive black hole (SMBH) based on a three-dimensional smoothed particle hydrodynamics code with radiative transfer. We find that such a tidally disrupted star fragment and form clumps soon after its tidal disruption. The fragmentation results from the endothermic processes of ionization and dissociation that reduce the gas pressure, leading to local gravitational collapse. Radiative cooling is less effective because the stellar debris is still highly optically thick …
Evolution of dust in a protoplanetary disc driven by stellar flybys: implications for the streaming instability
Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Graduate Institute of Astrophysics, National Taiwan University（國立台灣大學天文研究所）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（歐克拉荷馬大學霍默·L·道奇物理與天文學系）；Department of Physics and Astronomy, The University of Alabama（阿拉巴馬大學物理與天文學系）；Univ. Grenoble Alpes, CNRS, IPAG（格勒諾布爾阿爾卑斯大學、法國國家科學研究中心、IPAG）
We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as ``coagulation instability" and regard it as a promising mechanism to concentrate dust particles and assist planetesimal formation in the very early stages of disk evolution. Because of dust-density dependence of collisional coagulation efficiency, dust particles efficiently (inefficiently) grow in a region of positive (negative) dust density perturbations, which lead to a small radial variation of dust sizes and as a result radial velocity perturbations. The r…
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…
The stochastic nature of migration of disc instability protoplanets in three-dimensional hydrodynamical and MHD simulations of fragmenting discs
University of Zurich（苏黎世大学）；Shanghai Astronomical Observatory, Chinese academy of Science（中国科学院上海天文台）；Department of Astronomy and Astrophysics, University of California, Santa Cruz（加州大学圣克鲁兹分校天体物理学系）；Institute for Advanced Studies, Tsinghua University（清华大学高等研究院）
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…
We investigate streaming instability using two-fluid approximation (neutral gas and dust) in a quasi-global, unstratified protoplanetary disc, with the help of PIERNIK code. We compare amplification rate of the eigen-mode in numerical simulations, with the corresponding growth resulting from the linear stability analysis of full system of Euler's equation including aerodynamic drag. Following Youdin & Goodman (2005) we show that (1) rapid dust clumping occurs due to the difference in azimuthal velocities of gas and dust, coupled by the drag force, (2) initial density perturbations are amplifie…
We study stability of a dust layer in a gaseous disc subject to the linear axisymmetric perturbations. Instead of considering single-size particles, however, the population of dust particles is assumed to consist of two grain species. Dust grains exchange momentum with the gas via the drag force and their self-gravity is also considered. We show that the presence of two grain sizes can increase the efficiency of the linear growth of drag-driven instability in the protoplanetary discs. A second dust phase with a small mass, comparing to the first dust phase, would reduce the growth timescale ev…
We explore the initial conditions for fragments in the extended regions ($r\gtrsim 50$ AU) of gravitationally unstable disks. We combine analytic estimates for the fragmentation of spiral arms with 3D SPH simulations to show that initial fragment masses are in the gas giant regime. These initial fragments will have substantial angular momentum, and should form disks with radii of a few AU. We show that clumps will survive for multiple orbits before they undergo a second, rapid collapse due to H$_2$ dissociation and that it is possible to destroy bound clumps by transporting them into the inner…
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…
We study the origin of tail-like structures recently detected around the disk of SU Aurigae and several FU~Orionis-type stars. Dynamic protostellar disks featuring ejections of gaseous clumps and quiescent protoplanetary disks experiencing a close encounter with an intruder star were modeled using the numerical hydrodynamics code FEOSAD. Both the gas and dust dynamics were taken into account, including dust growth and mutual friction between the gas and dust components. Only plane-of-the-disk encounters were considered. Ejected clumps produce a unique type of tail that is characterized by a bo…
Radiation Hydrodynamics of Self-gravitating Protoplanetary Disks II. Accretion, Migration, Spin, and Internal Structure of GI Fragments
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Department of Astronomy, Tsinghua University（清华大学天文系）
Recent observations have revealed that protoplanetary discs often exhibit cavities and azimuthal asymmetries such as dust traps and clumps. The presence of a stellar binary system in the inner disc regions has been proposed to explain the formation of these structures. Here, we study the dust and gas dynamics in circumbinary discs around eccentric and inclined binaries. This is done through two-fluid simulations of circumbinary discs, considering different values of the binary eccentricity and inclination. We find that two kinds of dust structures can form in the disc: a single horseshoe-shape…
The size distribution of asteroids in the solar system suggests that they formed top-down, with 100-1000 km bodies forming from the gravitational collapse of dense clumps of small solid particles. We investigate the conditions under which solid particles can form dense clumps in a protoplanetary disc. We used a hydrodynamic code to model the solid-gas interaction in disc. We found that particles down to millimeter size can form dense clumps, but only in regions where solids make $\sim$ 8% of the local surface density. More generally, we mapped the range of particle sizes and concentrations tha…
We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $α\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flow…
Using local three dimensional radiation hydrodynamics simulations, the nonlinear outcome of gravitational instability in an irradiated protoplanetary disc is investigated in a parameter space of the surface density $Σ$ and the radius $r$. Starting from laminar flow, axisymmetric self-gravitating density waves grow first. Their self-gravitating degree becomes larger when $Σ$ is larger or the cooling time is shorter at larger radii. The density waves eventually collapse owing to non-axisymmetric instability, which results in either fragmentation or gravito-turbulence after a transient phase. The…
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…
We investigate the conditions required for planet formation via gravitational instability (GI) and protoplanetary disk (PPD) fragmentation around M-dwarfs. Using a suite of 64 SPH simulations with $10^6$ particles, the parameter space of disk mass, temperature, and radius is explored, bracketing reasonable values based on theory and observation. Our model consists of an equilibrium, gaseous, and locally isothermal disk orbiting a central star of mass $M_*=M_{sol}/3$. Disks with a minimum Toomre $Q$ of $Q_{min} \lesssim 0.9$ will fragment and form gravitationally bound clumps. Some previous lit…
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…
The development of perturbations in the circumstellar disks of pre-main-sequence stars caused by clumpy accretion was investigated. Here we perform 3D hydrodynamical smoothed particle hydrodynamics simulations of disks perturbed by a recent clump accretion event. These simulations are further explored by radiative transfer calculations to quantify the observational appearance of such disks. It was shown that the density waves in the disks were formed at the fall of the clump. After several revolutions they can transform into spirals and ring structures. Their images in millimeter wavelengths a…
The processes that led to the formation of the planetary bodies in the Solar System are still not fully understood. Using the results obtained with the comprehensive suite of instruments on-board ESA's Rosetta mission, we present evidence that comet 67P/Churyumov-Gerasimenko likely formed through the gentle gravitational collapse of a bound clump of mm-sized dust aggregates ("pebbles"), intermixed with microscopic ice particles. This formation scenario leads to a cometary make-up that is simultaneously compatible with the global porosity, homogeneity, tensile strength, thermal inertia, vertica…
The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping…
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…
There has been disagreement currently about whether cooling in protoplanetary disks can be sufficiently fast to induce the formation of gas giant protoplanets via gravitational instabilities. Simulations by our own group and others indicate that this method of planet formation does not work for disks around young, low- mass stars inside several tens of AU, while simulations by other groups show fragmentation into protoplanetary clumps in this region. To allow direct comparison in hopes of isolating the cause of the differences, we here present a high resolution three-dimensional hydrodynamics …
We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary disks, which may be important for planetesimal formation. The study is based on the recognition that dust-gas mixtures are generically unstable to a Resonant Drag Instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the "streaming instability" is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest-growing wavelengths. We extend this ana…
Direct imaging observations constrain the fraction of stars orbited by gas giant planets with separations greater than 10 au to about 0.01 only. This is widely believed to indicate that massive protoplanetary discs rarely fragment on planetary mass objects. I use numerical simulations of gas clumps embedded in massive gas discs to show that these observations are consistent with $\sim 0.2 - 10$ planetary mass clumps per star being born in young gravitationally unstable discs. A trio of processes -- rapid clump migration, tidal disruption and runaway gas accretion -- destroys or transforms all …
The streaming instability is a promising mechanism to induce the formation of planetesimals. Nonetheless, this process has been found in previous studies to require either a dust-to-gas surface density ratio or a dust size that is enhanced compared to observed values. Employing two-dimensional global simulations of protoplanetary disks, we show that the vertical shear instability and the streaming instability in concert can cause dust concentration that is sufficient for planetesimal formation for lower surface density ratios and smaller dust sizes than the streaming instability in isolation, …
Core Accretion, the most widely accepted scenario for planet formation, postulates existence of km-sized solid bodies, called planetesimals, arranged in a razor-thin disc in the earliest phases of planet formation. In the Tidal Downsizing hypothesis, an alternative scenario for formation of planets, grain growth, sedimentation and formation of planetary cores occur inside dense and massive gas clumps formed in the outer cold disc by gravitational instability. As a clump migrates inward, tidal forces of the star remove all or most of the gas from the clump, downsizing it to a planetary mass bod…
We study the utility of the [OI] 6300$\mathring{\mathrm A}$ forbidden line for identifying and interpreting externally driven photoevaporative winds in different environments and at a range of distances. Thermally excited [OI] 6300$\mathring{\mathrm A}$ is a well known tracer of inner disc winds, so any external contribution needs to be distinguishable. In external winds, the line is not thermally excited and instead results from the dissociation of OH and we study how the line luminosity resulting from that process scales with the disc/environmental parameters. We find that the line luminosit…
Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1-D models and 3-D simulations to calculate the envelopes around low-mass cores (several to tens of $M_{\oplus}$) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is opt…
(Abridged) We present local 2D and 3D hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time tau_s=Omega t_stop=1e-4 to marginally coupl…
We present molecular line observations of 13CO and C18O J=3-2, CN N = 3 - 2, and CS J=7-6 lines in the protoplanetary disk around TW Hya at a high spatial resolution of ~9 au (angular resolution of 0.15''), using the Atacama Large Millimeter/Submillimeter Array. A possible gas gap is found in the deprojected radial intensity profile of the integrated C18O line around a disk radius of ~58 au, slightly beyond the location of the au-scale dust clump at ~52 au, which resembles predictions from hydrodynamic simulations of planet-disk interaction. In addition, we construct models for the physical an…
It is shown that gas-dust perturbations in a disc with dust settling to the disc midplane exhibit the non-linear three-wave resonant interactions between streaming dust wave (SDW) and two inertial waves (IW). In the particular case considered in this paper, SDW at the wavenumber $k^\bullet = 2κ/ (g_z t_s)$, where $κ$, $g_z$ and $t_s$ are, respectively, epicyclic frequency, vertical gravitational acceleration and particle's stopping time, interacts with two IW at the lower wavenumbers $k^\prime$ and $k^{\prime\prime}$ such that $k^\prime < k_{\rm DSI} < k^{\prime\prime} < k^\bullet$, where $k_{…
Observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability, but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear. The controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process. The latter refers largely to the handling of radiative transfer in three dimensional (3D) hydrodynamical models, which controls heating and cooling processes in gravitationally unstable disks, and hence de…
In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. MHD disc models also suggest the existence of a dead-zone at $R\lesssim 10$ AU, where the regions close to the midplane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet ($\sim 1.7 \;{\rm M_\oplus}$) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio $ε\ge 0.5$. For pebbles with Stokes numbers St=0.1, 0.5, multiple dusty …
