scholarly journals A Lagrangian model for dust evolution in protoplanetary disks: formation of wet and dry planetesimals at different stellar masses

2018 ◽  
Vol 620 ◽  
pp. A134 ◽  
Author(s):  
Djoeke Schoonenberg ◽  
Chris W. Ormel ◽  
Sebastiaan Krijt
Keyword(s):  
Accretion Rate ◽  
Protoplanetary Disks ◽  
Particle Method ◽  
Solid Particles ◽  
Lagrangian Model ◽  
Low Mass Stars ◽  
Streaming Instability ◽  
Mass Fluxes ◽  
Gas Accretion ◽  
Stellar Masses

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 following 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 a recent publication. We validated our model by reproducing earlier results from the literature and apply our model to steady-state viscous gas disks (with constant gas accretion rate) around stars with different masses. We also present various other models where we explore the effects of pebble accretion, the fragmentation velocity threshold, the global metallicity of the disk, and a time-dependent gas accretion rate. We find that planetesimals preferentially form in a local annulus outside the water snowline, at early times in the lifetime of the disk (≲105 yr), when the pebble mass fluxes are high enough to trigger the streaming instability. During this first phase in the planet formation process, the snowline location hardly changes due to slow viscous evolution, and we conclude that assuming a constant gas accretion rate is justified in this first stage. The efficiency of converting the solids reservoir of the disk to planetesimals depends on the location of the water snowline. Cooler disks with a closer-in water snowline are more efficient at producing planetesimals than hotter disks where the water snowline is located further away from the star. Therefore, low-mass stars tend to form planetesimals more efficiently, but any correlation may be overshadowed by the spread in disk properties.

scholarly journals Dust clearing by radial drift in evolving protoplanetary discs

2020 ◽  
Vol 638 ◽  
pp. A156 ◽  
Author(s):  
Johan Appelgren ◽  
Michiel Lambrechts ◽  
Anders Johansen
Keyword(s):  
Accretion Rate ◽  
Stellar Mass ◽  
Dust Particles ◽  
Occurrence Rate ◽  
Linear Scaling ◽  
Streaming Instability ◽  
Dust Mass ◽  
Gas Accretion ◽  
Gas Ratio ◽  
Protoplanetary Discs

Recent surveys have revealed that protoplanetary discs typically have dust masses that appear to be insufficient to account for the high occurrence rate of exoplanet systems. We demonstrate that this observed dust depletion is consistent with the radial drift of pebbles. Using a Monte Carlo method we simulate the evolution of a cluster of protoplanetary discs using a 1D numerical method to viscously evolve each gas disc together with the radial drift of dust particles that have grown to 100 μm in size. For a 2 Myr-old cluster of stars, we find a slightly sublinear scaling between the gas disc mass and the gas accretion rate (Mg ∝ Ṁ0.9). However, for the dust mass we find that evolved dust discs have a much weaker scaling with the gas accretion rate, with the precise scaling depending on the age at which the cluster is sampled and the intrinsic age spread of the discs in the cluster. Ultimately, we find that the dust mass present in protoplanetary discs is on the order of 10–100 M⊕ in 1–3 Myr-old star-forming regions, a factor of 10–100 depleted from the original dust budget. As the dust drains from the outer disc, pebbles pile up in the inner disc and locally increase the dust-to-gas ratio by up to a factor of four above the initial value. In these regions of high dust-to-gas ratio we find conditions that are favourable for planetesimal formation via the streaming instability and subsequent growth by pebble accretion. We also find the following scaling relations with stellar mass within a 1–2 Myr-old cluster: a slightly super-linear scaling between the gas accretion rate and stellar mass (Ṁ ∝ M⋆1.4), a slightly super-linear scaling between the gas disc mass and the stellar mass (Mg ∝ M⋆1.4), and a super-linear relation between the dust disc mass and stellar mass (Md ∝ M⋆1.4−4.1).

scholarly journals Phylogeny of the Milky Way’s inner disk and bulge populations: Implications for gas accretion, (the lack of) inside-out thick disk formation, and quenching

2018 ◽  
Vol 618 ◽  
pp. A78 ◽  
Author(s):  
Misha Haywood ◽  
Paola Di Matteo ◽  
Matthew Lehnert ◽  
Owain Snaith ◽  
Francesca Fragkoudi ◽  
...  
Keyword(s):  
Star Formation ◽  
Accretion Rate ◽  
Large Fraction ◽  
Formation Rate ◽  
Thin Disk ◽  
Thick Disk ◽  
Star Formation History ◽  
Two Phase ◽  
Disk Formation ◽  
Gas Accretion

We show that the bulge and the disk of the Milky Way (MW) at R ≲ 7 kpc are well described by a unique chemical evolution and a two-phase star formation history (SFH). We argue that the populations within this inner disk, not the entire disk, are the same, and that the outer Lindblad resonance (OLR) of the bar plays a key role in explaining this uniformity. In our model of a two-phase SFH, the metallicity, [α/Fe] and [α/H] distributions, and age-metallicity relation are all compatible with the observations of both the inner disk and bulge. The dip at [Fe/H] ∼ 0 dex seen in the metallicity distributions of the bulge and inner disk reflects the quenching episode in the SFH of the inner MW at age ∼8 Gyr, and the common evolution of the bulge and inner disk stars. Our results for the inner region of the MW, R ≲ 7 kpc, are consistent with a rapid build-up of a large fraction of its total baryonic mass within a few billion years. We show that at z ≤ 1.5, when the MW was starting to quench, transitioning between the end of the α-enhanced thick disk formation to the start of the thin disk, and yet was still gas rich, the gas accretion rate could not have been significant. The [α/Fe] abundance ratio before and after this quenching phase would be different, which is not observed. The decrease in the accretion rate and gas fraction at z ≤ 2 was necessary to stabilize the disk allowing the transition from thick to thin disks, and for beginning the secular phase of the MW’s evolution. This possibly permitted a stellar bar to develop which we hypothesize is responsible for quenching the star formation. The present analysis suggests that MW history, and in particular at the transition from the thick to the thin disk – the epoch of the quenching – must have been driven by a decrease of the star formation efficiency. We argue that the decline in the intensity of gas accretion, the formation of the bar, and the quenching of the star formation rate (SFR) at the same epoch may be causally connected thus explaining their temporal coincidence. Assuming that about 20% of the gas reservoir in which metals are diluted is molecular, we show that our model is well positioned on the Schmidt-Kennicutt relation at all times.

scholarly journals Effect of hydrodynamic forces on mineral particles trajectories in gravimetric concentrator type JIG

2018 ◽  
Vol 14 (27) ◽  
pp. 68-79
Author(s):  
Manuel Alejandro Ospina ◽  
Liliana María Usuga Manco
Keyword(s):  
Pressure Gradient ◽  
Density Distribution ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
Solid Particles ◽  
Lagrangian Model ◽  
High Yield ◽  
Virtual Mass ◽  
Particle Trajectories ◽  
Continuity Equations

Hydrodynamic interaction is a sensitive process for gravity concentration equipment. Because of the nonlinearity and complexity of interaction dynamics due the solid particles and water, reliable mathematical models are needed to perform plant width design (PWD)-oriented tasks. To this end, in this paper we present a study of particle motion in a water oscillating flow subjected to a sinusoidal profile on a jig device, which is a high yield and high recovery gravimetric concentrator device widely used in minerals processing. A mathematical Eulerian-Lagrangian model (ELM) is used where fluid motion is calculated by solving the Navier-Stokes and continuity equations by a widely used numerical procedure call Semi-Implicit Method for Pressure Linked Equations algorithm (SIMPLE). The motion of individual particles is obtained by a forces balance applying the Newton’s second law of motion through the action of forces imposed by the water and gravity. Liquid-solid interactions forces are calculated by the mathematical Eulerian-Lagrangian model extended to a particle suspension having a wide size and density distribution. The calculation and comparison of Basset, pressure gradient and virtual mass forces with other forces (drag and buoyancy) acting on particle trajectories in water oscillating flows were carried out under turbulent regimen flow. It was found that Basset, pressure gradient and virtual mass forces have a significant effect on the particle’s trajectories affecting their subsequent stratification. Furthermore, the conditions under which these forces can be neglected in the jig’s hydrodynamic model were studied. The study demonstrates significant differences in the particle trajectories for various size and density distribution.

scholarly journals Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores

2021 ◽  
Vol 922 (1) ◽  
pp. 16
Author(s):  
Hiroshi Kobayashi ◽  
Hidekazu Tanaka
Keyword(s):  
Protoplanetary Disks ◽  
Central Star ◽  
Giant Planets ◽  
Solar Systems ◽  
Evolution Path ◽  
Planetary Cores ◽  
Rapid Formation ◽  
Gas Giant ◽  
Planetary Migration ◽  
Gas Accretion

Abstract Gas-giant planets, such as Jupiter, Saturn, and massive exoplanets, were formed via the gas accretion onto the solid cores, each with a mass of roughly 10 Earth masses. However, rapid radial migration due to disk–planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with a lot of effort, the full evolution path from dust to planets is still uncertain. Here we report the result of full simulations for collisional evolution from dust to planets in a whole disk. Dust growth with realistic porosity allows the formation of icy planetesimals in the inner disk (≲10 au), while pebbles formed in the outer disk drift to the inner disk and there grow to planetesimals. The growth of those pebbles to planetesimals suppresses their radial drift and supplies small planetesimals sustainably in the vicinity of cores. This enables rapid formation of sufficiently massive planetary cores within 0.2–0.4 million years, prior to the planetary migration. Our models shows the first gas giants form at 2–7 au in rather common protoplanetary disks, in agreement with the exoplanet and solar systems.

scholarly journals Streaming instability of multiple particle species in protoplanetary disks

2018 ◽  
Vol 618 ◽  
pp. A75 ◽  
Author(s):  
Noemi Schaffer ◽  
Chao-Chin Yang ◽  
Anders Johansen
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Protoplanetary Disks ◽  
Single Species ◽  
Stokes Number ◽  
Dust Particles ◽  
Particle Sizes ◽  
Particle Species ◽  
Streaming Instability ◽  
Large Particles

The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks, as well as the location and timing of planetesimal formation. In this paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We have considered three scenarios in terms of particle size ranges, one where the Stokes number τs = 10−1−100, one where τs = 10−4−10−1, and finally one where τs = 10−3−100. Moreover, we considered both discrete and continuous distributions in particle size. In accordance with previous works we find in our multispecies simulations that different particle sizes interact via the gas and as a result their dynamics changes compared to the single-species case. The larger species trigger the streaming instability and create turbulence that drives the diffusion of the solid materials. We measured the radial equilibrium velocity of the system and find that the radial drift velocity of the large particles is reduced in the multispecies simulations and that the small particle species move on average outwards. We also varied the steepness of the size distribution, such that the exponent of the solid number density distribution, dN∕da ∝ a−q, is either q = 3 or q = 4. Overall, we find that the steepness of the size distribution and the discrete versus continuous approach have little impact on the results. The level of diffusion and drift rates are mainly dictated by the range of particle sizes. We measured the scale height of the particles and observe that small grains are stirred up well above the sedimented midplane layer where the large particles reside. Our measured diffusion and drift parameters can be used in coagulation models for planet formation as well as to understand relative mixing of the components of primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their parent bodies.

scholarly journals The effect of gas accretion on the radial gas metallicity profile of simulated galaxies

2020 ◽  
Vol 495 (3) ◽  
pp. 2827-2843 ◽  
Author(s):  
Florencia Collacchioni ◽  
Claudia D P Lagos ◽  
Peter D Mitchell ◽  
Joop Schaye ◽  
Emily Wisnioski ◽  
...  
Keyword(s):  
Star Formation Rate ◽  
Accretion Rate ◽  
Formation Rate ◽  
Main Property ◽  
Stellar Mass ◽  
Effective Radius ◽  
Mass Star ◽  
Hydrodynamic Simulations ◽  
Gas Accretion ◽  
Gas Fractions

ABSTRACT We study the effect of the gas accretion rate ($\dot{M}_{\rm accr}$) on the radial gas metallicity profile (RMP) of galaxies using the eagle cosmological hydrodynamic simulations, focusing on central galaxies of stellar mass M⋆ ≳ 109 M⊙ at z ≤ 1. We find clear relations between $\dot{M}_{\rm accr}$ and the slope of the RMP (measured within an effective radius), where higher $\dot{M}_{\rm accr}$ are associated with more negative slopes. The slope of the RMPs depends more strongly on $\dot{M}_{\rm accr}$ than on stellar mass, star formation rate (SFR), or gas fraction, suggesting $\dot{M}_{\rm accr}$ to be a more fundamental driver of the RMP slope of galaxies. We find that eliminating the dependence on stellar mass is essential for pinning down the properties that shape the slope of the RMP. Although $\dot{M}_{\rm accr}$ is the main property modulating the slope of the RMP, we find that it causes other correlations that are more easily testable observationally: At fixed stellar mass, galaxies with more negative RMP slopes tend to have higher gas fractions and SFRs, while galaxies with lower gas fractions and SFRs tend to have flatter metallicity profiles within an effective radius.

scholarly journals Dependence of star formation on initial conditions and molecular cloud structure

2010 ◽  
Vol 6 (S270) ◽  
pp. 133-140
Author(s):  
Matthew R. Bate
Keyword(s):  
Star Formation ◽  
Molecular Cloud ◽  
Initial Conditions ◽  
Small Scale ◽  
Low Mass Stars ◽  
Cloud Structure ◽  
Low Mass ◽  
Stellar Properties ◽  
Stellar Masses ◽  
Formation Of Groups

AbstractI review what has been learnt so far regarding the origin of stellar properties from numerical simulations of the formation of groups and clusters of stars. In agreement with observations, stellar properties are found to be relatively robust to variations of initial conditions in terms of molecular cloud structure and kinetics, as long as extreme initial conditions (e.g. strong central condensation, weak or no turbulence) and small-scale driving are avoided, but properties may differ between bound and unbound clouds. Radiative feedback appears crucial for setting stellar masses, even for low-mass stars, while magnetic fields can provide low star formation rates.

Simulation of Particle-Wall Collisions in a Viscous Fluid Using a Resolved Discrete Particle Method

2010 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Efstathis E. Michaelides ◽  
Shaolin Mao
Keyword(s):  
Viscous Fluid ◽  
Numerical Method ◽  
Solid Wall ◽  
Particle Method ◽  
Solid Particles ◽  
Force Density ◽  
Model Parameters ◽  
Discrete Particle ◽  
Soft Sphere ◽  
Discrete Particle Method

The process of particle-wall collisions is very important in understanding and determining the fluid-particle behavior, especially near walls. Detailed information on particle-wall collisions can provide insight on the formulation of appropriate boundary conditions of the particulate phases in two-fluid models. We have developed a three-dimensional Resolved Discrete Particle Method (RDPM) that is capable of meaningfully handling particle-wall collisions in a viscous fluid. This numerical method makes use of a Finite-Difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum equations in the entire flow region. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, and a force density function is introduced to represent the momentum interactions between particle and fluid. We have used this numerical method to study both the central and oblique impact of a spherical particle with a wall in a viscous fluid. The particles are allowed to move in the fluid until they collide with the solid wall. The collision force on the particle is modeled by a soft-sphere collision scheme with a linear spring-dashpot system. The hydrodynamic force on the particle is solved directly from the RDPM. By following the trajectories of a particle, we investigate the effect of the collision model parameters to the dynamics of a particle close to the wall. We report in this paper the rebound velocity of the particle, the coefficient of restitution, and the particle slip velocity at the wall when a variety of different soft-sphere collision parameters are used.

scholarly journals Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy

2021 ◽  
Vol 922 (2) ◽  
pp. 184
Author(s):  
Yi-Xian Chen ◽  
Zhuoxiao Wang ◽  
Ya-Ping Li ◽  
Clément Baruteau ◽  
Douglas N. C. Lin
Keyword(s):  
Mass Distribution ◽  
Protoplanetary Disks ◽  
Mass Function ◽  
Low Viscosity ◽  
Mass Eccentricity ◽  
Tidal Perturbation ◽  
Ring Structures ◽  
Dust Distribution ◽  
Gas Accretion ◽  
Gap Width

Abstract The tidal perturbation of embedded protoplanets on their natal disks has been widely attributed to be the cause of gap-ring structures in submillimeter images of protoplanetary disks around T Tauri stars. Numerical simulations of this process have been used to propose scaling of characteristic dust-gap width/gap-ring distance with respect to planet mass. Applying such scaling to analyze observed gap samples yields a continuous mass distribution for a rich population of hypothetical planets in the range of several Earth to Jupiter masses. In contrast, the conventional core-accretion scenario of planet formation predicts a bimodal mass function due to (1) the onset of runaway gas accretion above ∼20 Earth masses and (2) suppression of accretion induced by gap opening. Here, we examine the dust disk response to the tidal perturbation of eccentric planets as a possible resolution of this paradox. Based on simulated gas and dust distributions, we show the gap-ring separation of Neptune-mass planets with small eccentricities might become comparable to that induced by Saturn-mass planets on circular orbits. This degeneracy may obliterate the discrepancy between the theoretical bimodal mass distribution and the observed continuous gap width distribution. Despite damping due to planet–disk interaction, modest eccentricity may be sustained either in the outer regions of relatively thick disks or through resonant excitation among multiple super Earths. Moreover, the ring-like dust distribution induced by planets with small eccentricities is axisymmetric even in low viscosity environments, consistent with the paucity of vortices in Atacama Large Millimeter/submillimeter Array images.

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