Catching drifting pebbles II. A stochastic equation of motions for pebbles

Abstract

Turbulence plays a key role in the transport of pebble-sized particles. It also affects the ability of pebbles to be accreted by protoplanets, because it stirs pebbles out of the disk midplane. In addition, turbulence can suppress pebble accretion once the relative velocities become too large for the settling mechanism to be viable. Following Paper I, we aim to quantify these effects by calculating the pebble accretion efficiency $\epsilon$ using three-body simulations. To model the effect of turbulence on the pebbles, we derive a stochastic equation of motion (SEOM) applicable to stratified disk configurations. In the strong coupling limit (ignoring particle inertia) the limiting form of this equation agrees with previous works. We conduct a parameter study and calculate $\epsilon$ in 3D, varying pebble and gas (turbulence) properties and accounting for the planet inclination. We find that strong turbulence suppresses pebble accretion through turbulent diffusion, agreeing within factors of order unity with previous works. Another reduction of $\epsilon$ occurs when the turbulent rms motions are large and the settling mechanism fails. Efficiency-wise, the outer disk regions are more affected by turbulence than the inner regions. At the location of the H${}_2$O iceline, planets around low-mass stars achieve much higher efficiencies. Including the results from Paper I, we present a framework to obtain $\epsilon$ under general circumstances.

arXiv commentaccepted version

References in corpus (38)

• Gas- and dust evolution in protoplanetary disks
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• Forming the cores of giant planets from the radial pebble flux in protoplanetary discs
• Separating gas-giant and ice-giant planets by halting pebble accretion
• Radial Flow of Dust Particles in Accretion Disks
• Linear and nonlinear evolution of the vertical shear instability in accretion discs
• An ALMA Survey of Protoplanetary Disks in the $\sigma$ Orionis Cluster
• Pebble isolation mass --- scaling law and implications for the formation of super-Earths and gas giants
• Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
• Weak Turbulence in the HD 163296 Protoplanetary Disk Revealed by ALMA CO Observations
• A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO${}^{+}$
• The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores
• Growing the gas-giant planets by the gradual accumulation of pebbles
• Planetesimal formation near the snowline: in or out?
• Inside-Out Planet Formation
• Evolution of Protoplanetary Discs with Magnetically Driven Disc Winds
• Dust Growth and Settling in Protoplanetary Disks and Disk Spectral Energy Distributions. I. Laminar Disks
• Lupus disks with faint CO isotopologues: low gas/dust or large carbon depletion?
• Vertical shear instability in accretion disc models with radiation transport
• Formation of dust-rich planetesimals from sublimated pebbles inside of the snow line
• Direct imaging of the water snow line at the time of planet formation using two ALMA continuum bands
• Accretion and destruction of planetesimals in turbulent disks
• Planetary Growth with Collisional Fragmentation and Gas Drag
• The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
• On the evolution of mean motion resonances through stochastic forcing: Fast and slow libration modes and the origin of HD128311
• On the dynamics of planetesimals embedded in turbulent protoplanetary discs
• Turbulent diffusion in protoplanetary discs: the effect of an imposed magnetic field
• Dead zones as safe-havens for planetesimals: influence of disc mass and external magnetic field
• The formation of systems with closely spaced low-mass planets and the application to Kepler-36
• Anisotropic hydrodynamic turbulence in accretion disks
• 3D Lagrangian turbulent diffusion of dust grains in a protoplanetary disk: method and first applications
• Effect of dust radial drift on viscous evolution of gaseous disk
• On the filtering and processing of dust by planetesimals 1. Derivation of collision probabilities for non-drifting planetesimals
• The steady-state flow pattern past gravitating bodies
• The growth of planets by pebble accretion in evolving protoplanetary discs
• Particle accretion onto planets in discs with hydrodynamic turbulence
• Steamworlds: atmospheric structure and critical mass of planets accreting icy pebbles
• Toward realistic simulations of magneto-thermal winds from weakly-ionized protoplanetary disks

Cited by in corpus (21)

• Super-Earth masses sculpted by pebble isolation around stars of different masses
• Pebbles versus Planetesimals: The case of Trappist-1
• A Balanced Budget View on Forming Giant Planets by Pebble Accretion
• Rapid formation of Gas Giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores
• Modeling the delivery of dust from discs to ionized winds
• Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets
• Are the observed gaps in protoplanetary discs caused by growing planets?
• Dust entrainment in photoevaporative winds: The impact of X-rays
• Survival of ALMA Rings in the Absence of Pressure Maxima
• Building the Galilean moons system via pebble accretion and migration: A primordial resonant chain
• The importance of thermal torques on the migration of planets growing by pebble accretion
• From Dust to Planets I: Planetesimal and Embryo Formation
• How planets grow by pebble accretion IV: Envelope opacity trends from sedimenting dust and pebbles
• Spinning up planetary bodies by pebble accretion
• Influences of three-dimensional gas flow induced by protoplanets on pebble accretion --$\mathrm{I}$. shear regime
• Promoted Mass Growth of Multiple, Distant Giant Planets through Pebble Accretion and Planet-Planet Collision
• Influences of protoplanet-induced three-dimensional gas flow on pebble accretion $\mathrm{I}\mathrm{I}$. Headwind regime
• On the settling of small grains in dusty discs: analysis and formulas
• On the origin of wide-orbit ALMA planets: giant protoplanets disrupted by their cores
• Pebble accretion in self-gravitating protostellar discs
• A pebble accretion model for the formation of the terrestrial planets in the Solar System