An Analytical Theory for the Growth from Planetesimals to Planets by Polydisperse Pebble Accretion

Abstract

Pebble accretion is recognized as a significant accelerator of planet formation. Yet, only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find 1-2 orders of magnitude higher accretion rates compared to monodisperse, also extending the onset of pebble accretion to 1-2 order of magnitude lower in mass. We find Myr-timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses $10^{-6}-10^{-4}{M}_{\oplus }$, over a significant range of the parameter space. This mass range overlaps with the high mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.

arXiv comment17 pages, 12 figures. Accepted to ApJ

References in corpus (62)

• Rapid planetesimal formation in turbulent circumstellar discs
• Streaming Instabilities in Protoplanetary Disks
• Rapid growth of gas-giant cores by pebble accretion
• A simple model for the evolution of the dust population in protoplanetary disks
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• Dust coagulation in protoplanetary disks: a rapid depletion of small grains
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
• Making other Earths: Dynamical Simulations of Terrestrial Planet Formation and Water Delivery
• 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
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods
• Concentrating small particles in protoplanetary disks through the streaming instability
• Oligarchic growth of giant planets
• How to form planetesimals from mm-sized chondrules and chondrule aggregates
• Formation of planetary systems by pebble accretion and migration: How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode
• Formation of planetary systems by pebble accretion and migration: Growth of gas giants
• The radial dependence of pebble accretion rates: A source of diversity in planetary systems I. Analytical formulation
• Thresholds for Particle Clumping by the Streaming Instability
• Impact Craters on Pluto and Charon Indicate a Deficit of Small Kuiper Belt Objects
• Steady state of dust distributions in disk vortices: Observational predictions and applications to transitional disks
• The Compositions of Kuiper Belt Objects
• Formation of sharp eccentric rings in debris disks with gas but without planets
• Tracing Slow Winds from T Tauri Stars via Low Velocity Forbidden Line Emission
• Embryos grown in the dead zone: Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids
• Erosion and the limits to planetesimal growth
• The Physics of Protoplanetesimal Dust Agglomerates. IV. Towards a Dynamical Collision Model
• Demographics of Planetesimals Formed by the Streaming Instability
• Diffusion and Concentration of Solids in the Dead Zone of a Protoplanetary Disk
• Rocky super-Earths or waterworlds: the interplay of planet migration, pebble accretion and disc evolution
• On the Feeding Zone of Planetesimal Formation by the Streaming Instability
• Pebble-driven Planet Formation around Very Low-mass Stars and Brown Dwarfs
• Geometrical Cross Sections of Dust Aggregates and a Compression Model for Aggregate Collisions
• How efficient is the streaming instability in viscous protoplanetary disks?
• How dust fragmentation may be beneficial to planetary growth by pebble accretion
• Prograde rotation of protoplanets by accretion of pebbles in a gaseous environment
• Giant planet formation at the pressure maxima of protoplanetary disks II. A hybrid accretion scenario
• On the coexistence of the streaming instability and the vertical shear instability in protoplanetary disks
• Testing the Jeans, Toomre and Bonnor-Ebert concepts for planetesimal formation: 3D streaming instability simulations of diffusion regulated formation of planetesimals
• Polydisperse Streaming Instability I. Tightly coupled particles and the terminal velocity approximation
• Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses
• From Planetesimals to Planets in Turbulent Protoplanetary Disks I. Onset of Runaway Growth
• Exploring the conditions for forming cold gas giants through planetesimal accretion
• The Mutual Orbit, Mass, and Density of the Large Transneptunian Binary System Varda and Ilmarë
• Streaming Instability of Multiple Particle Species in Protoplanetary Disks
• Streaming instability in the quasi-global protoplanetary discs
• Physical models of streaming instabilities in protoplanetary disks
• Polydisperse Streaming Instability III. Dust evolution encourages fast instability
• Stratified and vertically-shearing streaming instabilities in protoplanetary disks
• Numerical Simulations of Highly Porous Dust Aggregates in the Low-Velocity Collision Regime
• Dust clearing by radial drift in evolving protoplanetary discs
• Evolution of dust grain size distribution by shattering in the interstellar medium: robustness and uncertainty
• Influences of three-dimensional gas flow induced by protoplanets on pebble accretion --$\mathrm{I}$. shear regime
• Coagulation Instability in Protoplanetary Disks: A Novel Mechanism Connecting Collisional Growth and Hydrodynamical Clumping of Dust Particles
• The Growth of Protoplanets via the Accretion of Small Bodies in Disks Perturbed by the Planetary Gravity
• The radial structure of planetary bodies formed by the streaming instability
• Streaming instability in a global patch simulation of protoplanetary disks
• Growing the seeds of pebble accretion through planetesimal accretion
• Influences of protoplanet-induced three-dimensional gas flow on pebble accretion $\mathrm{I}\mathrm{I}$. Headwind regime

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• Planet formation throughout the Milky Way: Planet populations in the context of Galactic chemical evolution
• Formation of wide-orbit giant planets in protoplanetary disks with a decreasing pebble flux
• Filling in the Gaps: Can Gravitationally Unstable Discs Form the Seeds of Gas Giant Planets?
• Planetesimal and planet formation in transient dust traps
• From Planetesimals to Dwarf Planets by Pebble Accretion
• Planetesimal Growth in Evolving Protoplanetary Disks: Constraints from the Pebble Supply
• Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion
• How stellar mass and disc size shape the formation and migration of super-Earths
• Forming Earth-like and Low-Mass Rocky Exoplanets Through Pebble and Planetesimal Accretion
• A multi-fluid approach for polydisperse pebble accretion: From particles to fluids, establishing the multifluid framework