The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks

Abstract

Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by accreting particles of size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximations, however, enable us to cover an arbitrary large parameter space. The framework of the circularly restricted three body problem is used to numerically integrate particle trajectories and to derive their impact parameters. Three accretion modes can be distinguished: hyperbolic encounters, where the 2-body gravitational focusing enhances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters, where particles settle towards the protoplanet. An analysis of the observed behavior is presented; and we provide a recipe to analytically calculate the impact radius, which confirms the numerical findings. We apply our results to the sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of debris on small protoplanets (<50 km) is found to be slow, because the fragments are distributed over a rather thick layer. However, the newly found settling mechanism, which is characterized by much larger impact radii, becomes relevant for protoplanets of ~10^3 km in size and provides a much faster channel for growth.

accepted for publication in Astronomy & Astrophysics

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• Dynamical friction in an isentropic gas
• Planetesimal Growth in Evolving Protoplanetary Disks: Constraints from the Pebble Supply
• The New Generation Planetary Population Synthesis (NGPPS) VIII. Impact of host star metallicity on planet occurrence rates, orbital periods, eccentricities, and radius valley morphology
• Directly Detecting the Envelopes of Low-mass Planets Embedded In Protoplanetary Discs and The Case For TW Hydrae
• A "no-drift" runaway pile-up of pebbles in protoplanetary disks II. Characteristics of the resulting planetesimal belt
• Chondrule Accretion with a Growing Protoplanet
• Evidence of a primordial isotopic gradient in the inner region of the solar protoplanetary disc
• Forming equal mass planetary binaries via pebble accretion
• The PAIRS project: a global formation model for planets in binaries. I. Effect of disc truncation on the growth of S-type planets
• Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion
• Early Solar System Turbulence Constrained by High Oxidation States of the Oldest Non-Carbonaceous Planetesimals
• Architecture of planetary systems predicted from protoplanetary disks observed with ALMA II: evolution outcomes and dynamical stability
• The influence of a static planetary atmosphere on spin transfer during pebble accretion
• Planet Formation by Gas-Assisted Accretion of Small Solids
• Planets, debris and their host metallicity correlations
• Interpreting the atmospheric composition of exoplanets: sensitivity to planet formation assumptions
• Formation of super-Earths in icy dead zones around low-mass stars
• Diversity of Exoplanets
• Solid accretion onto planetary cores in radiative disks
• Water worlds in N-body simulations with fragmentation in systems without gaseous giants
• Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation
• Forming Earth-like and Low-Mass Rocky Exoplanets Through Pebble and Planetesimal Accretion
• Hypothesis about Enrichment of Solar System
• Interior dynamics of envelopes around disk-embedded planets
• Compositional Turbulence and Layering in the Gaseous Envelopes of Forming Planets
• Modelling dust coagulation, dynamical drag and turbulent mixing during star and disc formation
• Diversity in planetary architectures from pebble accretion: Water delivery to the habitable zone with pebble snow
• On the dynamics of pebbles in protoplanetary disks with magnetically-driven winds
• Long-term Hydrodynamic Simulations on the Planetesimals Trapped in the First-order Mean Motion Resonances
• Thermal emission spectra of the ultra-hot Jupiter WASP-33 b
• Inside-Out Planet Formation: VI. Oligarchic Coagulation of Planetesimals from a Pebble Ring?
• A close-encounter method for simulating the dynamics of planetesimals
• A large sub-Neptune transiting the thick-disk M4V TOI-2406
• A break in planet occurrence near the pebble isolation mass should be observable by the Roman microlensing survey
• The effect of late giant collisions on the atmospheres of protoplanets and the formation of cold sub-Saturns
• A multi-fluid approach for polydisperse pebble accretion: From particles to fluids, establishing the multifluid framework