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

By C. Ormel, H. Klahr. 2010

451 citations recorded by the source corpus.

Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by ac- creting particles of sizekm (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 en- hances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters ,w here 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/faa5ea933a17a70ed9b8d77b17d854ad445a7a80

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

Citations in the corpus

Fossilized condensation lines in the Solar System protoplanetary disk (2015, background): “The particles which would be potentially important are those mm-sized or larger, because for these sizes the pebble accretion process is efficient (Ormel and Klahr, 2010; Lambrechts and Johansen, 2012); however, for these particles the gaps barrier is effective.”
The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores (2015, methodology): “In a series of recent papers (Lambrechts and Johansen, 2012, 2014; Ormel and Klahr, 2010; Johansen and Lacerda, 2010; Murray-Clay et al., 2011; Morbidelli and Nesvorny, 2012; Kretke and Levison, 2014b), a new model has been proposed in which massive planetesimals accrete pebbles (particles cm to dm ”
Planetesimal formation near the snowline: in or out? (2017, background): “After planetesimals of a certain size have formed, they can subsequently accrete pebbles and quickly grow to larger bodies (e.g., Ormel & Klahr 2010; Lambrechts & Johansen 2012, 2014; Bitsch et al. 2015; Visser & Ormel 2016).”
Dust Evolution and the Formation of Planetesimals (2016, background): “As Ormel & Klahr (2010) have demonstrated, pebbles can efficiently be accreted by growing proto-planets as the drag force around them effectively increases their cross section.”
The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics from 10 to 100 au (2019, background): “…regime, with particle trajectories more strongly gravitationally focused, as opposed to the less efficient “hyperbolic” regime that obtains farther out (Ormel & Klahr 2010; Lin et al. 2018, in particular their Figure15 which contrasts fast settling accretion at 5 au with slow hyperbolic accretion…”
The nature of the TRAPPIST-1 exoplanets. (2018, background): “Next, the largest planetesimals grow rapidly by accreting inwards-drifting pebbles (Ormel & Klahr 2010; Lambrechts & Johansen 2012).”
The Compositional Structure of the Asteroid Belt (2015, background): “…that planetesimal formation relies on clumps of “pebbles” collapsing, which could lead to a small number of planetesimals amidst a huge number of remnant pebbles – where only a few of the formed planetesimals are large enough to rapidly accrete the remaining pebbles (see Ormel and Klahr 2010).”
Rapid growth of gas-giant cores by pebble accretion (2012, methodology): “The influence of gas drag on the interaction of single small bodies and low-mass planets was explored by Ormel & Klahr (2010).”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, background): “In recent years, a new paradigm of solid accretion has emerged: pebble accretion (Johansen & Lacerda 2010; Ormel & Klahr 2010; Lambrechts & Johansen 2012; Morbidelli & Nesvorny 2012).”
Close-in planetesimal formation by pile-up of drifting pebbles (2016, background): “Pebbles corresponding to Stokes number of 10−2−1 may be accreted very efficiently onto planetary embryos (Ormel & Klahr 2010; Lambrechts & Johansen 2012).”
Planetesimal formation starts at the snow line (2017, unknown): “The radial dependence of sizes and radial flux of pebbles that we can extract from our results are important parameters of the pebble accretion models (Ormel & Klahr 2010; Lambrechts & Johansen 2014; Levison et al. 2015; Visser & Ormel 2016).”
RINGED SUBSTRUCTURE AND A GAP AT 1 au IN THE NEAREST PROTOPLANETARY DISK (2016, background): “The millimeter-sized particles needed to assemble larger planetesimals (Ormel & Klahr 2010; Lambrechts & Johansen 2012) experience aerodynamic drag with the gas that results in their rapid migration toward the host star (Weidenschilling 1977; Takeuchi & Lin 2002).”
Separating gas-giant and ice-giant planets by halting pebble accretion (2014, background): “Previous studies (Johansen & Lacerda 2010; Ormel & Klahr 2010; Bromley & Kenyon 2011; Lambrechts & Johansen 2012; Morbidelli & Nesvorny 2012) demonstrate that this is the result of gas drag operating on pebbles, which dramatically increases the accretion cross section (Sect.”
Adding particle collisions to the formation of asteroids and Kuiper belt objects via streaming instabilities (2011, background): “…comparison to observed planetesimal belts is nevertheless complicated by a potentially very efficient accretion of unbound particles (pebbles and rocks) by the newly born planetesimals after their formation (Johansen & Lacerda 2010; Ormel & Klahr 2010), an epoch not captured in our simulations.”
Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations (2012, background): “…growth, which argues that, if the mass in the disk is predominantly carried by pebbles of a few decimeters in size, the largest planetesimals accrete pebbles very efficiently, rapidly growing to several Earth masses (see also Johansen & Lacerda 2010; Ormel & Klahr 2010; Murray-Clay et al. 2011).”