The effect of gas drag on the growth of protoplanets

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.

The Emerging Paradigm of Pebble Accretion

“…These expressions are, within orders of unity, consistent with recent works (Ormel and Klahr 2010;Ormel and Kobayashi 2012;Johansen 2012, 2014;Guillot et al 2014;Ida et al 2016). …”

“…Instead of the order-of-magnitude expressions derived above, I employ more precise expressions that have been calibrated to numerical integrations (Ormel and Klahr 2010;Ormel and Kobayashi 2012;Visser and Ormel 2016). But many of the key features highlighted in Fig.…”

On the filtering and processing of dust by planetesimals

“…The interactions of planetesimals and dust in a gas-rich disk have been the focus of less attention, apart from some works to which this study will frequently refer (Rafikov 2004;Ormel & Klahr 2010;Ormel & Kobayashi 2012;Lambrechts & Johansen 2012). The need for an early formation of planetesimals and the prevalence of dust in disks leads us to consider a situation in which planetesimals are formed in a given region of the disk while dust drifts from the outer region.…”

Hiding in the Shadows. Ii. Collisional Dust as Exoplanet Markers

“…One notable result from the coupling of N-body and Hydro codes is the model of pebble accretion. Pebble accretion relies upon the imperfect (nonnegligible, but not dominating) coupling of centimeter-sized particles with gas to efficiently accrete mass onto seed planetesimals (Johansen & Lacerda 2010;Ormel & Klahr 2010;Lambrechts & Johansen 2012). The generation of dust from interactions between planetesimals has been investigated in relation to debris disks (see Wyatt 2008;Thebault et al 2014), the modeling of giant impacts (e.g., Kral et al 2013), and the simulation of the mid to late stages of planet formation (e.g., Leinhardt & Stewart 2012;Leinhardt et al 2015).…”