The steady-state flow pattern past gravitating bodies

TL;DR

This study models the flow pattern of gas around low-mass, embedded planets in protoplanetary disks, revealing how disc headwind influences atmosphere size and particle accretion, with implications for planet formation.

Contribution

It provides a simplified, combined numerical and analytical description of gas flow and particle trajectories around low-mass planets, highlighting the impact of disc headwind.

Findings

Atmosphere size decreases with increasing disc headwind.

Small particles follow streamlines and have low accretion rates.

Pebble-sized particles achieve high accretion rates.

Abstract

Gravitating bodies significantly alter the flow pattern (density and velocity) of the gas that attempts to stream past. Still, small protoplanets in the Mars--super-Earth range can only bind limited amounts of nebular gas; until the so-called critical core mass has been reached (~1-10 Earth masses) this gas is in near hydrostatic equilibrium with the nebula. Here we aim for a general description of the flow pattern surrounding these low-mass, embedded planets. Using various simplifying assumptions (subsonic, 2D, inviscid flow, etc), we reduce the problem to a partial differential equation that we solve numerically as well as approximate analytically. It is found that the boundary between the atmosphere and the nebula gas strongly depends on the value of the disc headwind (deviation from Keplerian rotation). With increasing headwind the atmosphere decreases in size and also becomes more asymmetrical. Using the derived flow pattern for the gas, trajectories of small solid particles, which experience both gas drag and gravitational forces, are integrated numerically. Accretion rates for small particles (dust) are found to be low, as they closely follow the streamlines, which curl away from the planet. However, pebble-size particles achieve large accretion rates, in agreement with previous numerical and analytical works.