  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.
