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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.
In this paper, we show that in the vicinity of certain astronomical bodies, e.g., a Neutron Star, a Black Hole, there exist significant enhancements of Dark Matters density and current, due to its interaction with the gravitational field of the bodie
We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than that for the
We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the in
Context. More than 60 planets have been discovered so far in systems that harbour two stars, some of which have binary semi-major axes as small as 20 au. It is well known that the formation of planets in such systems is strongly influenced by the ste
Impacts between planetary-sized bodies can explain the origin of satellites orbiting large ($R>500$~km) trans-Neptunian objects. Their water rich composition, along with the complex phase diagram of water, make it important to accurately model the wi