Dynamical friction for supersonic motion in a homogeneous gaseous medium

Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: daniel.thun@uni-tuebingen.de; rolf.kuiper@uni-tuebingen.de; schmidtstudent@uni-tuebingen.de; wilhelm.kley@uni-tuebingen.de

Received: 23 October 2015
Accepted: 27 January 2016

Abstract

Context. The supersonic motion of gravitating objects through a gaseous ambient medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planetesimals, planets, and all kind of stars up to galaxies and black holes. In particular, the dynamical friction caused by the wake that forms behind the object plays an important role for the dynamics of the system. To calculate the dynamical friction for a particular system, standard formulae based on linear theory are often used.

Aims. It is our goal to check the general validity of these formulae and provide suitable expressions for the dynamical friction acting on the moving object, based on the basic physical parameters of the problem: first, the mass, radius, and velocity of the perturber; second, the gas mass density, soundspeed, and adiabatic index of the gaseous medium; and finally, the size of the forming wake.

Methods. We perform dedicated sequences of high-resolution numerical studies of rigid bodies moving supersonically through a homogeneous ambient medium and calculate the total drag acting on the object, which is the sum of gravitational and hydrodynamical drag. We study cases without gravity with purely hydrodynamical drag, as well as gravitating objects. In various numerical experiments, we determine the drag force acting on the moving body and its dependence on the basic physical parameters of the problem, as given above. From the final equilibrium state of the simulations, for gravitating objects we compute the dynamical friction by direct numerical integration of the gravitational pull acting on the embedded object.

Results. The numerical experiments confirm the known scaling laws for the dependence of the dynamical friction on the basic physical parameters as derived in earlier semi-analytical studies. As a new important result we find that the shock’s stand-off distance is revealed as the minimum spatial interaction scale of dynamical friction. Below this radius, the gas settles into a hydrostatic state, which – owing to its spherical symmetry – causes no net gravitational pull onto the moving body. Finally, we derive an analytic estimate for the stand-off distance that can easily be used when calculating the dynamical friction force.