1998/10/20 by Eve C. Ostriker · 573 citations
Chemistry · Physics and Astronomy · #Astronomy #Astrophysics #Astrophysics and Star Formation Studies #Circular orbit #Classical mechanics #Drag #Dynamical friction #Hydrostatic equilibrium #Mechanics #Molecular Spectroscopy and Structure #Perturbation (astronomy) #Physics #RADIUS #Stellar, planetary, and galactic studies #Supersonic speed #Wake #astro-ph
paper · pdf · doi:10.1086/306858
published in The Astrophysical Journal 513(1), 252-258 (IOP Publishing) · 17 pages, 5 postscript figures, to appear in ApJ 3/1/99
arxiv created 1998/10/20 · openalex publication_date 1999/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber M p traveling at velocity V through a uniform gaseous medium of density ρ 0 and sound speed c s . This drag force acts in the direction - and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion ( ≡ V / c s >1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion ( <1), the wake is confined to a sphere of radius c s t centered a distance Vt behind the perturber. Inside the wake, surfaces of constant density are hyperboloids or oblate spheroids for supersonic or subsonic perturbers, respectively, with the density maximal nearest the perturber. The dynamical drag force has the form F DF =- I × 4π( GM p ) 2 ρ 0 / V 2 . We evaluate I analytically; its limits are I → 3 /3 for ≪1, and I →ln( Vt / r min ) for ≫1. We compare our results to the Chandrasekhar formula for dynamical friction in a collisionless medium, noting that the gaseous drag is generally more efficient when >1, but is less efficient when <1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal ρ∝ r −2 halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.