1999/06/30 by Dong Lai, Peter Goldreich · 97 citations
Physics and Astronomy · #Accretion (finance) #Astronomy #Astrophysics #Circular symmetry #Classical mechanics #Cosmology and Gravitation Theories #Gamma-ray bursts and supernovae #Geometry #Gravitational collapse #Homogeneous #Mechanics #Perturbation (astronomy) #Physics #Pulsars and Gravitational Waves Research #RADIUS #Scaling #Statistical physics #Supernova #Supersonic speed #astro-ph
paper · pdf · doi:10.1086/308821
published in The Astrophysical Journal 535(1), 402-411 (IOP Publishing) · 23 pages including 6 ps figures; Minor changes and update; To appear in ApJ, 2000
arxiv created 1999/12/27 · openalex publication_date 2000/05/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile ρ ∝ r -3/2 and the velocity approaches free fall. We show that in this region nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as r -1 , while the Lagrangian density perturbation, Δρ/ρ, grows as r -1/2 . Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case Δρ/ρ increases as r - l , where l specifies the angular degree of the perturbation. These scaling relations are different from those obtained for the collapse of a homogeneous cloud. Our numerical calculations indicate that nonspherical perturbations are damped in the subsonic region and that they grow and approach the asymptotic scalings in the supersonic region. The implications of our results to asymmetric supernova collapse and to black hole accretion are briefly discussed.