Stablest shapes for an axisymmetric body of gravitating, incompressible fluid

Journal Article · Wed Jun 01 04:00:00 EDT 1977 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/155284· OSTI ID:7110029

Marcus, P S; Press, W H; Teukolsky, S A

A numerical method for computing the total energy of self-gravitating, incompressible, rotating, axisymmetric fluid bodies is presented. Then, using a minimization technique, the stablest axisymmetric shapes are found for fluids having the same angular momentrum distribution as the Maclaurin spheroids. For small angular momenta the Maclaurin spheroid is a minimum-energy configuration; above a certain value a new, toroidal family of differentially rotating figures becomes the stable minimum-energy shape. Just below this critical value the spheroids are stable to small perturbations, but the corresponding toroids have lower energy. The family of ''Mestel disks'' (mass proportional 1/r, flat rotation curve) with this same angular momentum distribution are equilibria, but they are always unstable. Similar conclusions hold for other angular momentum distributions also investigated. These results may clarify the ''ring formation'' stage of some realistic collapse models, and may also support the hypothesis of massive galactic halos.

• Research Organization: Joseph Henry Laboratories, Princeton University
• OSTI ID: 7110029
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 214:2; ISSN ASJOA
• Country of Publication: United States
• Language: English

Related Subjects

640102* -- Astrophysics & Cosmology-- Stars & Quasi-Stellar
Radio & X-Ray Sources
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
DISTRIBUTION
FLUID MECHANICS
GALACTIC EVOLUTION
GALAXIES
GRAVITATIONAL COLLAPSE
HYDRODYNAMICS
MATHEMATICAL MODELS
MECHANICS
MOTION
ROTATION
SPHEROIDS
STARS