Secular instability of rotating Newtonian stars

Journal Article · Mon May 15 04:00:00 EDT 1978 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/156143· OSTI ID:7054760

Friedman, J L; Schutz, B F

The effect of gravitational radiation and of viscosity on the stability of rotating self-gravitating fluids is considered. Previous cirteria governing secular stability to radiation are shown to fail as a result of the trival displacements introduced in a previous paper (1). The required modification is obtained by describing perturbations in terms of canonical displacements (displacements orthogonal to the trivials). There nevertheless remain physical perturbations having angular dependence e/sup i/mphi which, for sufficiently large m, make the stability functional (the canonical energy E/sub c/) negative, and it follows that all rotating stars are unstable or marginally unstable to gravitational radiation. In the case of stability against viscosity, the corresponding stability criterion is shown to involve the the canonical energy in a rotating frame, E/sub c/,R, a functional invariant under gauge transformations associated with the trival displacements. By using the functional E/sub c/,R to analyze local stability, it is found that a star is locally stable against viscosity if and only if the special entropy increases outward (in the sense of decreasing pressure). Finally, the behavior of normal modes is discussed and used to elucidate the generic radiation-induced instability; and certain orthogonality properties are derived.

• Research Organization: Department of Physics, University of Wisconsin--Milwaukee
• OSTI ID: 7054760
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 222:1; 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
DIFFERENTIAL EQUATIONS
DISTURBANCES
EQUATIONS
EQUATIONS OF MOTION
FLUID FLOW
FLUID MECHANICS
GRAVITATIONAL RADIATION
HYDRODYNAMICS
INSTABILITY
MATHEMATICAL MODELS
MECHANICS
MOTION
RADIATIONS
ROTATION
STABILITY
STAR MODELS
STARS
VISCOSITY