Improved secular stability limits for differentially rotating polytropes and degenerate dwarfs

Journal Article · Thu Jan 15 04:00:00 EST 1981 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/158626· OSTI ID:6499362

Durisen, R H; Imamura, J N

The second-order tensor virial equation (TVE) method applied to rotating polytropes and degenerated dwarfs has indicated that the Kelvin bar modes becomes secularly unstable when T/Vertical BarWVertical Bar> or approx. =0.14, where T is the rotational kinetic energy and W is the total gravitational energy, for a wide variety of rotation laws and equations of state. However, recent advances in Lagrangian perturbation techniques have shwon that the TVE method provides neither a necessary nor a sufficient condition for secular stability in differentially rotating stars, because the trial eigenfunction has recently been suggested which satisfies the Kelvin circulation theorem. When used a Lagrangian variational formulation this trial eigenfunction yields a sufficient condition for secular instability. We find that the application of this sufficient condition for secular instability of barlike modes gives substantially the same result as the TVE method: differentially rotating polytropes and degenerate dwarfs are secularly unstable for T/Vertical BarWVertical Bar> or approx. =0.14 for a wide range of compressibilities and rotation laws. The difference between our improved secular stability limits and the TVE limits ranges from 1 to 7% and increases with the degree of central concentration of mass and angular momentum of the equilibrium model.

• Research Organization: Department of Astronomy, Indiana University, Bloomington
• OSTI ID: 6499362
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 243:2; 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
DWARF STARS
ENERGY
EQUATIONS
EQUATIONS OF STATE
EQUILIBRIUM
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
KINETIC ENERGY
MATHEMATICAL MODELS
MECHANICS
MOTION
ROTATION
SPHEROIDS
STAR MODELS
STARS
VIRIAL EQUATION
WHITE DWARF STARS