Nonaxisymmetric normal modes and secular instabilities of rotating stars

1986 ◽  
Vol 309 ◽  
pp. 598 ◽  
Author(s):  
Robert A. Managan
Keyword(s):  
Normal Modes ◽  
Rotating Stars

Rapidly rotating relativistic stars

1992 ◽  
Vol 340 (1658) ◽  
pp. 391-422 ◽  
Keyword(s):  
Neutron Stars ◽  
Numerical Models ◽  
Normal Modes ◽  
Rotating Stars ◽  
Relativistic Stars ◽  
Small Oscillations ◽  
Perfect Fluids ◽  
Upper Limits ◽  
Viscosity Limit

Within the last decade, significant progress has been made in modelling rotating stars in general relativity and in relating observable properties to the equation of state of matter at high density. A formalism describing rotating perfect fluids is presented and numerical models of neutron stars are briefly discussed, with emphasis on upper limits on mass and rotation. The equations governing small oscillations are reviewed, and a variational principle appropriate both to eulerian and lagrangian perturbations is obtained. This extends to relativity an eulerian principle used to find non-axisymmetric stability points for perfect fluids. A related eulerian approach has been recently used to obtain normal modes of rotating newtonian stars. The review concludes with an outline of this work and of the two types of instability that can restrict the range of neutron stars. In particular, current work shows that several kinds of effective viscosity limit the possible role of a non-axisymmetric instability driven by gravitational waves.

On the non-radial oscillations of slowly rotating stars induced by the Lense-Thirring effect

1991 ◽  
Vol 433 (1888) ◽  
pp. 423-440 ◽  
Keyword(s):  
Neutron Stars ◽  
Characteristic Frequency ◽  
Selection Rule ◽  
Inertial Frame ◽  
Normal Modes ◽  
Decisive Factor ◽  
Rotating Stars ◽  
Opposite Parity ◽  
Axial Mode ◽  
Polar Mode

In a star that is rotating so slowly that the distortion of its figure may be ignored, the axial modes of non-radial oscillation exhibiting resonance can be excited by the polar modes of perturbation by the coupling derived from the dragging of the inertial frame by the rotation of the star (i. e. by the Lense-Thirring effect). The coupling of these two modes of opposite parity is subject to the standard selection rule, ∆ l = ±1. Also, the excitation of ( l + 1)-axial mode by the l -polar mode is favoured relative to the excitation of the ( l - 1)-axial mode, in conformity with the ‘propensity’ rule. As an illustrative example, the excitation of the sextupole axial modes of oscillation by the quadrupole polar perturbations is considered in some detail; and it is shown that both the real and the imaginary parts of the characteristic frequency of the quasi­-normal modes decrease dramatically with the amplitude of the coupling. The relatively very long damping times of these rotationally induced oscillations may be a decisive factor in their eventual detection in neutron stars following the glitches.

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