r-mode instability: Analytical solution with gravitational radiation reaction

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.024020· OSTI ID:20711142

Dias, Oscar J.C.; Sa, Paulo M ^[1]

---

1. Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)

Analytical r-mode solutions are investigated within the linearized theory in the case of a slowly rotating, Newtonian, barotropic, nonmagnetized, perfect-fluid star in which the gravitational radiation (GR) reaction force is present. For the GR reaction term we use the 3.5 post-Newtonian order expansion of the GR force, in order to include the contribution of the current quadrupole moment. We find the explicit expression for the r-mode velocity perturbations and we conclude that they are sinusoidal with the same frequency as the well-known GR force-free linear r-mode solution, and that the GR force drives the r-modes unstable with a growth time scale that agrees with the expression first found by Lindblom, Owen, and Morsink. We also show that the amplitude of these velocity perturbations is corrected, relatively to the GR force-free case, by a term of order {omega}{sup 6}, where {omega} is the angular velocity of the star.

• OSTI ID: 20711142
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANALYTICAL SOLUTION
ANGULAR VELOCITY
COSMOLOGY
DISTURBANCES
GENERAL RELATIVITY THEORY
GRAVITATIONAL RADIATION
GRAVITATIONAL WAVES
IDEAL FLOW
INSTABILITY
QUADRUPOLE MOMENTS
ROTATION
STARS