Differential rotation of nonlinear r-modes

Details Differential rotation of nonlinear r-modes Differential rotation of nonlinear r-modes

2003-02-27

arxiv.org/abs/gr-qc/0302115v2

Phys.Rev. D69 (2004) 084001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, revtex4; section III revised, comments added in Introduction and Conclusions, references updated; to appear in Phys.

Scientific paper

10.1103/PhysRevD.69.084001

Differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly-rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one which is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlikely the situation in the linearized theory, r-modes do not preserve vorticity of fluid elements at second-order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.

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