Nonlinear coupling and saturation of r-modes in newly born neutron stars

Details Nonlinear coupling and saturation of r-modes in newly born neutron stars Nonlinear coupling and saturation of r-modes in newly born neutron stars

Mar 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001phdt........12s&link_type=abstract

Thesis (PhD). CORNELL UNIVERSITY, Source DAI-B 61/09, p. 4776, Mar 2001, 155 pages.

Computer Science

Scientific paper

This thesis describes the effect of rotation on both the linear and nonlinear oscillations of stars. The intended application is the saturation of the r-mode instability in rapidly rotating young neutron stars. We employ degenerate perturbation theory and an expansion in powers of the rotation frequency Ω to derive the oscillation modes of a rotating star. An eigenvalue equation for the modes for which the Coriolis force is the dominant restoring force is derived. These modes have been described as the r-modes [1] or r-g hybrid modes [2] depending on the size of the buoyancy force as compared to the Coriolis force. The standard corrections to ``spherical star'' modes whose frequencies are nonzero as Ω --> 0 are also derived. We show how to decompose a general motion of the star as a sum over modes, and obtain uncoupled equations of motion for the mode coefficients, q α(t). Our formalism improves on previous investigations by proving that, at linear order in the displacement vector, the free oscillations of the mode amplitudes are uncoupled. Next, we turn to the nonlinear hydrodynamical mode-mode coupling. For clarity, we derive the nonlinear equations of motion for the mode amplitudes and mode coupling coefficients in several ways. We find that to all orders in perturbation theory (coupling of any number of modes) the form of the mode-mode coupling coefficients for slowly rotating stars is exactly the same as for a nonrotating star, although the eigenfunctions and background star quantities inserted into these expressions may differ. We describe a novel, efficient method to compute the nonlinear mode coupling coefficients using the spin-weighted spherical harmonics formalism of [3], and give a simple, illustrative example of how the Coriolis-driven modes couple differently than the spherical star modes.

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