Properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>r</mml:mi></mml:math>modes in rotating magnetic neutron stars. I. Kinematic secular effects and magnetic evolution equations

The instability of r-mode oscillations in rapidly rotating neutron stars has attracted attention as a potential mechanism for producing high frequency, almost periodic gravitational waves. The analyses carried so far have shown the existence of these modes and have considered damping by shear and bulk viscosity. However, the magnetohydrodynamic coupling of the modes with a stellar magnetic field and its role in the damping of the instability has not been fully investigated yet. Following our introductory paper [L. Rezzolla, F. K. Lamb, and S. L. Shapiro, Astrophys. J. Lett. 531, L141 (2000)], we here discuss in more detail the existence of secular higher-order kinematical effects which will produce toroidal fluid drifts. We also define the sets of equations that account for the time evolution of the magnetic fields produced by these secular velocity fields and show that the magnetic fields produced can reach equipartition in less than a year. The full numerical calculations as well as the evaluation of the impact of strong magnetic fields on the onset and evolution of the r-mode instability will be presented in a companion paper [L. Rezzolla, F. K. Lamb, D. Markovi\ifmmode \acute{c}\else \'{c}\fi{}, and S. L. Shapiro, following paper, Phys. Rev. D 64, 104014 (2001)].

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