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The instability of r-mode oscillations in rapidly rotating neutron stars hasattracted attention as a potential mechanism for producing high frequency,almost periodic gravitational waves. The analyses carried so far have shown theexistence of these modes and have considered damping by shear and bulkviscosity. However, the magnetohydrodynamic coupling of the modes with astellar magnetic field and its role in the damping of the instability has notbeen fully investigated yet. Following our introductory paper (Rezzolla, Lamband Shapiro 2000), we here discuss in more detail the existence of secularhigher-order kinematical effects which will produce toroidal fluid drifts. Wealso define the sets of equations that account for the time evolution of themagnetic fields produced by these secular velocity fields and show that themagnetic fields produced can reach equipartition in less than a year. The fullnumerical calculations as well as the evaluation of the impact of strongmagnetic fields on the onset and evolution of the r-mode instability will bepresented in a companion paper.Comment: 15 pages, 4 figures. To appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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

Properties ofrmodes in rotating magnetic neutron stars. I. Kinematic secular effects and magnetic evolution equations