R-Modes in the ocean of a magnetic neutron star

We study the dynamics of r-modes in the ocean of a magnetic neutron star. We modeled the star’s ocean with a spherical rotating thin shell and assumed that the magnetic field symmetry axis is not aligned to the shell’s spin axis. In the magnetohydrodynamic approximation, we calculate the frequency of ` = m rmodes in the shell of an incompressible fluid. Different r-modes with ` and `±2 are coupled by the inclined magnetic field. Kinematical secular effects for the motion of a fluid element in the shell undergoing ` = m = 2 r-mode are studied. The magnetic corrected drift velocity of a given fluid element undergoing the ` = m r-mode oscillations is obtained. The magnetic field increases the magnitude of the fluid drift produced by the r-mode oscillations. The drift velocity is strongly modulated by the inclined magnetic field. We show that the magnetic field is distorted by the high-` magnetic r-modes more strongly than by the low-` modes. Further, due to the shear produced by the r-mode drift velocity, the high-` modes in the ocean fluid will damp faster than the low-` ones. Subject headings: stars: neutron – stars: magnetic – stars: rotation – stars: oscillations