Effect of magnetic fields on the r-modes of slowly rotating relativistic neutron stars

We study here the r-modes in the Cowling approximation of a slowly rotating and magnetized neutron star with a poloidal magnetic field, where we neglect any deformations of the spherical symmetry of the star. We were able to quantify the influence of the magnetic field in both the oscillation frequency sigma(r) of the r-modes and the growth time t(gw) of the gravitational radiation emission. We conclude that magnetic fields of the order 10(15) G at the center of the star are necessary to produce any changes. Our results for sigma(r) show a decrease of up to similar to 5% in the frequency with increasing magnetic field, with a B-2 dependence for rotation rates Omega/Omega(K) greater than or similar to 0.07 and B-4 for Omega/Omega(K) less than or similar to 0.07. (These results should be trusted only within the slow rotation approximation, and we kept Omega/Omega(K) < 0.3.) For t(gw), we find that it is approximately 30% smaller than previous Newtonian results for nonmagnetized stars, which would mean a faster growth of the emission of gravitational radiation. The effect of the magnetic field in t(gw) causes a nonmonotonic effect that first slightly increases t(gw) and then decreases it further by another similar to 5%. (The value of the magnetic field for which t(gw) starts to decrease depends on the rotational frequency, but it is generally around 10(15) G.) Future work should be dedicated to the study of the effect of viscosity in the presence of magnetic fields, in order to establish the magnetic correction to the instability window.