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

Abstract

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 $\sim$ $5\%$ in the frequency with increasing magnetic field, with a $B^2$ dependence for rotation rates $\Omega /{\Omega }_K\gtrsim 0.07$ and $B^4$ for $\Omega /{\Omega }_K\lesssim 0.07$. (These results should be trusted only within 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 non-magnetized stars, which would mean a faster growth of the emission of gravitational radiation. The effect of the magnetic field in $t_{gw}$ causes a non-monotonic effect, that first slightly increases $t_{gw}$ and then decreases it further by another $\sim$ $5\%$. (The value of 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.

14 pages, 11 figures, v2: final version accepted for publication in Phys.Rev.D

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• Limits on Magnetic Field Amplification from the r-Mode Instability
• Torsional oscillations of magnetized neutron stars with mixed poloidal-toroidal fields
• $M/R$ estimates for two neutron stars in LMXBs with possible r-mode frequencies detected
• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales
• Inferring neutron star properties through gravitational waves from r-modes and their relativistic counterparts
• Instability windows of relativistic r-modes in stably stratified neutron stars with hyperonic cores
• Hadronic matter phases and their application to rapidly rotating neutron stars
• Impact of Rotation on Quark-Hadron Hybrid Stars