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

TL;DR

This study investigates how strong magnetic fields influence the r-modes of slowly rotating relativistic neutron stars, revealing that magnetic fields of around 10^{15} G can significantly alter oscillation frequencies and gravitational wave emission timescales.

Contribution

It provides the first quantification of magnetic field effects on r-mode frequencies and gravitational wave growth times in relativistic neutron stars within the Cowling approximation.

Findings

Magnetic fields of 10^{15} G cause up to 5% decrease in r-mode frequency.

Magnetic fields reduce gravitational wave growth time by about 30%.

Magnetic effects on growth time are non-monotonic, first increasing then decreasing it.

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.