Axisymmetric magnetic modes of neutron stars having mixed poloidal and toroidal magnetic fields

TL;DR

This study models axisymmetric magnetic oscillations in neutron stars with mixed poloidal and toroidal magnetic fields, revealing how mode frequencies depend on magnetic field strength and field configuration without detecting instabilities.

Contribution

It provides the first detailed analysis of axisymmetric magnetic modes in neutron stars with combined poloidal and toroidal fields, considering their coupling and frequency behavior.

Findings

Magnetic mode frequencies decrease as the toroidal component increases.

Spheroidal mode frequencies are proportional to surface magnetic field strength for small toroidal fields.

No unstable magnetic modes were found in the analyzed parameter range.

Abstract

We calculate axisymmetric magnetic modes of a neutron star possessing a mixed poloidal and toroidal magnetic field, where the toroidal field is assumed to be proportional to a dimensionless parameter $\zeta_0$. Here, we assume an isentropic structure for the neutron star and consider no effects of rotation. Ignoring the equilibrium deformation due to the magnetic field, we employ a polytrope of the index $n=1$ as the background model for our modal analyses. For the mixed poloidal and toroidal magnetic field with $\zeta_0\not=0$, axisymmetric spheroidal and toroidal modes are coupled. We compute axisymmetric spheroidal and toroidal magnetic modes as a function of the parameter $\zeta_0$ from $0$ to $\sim 1$ for the surface field strengths $B_S=10^{14}$G and $10^{15}$G. We find that the frequency $\omega$ of the magnetic modes decreases with increasing $\zeta_0$. We also find that the frequency of the spheroidal magnetic modes is almost exactly proportional to $B_S$ for $\zeta_0\lesssim 1$ but that this proportionality holds only when $\zeta_0\ll 1$ for the toroidal magnetic modes. The wave patterns of the spheroidal magnetic modes and toroidal magnetic modes are not strongly affected by the coupling so long as $\zeta_0\lesssim 1$. We find no unstable modes having $\omega^2<0$.