Alfven node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

TL;DR

This paper explores the vibrational properties of non-magnetic white dwarfs with internal toroidal magnetic fields, deriving analytical formulas for Alfven modes and comparing them with other magnetic configurations.

Contribution

It introduces a model for node-free Alfven vibrations in solid white dwarfs with purely toroidal magnetic fields, providing analytical spectral formulas and insights into magnetic effects on seismic modes.

Findings

Analytical expressions for Alfven mode frequencies in toroidal magnetic fields.

Demonstration that buried magnetic fields influence seismic vibrations.

Comparison with poloidal magnetic field models to understand magnetic effects.

Abstract

In the context of the white dwarf asteroseismology, we investigate vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on regime of node-free global Lorentz-force-driven vibrations about symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke's force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfven modes whose frequency spectra are computed in analytic form showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The obtained spectral formulae are discussed in juxtaposition with those for Alfven modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfven vibrations in magnetic white dwarfs.