Non-radial oscillations of the magnetized rotating stars with purely toroidal magnetic fields

Abstract

We calculate non-axisymmetric oscillations of uniformly rotating polytropes magnetized with a purely toroidal magnetic field, taking account of the effects of the deformation due to the magnetic field. As for rotation, we consider only the effects of Coriolis force on the oscillation modes, ignoring those of the centrifugal force, that is, of the rotational deformation of the star. Since separation of variables is not possible for the oscillation of rotating magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We calculate magnetically modified normal modes such as $g$-, $f$-, $p$-, $r$-, and inertial modes. In the lowest order, the frequency shifts produced by the magnetic field scale with the square of the characteristic Alfvén frequency. As a measure of the effects of the magnetic field, we calculate the proportionality constant for the frequency shifts for various oscillation modes. We find that the effects of the deformation are significant for high frequency modes such as $f$- and $p$-modes but unimportant for low frequency modes such as $g$-, $r$-, and inertial modes.

References in corpus (16)

• The strongest cosmic magnets: Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars
• Torsional Oscillations of Relativistic Stars with Dipole Magnetic Fields
• QPOs during magnetar flares are not driven by mechanical normal modes of the crust
• On the theory of magnetar QPOs
• Elastic or magnetic? A toy model for global magnetar oscillations with implications for QPOs during flares
• Alfvén QPOs in Magnetars
• Relativistic models of magnetars: structure and deformations
• Magnetars oscillations in the presence of a crust
• Hydromagnetic Instabilities in Neutron Stars
• Variability from Nonaxisymmetric Fluctuations Interacting with Standing Shocks in Tilted Black Hole Accretion Disks
• Relativistic stars with purely toroidal magnetic fields
• Constraints on the Magnetic Field Geometry of Magnetars
• Quasi-Periodic Oscillations in Short Recurring Bursts of the Soft-Gamma Repeater J1550-5418
• Axisymmetric oscillations of magnetic neutron stars
• Axisymmetric toroidal modes of magnetized neutron stars
• Axisymmetric toroidal modes of general relativistic magnetized neutron star models

Cited by in corpus (5)

• Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimuthal magnetic field
• Quasi-periodic oscillations in superfluid, relativistic magnetars with nuclear pasta phases
• Oscillations of Highly Magnetized Non-rotating Neutron Stars
• Evolution of newborn rapidly rotating magnetars: effects of r-mode and fall-back accretion
• Axisymmetric spheroidal modes of neutron stars magnetized with poloidal magnetic fields