Axisymmetric spheroidal modes of neutron stars magnetized with poloidal magnetic fields

Abstract

We calculate axisymmetric spheroidal modes of neutron stars magnetized with an axisymmetric poloidal magnetic field. We use polytropes of the indices $n\sim 1$ as background equilibrium models of neutron stars where we ignore the deformation due to the magnetic fields. For a poloidal magnetic field, axisymmetric normal modes of non-rotating stars are decoupled into spheroidal modes and toroidal modes, and we can treat spheroidal modes separately from toroidal modes. For the surface field strength $B_S$ ranging from $10^{14}$G to $10^{16}$G, we calculate axisymmetric spheroidal magnetic modes whose oscillation frequency is proportional to $B_S$. The typical oscillation frequency of the magnetic modes is $\sim 0.01\times \sqrt{GM/R^3}$ for $B_S\sim 10^{15}$G, where $M$ and $R$ are respectively the mass and radius of the star and $G$ is the gravitational constant. For $M=1.4M_{\odot }$ and $R=10^6$cm, this frequency is $\sim 20$Hz, which may explain low frequency QPOs found for SGR 1806-204 and SGR 1900+14. We also find modes of frequency $>\sqrt{GM/R^3}$ corresponding to the radial fundamental and first harmonic modes. No unstable magnetic modes are found for axisymmetric spheroidal oscillations of magnetized stars.

arXiv commentsubmitted to MNRAS, 6 figures, 2 tables

References in corpus (32)

• The strongest cosmic magnets: Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars
• Discovery of Rapid X-ray Oscillations in the Tail of the SGR 1806-20 Hyperflare
• Discovery of Fast X-ray Oscillations During the 1998 Giant Flare from SGR 1900+14
• Global Seismic Oscillations in Soft Gamma Repeaters
• The 2004 Hyperflare from SGR 1806-20: Further Evidence for Global Torsional Vibrations
• Detection with RHESSI of high frequency X-ray oscillations in the tail of the 2004 hyperflare from SGR 1806-20
• QPOs during magnetar flares are not driven by mechanical normal modes of the crust
• Stability of magnetic fields in non-barotropic stars: an analytic treatment
• Magneto-elastic oscillations of neutron stars with dipolar magnetic fields
• On the theory of magnetar QPOs
• Alfvén QPOs in Magnetars
• Magnetars oscillations in the presence of a crust
• Magneto-elastic oscillations and the damping of crustal shear modes in magnetars
• Alfven QPOs in magnetars in the anelastic approximation
• Constraints on the Magnetic Field Geometry of Magnetars
• Magnetar Oscillations I: strongly coupled dynamics of the crust and the core
• Magneto-elastic oscillations of neutron stars: exploring different magnetic field configurations
• Quasi-periodic oscillations in superfluid magnetars
• Oscillations and instabilities in neutron stars with poloidal magnetic fields
• Alfvén Polar Oscillations of Relativistic Stars
• Stratification, superfluidity and magnetar QPOs
• Axisymmetric oscillations of magnetic neutron stars
• Magnetar Oscillations II: spectral method
• Axisymmetric toroidal modes of magnetized neutron stars
• Inertial modes of slowly rotating isentropic stars
• Oscillations of rotating magnetised neutron stars with purely toroidal magnetic fields
• R-modes of a neutron star with a magnetic dipole field
• Stability Analysis of Magnetised Neutron Stars - A Semi-analytic Approach
• Non-radial oscillations of the magnetized rotating stars with purely toroidal magnetic fields
• Axisymmetric toroidal modes of general relativistic magnetized neutron star models
• Non-axisymmetric magnetic modes of neutron stars with purely poloidal magnetic fields
• Neutron starquakes and the dynamic crust

Cited by in corpus (2)

• Effects of a strong magnetic field on internal gravity waves: trapping, phase mixing, reflection and dynamical chaos
• Axisymmetric magnetic modes of neutron stars having mixed poloidal and toroidal magnetic fields