Torsional Nodeless Vibrations of a Quaking Neutron Star Restored by the Combined Forces of Shear Elastic and Magnetic Field Stresses

Abstract

Within the framework of Newtonian magneto-solid mechanics, relying on equations appropriate for a perfectly conducting elastic continuous medium threaded by a uniform magnetic field, the asteroseismic model of a neutron star undergoing axisymmetric global torsional nodeless vibrations under the combined action of Hooke's elastic and Lorentz magnetic forces is considered with emphasis on a toroidal Alfvén mode of differentially rotational vibrations about the dipole magnetic-moment axis of the star. The obtained spectral equation for frequency is applied to -pole identification of quasi-periodic oscillations (QPOs) of the X-ray flux during the giant flares of SGR 1806-20 and SGR 1900+14. Our calculations suggest that detected QPOs can consistently be interpreted, within the framework of this model, as being produced by global torsional nodeless vibrations of a quaking magnetar if they are considered to be restored by the joint action of bulk forces of shear elastic and magnetic field stresses.

Self-Gravitating Astrophysical Mass With Singular Central Density Vibrating in Fundamental Mode

“…These are stellar objects whose asteroseismology is adequately modeled by equations of fluid-dynamics, contrary to the extremely dense compact objects of finale stage of evolution track, white dwarfs and pulsars, the seismic vibrations of which are studied within the framework of solid star models relying on equations of solid mechanics, as reported in Refs. [13,[17][18][19]. Understandably, therefore, that mathematical treatment of node-free vibrations of a solid star in fundamental mode is different from the considered here fluid-dynamical theory of fundamental mode in liquid star models and this difference will be the subject our forthcoming paper.…”

On Hoyle-Narlikar-Wheeler mechanism of vibration energy powered magneto-dipole emission of neutron stars

“…It should be noted that above equations of solid-star model are applicable not only to neutron stars but also for white dwarfs Bastrukov et al 2010) and quark stars (Xu 2003(Xu , 2009. In this work, continuing investigations reported in Bastrukov et al (2009aBastrukov et al ( , 2009bBastrukov et al ( , 2010, we relax the assumption about constant-in-time undisturbed magnetic field and examine the impact of its decay on quake-induced vibrations and resultant magneto-dipole radiation.…”

“…The starting point in the study of node-free Alfvén (noncompression magneto-mechanical) vibrations of a neutron star (thought of as a spherical solid mass of a perfectly conducting non-flowing continuous matter with frozen-in constant-in-time magnetic field) are equations of magnetosolid-mechanics (Bastrukov et al 2009a(Bastrukov et al , 2009bMolodtsova et al 2010)…”

Frequency spectrum of toroidal Alfvén mode in a neutron star with Ferraro’s form of nonhomogeneous poloidal magnetic field

“…In the context of recent discovery of quasi-periodic oscillations (QPOs) in the X-ray luminosity during the giant flare of SGR 1806−20 and SGR 1900+14 that were interpreted as being produced by torsional vibrations of quaking magnetars (Israel et al 2005;Watts and Strohmayer 2006), in Bastrukov et al (2009aBastrukov et al ( , 2009b (3)…”

“…The most conspicuous feature of this regime is that the radial dependence of oscillating material displacements field u has no nodes. In a star undergoing global nodeless torsional oscillations, which are of particular interest for our present discussion, the fluctuating material displacements are described by the toroidal field of the form (Bastrukov et al 2007a(Bastrukov et al , 2007b(Bastrukov et al , 2009a …”