Torsional shear oscillations in the neutron star crust driven by restoring force of elastic stresses

TL;DR

This paper provides exact solutions for torsional shear oscillations in neutron star crusts, analyzing their frequencies and boundary conditions, with implications for interpreting observed quasiperiodic oscillations during stellar flares.

Contribution

It introduces analytical models for torsional shear vibrations in neutron star crusts, emphasizing the effects of boundary conditions and crustal depth on oscillation frequencies.

Findings

Analytical expressions for torsional oscillation frequencies derived.

Frequency dependence on crustal depth and boundary conditions analyzed.

Models relevant to observed quasiperiodic oscillations in magnetar flares.

Abstract

We present several exact solutions of the eigenfrequency problem for torsional shear vibrations in homogeneous and non-homogeneous models of the neutron star crust governed by canonical equation of solid mechanics with a restoring force of Hookean elasticity. Particular attention is given to regime of large lengthscale nodeless axisymmetric differentially rotational oscillations which are treated in spherical polar coordinates reflecting real geometry of the neutron star crust. Highlighted is the distinction between analytic forms and numerical estimates of the frequency, computed as a function of multipole degree of nodeless torsional oscillations and fractional depth of the crust, caused by different boundary conditions imposed on the toroidal field of material displacements. The relevance of considered models to quasiperiodic oscillations, recently detected during the flare of SGR 1806-20 and SGR 1900+14, is discussed.