Self-similarity relations for torsional oscillations of neutron stars

Abstract

ABSTRACT Self-similarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wavefunction, i.e. at n = 0, and at all possible angular wave numbers ℓ ≥ 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n > 0 with ℓ ≥ 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants for a star of fixed mass can be accurately interpolated for stars of various masses (but the same equation of state). In addition, the torsional oscillations can be accurately studied in the flat space–time approximation within the crust. The results can be useful for investigating magneto-elastic oscillations of magnetars which are thought to be observed as quasi-periodic oscillations after flares of soft-gamma repeaters.