Nonradial oscillations of neutron stars with a solid crust

Abstract

Abstract. Nonradial oscillations of relativistic neutron stars with a solid crust are computed in the relativistic Cowling approximation, in which all metric perturbations are ignored. For the modal analysis, we employ three-component relativistic neutron star models with a solid crust, a fluid core, and a fluid ocean. As a measure for the relativistic effects on the oscillation modes, we calculate the relative frequency difference defined as δσ/σ ≡ (σ GR − σ N )/σ GR , where σ GR and σ R are, respectively, the relativistic and the Newtonian oscillation frequencies. The relative difference δσ/σ takes various values for different oscillation modes of the neutron star model, and the value of δσ/σ for a given mode depends on the physical properties of the models. We find that |δσ/σ| is less than ∼0.1 for most of the oscillation modes we calculate, although there are a few exceptions such as the fundamental (nodeless) toroidal torsional modes in the crust, the surface gravity modes confined in the surface ocean, and the core gravity modes trapped in the fluid core. We also find that the modal properties, represented by the eigenfunctions, are not strongly affected by introducing general relativity. It is however shown that the mode characters of the two interfacial modes, associated with the core/crust and crust/ocean interfaces, have been interchanged between the two through an avoided crossing when we move from Newtonian dynamics to general relativistic dynamics.

Nonradial oscillation modes of compact stars with a crust

“…The Cowling approximation is expected to make at most 10% difference to the calculation of the eigenfrequencies of the p and f modes, and is widely used in the literature [24,32,60,61]. The calculation with the complete linearized system of equations in General Relativity without the Cowling approximation, which also yields the damping times for these modes, will be taken up in a following work.…”

“…The calculation with the complete linearized system of equations in General Relativity without the Cowling approximation, which also yields the damping times for these modes, will be taken up in a following work. The system of 4 fluid equations in General Relativity that we solve for the coupled core and crust are detailed in [32], as well as the Appendix of this paper for the sake of completeness. For a 2-component star, the crust eigenfunctions (2 for the fluid displacement and 2 for the tractions) are connected to those in the core through the condition of continuity of the radial displacement and tractions, while the horizontal component of the traction vanishes for an ideal fluid [33].…”

Neutron star asteroseismology. Axial crust oscillations in the Cowling approximation

“…In the isotropic limit these perturbation equations are equivalent to, e.g. those used by Yoshida & Lee (2002).…”

Crustal oscillations of slowly rotating relativistic stars

“…As in Yoshida & Lee (2002), the functions that appear in are In the Newtonian limit, ɛ→ 0, and dν/d r → g where g = M ( r )/ r 2 is the gravitational acceleration with d p /d r →−ρg. Therefore, the functions reduce to The functions V , U and c 1 are well known from the Newtonian theory, see e.g.…”

“…To describe the oscillations in the fluid‐core region, we use the following functions: The zeroth and first‐order spheroidal radial functions H 0 and H 1 are given by the relations: cf. relations of Yoshida & Lee (2002) for non‐rotating relativistic stars and relations (81), (86) and (87) of Lee & Strohmayer (1996) for rotating Newtonian stars.…”