Inertial modes of rigidly rotating neutron stars in Cowling approximation

Journal Article · Sun Jun 15 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.124019· OSTI ID:21212029

Kastaun, Wolfgang ^[1]

---

1. Department of Theoretical Astrophysics, Universitaet Tuebingen, 72076 Tuebingen (Germany)

In this article, we investigate inertial modes of rigidly rotating neutron stars, i.e. modes for which the Coriolis force is dominant. This is done using the assumption of a fixed spacetime (Cowling approximation). We present frequencies and eigenfunctions for a sequence of stars with a polytropic equation of state, covering a broad range of rotation rates. The modes were obtained with a nonlinear general relativistic hydrodynamic evolution code. We further show that the eigenequations for the oscillation modes can be written in a particularly simple form for the case of arbitrary fast but rigid rotation. Using these equations, we investigate some general characteristics of inertial modes, which are then compared to the numerically obtained eigenfunctions. In particular, we derive a rough analytical estimate for the frequency as a function of the number of nodes of the eigenfunction, and find that a similar empirical relation matches the numerical results with unexpected accuracy. We investigate the slow rotation limit of the eigenequations, obtaining two different sets of equations describing pressure and inertial modes. For the numerical computations we only considered axisymmetric modes, while the analytic part also covers nonaxisymmetric modes. The eigenfunctions suggest that the classification of inertial modes by the quantum numbers of the leading term of a spherical harmonic decomposition is artificial in the sense that the largest term is not strongly dominant, even in the slow rotation limit. The reason for the different structure of pressure and inertial modes is that the Coriolis force remains important in the slow rotation limit only for inertial modes. Accordingly, the scalar eigenequation we obtain in that limit is spherically symmetric for pressure modes, but not for inertial modes.

• OSTI ID: 21212029
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
AXIAL SYMMETRY
CLASSIFICATION
CORIOLIS FORCE
DECOMPOSITION
EIGENFUNCTIONS
EQUATIONS OF STATE
EVOLUTION
NEUTRON STARS
NONLINEAR PROBLEMS
OSCILLATION MODES
QUANTUM NUMBERS
RELATIVISTIC RANGE
ROTATION
SPACE-TIME
SPHERICAL CONFIGURATION