2008/04/30 by W. Kastaun, Wolfgang Kastaun · 4 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Geophysics and Gravity Measurements #Inertial frame of reference #Mathematics #Nonlinear system #Normal mode #Oscillation (cell signaling) #Physics #Polytropic process #Pulsars and Gravitational Waves Research #Quantum mechanics #Rotation (mathematics) #Stellar, planetary, and galactic studies #Vibration #astro-ph
paper · pdf · doi:10.1103/physrevd.77.124019
published as Phys.Rev.D77:124019,2008 · 13 pages, 10 figures Fixed some typos, reformulated a few paragraphs, added 3 references
arxiv created 2008/05/22 · openalex publication_date 2008/06/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.