The oscillation and stability of differentially rotating spherical shells: The normal mode problem

Abstract

An understanding of the dynamics of differentially rotating systems is key to many areas of astrophysics. We investigate the oscillations of a simple system exhibiting differential rotation, and discuss issues concerning the role of corotation points and the emergence of dynamical instabilities. This problem is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess significant differential rotation immediately after birth or binary merger.

14 pages, 6 figures, minor error corrected, MNRAS in press

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Cited by in corpus (19)

• Gravitational waves from instabilities in relativistic stars
• The 2004 Hyperflare from SGR 1806-20: Further Evidence for Global Torsional Vibrations
• The nature of low T/|W| dynamical instabilities in differentially rotating stars
• Neutron star oscillations and QPOs during magnetar flares
• Differentially-rotating neutron star models with a parametrized rotation profile
• On the Shear Instability in Relativistic Neutron Stars
• Low T/|W| dynamical instability in differentially rotating stars: Diagnosis with canonical angular momentum
• Numerical-relativity simulations of long-lived remnants of binary neutron star mergers
• AMR simulations of the low T/|W| bar-mode instability of neutron stars
• Non-axisymmetric instability and fragmentation of general relativistic quasi-toroidal stars
• The oscillation and stability of differentially rotating spherical shells: The normal mode problem
• Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimuthal magnetic field
• Regularizing the r-mode problem for nonbarotropic relativistic stars
• Latitudinal Shear Instabilities during Type I X-ray Bursts
• The oscillation and stability of differentially rotating spherical shells: The initial value problem
• Inertial waves near corotation in 3D hydrodynamical disks
• On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars
• Stability of latitudinal differential rotation in stars
• The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation