New approach to the evolution of neutron star oscillations

Abstract

We present a new derivation of the perturbation equations governing the oscillations of relativistic non-rotating neutron star models using the ADM-formalism. This formulation has the advantage that it immediately yields the evolution equations in a hyperbolic form, which is not the case for the Einstein field equations in their original form. We show that the perturbation equations can always be written in terms of spacetime variables only, regardless of any particular gauge. We demonstrate how to obtain the Regge-Wheeler gauge, by choosing appropriate lapse and shift. In addition, not only the 3-metric but also the extrinsic curvature of the initial slice have to satisfy certain conditions in order to preserve the Regge-Wheeler gauge throughout the evolution. We discuss various forms of the equations and show their relation to the formulation of Allen et al. New results are presented for polytropic equations of state. An interesting phenomenon occurs in very compact stars, where the first ring-down phase in the wave signal corresponds to the first quasinormal mode of an equal mass black hole, rather than to one of the proper quasinormal modes of the stellar model. A somewhat heuristic explanation to account for this phenomenon is given. For realistic equations of state, the numerical evolutions exhibit an instability, which does not occur for polytropic equations of state. We show that this instability is related to the behavior of the sound speed at the neutron drip point. As a remedy, we devise a transformation of the radial coordinate $r$ inside the star, which removes this instability and yields stable evolutions for any chosen numerical resolution.

25 pages, 8 figures, final version

References in corpus (6)

• Towards gravitational-wave asteroseismology
• Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star
• Nonlinear hydrodynamical evolution of rotating relativistic stars: Numerical methods and code tests
• Excitation of Neutron Star Oscillations by an Orbiting Particle
• The close-limit approximation to Neutron Star Collisions
• Construction of Astrophysical Initial Data for Perturbations of Relativistic Stars

Cited by in corpus (22)

• Extraction of Gravitational Waves in Numerical Relativity
• Gravitational Waves from Nonlinear Couplings of Radial and Polar Nonradial Modes in Relativistic Stars
• Parameter estimation of gravitational wave echoes from exotic compact objects
• Coupling of Radial and Axial non-Radial Oscillations of Compact Stars: Gravitational Waves from first-order Differential Rotation
• Gravitational-Wave Extraction from Neutron Star Oscillations: comparing linear and nonlinear techniques
• Scalar field induced oscillations of neutron stars and gravitational collapse
• On the r-mode spectrum of relativistic stars in the low-frequency approximation
• Spin-induced scalarization of Kerr black holes with a massive scalar field
• Accretion-driven gravitational radiation from nonrotating compact objects. Infalling quadrupolar shells
• On the r-mode spectrum of relativistic stars: Inclusion of the radiation reaction
• Coupling of radial and non-radial oscillations of relativistic stars: gauge-invariant formalism
• Dynamics of Fast Rotating Neutron Stars: An Approach in the Hilbert Gauge
• Excitation of Neutron Star Oscillations by an Orbiting Particle
• Fast Rotating Neutron Stars: Oscillations and Instabilities
• Evolution equations for the perturbations of slowly rotating relativistic stars
• Gravitational waves from pulsations of neutron stars described by realistic Equations of State
• Dynamical excitation of space-time modes of compact objects
• Massive scalar field perturbation on Kerr black holes in dynamical Chern-Simons gravity
• Gravitational waves from a dust disk around a Schwarzschild black hole
• Magnetic-induced Spontaneous Scalarization in Dynamcial Chern-Simons Gravity
• Separation of spacetime and matter in polar oscillations of compact stars
• Non-linear Oscillations of Compact Stars and Gravitational Waves