Dynamical Bar Instability in Rotating Stars: Effect of General Relativity

Abstract

We study the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in the first post-Newtonian approximation of general relativity. We vary the compaction of the star $M/R$ (where $M$ is the gravitational mass and $R$ the equatorial circumferential radius) between 0.01 and 0.05 to isolate the influence of relativistic gravitation on the instability. For compactions in this moderate range, the critical value of $\beta \equiv T/W$ for the onset of the dynamical instability (where $T$ is the rotational kinetic energy and $W$ the gravitational binding energy) slightly decreases from $\sim 0.26$ to $\sim 0.25$ with increasing compaction for our choice of the differential rotational law. Combined with our earlier findings based on simulations in full general relativity for stars with higher compaction, we conclude that relativistic gravitation {\em enhances} the dynamical bar-mode instability, i.e. the onset of instability sets in for smaller values of $\beta$ in relativistic gravity than in Newtonian gravity. We also find that once a triaxial structure forms after the bar-mode perturbation saturates in dynamically unstable stars, the triaxial shape is maintained, at least for several rotational periods. To check the reliability of our numerical integrations, we verify that the general relativistic Kelvin-Helmholtz circulation is well-conserved, in addition to rest-mass energy, total mass-energy, linear and angular momentum. Conservation of circulation indicates that our code is not seriously affected by numerical viscosity. We determine the amplitude and frequency of the quasi-periodic gravitational waves emitted during the bar formation process using the quadrupole formula.

10 pages with 10 gif figures, emulateapj5.sty. Accepted for publication in The Astrophysical Journal

References in corpus (5)

• The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity
• Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests
• Gravitational Waves from Long-Duration Simulations of the Dynamical Bar Instability
• Fully general relativistic simulation of merging binary clusters -- Spatial gauge condition --
• Gravitational Waves from the Dynamical Bar Instability in a Rapidly Rotating Star

Cited by in corpus (47)

• Rotating Stars in Relativity
• Binary Neutron Star Mergers
• The astrophysical gravitational wave stochastic background
• Rotating Stars in Relativity
• Accurate simulations of the dynamical bar-mode instability in full General Relativity
• Anisotropic Hydrodynamics, Bulk Viscosities and R-Modes of Strange Quark Stars with Strong Magnetic Fields
• Gravitational Waves from Gravitational Collapse
• Phase transition effects on the dynamical stability of hybrid neutron stars
• Three-dimensional simulations of stellar core collapse in full general relativity: Nonaxisymmetric dynamical instabilities
• One-Armed Spiral Instability in Differentially Rotating Stars
• Hydrodynamic Simulations in 3+1 General Relativity
• Phase transitions in neutron stars and their links to gravitational waves
• On the Shear Instability in Relativistic Neutron Stars
• Dynamical non-axisymmetric instabilities in rotating relativistic stars
• Low T/|W| dynamical instability in differentially rotating stars: Diagnosis with canonical angular momentum
• Formation of an evanescent proto-neutron star binary and the origin of pulsar kicks
• The Transient Gravitational-Wave Sky
• Modeling differential rotations of compact stars in equilibriums
• Models of Rapidly Rotating Neutron Stars: Remnants of Accretion Induced Collapse
• Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity
• Testing the nonlinear stability of Kerr-Newman black holes
• Dynamical bar-mode instability in rotating and magnetized relativistic stars
• Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars
• Post-Newtonian SPH calculations of binary neutron star coalescence. III. Irrotational systems and gravitational wave spectra
• Gravitational wave background from sub-luminous GRBs: prospects for second and third generation detectors
• Dynamical instability of new-born neutron stars as sources of gravitational radiation
• Dynamical $\ell$-boson stars: generic stability and evidence for non-spherical solutions
• Are rotating strange quark stars good sources of gravitational waves?
• Non-axisymmetric instability and fragmentation of general relativistic quasi-toroidal stars
• Numerical evolution of secular bar-mode instability induced by the gravitational radiation reaction in rapidly rotating neutron stars
• The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations
• Head-on collisions of $\ell$-boson stars
• Quasi-equilibrium models for triaxially deformed rotating compact stars
• Instabilities in neutron-star postmerger remnants
• The Gravitational Wave Signature of Core-Collapse Supernovae
• The Formation of Supermassive Black Holes and the Evolution of Supermassive Stars
• Lower limits on the maximum orbital frequency around rotating strange stars
• Low-$T/|W|$ instabilities in differentially rotating proto-neutron stars with magnetic fields
• Gravitational Wave Astronomy
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• Dynamical bar instability in a relativistic rotational core collapse
• On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars
• Faraday resonance in dynamical bar instability of differentially rotating stars
• General-relativistic resistive-magnetohydrodynamics simulations of self-consistent magnetized rotating neutron stars
• Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars
• Spinning solutions in general relativity with infinite central density
• MIR: a general-relativistic resistive-magneto-hydrodynamic code to study the effect of resistivity in Neutron Star dynamics