Effect of hyperon bulk viscosity on neutron-star r-modes

Neutron stars are expected to contain a significant number of hyperons in addition to protons and neutrons in the highest density portions of their cores. Following the work of Jones, we calculate the coefficient of bulk viscosity due to nonleptonic weak interactions involving hyperons in neutron-star cores, including new relativistic and superfluid effects. We evaluate the influence of this new bulk viscosity on the gravitational radiation driven instability in the r-modes. We find that the instability is completely suppressed in stars with cores cooler than a few times 10^9 K, but that stars rotating more rapidly than 10-30% of maximum are unstable for temperatures around 10^10 K. Since neutron-star cores are expected to cool to a few times 10^9 K within seconds (much shorter than the r-mode instability growth time) due to direct Urca processes, we conclude that the gravitational radiation instability will be suppressed in young neutron stars before it can significantly change the angular momentum of the star.Comment: final PRD version, minor typos etc correcte

Solving Einstein's Equations With Dual Coordinate Frames

A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original ``inertial'' coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein's equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.Comment: Updated to agree with published versio

Non-equilibrium beta processes in superfluid neutron star cores

The influence of nucleons superfluidity on the beta relaxation time of degenerate neutron star cores, composed of neutrons, protons and electrons, is investigated. We numerically calculate the implied reduction factors for both direct and modified Urca reactions, with isotropic pairing of protons or anisotropic pairing of neutrons. We find that due to the non-zero value of the temperature and/or to the vanishing of anisotropic gaps in some directions of the phase-space, superfluidity does not always completely inhibit beta relaxation, allowing for some reactions if the superfluid gap amplitude is not too large in respect to both the typical thermal energy and the chemical potential mismatch. We even observe that if the ratio between the critical temperature and the actual temperature is very small, a suprathermal regime is reached for which superfluidity is almost irrelevant. On the contrary, if the gap is large enough, the composition of the nuclear matter can stay frozen for very long durations, unless the departure from beta equilibrium is at least as important as the gap amplitude. These results are crucial for precise estimation of the superfluidity effect on the cooling/slowing-down of pulsars and we provide online subroutines to be implemented in codes for simulating such evolutions.Comment: 11 pages, 6 Figs., published, minor changes, subroutines can be found on line at http://luth2.obspm.fr/~etu/villain/Micro/Resolution.htm

Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.Comment: Published in Phys. Rev. D Rapid Comm. 66, 041303(R) (2002

Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found to be stable, except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure

Second-order rotational effects on the r-modes of neutron stars

Techniques are developed here for evaluating the r-modes of rotating neutron stars through second order in the angular velocity of the star. Second-order corrections to the frequencies and eigenfunctions for these modes are evaluated for neutron star models. The second-order eigenfunctions for these modes are determined here by solving an unusual inhomogeneous hyperbolic boundary-value problem. The numerical techniques developed to solve this unusual problem are somewhat non-standard and may well be of interest beyond the particular application here. The bulk-viscosity coupling to the r-modes, which appears first at second order, is evaluated. The bulk-viscosity timescales are found here to be longer than previous estimates for normal neutron stars, but shorter than previous estimates for strange stars. These new timescales do not substantially affect the current picture of the gravitational radiation driven instability of the r-modes either for neutron stars or for strange stars.Comment: 13 pages, 5 figures, revte

Nonlinear Development of the Secular Bar-mode Instability in Rotating Neutron Stars

We have modelled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation-reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating, axisymmetric $n=1/2$ polytropic star with a ratio of rotational to gravitational potential energy $T/|W| = 0.181$ is driven by GRR forces to a bar-like structure, as predicted by linear theory. The pattern frequency of the bar slows to nearly zero, that is, the bar becomes almost stationary as viewed from an inertial frame of reference as GRR removes energy and angular momentum from the star. In this ``Dedekind-like'' state, rotational energy is stored as motion of the fluid in highly noncircular orbits inside the bar. However, in less than 10 dynamical times after its formation, the bar loses its initially coherent structure as the ordered flow inside the bar is disrupted by what appears to be a purely hydrodynamical, short-wavelength, ``shearing'' type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented.Comment: 25 pages, 9 figures, accepted for publication in ApJ, refereed version, updated, for quicktime movie, see http://www.phys.lsu.edu/~ou/movie/fmode/new/fmode.b181.om4.2e5.mo

Toward stable 3D numerical evolutions of black-hole spacetimes

Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about 8000M, where M is the mass of the black hole. This degree of stability is achieved by using growth-rate estimates to guide the fine tuning of the parameters in a multi-parameter family of symmetric hyperbolic representations of the Einstein evolution equations. These evolutions were performed using a fixed gauge in order to separate the intrinsic stability of the evolution equations from the effects of stability-enhancing gauge choices.Comment: 4 pages, 5 figures. To appear in Phys. Rev. D. Minor additions to text for clarification. Added short paragraph about inner boundary dependenc

The rotational modes of relativistic stars: Numerical results

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure