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

Bulk viscosity in superfluid neutron star cores. I. Direct Urca processes in npe\mu matter

The bulk viscosity of the neutron star matter due to the direct Urca processes involving nucleons, electrons and muons is studied taking into account possible superfluidity of nucleons in the neutron star cores. The cases of singlet-state pairing or triplet-state pairing (without and with nodes of the superfluid gap at the Fermi surface) of nucleons are considered. It is shown that the superfluidity may strongly reduce the bulk viscosity. The practical expressions for the superfluid reduction factors are obtained. For illustration, the bulk viscosity is calculated for two models of dense matter composed of neutrons, protons,electrons and muons. The presence of muons affects the bulk viscosity due to the direct Urca reactions involving electrons and produces additional comparable contribution due to the direct Urca reactions involving muons. The results can be useful for studying damping of vibrations of neutron stars with superfluid cores.Comment: 14 pages, 7 figures, latex, uses aa.cls, to be published in Astronomy and Astrophysic

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

On the black hole limit of rotating fluid bodies in equilibrium

Recently, it was shown that the extreme Kerr black hole is the only candidate for a (Kerr) black hole limit of stationary and axisymmetric, uniformly rotating perfect fluid bodies with a zero temperature equation of state. In this paper, necessary and sufficient conditions for reaching the black hole limit are presented.Comment: 8 pages, v2: one footnote and one reference added, accepted for publication in CQ

Elastic Stars in General Relativity: II. Radial perturbations

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a Sturm-Liouville type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalisation of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in Paper I of this series.Comment: 22 pages, no figures, final version accepted for publication in Class. Quantum Grav. The treatment of the junction conditions has been improve

R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism

We derive the hydrodynamical equations of r-mode oscillations in neutron stars in presence of a novel damping mechanism related to particle number changing processes. The change in the number densities of the various species leads to new dissipative terms in the equations which are responsible of the {\it rocket effect}. We employ a two-fluid model, with one fluid consisting of the charged components, while the second fluid consists of superfluid neutrons. We consider two different kind of r-mode oscillations, one associated with comoving displacements, and the second one associated with countermoving, out of phase, displacements.Comment: 10 page

Gravitational Helioseismology?

The magnitudes of the external gravitational perturbations associated with the normal modes of the Sun are evaluated to determine whether these solar oscillations could be observed with the proposed Laser Interferometer Space Antenna (LISA), a network of satellites designed to detect gravitational radiation. The modes of relevance to LISA---the $l=2$, low-order $p$, $f$ and $g$-modes---have not been conclusively observed to date. We find that the energy in these modes must be greater than about $10^{30} \rm{ergs}$ in order to be observable above the LISA detector noise. These mode energies are larger than generally expected, but are much smaller than the current observational upper limits. LISA may be confusion-limited at the relevant frequencies due to the galactic background from short-period white dwarf binaries. Present estimates of the number of these binaries would require the solar modes to have energies above about $10^{33} \rm{ergs}$ to be observable by LISA.Comment: 8 pages; prepared with REVTEX 3.0 LaTeX macro

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling coefficients, added new selection rule and an appendix on energy and angular momentum of mode

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala