Gregory B. Cook

Rapidly Rotating Neutron Stars in General Relativity: Realistic Equations of State

We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for fourteen nuclear matter equations of state. We determine a number of important physical parameters for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well-suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian evolutionary sequences, and supramassive sequences, which exist solely because of relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves towards eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole. Keywords: pulsar, stars, neutron, rotation

Initial Data for Numerical Relativity

Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein’s equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3 + 1 decomposition of Einstein’s equations. We will then explore how these formalisms have been used in constructing initial data for spacetimes containing black holes and neutron stars. In the topics discussed, emphasis is placed on those issues that are important for obtaining astrophysically realistic initial data for compact binary coalescence.

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first ~15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%–7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly (<1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

Rapidly Rotating Polytropes in General Relativity

We construct an extensive set of equilibrium sequences of rotating polytropes in general relativity. We determine a number of important physical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial perturbations is diagnosed. Two classes of evolutionary sequences of fixed rest mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leading to loss of angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Proir to collapse, the star must spin up as it loses angular momentum, an effect which may provide an observational precursor to gravitational collapse to a black hole. Keywords: pulsars, stars, neutron, rotation

Excision boundary conditions for black-hole initial data

We define and extensively test a set of boundary conditions that can be applied at black-hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasicircular orbits and the determination of the innermost stable circular orbit. Our tests show that the boundary conditions work well.

Corotating and irrotational binary black holes in quasicircular orbits

A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the time scale for orbital decay is much longer than the orbital period, a binary can be considered to be in quasiequilibrium. If each black hole is assumed to be in quasiequilibrium, then a complete set of boundary conditions for all initial data variables can be developed. These boundary conditions are applied on the apparent horizon of each black hole, and in fact force a specified surface to be an apparent horizon. A global assumption of quasiequilibrium is also used to fix some of the freely specifiable pieces of the initial data and to uniquely fix the asymptotic boundary conditions. This formalism should allow for the construction of completely general quasiequilibrium black hole binary initial data.

Three-dimensional initial data for the collision of two black holes. II. Quasicircular orbits for equal-mass black holes.

The construction of initial-data sets representing binary black-hole configurations in quasi-circular orbits is studied in the context of the conformal-imaging formalism. An effective-potential approach for locating quasi-circular orbits is outlined for the general case of two holes of arbitrary size and with arbitrary spins. Such orbits are explicitly determined for the case of two equal-sized nonrotating holes, and the innermost stable quasi-circular orbit is located. The characteristics of this innermost orbit are compared to previous estimates for it, and the entire sequence of quasi-circular orbits is compared to results from the post-Newtonian approximation. Some aspects of the numerical evolution of such data sets are explored.

Binary neutron stars in general relativity: Quasiequilibrium models

We perform fully relativistic calculations of binary neutron stars in quasiequilibrium circular orbits. We integrate Einsteins equations together with the relativistic equation of hydrostatic equilibrium to solve the initial-value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasiequilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.

Roles of hyperons in neutron stars

We examine the roles the presence of hyperons in the cores of neutron stars may play in determining global properties of these stars. The study is based on estimates that hyperons appear in neutron star matter at about twice the nuclear saturation density, and emphasis is placed on effects that can be attributed to the general multi-species composition of the matter, hence being only weakly dependent on the specific modeling of strong interactions. Our analysis indicates that hyperon formation not only softens the equation of state but also severely constrains its values at high densities. Correspondingly, the valid range for the maximum neutron star mass is limited to about 1.5-1.8

Effects of Rapid Stellar Rotation on Equation-of-State Constraints Derived from Quasi-periodic Brightness Oscillations

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