Truncated post-Newtonian neutron star model

As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and truncate at the various order. We solve the system using the polytropic equation of state with index $\Gamma=5/3, 2$ and 3, and show how this approximation converges together with mass-radius relations. Next, we solve the Hamiltonian constraint equation with these density profiles as trial functions, and examine the differences in the final metric. We conclude the second `post-Newtonian' approximation is close enough to describe general relativistic single star. The result of this report will be useful for further binary studies. (Note to readers) This paper was accepted for publication in Physical Review D. [access code dsj637]. However, since I was strongly suggested that the contents of this paper should be included as a section in our group's future paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in PRD (Brief Report), but will not appea

General Relativistic Models of Binary Neutron Stars in Quasiequilibrium

We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit (ISCO) and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft >= 1.5. A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.Comment: 14 pages, 8 figures, RevTe

A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity

We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation to assume that (1) the binary star system is irrotational, i.e. the vorticity of the flow field inside component stars vanishes everywhere (irrotational flow), and (2) the binary star system is in quasi-equilibrium, for an inspiraling binary neutron star system just before the coalescence as a result of gravitational wave emission. We can introduce the velocity potential for such an irrotational flow field, which satisfies an elliptic partial differential equation (PDE) with a Neumann type boundary condition at the stellar surface. For a treatment of general relativistic gravity, we use the Wilson--Mathews formulation, which assumes conformal flatness for spatial components of metric. In this formulation, the basic equations are expressed by a system of elliptic PDEs. We have developed a method to solve these PDEs with appropriate boundary conditions. The method is based on the established prescription for computing equilibrium states of rapidly rotating axisymmetric neutron stars or Newtonian binary systems. We have checked the reliability of our new code by comparing our results with those of other computations available. We have also performed several convergence tests. By using this code, we have obtained quasi-equilibrium sequences of irrotational binary star systems with strong gravity as models for final states of real evolution of binary neutron star systems just before coalescence. Analysis of our quasi-equilibrium sequences of binary star systems shows that the systems may not suffer from dynamical instability of the orbital motion and that the maximum density does not increase as the binary separation decreases.Comment: 20 pages, 18 figures, more results of convergence tests are added, revised version accepted for publication in PR

Coalescing Binary Neutron Stars

Coalescing compact binaries with neutron star or black hole components provide the most promising sources of gravitational radiation for detection by the LIGO/VIRGO/GEO/TAMA laser interferometers now under construction. This fact has motivated several different theoretical studies of the inspiral and hydrodynamic merging of compact binaries. Analytic analyses of the inspiral waveforms have been performed in the Post-Newtonian approximation. Analytic and numerical treatments of the coalescence waveforms from binary neutron stars have been performed using Newtonian hydrodynamics and the quadrupole radiation approximation. Numerical simulations of coalescing black hole and neutron star binaries are also underway in full general relativity. Recent results from each of these approaches will be described and their virtues and limitations summarized.Comment: Invited Topical Review paper to appear in Classical and Quantum Gravity, 35 pages, including 5 figure

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

Damages of the tibial post in constrained total knee prostheses in the early postoperative course – a scanning electron microscopic study of polyethylene inlays

<p>Abstract</p> <p>Background</p> <p>Investigation of the risk of fracture of the polyethylene (PE) inlay in constrained total knee prostheses.</p> <p>Methods</p> <p>Three unused and seven polyethylene inlays that had been implanted in a patient's knee for an average of 25.4 months (min 1.1 months, max 50.2 months) were investigated using scanning electron microscopy (SEM). All inlays were of the same type and size (Genesis II constrained, Smith & Nephew). The PE surface at the transition from the plateau to the post was analyzed.</p> <p>Results</p> <p>The unused inlays had fissure-free surfaces. All inlays that had been implanted in a patient's knee already had distinct fissures at the front and backside of the post.</p> <p>Conclusion</p> <p>The fissures of the transition from the plateau to the post indicated a loading-induced irreversible mechanical deformation and possibly cause the fracture of the inlay.</p

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that stellar birth is primarily controlled by the interplay between gravity and magnetostatic support, modulated by ambipolar diffusion. Recently, however, both observational and numerical work has begun to suggest that support by supersonic turbulence rather than magnetic fields controls star formation. In this review we outline a new theory of star formation relying on the control by turbulence. We demonstrate that although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic scale star formation. (ABSTRACT ABBREVIATED)Comment: Invited review for "Reviews of Modern Physics", 87 pages including 28 figures, in pres