Stationary structures of irrotational binary systems -- models for close binary systems of compact stars

We propose a new numerical method to calculate irrotational binary systems composed of compressible gaseous stars in Newtonian gravity. Assuming irrotationality, i.e. vanishing of the vorticity vector everywhere in the star in the inertial frame, we can introduce the velocity potential for the flow field. Using this velocity potential we can derive a set of basic equations for stationary states which consist of (i) the generalized Bernoulli equation, (ii) the Poisson equation for the Newtonian gravitational potential and (iii) the equation for the velocity potential with the Neumann type boundary condition. We succeeded in developing a new code to compute numerically exact solutions to these equations for the first time. Such irrotational configurations of binary systems are appropriate models for realistic neutron star binaries composed of inviscid gases, just prior to coalescence of two stars caused by emission of gravitational waves. Accuracies of our numerical solutions are so high that we can compute reliable models for fully deformed final stationary configurations and hence determine the inner most stable circular orbit of binary neutron star systems under the approximations of weak gravity and inviscid limit.Comment: 32 pages, 25 bitmapped ps files, to appear in ApJ supplemen

Pattern Matching and Discourse Processing in Information Extraction from Japanese Text

Information extraction is the task of automatically picking up information of interest from an unconstrained text. Information of interest is usually extracted in two steps. First, sentence level processing locates relevant pieces of information scattered throughout the text; second, discourse processing merges coreferential information to generate the output. In the first step, pieces of information are locally identified without recognizing any relationships among them. A key word search or simple pattern search can achieve this purpose. The second step requires deeper knowledge in order to understand relationships among separately identified pieces of information. Previous information extraction systems focused on the first step, partly because they were not required to link up each piece of information with other pieces. To link the extracted pieces of information and map them onto a structured output format, complex discourse processing is essential. This paper reports on a Japanese information extraction system that merges information using a pattern matcher and discourse processor. Evaluation results show a high level of system performance which approaches human performance.Comment: See http://www.jair.org/ for any accompanying file

Dynamical instability of differentially rotating stars

We study the dynamical instability against bar-mode deformation of differentially rotating stars. We performed numerical simulation and linear perturbation analysis adopting polytropic equations of state with the polytropic index $n=1$. It is found that rotating stars of a high degree of differential rotation are dynamically unstable even for the ratio of the kinetic energy to the gravitational potential energy of $O(0.01)$. Gravitational waves from the final nonaxisymmetric quasistationary states are calculated in the quadrupole formula. For rotating stars of mass $1.4M_{\odot}$ and radius several 10 km, gravitational waves have frequency several 100 Hz and effective amplitude $\sim 5 \times 10^{-22}$ at a distance of $\sim 100$ Mpc.Comment: 5 pages, 7 figures, accepted for publication in MNRA

Possible evolutionary transition from rapidly rotating neutron stars to strange stars due to spin-down

We present a scenario of formation of strange stars due to spin-down of {\it rapidly rotating} neutron stars left after supernova explosions . By assuming a process where the total baryon mass is conserved but the angular momentum is lost due to emission of gravitational waves and/or the magnetic braking, we find that the transition from rapidly rotating neutron stars to slowly rotating strange stars is possible; a large amount of energy $\sim 10^{53} ergs$ could be released. The liberated energy might become a new energy source for a delayed explosion of supernova. Furthermore, our scenario suggests that the supernova associated with gamma-ray bursts could become candidates for targets in the future observation of gravitational waves.Comment: 11 pages, 3 figures, Received November 5, 200

Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity

Using a multi domain spectral method, we investigate systematically the general-relativistic model for axisymmetric uniformly rotating, homogeneous fluid bodies generalizing the analytically known Maclaurin and Schwarzschild solutions. Apart from the curves associated with these solutions and a further curve of configurations that rotate at the mass shedding limit, two more curves are found to border the corresponding two parameter set of solutions. One of them is a Newtonian lens shaped sequence bifurcating from the Maclaurin spheroid sequence, while the other one corresponds to highly relativistic bodies with an infinite central pressure. The properties of the configuration for which both the gravitational and the baryonic masses, moreover angular velocity, angular momentum as well as polar red shift obtain their maximal values are discussed in detail. In particular, by comparison with the static Schwarzschild solution, we obtain an increase of 34.25% in the gravitational mass. Moreover, we provide exemplarily a discussion of angular velocity and gravitational mass on the entire solution class.Comment: 4 pages, 4 figures, 1 table, submitted to A&A, corrected eq. for W, W' in 3.

Dynamical bar-mode instability of differentially rotating stars: Effects of equations of state and velocity profiles

As an extension of our previous work, we investigate the dynamical instability against nonaxisymmetric bar-mode deformations of differentially rotating stars in Newtonian gravity varying the equations of state and velocity profiles. We performed the numerical simulation and the followup linear stability analysis adopting polytropic equations of state with the polytropic indices n=1, 3/2, and 5/2 and with two types of angular velocity profiles (the so-called j-constant-like and Kepler-like laws). It is confirmed that rotating stars of a high degree of differential rotation are dynamically unstable against the bar-mode deformation, even for the ratio of the kinetic energy to the gravitational potential energy $\beta$ of order 0.01. The criterion for onset of the bar-mode dynamical instability depends weakly on the polytropic index n and the angular velocity profile as long as the degree of differential rotation is high. Gravitational waves from the final nonaxisymmetric quasi-stationary states are calculated in the quadrupole formula. For proto-neutron stars of mass $1.4M_{\odot}$, radius $\sim 30$ km and \beta \alt 0.1, such gravitational waves have the frequency of $\sim$ 600--1,400 Hz, and the effective amplitude is larger than $10^{-22}$ at a distance of about 100 Mpc irrespective of n and the angular velocity profile.Comment: 9 pages, 14 figures, accepted to MNRA

Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Black Holes Surrounded by Uniformly Rotating Rings

Highly accurate numerical solutions to the problem of Black Holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some detail. Related Newtonian problems are described and numerical results provided, which show that configurations can reach an inner mass-shedding limit as the mass of the central object increases. Exemplary results for the full relativistic problem for rings of constant density are given and the deformation of the event horizon due to the presence of the ring is demonstrated. Finally, we provide an example of a system for which the angular momentum of the central Black Hole divided by the square of its mass exceeds one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected, corresponds to version in PR

Highly accurate calculation of rotating neutron stars

A new spectral code for constructing general-relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with those obtained by several previous codes. Moreover, representative relativistic examples corresponding to highly flattened rotating bodies are given.Comment: 4 pages, submitted to Astronomy & Astrophysic