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

Quasi-radial modes of rotating stars in general relativity

By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing functions of the rotational frequency. The eigenfrequency curve of each mode as a function of the rotational frequency has discontinuities, which arise from the avoided crossing with other curves of axisymmetric modes.Comment: 7 pages, 10 figures, submitted to MNRAS. (revisions: new results are presented

Multi-Dimensional Astrophysical Structural and Dynamical Analysis I. Development of a Nonlinear Finite Element Approach

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.). The technique employed is the Finite Element Method (FEM), commonly used to solve engineering structural problems. The approach developed herein has the following key features: 1. The computational mesh can extend into the time dimension, as well as space, perhaps only a few cells, or throughout spacetime. 2. Virtually all equations describing the astrophysics of continuous media, including the field equations, can be written in a compact form similar to that routinely solved by most engineering finite element codes. 3. The transformations that occur naturally in the four-dimensional FEM possess both coordinate and boost features, such that (a) although the computational mesh may have a complex, non-analytic, curvilinear structure, the physical equations still can be written in a simple coordinate system independent of the mesh geometry. (b) if the mesh has a complex flow velocity with respect to coordinate space, the transformations will form the proper arbitrary Lagrangian- Eulerian advective derivatives automatically. 4. The complex difference equations on the arbitrary curvilinear grid are generated automatically from encoded differential equations. This first paper concentrates on developing a robust and widely-applicable set of techniques using the nonlinear FEM and presents some examples.Comment: 28 pages, 9 figures; added integral boundary conditions, allowing very rapidly-rotating stars; accepted for publication in Ap.

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

Analytical approximation for the structure of differentially rotating barotropes

Approximate analytical formula for density distribution in differentially rotating stars is derived. Any barotropic EOS and conservative rotation law can be handled with use of this method for wide range of differential rotation strength. Results are in good qualitative agreement with comparison to the other methods. Some applications are suggested and possible improvements of the formula are discussed.Comment: 10 pages, 13 figures, accepted for publication in Monthly Notice