arXiv subjects

Koji Uryu

Publications and source records attributed to Koji Uryu.

52 records · Page 3Linked to original sources

arXiv2002

Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation

We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large scale supercomputer. We take the typical grid size as (505,505,253) for (x,y,z) and the maximum grid size as (633,633,317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within $\sim 10%$ error) for the first time. To model neutron stars, we adopt a $Γ$-law equation of state in the form $P=(Γ-1)ρε$, where P, $ρ$, $\varep$ and $Γ$ are the pressure, rest mass density, specific internal energy, and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain.

gr-qc↗

arXiv2001

Thermodynamics of binary black holes and neutron stars

We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^α, heuristically, the generator of time-translations in a corotating frame. Systems that are stationary in this sense are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation. For black-hole binaries, a rigidity theorem implies that the Killing vector lies along the horizon's generators, and from this one can deduce the zeroth law (constant surface gravity of the horizon). Remarkably, although the mass and angular momentum of such a system are not defined, there is an exact first law, relating the change in the asymptotic Noether charge to the changes in the vorticity, baryon mass, and entropy of the fluid, and in the area of black holes. Binary systems with MΩsmall have an approximate asymptopia in which one can write the first law in terms of the asymptotic mass and angular momentum. Asymptotic flatness is precise in two classes of solutions used to model binary systems: spacetimes satisfying the post-Newtonian equations, and solutions to a modified set of field equations that have a spatially conformally flat metric. (The spatial conformal flatness formalism with helical symmetry, however, is consistent with maximal slicing only if replaces the extrinsic curvature in the field equations by an artificially tracefree expression in terms of the shift vector.) For these spacetimes, nearby equilibria whose stars have the same vorticity obey the relation δM = ΩδJ, from which one can obtain a turning point criterion that governs the stability of orbits.

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arXiv2001

Comparing the inspiral of irrotational and corotational binary neutron stars

We model the adiabatic inspiral of relativistic binary neutron stars in a quasi-equilibrium (QE) approximation, and compute the gravitational wavetrain from the late phase of the inspiral. We compare corotational and irrotational sequences and find a significant difference in the inspiral rate, which is almost entirely caused by differences in the binding energy. We also compare our results with those of a point-mass post-Newtonian calculation. We illustrate how the late inspiral wavetrain computed with our QE numerical scheme can be matched to the subsequent plunge and merger waveform calculated with a fully relativistic hydrodynamics code.

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arXiv2001

Computation of gravitational waves from inspiraling binary neutron stars in quasiequilibrium circular orbits : Formulation and calibration

Gravitational waves from binary neutron stars in quasiequilibrium circular orbits are computed using an approximate method which we propose in this paper. In the first step of this method, we prepare general relativistic irrotational binary neutron stars in a quasiequilibrium circular orbit, neglecting gravitational waves. We adopt the so-called conformal flatness approximation for a three-metric to obtain the quasiequilibrium states in this paper. In the second step, we compute gravitational waves, solving linear perturbation equations in the background spacetime of the quasiequilibrium states. Comparing numerical results with post Newtonian waveforms and luminosity of gravitational waves from two point masses in circular orbits, we demonstrate that this method can produce accurate waveforms and luminosity of gravitational waves. It is shown that the effects of tidal deformation of neutron stars and strong general relativistic gravity modify the post Newtonian results for compact binary neutron stars in close orbits. We indicate that the magnitude of a systematic error in quasiequilibrium states associated with the conformal flatness approximation is fairly large for close and compact binary neutron stars. Several formulations for improving the accuracy of quasiequilibrium states are proposed.

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arXiv2001

Gravitational Wave Emission by Cataclysmic Variables: numerical models of semi-detached binaries

Gravitational wave emission is considered to be the driving force for the evolution of short-period cataclysmic binary stars, making them a potential test for the validity of General Relativity. In spite of continuous refinements of the physical description, a 10% mismatch exists between the theoretical minimum period ($P_{\rm turn} \simeq 70$ min) and the short-period cut-off ($P_{\rm min} \simeq 80$ min) observed in the period distribution for cataclysmic variable binaries. A possible explanation for this mismatch was associated with the use of the Roche model. We here present a systematic comparison between self-consistent, numerically constructed sequences of hydrostatic models of binary stars and Roche models of semi-detached binaries. On the basis of our approach, we also derive a value for the minimum period of cataclysmic variable binaries. The results obtained through the comparison indicate that the Roche model is indeed very good, with deviations from the numerical solution which are of a few percent at most. Our results therefore suggest that additional sources of angular momentum loss or alternative explanations need to be considered in order to justify the mismatch.

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arXiv2001

Binary neutron star mergers in fully general relativistic simulations

We perform 3D numerical simulations for merger of equal mass binary neutron stars in full general relativity preparing irrotational binary neutron stars in a quasiequilibrium state as initial conditions. Simulations have been carried out for a wide range of stiffness of equations of state and compactness of neutron stars, paying particular attention to the final products and gravitational waves. We take a fixed uniform grid in Cartesian coordinates with typical grid size $(293,293,147)$ in $(x,y,z)$ assuming a plane symmetry with respect to the equatorial plane. A result of one new large-scale simulation performed with grid size $(505,505,253)$ is also presented. We find that the final product depends sensitively on the initial compactness of the neutron stars: In a merger between sufficiently compact neutron stars, a black hole is formed in a dynamical timescale. As the compactness is decreased, the formation timescale becomes longer and longer. For less compact cases, a differentially rotating massive neutron star is formed instead of a black hole. In the case of black hole formation, the disk mass around the black hole appears to be smaller than 1% of the total rest mass. It is also indicated that waveforms of high-frequency gravitational waves after merger depend strongly on the compactness of neutron stars.

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arXiv2001

Equilibrium and stability of supermassive stars in binary systems

We investigate the equilibrium and stability of supermassive stars of mass $M \agt 10^5M_{\odot}$ in binary systems. We find that corotating binaries are secularly unstable for close, circular orbits with $r \alt 4R(M/10^6M_{\odot})^{1/6}$ where $r$ is the orbital separation and $R$ the stellar radius. We also show that corotation cannot be achieved for distant orbits with $r \agt 12 R (M/10^6M_{\odot})^{-11/24}$, since the timescale for viscous angular momentum transfer associated with tidal torques is longer than the evolution timescale due to emission of thermal radiation. These facts suggest that the allowed mass range and orbital separation for corotating supermassive binary stars is severely restricted. In particular, for supermassive binary stars of large mass $M \agt 6\times 10^6M_{\odot}$, corotation cannot be achieved, as viscosity is not adequate to mediate the transfer between orbital and spin angular momentum. One possible outcome for binary supermassive stars is the onset of quasi-radial, relativistic instability which drives each star to collapse prior to merger: We discuss alternative outcomes of collapse and possible spin states of the resulting black holes. We estimate the frequency and amplitude of gravitational waves emitted during several inspiral and collapse scenarios.

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arXiv2000

Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits : Polytropic equations of state

We investigate close binary neutron stars in quasiequilibrium states in a general relativistic framework. We assume conformal flatness for the spatial metric and irrotational velocity field for the neutron stars. We adopt the polytropic equation of state. The computation is performed for the polytropic index n(=0.5, 0.66667, 0.8, 1, 1.25), and compactness of neutron stars M/R(=0.03 - 0.3). Results of this paper are as follows. (i) The sequences of the irrotational binary are always terminated at an innermost orbit where a cusp (inner Lagrange point)appears at the inner edges of the stellar surface. The binaries with cusps are found to be dynamically unstable for n=0.5 and stable for n > 0.8 irrespective of M/R < 0.2. For n=0.66667, the stability changes depending on M/R. (ii) The gravitational wave frequency at the innermost orbit turns out to be between 800 and 1500 Hz for realistic compactness 0.14 < M/R < 0.2. (iii) The ISCO for n=0.5 appears to be determined by a hydrodynamic instability for M/R < 0.2. We derive fitting formulae for the relation between the orbital angular velocity at the ISCO and the compactness to clarify it. (iv) The maximum density of neutron stars in binary systems slightly decreases with decreasing the orbital separation and hence they are stable against individual radial collapse during the inspiral. (v) q = J_tot/M_ADM^2 at the innermost orbits is always less than unity for M/R > 0.13 irrespective of n, which indicates that the realistic binary neutron stars satisfy a necessary condition (q<1) for formation of a black hole before the merger. (vi) The specific angular momentum of any mass element in irrotational binary neutron stars at the innermost orbit appears to be too small to form a disk around black holes formed after the merger.

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arXiv2000

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.

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arXiv1999

Simulation of merging binary neutron stars in full general relativity: $Γ=2$ case

We have performed 3D numerical simulations for merger of equal mass binary neutron stars in full general relativity. We adopt a $Γ$-law equation of state in the form $P=(Γ-1)ρε$ where P, $ρ$, $\varep$ and $Γ$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant with $Γ=2$. As initial conditions, we adopt models of corotational and irrotational binary neutron stars in a quasi-equilibrium state which are obtained using the conformal flatness approximation for the three geometry as well as an assumption that a helicoidal Killing vector exists. In this paper, we pay particular attention to the final product of the coalescence. We find that the final product depends sensitively on the initial compactness parameter of the neutron stars : In a merger between sufficiently compact neutron stars, a black hole is formed in a dynamical timescale. As the compactness is decreased, the formation timescale becomes longer and longer. It is also found that a differentially rotating massive neutron star is formed instead of a black hole for less compact binary cases, in which the rest mass of each star is less than 70-80% of the maximum allowed mass of a spherical star. In the case of black hole formation, we roughly evaluate the mass of the disk around the black hole. For the merger of corotational binaries, a disk of mass $\sim 0.05-0.1M_*$ may be formed, where M_* is the total rest mass of the system. On the other hand, for the merger of irrotational binaries, the disk mass appears to be very small : < 0.01M_*.

gr-qc↗

arXiv1999

Darwin-Riemann Problems in Newtonian Gravity

In this paper, we have reviewed the present status of the theory of equilibrium configurations of compact binary star systems in Newtonian gravity. Evolutionary processes of compact binary star systems due to gravitational wave emission can be divided into three stages according to the time scales and configurations. The evolution is quasi-stationary until a merging process starts, since the time scale of the orbital change due to gravitational wave emission is longer than the orbital period. In this stage, equilibrium sequences can be applied to evolution of compact binary star systems. Along the equilibrium sequences, there appear several critical states where some instability sets in or configuration changes drastically. We have discussed relations among these critical points and have stressed the importance of the mass overflow as well as the dynamical instability of orbital motions. Concerning the equilibrium sequences of binary star systems, we have summarized classical results of incompressible ellipsoidal configurations. Recent results of compressible binary star systems obtained by the ellipsoidal approximation and by numerical computations have been shown and discussed. It is important to note that numerical computational solutions to {\it exact equations} show that compressibility may lead realistic neutron star binary systems to mass overflows instead of dynamical disruptions for a wide range of parameters.

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arXiv1999

A new numerical scheme to compute 3D configurations of quasiequilibrium compact stars in general relativity -- Application to synchronously rotating binary star systems --

We have developed a new numerical scheme to obtain quasiequilibrium structures of nonaxisymmetric compact stars such as binary neutron star systems as well as the spacetime around those systems in general relativity. Concerning quasiequilibrium states of binary systems in general relativity, several investigations have been already carried out by assuming conformal flatness of the spatial part of the metric. However, the validity of the conformally flat treatment has not been fully analyzed except for axisymmetric configurations. Therefore it is desirable to solve quasiequilibrium states by developing totally different methods from the conformally flat scheme. In this paper we present a new numerical scheme to solve directly the Einstein equations for 3D configurations without assuming conformal flatness, although we make use of the simplified metric for the spacetime. This new formulation is the extension of the scheme which has been successfully applied for structures of axisymmetric rotating compact stars in general relativity. It is based on the integral representation of the Einstein equations by taking the boundary conditions at infinity into account. We have checked our numerical scheme by computing equilibrium sequences of binary polytropic star systems in Newtonian gravity and those of axisymmetric polytropic stars in general relativity. We have applied this numerical code to binary star systems in general relativity and have succeeded in obtaining several equilibrium sequences of synchronously rotating binary polytropes with the polytropic indices N = 0.0, 0.5 and 1.0.

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arXiv1998

Newtonian models for black hole-gaseous star close binary systems

Circularly orbiting black hole-gaseous star close binary systems are examined by using numerically exact stationary configurations in the framework of Newtonian gravity. We have chosen a polytropic star for the fluid component of the binary system and considered two ideal situations: 1) a synchronously rotating star and 2) an irrotationally rotating star. They correspond to a rotating star under the influence of viscosity and to that in the inviscid limit, respectively. By analyzing the stationary sequences of binary systems with small separations, we can discuss the final stages of black hole-gaseous star close binary systems. Our computational results show that the binary systems reach the Roche(-Riemann) limit states or the Roche lobe filling states without suffering from hydrodynamical instability due to tidal force for a large parameter range of the mass ratio and the polytropic index. It is very likely that such stable Roche(-Riemann) limits or Roche lobe filling states survive even under the general relativistic effect. Therefore, at the final stage of the evolution which is caused by the emission of gravitational waves, the Roche overflow will occur instead of merging of a black hole and a star.

astro-ph↗

arXiv1998

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.

astro-ph↗

arXiv1998

Incompressible fluid binary systems with internal flows -- models of close binary neutron star systems with spin

In this paper we have examined numerically exact configurations of close binary systems composed of incompressible fluids with internal flows. Component stars of binary systems are assumed to be circularly orbiting each other but rotating nonsynchronously with the orbital motion, i.e. stars in binary systems have steady motions seen from a rotational frame of reference. We have computed several equilibrium sequences by taking fully into account the tidal effect of Newtonian gravity without approximation. We consider two binary systems consisting of either 1) a point mass and a fluid star or 2) a fluid star and a fluid star. Each of them corresponds to generalization of the Roche--Riemann or the Darwin--Riemann problem, respectively. Our code can be applied to various types of incompressible binary systems with various mass ratios and spin as long as the vorticity is constant. We compare these equilibrium sequences of binaries with approximate solutions which were studied extensively by Lai, Rasio and Shapiro (LRS) as models for neutron star--neutron star (NS--NS) binary systems or black hole--neutron star (BH--NS) binary systems. Our results coincide qualitatively with those of LRS but are different from theirs for configurations with small separations. For these binary systems, our sequences show that dynamical or secular instability sets in as the separation decreases. The quantitative errors of the ellipsoidal approximation amount to 2\sim 10% for configurations near the instability point. Compared to the results of LRS, the separation of the stars at the point where the instability sets in is larger and correspondingly the orbital frequency at the critical state is smaller for our models.

astro-ph↗

arXiv1997

Stationary states of irrotational binary neutron star systems and their evolution due to gravitational wave emission

We have succeeded in obtaining exact configurations of irrotational binary systems for compressible (polytropic) equations of state. Our models correspond to binaries of equal mass neutron star systems in the viscosity free limit. By using the obtained sequences of stationary states, the evolution of binary systems of irrotational neutron stars due to gravitational wave emission has been examined. For inviscid binary systems the spin angular velocity of each component in a detached phase is smaller than the orbital angular velocity at a contact phase. Thus the irrotational approximation during evolution of binary neutron stars due to gravitational wave emission can be justified. Our computational results show that the binary will never reach a dynamically unstable state before a contact phase even for rather stiff polytropes with the index N > 0.7, as the separation of two components decreases due to gravitational wave emission. This conclusion is quantitatively different from that of Lai, Rasio & Shapiro who employed approximate solutions for polytropic binary systems.

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