arXiv subjects

Koji Uryu

Publications and source records attributed to Koji Uryu.

At least 37 records · Page 2Linked to original sources

arXiv2011

A new code for equilibriums and quasiequilibrium initial data of compact objects

We present a new code, named COCAL - Compact Object CALculator, for the computation of equilibriums and quasiequilibrium initial data sets of single or binary compact objects of all kinds. In the cocal code, those solutions are calculated on one or multiple spherical coordinate patches covering the initial hypersurface up to the asymptotic region. The numerical method used to solve field equations written in elliptic form is an adaptation of self-consistent field iterations in which Green's integral formula is computed using multipole expansions and standard finite difference schemes. We extended the method so that it can be used on a computational domain with excised regions for a black hole and a binary companion. Green's functions are constructed for various types of boundary conditions imposed at the surface of the excised regions for black holes. The numerical methods used in cocal are chosen to make the code simpler than any other recent initial data codes, accepting the second order accuracy for the finite difference schemes. We perform convergence tests for time symmetric single black hole data on a single coordinate patch, and binary black hole data on multiple patches. Then, we apply the code to obtain spatially conformally flat binary black hole initial data using boundary conditions including the one based on the existence of equilibrium apparent horizons.

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arXiv2011

Neutron star equation of state via gravitational wave observations

Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence.

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arXiv2011

Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach

A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in GRMHD. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

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arXiv2010

Thermodynamics of magnetized binary compact objects

Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically-symmetric perfect-fluid spacetimes are extended to include the electromagnetic fields, and electric currents and charges; the first law is written as a relation between the change in the asymptotic Noether charge $\dl Q$ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetized fluid. Using the conservation laws of the circulation of magnetized flow found by Bekenstein and Oron for the ideal magnetohydrodynamic (MHD) fluid, and also for the flow with zero conducting current, we show that, for nearby equilibria that conserve the quantities mentioned above, the relation $\dl Q=0$ is satisfied. We also discuss a formulation for computing numerical solutions of magnetized binary compact objects in equilibrium with emphasis on a first integral of the ideal MHD-Euler equation.

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arXiv2010

Inferring the neutron star equation of state from binary inspiral waveforms

The properties of neutron star matter above nuclear density are not precisely known. Gravitational waves emitted from binary neutron stars during their late stages of inspiral and merger contain imprints of the neutron-star equation of state. Measuring departures from the point-particle limit of the late inspiral waveform allows one to measure properties of the equation of state via gravitational wave observations. This and a companion talk by J. S. Read reports a comparison of numerical waveforms from simulations of inspiraling neutron-star binaries, computed for equations of state with varying stiffness. We calculate the signal strength of the difference between waveforms for various commissioned and proposed interferometric gravitational wave detectors and show that observations at frequencies around 1 kHz will be able to measure a compactness parameter and constrain the possible neutron-star equations of state.

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arXiv2009

Non-conformally flat initial data for binary compact objects

A new method is described for constructing initial data for a binary neutron-star (BNS) system in quasi-equilibrium circular orbit. Two formulations for non-conformally flat data, waveless (WL) and near-zone helically symmetric (NHS), are introduced; in each formulation, the Einstein-Euler system, written in 3+1 form on an asymptotically flat spacelike hypersurface, is exactly solved for all metric components, including the spatially non-conformally flat potentials, and for irrotational flow. A numerical method applicable to both formulations is explained with an emphasis on the imposition of a spatial gauge condition. Results are shown for solution sequences of irrotational BNS with matter approximated by parametrized equations of state that use a few segments of polytropic equations of state. The binding energy and total angular momentum of solution sequences computed within the conformally flat -- Isenberg-Wilson-Mathews (IWM) -- formulation are closer to those of the third post-Newtonian (3PN) two point particles up to the closest orbits, for the more compact stars, whereas sequences resulting from the WL/NHS formulations deviate from the 3PN curve even more for the sequences with larger compactness. We think it likely that this correction reflects an overestimation in the IWM formulation as well as in the 3PN formula, by $\sim 1$ cycle in the gravitational wave phase during the last several orbits. The work suggests that imposing spatial conformal flatness results in an underestimate of the quadrupole deformation of the components of binary neutron-star systems in the last few orbits prior to merger.

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arXiv2009

Measuring the neutron star equation of state with gravitational wave observations

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc.

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arXiv2008

Quasi-equilibrium models for triaxially deformed rotating compact stars

Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state. Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids, centered at the source, in all angular directions up to a large truncation radius. Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations. Selected parameters are to model (proto-) neutron stars; the compactness is M/R = 0.001, 0.1, 0.14, 0.2 for polytropic index n = 0.3 and M/R = 0.001, 0.1, 0.12, 0.14 for n = 0.5. We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes. However, it is also found that the triaxial sequences become shorter for higher compactness, and those may disappear at a certain large compactness for the n = 0.5 case. In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling, it is plausible that, once the viscosity driven secular instability sets in during the contraction, the proto-neutron stars are always maximally deformed triaxial configurations, as long as the compactness and the equation of state parameters allow such triaxial sequences. Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state.

astro-ph↗

arXiv2007

Circular solution of two unequal mass particles in post-Minkowski approximation

A Fokker action for post-Minkowski approximation with the first post-Newtonian correction is introduced in our previous paper, and a solution for the helically symmetric circular orbit is obtained. We present supplemental results for the circular solution of two unequal mass point-particles. Circular solutions for selected mass ratios are found numerically, and analytic formulas in the extreme mass ratio limit are derived. The leading terms of the analytic formulas agree with the first post-Newtonian formulas in this limit.

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arXiv2007

Numerical method for binary black hole/neutron star initial data: Code test

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.

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arXiv2006

Merger of black hole-neutron star binaries: nonspinning black hole case

We perform a simulation for merger of a black hole (BH)-neutron star (NS) binary in full general relativity preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $Γ$-law equation of state with $Γ=2$. Corotating velocity field is assumed for the NS. The mass of the BH and the rest-mass of the NS are chosen to be $\approx 3.2 M_{\odot}$ and $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 14$ km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80%$ of the material is swallowed into the BH with small disk mass $\sim 0.3M_{\odot}$ even for such small BH mass $\sim 3M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome.

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arXiv2006

Merger of black hole-neutron star binaries in full general relativity

We present our latest results for simulation for merger of black hole (BH)-neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $Γ$-law equation of state with $Γ=2$ and corotating velocity field as a first step. The mass of the BH is chosen to be $\approx 3.2 M_{\odot}$ or $4.0M_{\odot}$, and the rest-mass of the NS $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 13$--14 km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80$--90% of the material is swallowed into the BH and resulting disk mass is not very large as $\sim 0.3M_{\odot}$ even for small BH mass $\sim 3.2M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries irrespective of BH mass, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome for this relatively small BH mass range as $\sim 3$--4$M_{\odot}$. Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.

astro-ph↗

arXiv2006

Binary neutron stars: Equilibrium models beyond spatial conformal flatness

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the 4-metric and an extrinsic curvature whose time derivative vanishes in a comoving frame. Two independent numerical codes are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are successfully computed. The binding energy of the system near its final orbit deviates from earlier results of third post-Newtonian and of spatially conformally flat calculations. The new solutions may serve as initial data for merger simulations and as members of quasiequilibrium sequences to generate gravitational wave templates, and may improve estimates of the gravitational-wave cutoff frequency set by the last inspiral orbit.

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arXiv2006

Models of helically symmetric binary systems

Results from helically symmetric scalar field models and first results from a convergent helically symmetric binary neutron star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity omega. In the scalar field models and the neutron star code, helical symmetry leads to a system of mixed elliptic-hyperbolic character. The scalar field models involve nonlinear terms that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used; and it improves with an outer boundary in the near zone. In the neutron star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than approximately 1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves; and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.

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arXiv2006

Post-Minkowski action for point particles and a helically symmetric binary solution

Two Fokker actions and corresponding equations of motion are obtained for two point particles in a post-Minkowski framework, in which the field of each particle is given by the half-retarded + half-advanced solution to the linearized Einstein equations. The first action is parametrization invariant, the second a generalization of the affinely parametrized quadratic action for a relativistic particle. Expressions for a conserved 4-momentum and angular momentum tensor are obtained in terms of the particles' trajectories in this post-Minkowski approximation. A formal solution to the equations of motion is found for a binary system with circular orbits. For a bound system of this kind, the post-Minkowski solution is a toy model that omits nonlinear terms of relevant post-Newtonian order; and we also obtain a Fokker action that is accurate to first post-Newtonian order, by adding to the post-Minkowski action a term cubic in the particle masses. Curiously, the conserved energy and angular momentum associated with the Fokker action are each finite and well-defined for this bound 2-particle system despite the fact that the total energy and angular momentum of the radiation field diverge. Corresponding solutions and conserved quantities are found for two scalar charges (for electromagnetic charges we exhibit the solution found by Schild). For a broad class of parametrization-invariant Fokker actions and for the affinely parametrized action, binary systems with circular orbits satisfy the relation $dE = ΩdL$ (a form of the first law of thermodynamics), relating the energy, angular velocity and angular momentum of nearby equilibrium configurations.

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arXiv2005

Merger of binary neutron stars with realistic equations of state in full general relativity

We present numerical results of three-dimensional simulations for the merger of binary neutron stars (BNSs) in full general relativity. Hybrid equations of state (EOSs) are adopted to mimic realistic nuclear EOSs. In this approach, we divide the EOSs into two parts, i.e., the thermal part and the cold part. For the cold part, we assign a fitting formula for realistic EOSs of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS EOSs for which the maximum allowed ADM mass of cold and spherical neutron stars (NSs) is ~ 2.04Mo and 1.80Mo, respectively. Simulations are performed for BNSs of the total ADM mass in the range between 2.4Mo and 2.8Mo with the rest-mass ratio Q_M to be in the range 0.9 < Q_M < 1. It is found that if the total ADM mass of the system is larger than a threshold M_{thr}, a black hole (BH) is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive NS of a large ellipticity, which results from the large adiabatic index of the realistic EOSs adopted. The value of M_{thr} depends on the EOS: ~ 2.7Mo and ~ 2.5Mo for the SLy and FPS EOSs, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive NS, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is < 100 ms, after which the hypermassive NS collapses to a BH. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than ~ 100 Mpc.

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arXiv2004

Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits

Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first law in the form $δM_{\rm ADM}=ΩδJ$, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and $Ω$ are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $δ$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $δM_{\rm ADM}$ and $ΩδJ$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

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arXiv2003

Merger of binary neutron stars of unequal mass in full general relativity

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A $Γ$-law equation of state $P=(Γ-1)ρε$ is adopted, where $P$, $ρ$, $\varep$, and $Γ$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take $Γ=2$ and the baryon rest-mass ratio $Q_M$ to be in the range 0.85--1. The typical grid size is $(633,633,317)$ for $(x,y,z)$ . We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest-mass of the system is more than $\sim 1.7$ times of the maximum allowed rest-mass of spherical neutron stars, a black hole is formed after the merger irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range $Q_M= 0.85$--1.

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