Irrotational Binary Neutron Stars Research Articles

Binary neutron stars with arbitrary spins in numerical relativity

We present a code to construct initial data for binary neutron star systems in which the stars are rotating. Our code, based on a formalism developed by Tichy, allows for arbitrary rotation axes of the neutron stars and is able to achieve rotation rates near rotational breakup. We compute the neutron star angular momentum through quasi-local angular momentum integrals. When constructing irrotational binary neutron stars, we find a very small residual dimensionless spin of $\sim 2\times 10^{-4}$. Evolutions of rotating neutron star binaries show that the magnitude of the stars' angular momentum is conserved, and that the spin- and orbit-precession of the stars is well described by post-Newtonian approximation. We demonstrate that orbital eccentricity of the binary neutron stars can be controlled to $\sim 0.1\%$. The neutron stars show quasi-normal mode oscillations at an amplitude which increases with the rotation rate of the stars.

Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

We calculate quasiequilibrium sequences of equal-mass, irrotational binary neutron stars (BNSs) in a scalar-tensor (ST) theory of gravity that admits dynamical scalarization. We model neutron stars with realistic equations of state (notably through piecewise polytropic equations of state). Using these quasiequilibrium sequences we compute the binary's scalar charge and binding energy versus orbital angular frequency. We find that the absolute value of the binding energy is smaller than in general relativity (GR), differing at most by ~14% at high frequencies for the cases considered. We use the newly computed binding energy and the balance equation to estimate the number of gravitational-wave (GW) cycles during the adiabatic, quasicircular inspiral stage up to the end of the sequence, which is the last stable orbit or the mass-shedding point, depending on which comes first. We find that, depending on the ST parameters, the number of GW cycles can be substantially smaller than in GR. In particular, we obtain that when dynamical scalarization sets in around a GW frequency of ~130 Hz, the sole inclusion of the ST binding energy causes a reduction of GW cycles from ~120 Hz up to the end of the sequence (~1200 Hz) of ~11% with respect to the GR case. We estimate that when the ST energy flux is also included the reduction in GW cycles becomes of ~24%. Quite interestingly, dynamical scalarization can produce a difference in the number of GW cycles with respect to the GR point-particle case that is much larger than the effect due to tidal interactions, which is on the order of only a few GW cycles. These results further clarify and confirm recent studies that have evolved BNSs either in full numerical relativity or in post-Newtonian theory, and point out the importance of developing accurate ST-theory waveforms for systems composed of strongly self-gravitating objects, such as BNSs.

Compact binary evolutions with the Z4c formulation

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to truncation errors are between one and three orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of four smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the ADM mass from surface integrals. For equal-mass non-spinning binary puncture black hole evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of two smaller. In the same evolutions we find that away from the punctures the Hamiltonian constraint violation is reduced by between one and two orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirm earlier results in spherical symmetry. The boundary conditions avoid spurious and non-convergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge.

Numerical relativity simulations of binary neutron stars

We present a new numerical relativity code designed for simulations of compact binaries involving matter. The code is an upgrade of the BAM code to include general relativistic hydrodynamics and implements state-of-the-art high-resolution-shock-capturing schemes on a hierarchy of mesh refined Cartesian grids with moving boxes. We test and validate the code in a series of standard experiments involving single neutron star spacetimes. We present test evolutions of quasiequilibrium equal-mass irrotational binary neutron star configurations in quasicircular orbits which describe the late inspiral to merger phases. Neutron star matter is modeled as a zero-temperature fluid; thermal effects can be included by means of a simple ideal gas prescription. We analyze the impact that the use of different values of damping parameter in the Gamma-driver shift condition has on the dynamics of the system. The use of different reconstruction schemes and their impact in the post-merger dynamics is investigated. We compute and characterize the gravitational radiation emitted by the system. Self-convergence of the waves is tested, and we consistently estimate error bars on the numerically generated waveforms in the inspiral phase.

Impact of the nuclear equation of state on the last orbits of binary neutron stars

We present calculations of quasiequilibrium sequences of irrotational binary neutron stars based on realistic equations of state (EOS) for the whole neutron star interior. Three realistic nuclear EOSs of various softness and based on different microscopic models have been joined with a recent realistic EOS of the crust, giving in this way three different EOSs of neutron-star interior. Computations of quasiequilibrium sequences are performed within the Isenberg-Wilson-Mathews approximation to general relativity. For all evolutionary sequences, the innermost stable circular orbit (ISCO) is found to be given by mass-shedding limit (Roche lobe overflow). The EOS dependence on the last orbits is found to be quite important: for two 1.35 M_sol neutron stars, the gravitational wave frequency at the ISCO (which marks the end of the inspiral phase) ranges from 800 Hz to 1200 Hz, depending upon the EOS. Detailed comparisons with 3rd order post-Newtonian results for point-mass binaries reveals a very good agreement until hydrodynamical effects (dominated by high-order functions of frequency) become important, which occurs at a frequency ranging from 500 Hz to 1050 Hz, depending upon the EOS.

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.

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.

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. II. Newtonian limits

We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity. The solving method is a multidomain spectral method which we have recently developed. An improvement is introduced here for accurate computations of binary systems with a stiff equation of state $(\ensuremath{\gamma}>2).$ The computations are performed for both cases of synchronized and irrotational binary systems with adiabatic indices $\ensuremath{\gamma}=3, 2.5, 2.25, 2,$ and $1.8.$ It is found that the turning points of total energy along a constant-mass sequence appear only for $\ensuremath{\gamma}>~1.8$ for synchronized binary systems and $\ensuremath{\gamma}>~2.3$ for irrotational ones. In the synchronized case, the equilibrium sequences terminate by the contact between the two stars. On the other hand, for irrotational binaries, it is found that the sequences terminate at a mass shedding limit which corresponds to a detached configuration.

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests

We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with gamma=2.

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. The configurations are numerically computed assuming (1) the existence of a helicoidal Killing vector, (2) conformal flatness for spatial components of the metric, (3) irrotational velocity field for the neutron stars, and (4) masses of neutron stars to be identical. We adopt the polytropic equation of state and the computation is performed for a wide range of the polytropic index $n(=0.5,0.66667,0.8,1,1.25),$ and compactness of neutron stars ${(M/R)}_{\ensuremath{\infty}}(=0.03\ensuremath{-}0.3),$ where M and R denote the mass and radius of neutron stars in isolation. Because of the assumption of the irrotational velocity field, a sequence of fixed rest mass can be identified as an evolutionary track as a result of the radiation reaction of gravitational waves. Such solution sequences are computed from distant detached to innermost orbits where a cusp (inner Lagrange point) appears at the inner edges of the stellar surface. The stability of the orbital motions and the gravitational wave frequency at the innermost orbits are investigated. It is found that the innermost stable circular orbits (ISCO) appear for the case of a stiff equation of state with $n\ensuremath{\lesssim}2/3.$ We carefully analyze the ISCO for $n=0.5$ and show that the ISCO are mainly determined by a hydrodynamic instability for ${(M/R)}_{\ensuremath{\infty}}\ensuremath{\lesssim}0.2.$ We also investigate the total angular momentum and the specific angular momentum distribution of the binary configuration at the innermost orbits, where the final merger process starts. From these quantities, we expect the final outcomes of the binary neutron star coalescence.

New numerical method for constructing quasiequilibrium 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.

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

We have performed 3D numerical simulations for merger of equal mass binary neutron stars in full general relativity. We adopt a $\Gamma$-law equation of state in the form $P=(\Gamma-1)\rho\epsilon$ where P, $\rho$, $\varep$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant with $\Gamma=2$. 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_*.

Irrotational binary neutron stars in quasiequilibrium

We report on numerical results from an independent formalism to describe the quasi-equilibrium structure of nonsynchronous binary neutron stars in general relativity. This is an important independent test of controversial numerical hydrodynamic simulations which suggested that nonsynchronous neutron stars in a close binary can experience compression prior to the last stable circular orbit. We show that, for compact enough stars the interior density increases slightly as irrotational binary neutron stars approach their last orbits. The magnitude of the effect, however, is much smaller than that reported in previous hydrodynamic simulations.

Numerical Models of Irrotational Binary Neutron Stars in General Relativity

We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.

Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states

We present relativistic hydrostatic equations for obtaining irrotational binary neutron stars in quasi equilibrium states in 3+1 formalism. Equations derived here are different from those previously given by Bonazzola, Gourgoulhon, and Marck, and have a simpler and more tractable form for computation in numerical relativity. We also present hydrostatic equations for computation of equilibrium irrotational binary stars in first post-Newtonian order.

Irrotational Binary Neutron Stars in Quasi‐Equilibrium in General Relativity

Neutron stars in binary orbit emit gravitational waves and spiral slowly together. During this inspiral, they are expected to have very little vorticity. It is in fact a good approximation to treat the system as having zero vorticity, i.e., as irrotational. Because the orbital period is much shorter than the radiation reaction time scale, it is also an excellent approximation to treat the system as evolving through a sequence of equilibrium states, in each of which the gravitational radiation is neglected. In Newtonian gravity, one can simplify the hydrodynamic equations considerably for an equilibrium irrotational binary by introducing a velocity potential. The equations reduce to a Poisson-like equation for the potential, and a Bernoulli-type integral for the density. We show that a similar simplification can be carried out in general relativity. The resulting equations are much easier to solve than other formulations of the problem.

Stationary states of irrotational binary neutron star systems and their evolution as a result of 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.