Quark Matter in Neutron Star Mergers

Binary neutron star mergers are expected to be one of the most promising source of gravitational waves (GW) for the network of laser interferometric and bar detectors becoming operational in the next few years. The merger wave signal is expected to be sensitive to the interior structure of the neutron star (NS). The structure of high density phases of matter is under current experimental investigation in heavy-ion collisions. We investigate the dependence of the merger process and its GW signal on the presence of quarks in these phases by performing numerical simulations, where the smoothed particle hydrodynamics (SPH) method and the conformally flat approximation for the 3-geometry in general relativistic gravity are implemented.Comment: 4 Pages, 4 Figures, Proc. Nuclei in the Cosmos 7, 200

The influence of quark matter at high densities on binary neutron star mergers

We consider the influence of potential quark matter existing at high densities in neutron star (NS) interiors on gravitational waves (GWs) emitted in a binary NS merger event. Two types of equations of state (EoSs) at zero temperature are used - one describing pure nuclear matter and the other nuclear matter with a phase transition to quark matter at very high densities. Binary equilibrium sequences close to the innermost stable circular orbit (ISCO) are calculated to determine the GW frequencies just before the merger. It is found that the effects of the EoSs begin to play a role when gravitational masses are larger than M∞≃ 1.5 M⊙. The difference in the GW frequency at the ISCO increases by up to ≃10 per cent for the maximum mass permitted by the EoSs. We then perform three-dimensional hydrodynamic simulations for each EoS while varying the initial mass and determine the characteristic GW frequencies of the merger remnant. The implications of the presence of quark matter show up mainly in the collapse behaviour of the merger remnant. If the collapse does not take place immediately after the merger, we find a phase difference between the two EoSs in the post-merger GW signal. We also compare the GW frequencies emitted by the remnant of the merger to values obtained from simulations using a polytropic EoS and find an imprint of the non-constant adiabatic index of our EoSs. All calculations are based on the conformally flat approximation to general relativity and the GW signal from the merger simulation is extracted up to quadrupole orde

The Influence of Quark Matter at High Densities on Binary Neutron Star Mergers

We consider the influence of potential quark matter existing at high densities in neutron star interiors on gravitational waves (GW) emitted in a binary neutron star merger event. Two types of equations of state (EoS) at zero temperatures are used, one describing pure nuclear matter, the other nuclear matter with a phase transition to quark matter at very high densities. Binary equilibrium sequences close to the innermost stable circular orbit (ISCO) are calculated to determine the GW frequencies just before merger. It is found that EoS effects begin to play a role for gravitational masses larger than $M_\infty\simeq1.5M_\odot$. The difference in the gravitational wave frequency at the ISCO grows to up to $\simeq 10$ for the maximal allowed mass given by the EoSs used. Then, we perform 3D hydrodynamic simulations for each EoS varying the initial mass and determine the characteristic GW frequencies of the merger remnants. The implications of quark matter show up mainly in a different collapse behaviour of the merger remnant. If the collapse does not take place immediately after merger, we find a phase difference between two EoS's in the post-merger GW signal. We also compare the GW frequencies emitted by the merger remnant to values from simulations using a polytropic EoS and find an imprint of the non-constant adiabatic index of our EoSs. All calculations are based on the conformally flat (CF) approximation to general relativity and the GW signal from the merger simulation is extracted up to quadrupole order.Comment: 13 pages, 8 figure

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 $\Gamma$-law equation of state with $\Gamma=2$ 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.Comment: 14 pages. To appear in a special issue of Classical and Quantum Gravity: New Frontiers in Numerical Relativit

Equilibrium sequences of irrotational binary polytropic stars : The case of double polytropic stars

Solutions to equilibrium sequences of irrotational binary polytropic stars in Newtonian gravity are expanded in a power of $\epsilon=a_0/R$, where R and $a_0$ are the orbital separation of the binary system and the radius of each star for $R=\infty$. For each order of $\epsilon$, we should solve ordinary differential equations for arbitrary polytropic indices n. We show solutions for polytropic indices n= 0.5, 1, 1.5 and 2 up to $\epsilon^6$ orders. Our semi-analytic solutions can be used to check the validity of numerical solutions.Comment: 59 pages including 15 tables and 13 figures, revtex, accepted to Phys. Rev.

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.Comment: 20 pages, 18 figures, more results of convergence tests are added, revised version accepted for publication in PR

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.Comment: 19 pages, 7 figures. Expanded version of article to be published in Class. Quantum Grav. special issue on Numerical Relativit

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

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.Comment: 26 pages, to be published in PR

Relativistic Models for Binary Neutron Stars with Arbitrary Spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an n=1 polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19) by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.Comment: 21 pages, 14 figures. A few explanatory sentences added and some typos corrected. Accepted for publication in Phys. Rev.