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

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_*.Comment: 27 pages, to appear in Phys. Rev.

Excitation of the odd-parity quasi-normal modes of compact objects

The gravitational radiation generated by a particle in a close unbounded orbit around a neutron star is computed as a means to study the importance of the $w$ modes of the neutron star. For simplicity, attention is restricted to odd parity (``axial'') modes which do not couple to the neutron star's fluid modes. We find that for realistic neutron star models, particles in unbounded orbits only weakly excite the $w$ modes; we conjecture that this is also the case for astrophysically interesting sources of neutron star perturbations. We also find that for cases in which there is significant excitation of quadrupole $w$ modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.

Relativistic neutron star merger simulations with non-zero temperature equations of state I. Variation of binary parameters and equation of state

An extended set of binary neutron star (NS) merger simulations is performed with an approximative conformally flat treatment of general relativity to systematically investigate the influence of the nuclear equation of state (EoS), the neutron star masses, and the NS spin states prior to merging. We employ the two non-zero temperature EoSs of Shen et al. (1998a,b) and Lattimer & Swesty (1991). In addition, we use the cold EoS of Akmal et al. (1998) with a simple ideal-gas-like extension according to Shibata & Taniguchi (2006), and an ideal-gas EoS with parameters fitted to the supernuclear part of the Shen-EoS. We estimate the mass sitting in a dilute high-angular momentum ``torus'' around the future black hole (BH). The dynamics and outcome of the models is found to depend strongly on the EoS and on the binary parameters. Larger torus masses are found for asymmetric systems (up to ~0.3 M_sun for a mass ratio of 0.55), for large initial NSs, and for a NS spin state which corresponds to a larger total angular momentum. We find that the postmerger remnant collapses either immediately or after a short time when employing the soft EoS of Lattimer& Swesty, whereas no sign of post-merging collapse is found within tens of dynamical timescales for all other EoSs used. The typical temperatures in the torus are found to be about 3-10 MeV depending on the strength of the shear motion at the collision interface between the NSs and thus depending on the initial NS spins. About 10^{-3}-10^{-2} M_sun of NS matter become gravitationally unbound during or right after the merging process. This matter consists of a hot/high-entropy component from the collision interface and (only in case of asymmetric systems) of a cool/low-entropy component from the spiral arm tips. (abridged)Comment: 20 pages, 15 figures, accepted for publication in A&A, included changes based on referee comment

Stable Topologies of Event Horizon

In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe

Matter flows around black holes and gravitational radiation

We develop and calibrate a new method for estimating the gravitational radiation emitted by complex motions of matter sources in the vicinity of black holes. We compute numerically the linearized curvature perturbations induced by matter fields evolving in fixed black hole backgrounds, whose evolution we obtain using the equations of relativistic hydrodynamics. The current implementation of the proposal concerns non-rotating holes and axisymmetric hydrodynamical motions. As first applications we study i) dust shells falling onto the black hole isotropically from finite distance, ii) initially spherical layers of material falling onto a moving black hole, and iii) anisotropic collapse of shells. We focus on the dependence of the total gravitational wave energy emission on the flow parameters, in particular shell thickness, velocity and degree of anisotropy. The gradual excitation of the black hole quasi-normal mode frequency by sufficiently compact shells is demonstrated and discussed. A new prescription for generating physically reasonable initial data is discussed, along with a range of technical issues relevant to numerical relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to Phys. Rev.

Gravitational waves from a test particle scattered by a neutron star: Axial mode case

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius $R \lesssim 3M$), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).Comment: 21 pages, revtex, 11 figures are attached with eps files Accepted to Phys. Rev.

Unusual magnetic-field dependence of partially frustrated triangular ordering in manganese tricyanomethanide

Manganese tricyanomethanide, Mn[C(CN)3]2, consists of two interpenetrating three-dimensional rutile-like networks. In each network, the tridentate C(CN)3- anion gives rise to superexchange interactions between the Mn2+ ions (S=5/2) that can be mapped onto the "row model" for partially frustrated triangular magnets. We present heat capacity measurements that reveal a phase transition at T_N = 1.18K, indicative of magnetic ordering. The zero-field magnetically ordered structure was solved from neutron powder diffraction data taken between 0.04 and 1.2 K. It consists of an incommensurate spiral with a temperature independent propagation vector Q=(2Q 0 0)=(+/-0.622 0 0), where different signs relate to the two different networks. This corresponds to (+/-0.311 +/-0.311 0) in a quasi-hexagonal representation. The ordered moment mu=3.3mu_B is about 2/3 of the full Mn2+ moment. From the values of T_N and Q, the exchange parameters J/k = 0.15 K and J'/J = 0.749 are estimated. The magnetic-field dependence of the intensity of the Bragg reflection, measured for external fields H||Q, indicates the presence of three different magnetic phases. We associate them with the incommensurate spiral (H < 13.5 kOe), an intermediate phase (13.5 kOe 16 kOe) proposed for related compounds. For increasing fields, Q continuously approaches the value 1/3, corresponding to the commensurate magnetic structure of the fully frustrated triangular lattice. This value is reached at H_c = 19 kOe. At this point, the field-dependence reverses and Q adopts a value of 0.327 at 26 kOe, the highest field applied in the experiment. Except for H_c, the magnetic ordering is incommensurate in all three magnetic phases of Mn[C(CN)3]2.Comment: accepted for publication in J. Phys.: Condens. Matte