Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes

Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes

We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an axisymmetric boundary condition, and the general relativistic hydrodynamic equations are solved using a high-resolution shock-capturing scheme based on an approximate Riemann solver. As tests, we performed the following simulations: (i) long-term evolution of non-rotating and rapidly rotating neutron stars, (ii) long-term evolution of neutron stars of a high-amplitude damping oscillation accompanied with shock formation, (iii) collapse of unstable neutron stars to black holes, and (iv) stellar collapses to neutron stars. The tests (i)--(iii) were carried out with the $\Gamma$-law equation of state, and the test (iv) with a more realistic parametric equation of state for high-density matter. We found that this new implementation works very well: It is possible to perform the simulations for stable neutron stars for more than 10 dynamical time scales, to capture strong shocks formed at stellar core collapses, and to accurately compute the mass of black holes formed after the collapse and subsequent accretion. In conclusion, this implementation is robust enough to apply to astrophysical problems such as stellar core collapse of massive stars to a neutron star and black hole, phase transition of a neutron star to a high-density star, and accretion-induced collapse of a neutron star to a black hole. The result for the first simulation of stellar core collapse to a neutron star started from a realistic initial condition is also presented.Comment: 28 pages, to appear in PRD 67, 0440XX (2003

Thermodynamic properties of the one-dimensional Kondo insulators studied by the density matrix renormalization group method

Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.Comment: 4 pages, 3 Postscript figures, REVTeX, submitted to J. Phys. Soc. Jp

A relativistic formalism for computation of irrotational binary stars in quasi equilibrium 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.Comment: 5 pages, corrected eqs.(2.10), (2.11) and (3.1

Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets

We derive a lattice $\beta$-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states

Black hole tidal problem in the Fermi normal coordinates

We derive a tidal potential for a self-gravitating fluid star orbiting Kerr black hole along a timelike geodesic extending previous works by Fishbone and Marck. In this paper, the tidal potential is calculated up to the third and fourth-order terms in $R/r$, where $R$ is the stellar radius and $r$ the orbital separation, in the Fermi-normal coordinate system following the framework developed by Manasse and Misner. The new formulation is applied for determining the tidal disruption limit (Roche limit) of corotating Newtonian stars in circular orbits moving on the equatorial plane of Kerr black holes. It is demonstrated that the third and fourth-order terms quantitatively play an important role in the Roche limit for close orbits with R/r \agt 0.1. It is also indicated that the Roche limit of neutron stars orbiting a stellar-mass black hole near the innermost stable circular orbit may depend sensitively on the equation of state of the neutron star.Comment: Correct typo

Thermodynamics of doped Kondo insulator in one dimension: Finite Temperature DMRG Study

The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature.Comment: 4 pages, 7 Postscript figures, REVTe

Possible explanation for star-crushing effect in binary neutron star simulations

A possible explanation is suggested for the controversial star-crushing effect seen in numerical simulations of inspiraling neutron star binaries by Wilson, Mathews and Marronetti (WMM). An apparently incorrect definition of momentum density in the momentum constraint equation used by WMM gives rise to a post-1-Newtonian error in the approximation scheme. We show by means of an analytic, post-1-Newtonian calculation that this error causes an increase of the stars' central densities which is of the order of several percent when the stars are separated by a few stellar radii, in agreement with what is seen in the simulations.Comment: 4 pages, 1 figure, uses revetx macros, minor revision

Mergers of binary stars: The ultimate heavy-ion experience

The mergers of black hole-neutron star binaries are calcuated using a pseudo-general relativistic potential that incorporates ${\mathcal O}(v^2/c^2)^3$ post-Newtonian corrections. Both normal matter neutron stars and self-bound strange quark matter stars are considered as black hole partners. As long as the neutron stars are not too massive relative to the black hole mass, orbital decay terminates in stable mass transfer rather than an actual merger. For a normal neutron star, mass transfer results in a widening of the orbit but the stable transfer ends before the minimum neutron star mass is reached. For a strange star, mass transfer does not result in an appreciable enlargement of the orbital separation, and the stable transfer continues until the strange star essentially disappears. These differences might be observable through their respective gravitational wave signatures.Comment: Contribution to QM04 proceedings. Submitted to Journal of Physics

Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.Comment: 5 pages, to appear in J. Phys. Soc. Jpn. Vol.73, No.8 (2004