Abstract:
We present the results of three-dimensional hydrodynamical simulations of the final stages of inspiral in a black hole-neutron star binary, when the separation is comparable to the stellar radius. We use a Newtonian Smooth Particle Hydrodynamics (SPH) code to model the evolution of the system, and take the neutron star to be a polytrope with a soft (adiabatic index G=2 and G=5/3) equation of state and the black hole to be a Newtonian point mass. The only non-Newtonian effect we include is a gravitational radiation back reaction force, computed in the quadrupole approximation for point masses. We use irrotational binaries as initial conditions for our dynamical simulations, which are begun when the system is on the verge of initiating mass transfer and followed for approximately 23 ms. For all the cases studied we find that the star is disrupted on a dynamical time-scale, and forms a massive (the disc mass is approximately 0.2 solar masses) accretion torus around the spinning (Kerr) black hole. The rotation axis is clear of baryons (less than 1.e-5 solar masses within 10 degrees) to an extent that would not preclude the formation of a relativistic fireball capable of powering a cosmological gamma ray burst. Some mass (the specific amount is sensitive to the stiffness of the equation of state) may be dynamically ejected from the system during the coalescence and could undergo r-process nucleosynthesis. We calculate the waveforms, luminosities and energy spectra of the gravitational radiation signal and show how they reflect the global outcome of the coalescence process.

Abstract:
We present a numerical study of the hydrodynamics in the final stages of inspiral of a black hole-neutron star binary, when the binary separation becomes comparable to the stellar radius. We use a Newtonian three-dimensional Smooth Particle Hydrodynamics (SPH) code, and model the neutron star with a soft (adiabatic index Gamma=5/3) polytropic equation of state and the black hole as a Newtonian point mass which accretes matter via an absorbing boundary at the Schwarzschild radius. Our initial conditions correspond to tidally locked binaries in equilibrium, and we have explored configurations with different values of the mass ratio q=Mns/Mbh, ranging from q=1 to q=0.1. The dynamical evolution is followed for approximately 23 ms, and in every case studied here we find that the neutron star is tidally disrupted on a dynamical timescale, forming a dense torus around the black hole that contains a few tenths of a solar mass. A nearly baryon-free axis is present in the system throughout the coalescence, and only modest beaming of a fireball that could give rise to a gamma-ray burst would be sufficient to avoid excessive baryon contamination. We find that some mass (on the order of 0.01 to 0.001 solar masses) may be dynamically ejected from the system, and could thus contribute substantially to the amount of observed r-process material in the galaxy. We calculate the gravitational radiation waveforms and luminosity in the quadrupole approximation.

Abstract:
Considering the importance of Lorentz invariance and chiral symmetry, we adopt the saturated Nambu-Jona-Lasinio (NJL) model to study the density dependence of the symmetry energy. The super-soft symmetry energy can be obtained from introducing a chiral isovector-vector interaction in the lagrangian, but should be ruled out by the neutron star (NS) stability in the mean-field approximation. It is found that the isovector-scalar interaction in the NJL model can play an important role in softening of the symmetry energy. We have investigated NS properties. The NS maximum mass obtained with various isovector-scalar couplings and momentum cutoffs is well above the $2M_\odot$, and the NS radius obtained well meets the limits extracted from recent measurements.

Abstract:
The recently discovery of a massive neutron star (PSR J1614-2230 of $1.97\pm0.04M_{\odot}$) rules out the soft equation of states (EOSs) such as those included hyperons or kaon condensates at high densities, while the nuclear theory or the terrestrial laboratory data prefer a soft EOS. Here we propose one possible mechanism to allow that the observed massive neutron star can be supported by a soft EOS, that is, if the the gravitational constant $G$ varies at super strong field, a soft EOS can support the massive neutron stars.

Abstract:
The class of Super Soft Sources has been established after discoveries performed with the Einstein and the ROSAT satellite. Only sources contributing to the class of super-soft X-ray binaries are considered. The X-ray emission in these sources is due to thermonuclear burning of accreted material on the surface of a white dwarf. The physical process of nuclear burning is described. The typical timescales of variability in these sources are discussed. The appearance and modeling of supersoft X-ray spectra are described. The phenomena related to the accretion disk in these sources are outlined. A discussion of the nature and appearance of the donor star is given. The evolutionary state of these sources and their likely progenitorship for Type Ia supernovae is shortly outlined. A summary of recent discoveries with Chandra and XMM-Newton of super-soft sources in nearby spiral and elliptical galaxies is given.

Abstract:
We present two of our efforts directed toward the numerical analysis of neutron star mergers, which are the most plausible sources for gravitational wave detectors that should begin operating in the near future. First we present Newtonian 3D simulations including radiation reaction (2.5PN) effects. We discuss the gravitational wave signals and luminosity from the merger with/without radiation reaction effects. Second we present the matching problem between post-Newtonian formulations and general relativity in numerical treatments. We prepare a spherical, static neutron star in a post-Newtonian matched spacetime, and find that discontinuities at the matching surface become smoothed out during fully relativistic evolution if we use a proper slicing condition.

Abstract:
Bursts from soft gamma repeaters have been shown to be super-Eddington by a factor of 1000 and have been persuasively associated with compact objects. Here, a model of super-Eddington radiation transfer on the surface of a strongly magnetic ($\geq 10^{13}$ gauss) neutron star is studied and related to the observational constraints on soft gamma repeaters. In strong magnetic fields, the cross-section to electron scattering is strongly suppressed in one polarization state, so super-Eddington fluxes can be radiated while the plasma remains in hydrostatic equilibrium. The model offers a somewhat natural explanation for the observation of similarity between spectra from bursts of varying intensity. The radiation produced in the model is found to be linearly polarized to about 1 part in 1000 in a direction determined by the local magnetic field, and the large intensity variations between bursts are understood as a change in the radiating area on the source. Therefore, the polarization may vary as a function of burst intensity, since the complex structure of the magnetic field may be more apparent for larger radiating areas. It is shown that for radiation transfer calculations in this limit of super-strong magnetic fields it is sufficient to solve the radiation transfer equations for the low opacity state rather than the coupled equations for both. With this approximation, standard stellar atmosphere techniques are utilized to calculate the model energy spectrum.

Abstract:
This article describes a comparison of two calculations of the merger of a binary neutron star (NS) system which is initially within the tidal instability as described by Rasio and Shapiro. The same initial data is used with one simulation involving a purely Newtonian evolution of the Euler equations for compressible fluids and another similarly evolved except there is an inclusion of a gravitational radiation reaction (GRR) term at the 2.5 Post-Newtonian (PN) order as prescribed by Blanchet, Damour, and Schafer. The inclusion of GRR is to allow an approximation of the full relativistic effect which forces the inspiral of binary systems. The initial data is identical at the start of each evolution and only the inclusion of the 2.5PN term differs in the evolutions. We chose two co-rotating, gamma=2 polytropic stars with masses 1.4M_Solar, radii R=9.56km and central densities of 2.5E15 g/cm3. The initial binary separation is 2.9R, inside the region where the dynamical tidal instability has been shown to cause the merger of the two stars. Comparisons between measured quantities will indicate a substantial difference between the two evolutions. It will be shown that the effect of GRR on the dynamics of the merger is significant.

Abstract:
As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and truncate at the various order. We solve the system using the polytropic equation of state with index $\Gamma=5/3, 2$ and 3, and show how this approximation converges together with mass-radius relations. Next, we solve the Hamiltonian constraint equation with these density profiles as trial functions, and examine the differences in the final metric. We conclude the second `post-Newtonian' approximation is close enough to describe general relativistic single star. The result of this report will be useful for further binary studies. (Note to readers) This paper was accepted for publication in Physical Review D. [access code dsj637]. However, since I was strongly suggested that the contents of this paper should be included as a section in our group's future paper, I gave up the publication.

Abstract:
Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc^2. We find that, for a given GM/Rc^2, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when n=0.5, and 20% larger when n=1. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases.