The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with differential rotation. We perform fully relativistic 3D simulations of compact stars with $M/R \geq 0.1$, where $M$ is the total gravitational mass and $R$ the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index $\Gamma=2$. As in Newtonian theory, we find that stars above a critical value of $\beta \equiv T/W$ (where $T$ is the rotational kinetic energy and $W$ the gravitational binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation profile, the critical value of $\beta = \beta_{dGR}$ is $\sim 0.24-0.25$, only slightly smaller than the well-known Newtonian value $\sim 0.27$ for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of differential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large $\beta$ subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large $\beta \gtrsim \beta_{dGR}$ do not develop spiral arms or eject mass but adjust to form dynamically stable ellipsoidal-like configurations. If the bar-mode instability is triggered in supernovae collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies.Comment: 17 pages, accepted for publication in AP

Numerical approach for high precision 3-D relativistic star models

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error reveals to be of the order of $10^{-10}$. This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres

The Magnetorotational Instability in Core Collapse Supernova Explosions

We investigate the action of the magnetorotational instability (MRI) in the context of iron-core collapse. Exponential growth of the field on the rotation time scale by the MRI will dominate the linear growth process of field line "wrapping" with the same characteristic time. We examine a variety of initial rotation states, with solid body rotation or a gradient in rotational velocity, that correspond to models in the literature. A relatively modest value of the initial rotation, a period of ~ 10 s, will give a very rapidly rotating PNS and hence strong differential rotation with respect to the infalling matter. We assume conservation of angular momentum on spherical shells. Results are discussed for two examples of saturation fields, a fiducial field that corresponds to Alfven velocity = rotational velocity and a field that corresponds to the maximum growing mode of the MRI. Modest initial rotation velocities of the iron core result in sub-Keplerian rotation and a sub-equipartition magnetic field that nevertheless produce substantial MHD luminosity and hoop stresses: saturation fields of order 10^{15} - 10^{16} G develop within 300 msec after bounce with an associated MHD luminosity of about 10^{52} erg/s. Bi-polar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae.Comment: 42 pages, including 15 figures. Accepted for publication in ApJ. We have revised to include an improved treatment of the convection, and some figures have been update

Neutron star properties and the equation of state of neutron-rich matter

We calculate total masses and radii of neutron stars (NS) for pure neutron matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We use realistic nucleon-nucleon (NN) interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.Comment: 13 pages, 9 figures, 1 table; Revised version, accepted for publication in Physical Review

Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests

We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems such as spherical dust collapse, stability test of perturbed spherical stars, and preservation of (approximate) equilibrium states of rapidly rotating neutron star and/or corotating binary neutron stars. These test simulations confirm that simulations of coalescing binary neutron stars are feasible in a numerical relativity code. It is illustrated that using our numerical code, simulations of these problems, in particular those of corotating binary neutron stars, can be performed stably and fairly accurately for a couple of dynamical timescales. These numerical results indicate that our formulation for solving the Einstein field equation and hydrodynamic equations are robust and make it possible to perform a realistic simulation of coalescing binary neutron stars for a long time from the innermost circular orbit up to formation of a black hole or neutron star.Comment: 36 pages, to be published in PRD 15, erase unnecessary figure

Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach

Minor modifications (text only); published version (28 pages)This work was supported by JSPS Grant-in-Aid for Scientific Research(C) under Grant No. 20540275, MEXT Grant-in-Aid for Scientific Research on Innovative Area under Grant No. 20105004, NSF Grant No. PHY100155, and ANR Grant No. 06-2-134423 Me´thodes mathe´matiques pour la relativite´ ge´ne´ral

Why NS and BH mass distribition is bimodal?

The observed mass distribution for the compact remnants of massive stars (neutron stars and black holes) and its relationship to possible mechanisms for the ejection of the envelopes of type II and Ib/c supernovae is analyzed. The conclusion is drawn that this distribution can be obtained only by a magneto-rotational mechanism for the supernovae with sufficiently long time of the field amplification, and a soft equation of state for neutron stars with limiting masses \sim1.5-1.6M_\odot. Some consequences of this hypothesis are discussed.Comment: latex, 4 pages, 5 figures, Talk given at 5th Int. Tsessevich Conf. "Variable Stars", Odessa, Ukraine, August 200