Motoyuki Saijo

ONE-ARMED SPIRAL INSTABILITY IN DIFFERENTIALLY ROTATING STARS

We investigate the dynamical one-armed spiral instability in differentially rotating stars with both eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We find that the one-armed spiral mode is generated around the corotation radius of the star, and the distribution of angular momentum shifts inwards the corotation radius during the growth of one-armed spiral mode. We also find by investigating the distribution of the canonical angular momentum density that the low T/|W| dynamical instability for both m=1 and m=2 mode, where T is the rotational kinetic energy and W is the gravitational potential energy, is generated around the corotation point. Finally, we discuss the feature of gravitational waves generated from these modes.

Dynamical bar instability in rotating stars: Effect of general relativity

We study the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in the first post-Newtonian approximation of general relativity. We vary the compaction of the star M/R (where M is the gravitational mass and

Collapse of a rotating supermassive star to a supermassive black hole: Post-Newtonian simulations

R

Low T/|W| dynamical instability in differentially rotating stars : diagnosis with canonical angular momentum

the equatorial circumferential radius) between 0.01 and 0.05 to isolate the influence of relativistic gravitation on the instability. For compactions in this moderate range, the critical value of

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

\beta \equiv T/W

Viscosity driven instability in rotating relativistic stars

for the onset of the dynamical instability (where T is the rotational kinetic energy and W the gravitational binding energy) slightly decreases from ~ 0.26 to ~ 0.25 with increasing compaction for our choice of the differential rotational law. Combined with our earlier findings based on simulations in full general relativity for stars with higher compaction, we conclude that relativistic gravitation {\em enhances} the dynamical bar-mode instability, i.e. the onset of instability sets in for smaller values of

Collapse of differentially rotating supermassive stars: Post black hole formation

\beta

The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations

in relativistic gravity than in Newtonian gravity. We also find that once a triaxial structure forms after the bar-mode perturbation saturates in dynamically unstable stars, the triaxial shape is maintained, at least for several rotational periods. To check the reliability of our numerical integrations, we verify that the general relativistic Kelvin-Helmholtz circulation is well-conserved, in addition to rest-mass energy, total mass-energy, linear and angular momentum. Conservation of circulation indicates that our code is not seriously affected by numerical viscosity. We determine the amplitude and frequency of the quasi-periodic gravitational waves emitted during the bar formation process using the quadrupole formula.

Dynamic black holes through gravitational collapse: Analysis of the multipole moment of the curvatures on the horizon

We study the gravitational collapse of a rotating supermassive star by means of a (3 + 1) hydrodynamic simulation in a post-Newtonian approximation of general relativity. This problem is particularly challenging because of the vast dynamic range in space that must be covered in the course of collapse. We evolve a uniformly rotating supermassive star from the onset of radial instability at Rp/M = 411, where Rp is the proper polar radius of the star and M is the total mass-energy, to the point at which the post-Newtonian approximation breaks down. We introduce a scale factor and a comoving coordinate to handle the large variation in radius during the collapse (8 Rp/M0 411, where M0 is the rest mass) and focus on the central core of the supermassive star. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/Rp for an n = 3 polytropic star throughout the collapse, the imploding star may ultimately exceed the critical value of T/W for dynamic instability to bar-mode formation. Analytic estimates suggest that this should occur near Rp/M ~ 12, at which point T/W ~ 0.27. For stars rotating uniformly at the onset of collapse, however, we do not find any unstable growth of bars prior to the termination of our simulation at Rp/M0 ~ 8. We do find that the collapse is likely to form a supermassive black hole coherently, with almost all of the matter falling into the hole, leaving very little ejected matter to form a disk. In the absence of nonaxisymmetric bar formation, the collapse of a uniformly rotating supermassive star does not lead to appreciable quasi-periodic gravitational wave emission by the time our integrations terminate. The coherent nature of the implosion, however, suggests that rotating supermassive star collapse will be a promising source of gravitational wave bursts. We also expect that, following black hole formation, long-wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by the Laser Interferometer Space Antenna.

Dynamical bar instability in a relativistic rotational core collapse

We study the nature of non-axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one-armed spiral instability, the low T/|W| bar instability, and the high T/|W| bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one-armed spiral and the low T/|W| bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high T/|W|. We also discuss the feature of gravitational waves generated from these three types of instability.