Rohta Takahashi

Numerical study of gamma-ray burst jet formation in collapsars

Two-dimensional MHD simulations are performed using the ZEUS-2D code to investigate the dynamics of a collapsar that generates a GRB jet, taking account of realistic equation of state, neutrino cooling and heating processes, magnetic fields, and gravitational force from the central black hole and self-gravity. It is found that neutrino heating processes are not efficient enough to launch a jet in this study. It is also found that a jet is launched mainly by B fields that are amplified by the winding-up effect. However, since the ratio of total energy relative to the rest-mass energy in the jet is not as high as several hundred, we conclude that the jets seen in this study are not GRB jets. This result suggests that general relativistic effects will be important to generating a GRB jet. Also, the accretion disk with magnetic fields may still play an important role in launching a GRB jet, although a simulation for much longer physical time (~10-100 s) is required to confirm this effect. It is shown that a considerable amount of 56Ni is synthesized in the accretion disk. Thus, there will be a possibility for the accretion disk to supply the sufficient amount of 56Ni required to explain the luminosity of a hypernova. Also, it is shown that neutron-rich matter due to electron captures with high entropy per baryon is ejected along the polar axis. Thus, there will be a possibility that r-process nucleosynthesis occurs at such a region. Finally, many neutrons will be ejected from the jet, which suggests that signals from the neutron decays may be observed as the delayed bump of the light curve of the afterglow or gamma rays.

Magnetohydrodynamics of Neutrino-Cooled Accretion Tori around a Rotating Black Hole in General Relativity

We present our first numerical results of axisymmetric magnetohydrodynamic simula- tions for neutrino-cooled accretion tori around rotating black holes in general relativity. We consider tori of mass ∼ 0.1-0.4Maround a black hole of mass M =4 Mand spin a =0 - 0.9M ; such systems are candidates for the central engines of gamma-ray bursts (GRBs) formed after the collapse of massive rotating stellar cores and the merger of a black hole and a neutron star. In this paper, we consider the short-term evolution of a torus for a duration of ≈ 60 ms, focusing on short-hard GRBs. Simulations were performed with a plausible microphysical equation of state that takes into account neutronization, the nuclear statistical equilibrium of a gas of free nucleons and α-particles, black body radiation, and a relativistic Fermi gas (neutrinos, electrons, and positrons). Neutrino-emission processes, such as e ± capture onto free nucleons, e ± pair annihilation, plasmon decay, and nucleon- nucleon bremsstrahlung are taken into account as cooling processes. Magnetic braking and the magnetorotational instability in the accretion tori play a role in angular momentum redistribution, which causes turbulent motion, resultant shock heating, and mass accretion onto the black hole. The mass accretion rate is found to be ˙ M∗ ∼ 1-10M� /s, and the shock heating increases the temperature to ∼ 10 11 K. This results in a maximum neutrino emission rate of Lν = several ×10 53 ergs/s and a conversion efficiency Lν / ˙ M∗c 2 on the order of a few percent for tori with mass Mt ≈ 0.1-0.4Mand for moderately high black hole spins. These results are similar to previous results in which the phenomenological α-viscosity prescription with the α-parameter of αv =0 .01-0.1 is used. It is also found that the neutrino luminosity can be enhanced by the black hole spin, in particular for large spins, i.e., a & 0.75M ;i f the accretion flow is optically thin with respect to neutrinos, the conversion efficiency may be & 10% for a & 0.9M. Angular momentum transport, and the resulting shock heating caused by magnetic stress induce time-varying neutrino luminosity, which is a favorable property for explaining the variability of the luminosity curve of GRBs.

Measuring spin of a supermassive black hole at the Galactic centre — implications for a unique spin

We determine the spin of a supermassive black hole in the context of discseismology by comparing newly detected quasi-periodic oscillations (QPOs) of radio emission in the Galactic centre, Sagittarius A* (Sgr A*), as well as infrared and X-ray emissions with those of the Galactic black holes. We find that the spin parameters of black holes in Sgr A* and in Galactic X-ray sources have a unique value of � 0:44 which is smaller than the generally accepted value for supermassive black holes, suggesting evidence for the angular momentum extraction of black holes during the growth of supermassive black holes. Our results demonstrate that the spin parameter approaches the equilibrium value where spin-up via accretion is balanced by spin-down via the Blandford-Znajek mechanism regardless of its initial spin. We anticipate that measuring the spin of black holes by using QPOs will open a new window for exploring the evolution of black holes in the Universe.

Observational testability of a Kerr bound in the x-ray spectrum of black hole candidates

The specific angular momentum of a Kerr black hole must not be larger than its mass. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. In order to investigate observational testability of this bound by using the x-ray energy spectrum of black hole candidates, we calculate energy spectra for a super-spinning object (or a naked singularity) which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. We assume an optically thick and geometrically thin disk around the super-spinning object and calculate its thermal energy spectrum seen by a distant observer by solving general relativistic radiative transfer equations including usual special and general relativistic effects, such as Doppler boosting, gravitational redshift, light bending and frame-dragging. Surprisingly, for a given black hole, we can always find its super-spinning counterpart with its spin a in the range whose observed spectrum is very similar to and practically indistinguishable from that of the black hole. As a result, we conclude that to confirm the Kerr bound we need more than the x-ray thermal spectrum of the black hole candidates.

TESTING THE ACCRETION FLOW WITH PLASMA WAVE HEATING MECHANISM FOR SAGITTARIUS A* BY THE 1.3 mm VLBI MEASUREMENTS

The vicinity of the supermassive black hole associated with the compact radio source Sagittarius (Sgr) A* is believed to dominate the observed emission at wavelengths near and shorter than similar to 1 millimeter. We show that a general relativistic accretion flow, heated via the plasma wave heating mechanism, is consistent with the polarization and recent millimeter-VLBI observations of Sgr A* for an inclination angle of similar to 45 degrees, position angle of similar to 140 degrees, and spin less than or similar to 0.9. Structure in visibilities produced by the black hole shadow can potentially be observed by 1.3 mm-VLBI on the existing Hawaii-CARMA and Hawaii-SMT baselines. We also consider eight additional potential millimeter-VLBI stations, including sites in Chile and New Zealand, finding that with these the basic geometry of the emission region can be reliably estimated.

Outflows from accreting super-spinars

In this paper we continue our study on the accretion process onto superspinning Kerr objects with no event horizon (super-spinars). We discuss the counterpart of the Bondi accretion onto black holes. We first report the results of our numerical simulations. We found a quasi-steady-state configuration for any choice of the parameters of our model. The most interesting feature is the presence of hot outflows. Unlike jets and outflows produced around black holes, which are thought to be powered by magnetic fields and emitted from the poles, here the outflows are produced by the repulsive gravitational force at a small distance from the super-spinar and are ejected around the equatorial plane. In some circumstances, the amount of matter in the outflow is considerable, which can indeed significantly reduce the gas mass accretion rate. Finally, we discuss a possible scenario of the accretion process in more realistic situations, which cannot be simulated by our code.

Equations of general relativistic radiation hydrodynamics in Kerr space–time

Equations of fully general relativistic radiation hydrodynamics in Kerr space-time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer-Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black holes rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF.

CONSTRAINING THE SIZE OF THE DARK REGION AROUND THE M87 BLACK HOLE BY SPACE-VLBI OBSERVATIONS

In order to examine if the next-generation space very long baseline interferometer (VLBI), such as VSOP-2 (VLBI Space Observatory Programme-2), will make it possible to obtain direct images of the accretion flow around the M87 black hole, we calculate the expected observed images by relativistic ray-tracing simulations under considerations of possible observational errors. We consider various cases of electron temperature profiles, as well various values for the distance, mass, and spin of the M87 black hole. We find it feasible to detect an asymmetric intensity profile around the black hole caused by rapid disk rotation, as long as the electron temperature does not rise steeply toward the black hole, as was predicted by the accretion disk theory and three-dimensional magnetohydrodynamic simulations. Further, we can detect a deficit in the observed intensity around the black hole when the apparent size of the gravitational radius is larger than 1.5 μas. In the cases that the inner edge of the disk is located at the radius of the innermost stable circular orbit (ISCO), moreover, even the black hole spin will be measured. We also estimate the required signal-to-noise ratio for achieving the scientific goals mentioned above, finding that it should be at least 10 at 22 GHz. To conclude, direct mapping observations by the next-generation space VLBI will provide us a unique opportunity to provide the best evidence for the presence of a black hole and to test the accretion disk theory.

Horizon-penetrating transonic accretion discs around rotating black holes

The stationary hydrodynamic equations for the transonic accretion discs and flows around rotating black holes are presented by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. We use two types of the causal viscosity prescription, and the boundary conditions for the transonic accretion flows are given at the sonic point. For one type of the causal viscosity prescription we also add the boundary conditions at the viscous point where the accreting radial velocity is nearly equal to the viscous diffusion velocity. Based on the formalism for the transonic accretion discs, after we present the calculation method of the transonic solutions, the horizon-penetrating transonic solutions which smoothly pass the event horizon are calculated for several types of the accretion flow models: the ideal isothermal flows, the ideal and the viscous polytropic flows, the advection-dominated accretion flows with the relativistic equation of state, the adiabatic accretion discs, the standard accretion discs, the supercritical accretion discs. These solutions are obtained for both non-rotating and rotating black holes. The calculated accretion flows plunge into black hole with finite three-velocity smaller than the speed of light even at the event horizon or inside the horizon, and the angular velocities of the accretion flow at the horizon are generally different from the angular velocity of the frame dragging due to the black holes rotation. These features contrast to the results obtained by using the Boyer-Lindquist coordinate with the coordinate singularity at the horizon.

Scalar field excited around a rapidly rotating black hole in Chern-Simons modified gravity

We discuss a Chern-Simons (CS) scalar field around a rapidly rotating black hole in dynamical CS modified gravity. The CS correction can be obtained perturbatively by considering the Kerr spacetime to be the background. We obtain the CS scalar field solution around the black hole analytically and numerically, assuming a stationary and axisymmetric configuration. The scalar field diverges on the inner horizon when we impose the boundary conditions that the scalar field be regular on the outer horizon and vanish at infinity. Therefore, the CS scalar field becomes problematic on the inner horizon.