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We develop the 3-dimensional general relativistic radiative transfer code: CARTOON (Calculation code of Authentic Radiative Transfer based On phOton Number conservation in curved space-time) which is improved from the 2-dimensional code: ARTIST developed by Takahashi & Umemura (2017). In CARTOON, the frequency-integrated general relativistic radiative transfer equation is solved in a photon number-conserving manner, and the isotropic and coherent scattering in the zero angular momentum observers (ZAMO) frame and the fluid rest frame is incorporated. By calculating the average energy of photons, energy conservation of the radiation is also guaranteed. With the test calculations in 2-dimensional and 3-dimensional space, we have demonstrated that the wavefront propagation in black hole space-time can be correctly solved in CARTOON conserving photon numbers. The position of the wavefront coincides with the analytical solution and the number of photons remains constant until the wavefront reaches the event horizon. We also solve the radiative transfer equation on the geodesic reaching the observer's screen. The time variation of the intensity map on the observer's screen can be simultaneously and consistently calculated with the time variation of the radiation field around the black hole. In addition, the black hole shadow can be reproduced in moderately optically thin situations., 12 pages, 12 figures. Accepted for publication in MNRAS

We consider the scattering of a quantum particle by two independent, successive parity-invariant point interactions in one dimension. The parameter space for the two point interactions is given by the direct product of two tori, which is described by four parameters. By investigating the effects of the two point interactions on the transmission probability of plane wave, we obtain the conditions for the parameter space under which perfect resonant transmission occur. The resonance conditions are found to be described by symmetric and anti-symmetric relations between the parameters., Comment: 8 pages, 8 figures, minor revision

We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space–Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr–Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ∼ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.

We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition., 24 pages, 9 figures, minor revision

We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2., Comment: 9 pages, 3 figures

We report the detection of radio QPOs with structure changes using the Very Long Baseline Array (VLBA) at 43 GHz. We found conspicuous patterned changes of the structure with P = 16.8 +/- 1.4, 22.2 +/- 1.4, 31.4 +/- 1.5, 56.4 +/- 6 min roughly in a 3:4:6:10 ratio. The first two periods show a rotating one-arm structure, while P = 31.4 min shows a rotating 3-arm structure, as if viewed edge-on. At the central 50 mu as the P = 56.4 min period shows a double-amplitude variation of those in its surroundings. The spatial distributions of the oscillation periods suggest that the disk of Sgr A* is roughly edge-on, rotating around an axis with PA = -10 degrees. Presumably, the observed VLBI images of Sgr A* at 43 GHz retain several features of the black hole accretion disk of Sgr A* in spite of being obscured and broadened by scattering of surrounding plasma.

We present a new formulation to compute numerically stationary and axisymmetric equilibria of magnetized and self-gravitating astrophysical fluids. Under the assumption of ideal MHD, the stream function for the flow can be chosen as a basic variable with which the Euler-Maxwell equations are cast into a set of basic equations, i.e. a generalized Bernoulli equation and a Grad-Shafranov-like equation by employing various integral conditions. A novel feature of this formulation is that systems with stars, disks and winds are treated in a simple unified picture and the magnetic field structures can contain both poloidal and toroidal components.

We show for the first time the direct time variable radio images in the context of shocked accretion flows around a black hole under the general relativistic treatment of both hydrodynamics and radiation transfer. Time variability around a black hole can be induced by the non-axisymmetric standing accretion shock instability (namely Black Hole SASI). Since the spiral arm shock waves generate the density and temperature waves at the post shock region, they cause time variability in the black hole vicinity. Based on our dynamical simulations, we discuss a possibility of detection for the time variable radio images of M87 by the future space telescope VSOP2/ASTRO-G satellite. The most luminous part of the images is predicted to be near 15 Schwarzschild radii for some snapshots. We show that our results are consistent with existing observational data such as timeaveraged radio spectra, VLBA images and variability timescale for M87. We also discuss observations of M87 with millimeter and sub-millimeter interferometers., 17 pages, 5 figures, Accepted to publication for ApJ

Equilibrium configurations of self-gravitating magnetized toroid–central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly 10 15 G if the mass of the c

Equations of fully general relativistic radiation hydrodynamics around a rotating black hole are derived by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. Since the radiation interacts with matter moving with relativistic velocities near the event horizon, the interplay between the radiation and the matter should be described fully relativistically. In the formalism used in this study, while the interactions between matter and radiation are introduced in the comoving frame, the equations and the equations and the derivatives for the description of the global evolution of both matter and the radiation are given in the Kerr-Schild frame (KSF) which is a frame fixed to the coordinate describing the central black hole. As a frame fixed to the coordinate, we use the locally non-rotating reference frame (LNRF) representing a radially falling frame when the Kerr-Schild coordinate is used. Around the rotating black hole, both the matter and the radiation are affected by the frame-dragging effects.

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 hole's 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.

Two-dimensional magnetohydrodynamic 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 so efficient to launch a jet in this study. It is also found that a jet is launched mainly by B_\phi 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 so high as several hundred, we conclude that the jets seen in this study are not be a GRB jet. This result suggests that general relativistic effects, which are not included in this study, will be important to generate a GRB jet. Also, the accretion disk with magnetic fields may still play an important role to launch a GRB jet, although a simulation for much longer physical time (\sim 10-100 s) is required to confirm this effect. It is shown that considerable amount of 56Ni is synthesized in the accretion disk. Thus there will be a possibility for the accretion disk to supply 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. Moreover, it is found that the electron fraction becomes larger than 0.5 around the polar axis near the black hole by \nu_e capture at the region. Thus there will be a possibility that r-process and r/p-process nucleosynthesis occur at these regions. Finally, much neutrons will be ejected from the jet, which suggests that signals from the neutron decays may be observed as the delayed bump of afterglow or gamma-rays.

We calculate eclipsing light curves for accretion flows around a rotating black hole taking into account the atmospheric effects of the companion star. In the cases of no atmospheric effects, the light curves contain the information of the black hole spin because most of the X-ray photons around 1 keV usually come from the blueshifted part of the accretion flow near the black hole shadow, and the size and the position of the black hole shadow depend on the spin. In these cases, when most of the emission comes from the vicinity of the event horizon, the light curves become asymmetric at ingress and egress. We next investigate the atmospheric absorption and scattering effects of the companion stars. By using the solar-type atmospheric model, we have taken into account the atmospheric effects of the companion star, such as the photoionization by HI and HeI. We found that the eclipsing light curves observed at 1 keV possibly contain the information of the black hole spin. However, in our atmospheric model, the effects of the atmosphere are much larger than the effects of the black hole spin. Therefore, even in the case that the light curves contain the information of the black hole spin, it may be difficult to extract the information of the black hole spin if we do not have the realistic atmospheric profiles, such as the temperature, and the number densities for several elements. Even in such cases, the light-curve asymmetries due to the rotation of the accretion disc exist. Only when we have the reliable atmospheric model, in principle, the information of the strong-gravity regions, such as the black hole spin, can be obtained from the eclipsing light curves., Comment: Takahashi R., Watarai K., 2007, MNRAS, 374, 1515

We propose a method for measuring the black hole charge by imaging a black hole shadow in a galactic center by future interferometers. Even when the black hole is uncharged, it is possible to confirm the charge neutrality by this method. We first derive the analytic formulae of the black hole shadow in an optically thin medium around a charged spinning black hole, and then investigate how contours of the black hole shadow depend on the spin and the charge of the black hole for several inclination angles between the rotation axis of the black hole and the observer. This method only assumes stationary black hole and general relativity. By fitting the formula of the contours of the shadow to the observed image of the shadow, in addition to the black hole charge, one can also determine the black hole spin and the inclination angle without any degeneracy among the charge, the spin, and the inclination angle unless the inclination angle is null.

Can we determine a spin parameter of a black hole by observation of a black hole shadow in an accretion disk? In order to answer this question, we make a qualitative analysis and a quantitative analysis of a shape and a position of a black hole shadow casted by a rotating black hole on an optically thick accretion disk and its dependence on an angular momentum of a black hole. We have found black hole shadows with a quite similar size and a shape for largely different black hole spin parameters and a same black hole mass. Thus, it is practically difficult to determine a spin parameter of a black hole from a size and a shape of a black hole shadow in an accretion disk. We newly introduce a bisector axis of a black hole shadow named a shadow axis. For a rotating black hole a shape and a position of a black hole shadow are not symmetric with respect to a rotation axis of a black hole shadow. So, in this case the minimum interval between a mass center of a black hole and a shadow axis is finite. An extent of this minimum interval is roughly proportional to a spin parameter of a black hole for a fixed inclination angle between a rotation axis of a black hole and a direction of an observer. In order to measure a spin parameter of a black hole, if a shadow axis is determined observationally, it is crucially important to determine a position of a mass center of a black hole in a region of a black hole shadow., 13 pages, 6 figures, accepted for publication in ApJ

Thanks to the revolutionary progress in the technique of astrometrical observation, a realistic possibility has emerged of elucidating the nature of baryonic dark matter (massive compact halo objects, small cold clouds) from the centroidal image trajectory of the microlens phenomena. To check if the size of lens objects can be determined by astrometrical observation, I have calculated astrometrical trajectories of microlensing phenomena caused by a spherical finite-size lens consisting of opaque material and found that these trajectories can be classified into three types according to occultation of the plus and minus images. All three types of trajectories have distinct features that reflect the effects of a finite-size lens. From these trajectories, the angular radius of the lens can be determined for two types of trajectories, and from the third type of trajectory, the upper and the lower limits of the angular radius can be determined if these features can be measured. I have investigated finite-lens effects in nearby high proper motion stars identified by Salim & Gould that could cause observable astrometric microlensing events during the Space Interferometry Mission's lifetime. None of them shows finite-lens effects with 10 μas positional accuracy, one event shows finite-lens effects with 1 μas positional accuracy, and six events show finite-lens effects with 0.1 μas positional accuracy.

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 condition that the scalar field is regular on the outer horizon and vanishes at infinity. Therefore, the CS scalar field becomes problematic on the inner horizon., 10 pages, 5 figures; Revised version, accepted for publication in PRD

We calculated the expected microlens light curves for several accretion-flow models and compared the results to find what aspects of distinct flow structures can be extracted from the microlens light curves. As for the flow models, we considered the standard disk, optically thin advection-dominated flow, and the disk-corona model by Kawaguchi et al., which can nicely reproduce the observed quasar spectra. The calculated microlens light curves of the disk-corona model exhibit rapid soft X-ray and slow hard X-ray variations. This is because the former is generated by Compton up-scattering of soft (optical -- UV) photons from the innermost part of the disk body, while the latter is emitted via bremsstrahlung within the corona at relatively large radii. Furthermore, an inhomogeneous emissivity distribution over the disk produces humps in the microlens light curves because of enhanced microlens amplification of the bright areas. It is hoped that black-hole accretion theory coupled with future multi-wavelength microlens observations will be able to reveal such spatial and temporal behaviors of flows in the vicinity of black holes., 12 pages, 4 Postscript figures

We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stationary structures of the toroidal gaseous configurations around central point masses in the framework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the poloidal magnetic fields are apt to elongate the density contours in a certain direction depending on the situation. Therefore, the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the stationary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems., 17 pages, 9 figures; published online in MNRAS

We report the results of multi-epoch observations of Sgr A* with VLBI Exploration of Radio Astrometry (VERA) at 43 GHz, carried out from 2004 to 2008. We detected a time variation of flux at 11 % level and intrinsic size at 19 %. In addition, comparisons with previous Very Long Baseline Array (VLBA) results shows that Sgr A* underwent the flaring event at least longer than 10 days in May 2007. The intrinsic size of Sgr A* remained unchanged within 1 $\sigma$ level from the size before/after the flaring event, indicating that the brightness temperature of Sgr A* was increased. The flaring event occurred within 31 d, which is shorter than the refractive time scale. Moreover it is difficult to explain the increase in the spectral index at the flaring event by the simple interstellar scattering model. Hence, the flaring event is most likely associated with the changes in intrinsic properties of Sgr A*. We considered the origin of the brightness temperature variation, and concluded that the flaring event of Sgr A* could be explained by the continuous heating of electrons, such as a standing shock in accretion flow., Comment: 13 pages, 7 figures, published in Publications of the Astronomical Society of Japan (PASJ)

We investigate non-inertial and gravitational effects on quantum states in electromagnetic fields and present the analytic solution for energy eigenstates for the Schr\"odinger equation including non-inertial, gravitational and electromagnetic effects. We find that in addition to the Landau quantization the rotation of spacetime itself leads to the additional quantization, and that the energy levels for an electron are different from those for a proton at the level of gravitational corrections., Comment: 4 pages, 1 figure

In this paper we continue our study on the accretion process onto super-spinning 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., 14 pages, 11 figures. v2: published version with typos corrected

Aims. In order to understand the anisotropic properties of local radiation field in the curved spacetime around a rotating black hole, we investigate the appearance of a black hole seen by an observer located near the black hole. When the black hole is in front of a source of illumination the black hole cast shadow in the illumination. Accordingly, the appearance of the black hole is called the black hole shadow. Methods. We first analytically describe the shape of the shadow in terms of constants of motion for a photon seen by the observer in the locally non-rotating reference frame (LNRF). Then, we newly derive the useful equation for the solid angle of the shadow. In a third step, we can easily plot the apparent image of the black hole shadow. Finally, we also calculate the ratio of the photon trapped by the hole and the escape photon to the distant region for photons emitted near the black hole. Results. From the shape and the size of the black hole shadow, we can understand the signatures of the curved spacetime; i.e., the mass and spin of the black hole. Our equations for the solid angle of the shadow has technical advantages in calculating the photon trapping ratio. That is, this equation is computationally very easy, and gives extremely precise results. This is because this equation is described by the one-parameter integration with given values of the spin and location for the black hole considered. After this, the solid angle can be obtained without numerical calculations of the null geodesics for photons., Accepted for publication in A&A

We present a model for high-energy emission sources generated by a standing magnetohydrodynamical (MHD) shock in a black hole magnetosphere. The black hole magnetosphere would be constructed around a black hole with an accretion disk, where a global magnetic field could be originated by currents in the accretion disk and its corona. Such a black hole magnetosphere may be considered as a model for the central engine of active galactic nuclei, some compact X-ray sources and gamma-ray bursts. The energy sources of the emission from the magnetosphere are the gravitational and electromagnetic energies of magnetized accreting matters and the rotational energy of a rotating black hole. When the MHD shock generates in MHD accretion flows onto the black hole, the plasma's kinetic energy and hole's rotational energy can convert to radiative energy. In this letter, we demonstrate the huge energy output at the shock front by showing negative energy postshock accreting MHD flows for a rapidly rotating black hole. This means that the extracted energy from the black hole can convert to the radiative energy at the MHD shock front. When axisymmetric shock front is formed, we expect a ring-shaped region with very hot plasma near the black hole; the look would be like an "aurora". The high energy radiation generated from there would carry to us the information for the curved spacetime due to the strong gravity., Comment: 9 pages, 3 figures, accepted to ApJL

The accretion process onto spinning objects in Kerr spacetimes is studied with numerical simulations. Our results show that accretion onto compact objects with Kerr parameter (characterizing the spin) $|a| < M$ and $|a| > M$ is very different. In the super-spinning case, for $|a|$ moderately larger than $M$, the accretion onto the central object is extremely suppressed due to a repulsive force at short distance. The accreting matter cannot reach the central object, but instead is accumulated around it, forming a high density cloud that continues to grow. The radiation emitted in the accretion process will be harder and more intense than the one coming from standard black holes; e.g. $��$-rays could be produced as seen in some observations. Gravitational collapse of this cloud might even give rise to violent bursts. As $|a|$ increases, a larger amount of accreting matter reaches the central object and the growth of the cloud becomes less efficient. Our simulations find that a quasi-steady state of the accretion process exists for $|a|/M \gtrsim 1.4$, independently of the mass accretion rate at large radii. For such high values of the Kerr parameter, the accreting matter forms a thin disk at very small radii. We provide some analytical arguments to strengthen the numerical results; in particular, we estimate the radius where the gravitational force changes from attractive to repulsive and the critical value $|a|/M \approx 1.4$ separating the two qualitatively different regimes of accretion. We briefly discuss the observational signatures which could be used to look for such exotic objects in the Galaxy and/or in the Universe., 11 pages, 5 figures. v2: with explanation of the origin of the critical value |a|/M = 1.4

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 $\sim$ 1 millimeter. We show that a general relativistic accretion flow, heated via the plasma wave heating mechanism, is consistent with the polarization and recent mm-VLBI observations of Sgr A* for an inclination angle of $\sim 45^\circ$, position angle of $\sim 140^\circ$, and spin $\lesssim 0.9$. 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 mm-VLBI stations, including sites in Chile and New Zealand, finding that with these the basic geometry of the emission region can be reliably estimated., ApJ accepted; 21 pages, 8 figures

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 $\approx 0.44$ 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., Comment: 5 pages, 3 figures, accepted by MNRAS LETTER

We present our first numerical results of axisymmetric magnetohydrodynamic simulations for neutrino-cooled accretion tori around rotating black holes in general relativity. We consider tori of mass $\sim 0.1$--0.4$M_{\odot}$ around a black hole of mass $M=4M_{\odot}$ and 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 $\approx 60$ 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 $\alpha$-particles, black body radiation, and a relativistic Fermi gas (neutrinos, electrons, and positrons). Neutrino-emission processes, such as $e^{\pm}$ capture onto free nucleons, $e^{\pm}$ 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 $\dot M_* \sim 1$--$10 M_{\odot}$/s, and the shock heating increases the temperature to $\sim 10^{11}$ K. This results in a maximum neutrino emission rate of $L_{\nu}=$ several $\times 10^{53}$ ergs/s and a conversion efficiency $L_{\nu}/\dot M_* c^2$ on the order of a few percent for tori with mass $M_{\rm t} \approx 0.1$--0.4$M_{\odot}$ and for moderately high black hole spins., Comment: Shibata, M., Sekiguchi, Y., Takahashi, R., Progress of Theoretical Physics, 118, 257 (2007)

The stationary hydrodynamic equations for the transonic accretion disks 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 disks, 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 (ADAFs) with the relativistic equation of state, the adiabatic accretion disks, the standard accretion disks, the supercritical accretion disks. 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 hole's rotation. These features contrast to the results obtained by using the Boyer-Lindquist coordinate with the coordinate singularity at the horizon., MNRAS accepted

Two‐dimensional magnetohydrodynamic 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 so efficient to launch a jet in this study. It is also found that a jet is launched mainly by Bφ 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 so high as several hundred, we conclude that the jets seen in this study are not be a GRB jet. This result suggests that general relativistic effects, which are not included in this study, will be important to generate a GRB jet.

We present the basic equations and sample solutions for the steady-state global transonic solutions of the advection-dominated accretion flows (ADAFs) with a causal viscosity prescription. The procedures for the stable numerical calculations and all explicit formula for obtaining the solutions of ADAFs are also presented. We solve the transonic solutions of ADAFs by using the explicit numerical integrations, as in the Runge-Kutta method. In this calculation method, we first solve the physical values at the sonic radius where L'Hopital's rule is used. Then, we numerically solve the coupled differential equations of the radial velocity, the angular momentum, and the sound speed from the sonic radius in the inward and outward directions. By the calculation procedures presented in this paper, we can cover all parameter spaces of the transonic solutions of ADAFs. Sample transonic solutions for ADAF-thick disk and ADAF-thin disk are presented. The explicit formula for the analytical expansion around the singular points, the sonic and the viscous points, are presented. If we set the diffusion timescale to null, the formalism in this study becomes the formalism of the acausal viscosity that is usually used in past studies for calculating of the ADAF structure., Comment: Takahashi R., 2007, A&A, 461, 393

We propose an eclipsing light-curve diagnosis for black-hole accretion flows. When emission from an inner accretion disk around a black hole is occulted by a companion star, the observed light curve becomes asymmetric at ingress and egress on a time scale of 0.1-1 seconds. This light-curve analysis provides a means of verifying the relativistic properties of the accretion flow, based on the special/general relativistic effects of black holes. The ``skewness'' for the eclipsing light curve of a thin disk is $\sim 0.08$, whereas that of a slim disk is $\sim 0$, since the innermost part is self-occulted by the disk's outer rim., 7 pages, 4 figures, PASJ accepted

We investigate the dependence of the viewing angle in supercritical accretion flows and discuss the observational implications of galactic black-hole candidates and ultraluminous X-ray sources. When the mass accretion rate exceeds the critical rate, then the shape of the disk is geometrically thick due to the enhanced radiation pressure. The model spectra of supercritical accretion flows strongly depend on the inclination angle. Because the outer disk blocks the emission from the disk inner region for high inclination angle. We also find that the spectral properties of low-inclination angle and low accretion-rate disks are very similar to those of high-inclination and high accretion rate disks. That is, if an object has a high inclination and high accretion rate, such a system suffers from self-occultation and the spectrum will be extremely soft. Therefore, we cannot discriminate these differences from spectrum shapes only. Conversely, if we use the self-occultation properties, we could constrain the inclination angle of the system. We suggest that some observed high temperature ultraluminous X-ray sources have near face-on geometry, i < 40, and Galactic black hole candidate, XTE J1550-564, possesses relatively high-inclination angles, i > 60., 13 pages, 6 figures, accepted for publication in PASJ

We investigate the dependence of the viewing angle in supercritical accretion flows and discuss the observational implications of galactic black‐hole candidates and ultraluminous X‐ray sources. We find that if an object has a high inclination and high accretion rate, such a system suffers from self‐occultation and the spectrum will be extremely soft even if we take into account the effect of general relativity (light bending, Doppler boosting). We therefore cannot discriminate these differences from spectrum shapes only. Conversely, if we use the self‐occultation properties, we could constrain the inclination angle of the system.

Mrk 766, a bright narrow-line Seyfert 1, has been observed eight times by the XMM-Newton satellite. We carried out the analysis of the composite data from all of these observations together by applying a dynamical method. Through this analysis, we noted a longer timescale variability in addition to rapid short-time variability. This longer term variability is manifested by the presence of two distinct branches in flux-flux plots. Moreover, the data show the presence of absorbing material whose average thickness decreases gradually from ~2 × 1023 cm–2 during the dim state to ~1022 cm–2 as the source brightens to brighter states. To explain this longer timescale behavior and others already found self-consistently, we offer a promising model. In this model, the source is dim when a small emission region is covered by a small, denser portion of a partial-covering cloud; the source brightens as it becomes larger and covered predominantly by a less dense, larger region of the covering cloud. The short rapid variability, in contrast, is consistent with the highly variable power-law component from the coronal primary emission region, which is superimposed onto a less variable, ionized relativistic reflection component. Last, a possible presence of some unique soft flares is suggested. Unlike many other flares seen in the light curves, these flares occur only in the 0.3-2.0 keV soft band. These soft flares may be attributed to "hot spots" on the accretion disk.

Can we determine spin parameters of black holes by observations of black hole shadows in accretion disks? In order to answer this question, we have investigated shapes and positions of black hole shadows in optically thick accretion disks around Kerr black holes. In conclusion, in order to measure black hole spin parameters from shapes and positions of black hole shadows, it is crucially important to determine a position of a mass centers of a black hole in a region of a black hole shadow. To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Thanks to the revolutionary progress in the technique of astrometrical observation, a realistic possibility has emerged of elucidating the nature of baryonic dark matter (massive compact halo objects, small cold clouds) from the centroidal image trajectory of the microlens phenomena. To check if the size of lens objects can be determined by astrometrical observation, I have calculated astrometrical trajectories of microlensing phenomena caused by a spherical finite-size lens consisting of opaque material and found that these trajectories can be classified into three types according to occultation of the plus and minus images. All three types of trajectories have distinct features that reflect the effects of a finite-size lens. From these trajectories, the angular radius of the lens can be determined for two types of trajectories, and from the third type of trajectory, the upper and the lower limits of the angular radius can be determined if these features can be measured. I have investigated finite-lens effects in nearby high proper motion stars identified by Salim & Gould that could cause observable astrometric microlensing events during the Space Interferometry Mission’s lifetime. None of them shows finite-lens effects with 10 las positional accuracy, one event shows finite-lens effects with 1 las positional accuracy, and six events show finite-lens effects with 0.1 las positional accuracy. Subject headings: astrometry — dark matter — gravitational lensing

Can we determine the spin parameters of black holes by observations of black hole shadows in accretion disks? In order to answer this question, we have investigated the shapes and positions of black hole shadows in optically thick accretion disks around Kerr black holes. In conclusion, in order to measure black hole spin parameters from shapes and positions of black hole shadows, it is crucially important to determine the position of the center of mass of a black hole in the region of a black hole shadow.

The specific angular momentum of a Kerr black hole must not be larger than its mass in the geometrical units. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. On the other hand, the violation of this bound may suggest the existence of a superspinning object which might be suggested from a string theory argument. In order to investigate observational testability of this bound by using the X-ray energy spectrum of black hole candidates, we calculate the energy spectra from an optically thick and geometrically thin accretion disk of a superspinning object 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. Based on this calculation, we present that the observational confirmation of the Kerr bound is very hard but the violation of it may be detectable if only the continuum X-ray spectrum of the disk is available.

In order to examine if the next generation space 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 the relativistic ray-tracing simulations under the considerations of possible observational errors. We consider various cases of electron temperature profiles, as well as a variety of 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 steeply rises towards the black hole, as was predicted by the accretion disk theory and the 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 $\gtrsim 1.5 \mu$ arcseconds. 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 $\mathcal{R}_{\rm SN}$ 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., Comment: 11 pages, 2 tables and 7 figures. Accepted version of Takahashi and Mineshige (2011, ApJ, 729, 86)

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 disc 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 $5/3, Comment: Accepted for publication in Classical and Quantum Gravity