Can we determine the spin parameter of a black hole by observing the black hole's shadow on an accretion disk? To answer this question, we make qualitative and quantitative analyses of the shape and position of the shadow cast by a rotating black hole on an optically thick accretion disk and its dependence on the angular momentum of the black hole. We consider two types of inner edges of accretion disks, an event horizon and a marginally stable orbit. We have found black hole shadows of quite similar sizes and shapes for very different black hole spin parameters and the same black hole mass. Thus, in practice it is difficult to determine the spin parameter of a black hole from the size and shape of its shadow on an accretion disk. On the other hand, a frame-dragging effect in the vicinity of a black hole causes a displacement of the shadow from the rotation axis of the black hole. The extent of the displacement largely depends on the black hole's spin parameter. However, it is difficult to determine the position of the rotation axis of a black hole observationally. So, we cannot practically use the displacement of the rotation axis of a black hole shadow to measure the spin parameter. We here introduce a bisector axis of black hole shadows that we call the ''shadow axis.'' We define this as the bisector perpendicular to a line segment of the maximum width of a black hole shadow. We can determine the position of a shadow axis through observation of a black hole shadow. For a nonrotating black hole, the minimum interval between the mass center of a black hole and the shadow axis is null. On the other hand, for a rotating black hole the shape and position of the shadow are not symmetric with respect to its rotation axis. So, in this case the minimum interval between the mass center of the black hole and the shadow axis is finite. The extent of this minimum interval is roughly proportional to the spin parameter of a black hole for a fixed inclination angle between a rotation axis and the direction of an observer. The maximum extent of these minimum intervals is about 1.5r g . Here r g is a gravitational radius. This is realized in the case of a maximum inclination angle and maximally rotating black hole in an accretion disk in which the inner edge is an event horizon. In order to measure the spin parameter of a black hole, if the shadow axis is determined observationally, it is crucially important to determine the position of the mass center in a region of the shadow. We also discuss how to determine a mass center of a black hole by observation of the shadow on an accretion disk.
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 φ 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 (∼ 10 − 100 s) is required to confirm this effect. It is shown that considerable amount of 56 Ni is synthesized in the accretion disk. Thus there will be a possibility for the accretion disk to supply sufficient amount of 56 Ni 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 ν 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 -2be 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 gammarays.
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 ∼ 0.1-0.4M around a black hole of mass M = 4M 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 ≈ 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 nucleonnucleon 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 beṀ * ∼ 1-10M /s, and the shock heating increases the temperature to ∼ 10 11 K. This results in a maximum neutrino emission rate of L ν = several ×10 53 ergs/s and a conversion efficiency L ν /Ṁ * c 2 on the order of a few percent for tori with mass M t ≈ 0.1-0.4M and 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 α v = 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 ; if 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. at East Tennessee State University on May 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from at East Tennessee State University on May 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from We numerically solved Eq. (2 . 33) in the same manner as Eq. (2 . 26). at East Tennessee State University on May 29, 2015http://ptp.oxfordjournals.org/ Downloaded from * ) In the realistic EOSs for high-density matter with ρ ≥ 10 7 g/cm 3 , ε is determined primarily by the radiation pressure for the high-temperature case, whereas it is determined by the electrondegenerate pressure for the low-temperature case. This implies that ε is proportional to T Downloaded from * ) As a result of the anisotropic emission, angular momentum is dissipated, but the magnitude of this effect is much smaller than the loss associated with the infal...
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