On Zermelo's theorem

A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all finite-stage two-player games of complete information with alternating moves. It is shown that in any such game either the first player has a winning strategy, or the second player has a winning strategy, or both have unbeatable strategies

Why Is Supercritical Disk Accretion Feasible?

Although the occurrence of steady supercritical disk accretion onto a black hole has been speculated about since the 1970s, it has not been accurately verified so far. For the first time, we previously demonstrated it through two-dimensional, long-term radiation-hydrodynamic simulations. To clarify why this accretion is possible, we quantitatively investigate the dynamics of a simulated supercritical accretion flow with a mass accretion rate of ~10^2 L_E/c^2 (with L_E and c being, respectively, the Eddington luminosity and the speed of light). We confirm two important mechanisms underlying supercritical disk accretion flow, as previously claimed, one of which is the radiation anisotropy arising from the anisotropic density distribution of very optically thick material. We qualitatively show that despite a very large radiation energy density, E_0>10^2L_E/(4 pi r^2 c) (with r being the distance from the black hole), the radiative flux F_0 cE_0/tau could be small due to a large optical depth, typically tau 10^3, in the disk. Another mechanism is photon trapping, quantified by vE_0, where v is the flow velocity. With a large |v| and E_0, this term significantly reduces the radiative flux and even makes it negative (inward) at r<70r_S, where r_S is the Schwarzschild radius. Due to the combination of these effects, the radiative force in the direction along the disk plane is largely attenuated so that the gravitational force barely exceeds the sum of the radiative force and the centrifugal force. As a result, matter can slowly fall onto the central black hole mainly along the disk plane with velocity much less than the free-fall velocity, even though the disk luminosity exceeds the Eddington luminosity. Along the disk rotation axis, in contrast, the strong radiative force drives strong gas outflows.Comment: 8 pages, 7 figures, accepted for publication in Ap

Ergoregion in Metamaterials Mimicking a Kerr Spacetime

We propose a simple singularity-free coordinate transformation that could be implemented in Maxwell's equations in order to simulate one aspect of a Kerr black hole. Kerr black holes are known to force light to rotate in a predetermined direction inside the ergoregion. By making use of cosmological analogies and the theoretical framework of transformation optics, we have designed a metamaterial that can make light behave as if it is propagating around a rotating cosmological massive body. We present numerical simulations involving incident Gaussian beams interacting with the materials to verify our predictions. The ergoregion is defined through the dispersion curve of the off-axis permittivities components.Comment: 10 pages, 4 figures, presented at FiO 201

A systematic search for massive black hole binaries in SDSS spectroscopic sample

We present the results of a systematic search for massive black hole binaries in the Sloan Digital Sky Survey spectroscopic database. We focus on bound binaries, under the assumption that one of the black holes is active. In this framework, the broad lines associated to the accreting black hole are expected to show systematic velocity shifts with respect to the narrow lines, which trace the rest-frame of the galaxy. For a sample of 54586 quasars and 3929 galaxies at redshifts 0.1<z<1.5 we brute-force model each spectrum as a mixture of two quasars at two different redshifts. The spectral model is a data-driven dimensionality reduction of the SDSS quasar spectra based on a matrix factorization. We identified 32 objects with peculiar spectra. Nine of them can be interpreted as black hole binaries. This doubles the number of known black hole binary candidates. We also report on the discovery of a new class of extreme double-peaked emitters with exceptionally broad and faint Balmer lines. For all the interesting sources, we present detailed analysis of the spectra, and discuss possible interpretations.Comment: 10 pages, 2 figures, accepted for publication in Ap

A Magnetohydrodynamic Model for the Formation of Episodic Jets

Episodic ejection of plasma blobs have been observed in many black hole systems. While steady, continuous jets are believed to be associated with large-scale open magnetic fields, what causes the episodic ejection of blobs remains unclear. Here by analogy with the coronal mass ejection on the Sun, we propose a magnetohydrodynamical model for episodic ejections from black holes associated with the closed magnetic fields in an accretion flow. Shear and turbulence of the accretion flow deform the field and result in the formation of a flux rope in the disk corona. Energy and helicity are accumulated and stored until a threshold is reached. The system then loses its equilibrium and the flux rope is thrust outward by the magnetic compression force in a catastrophic way. Our calculations show that for parameters appropriate for the black hole in our Galactic center, the plasmoid can attain relativistic speeds in about 35 minutes.Comment: 8 pages, 2 figures; the finalized version to appear in MNRA

An introduction to the game of hex

Hex is a tree game (defined in chapter II) with several interesting properties. Hex never ends in a draw. Either White, the player who moves first, or Black, the other player, can force a win. If Black can force a win, then White can force a win. This leads to the conclusion that White can force a win. All of this is established in chapter II. Although it Is known that White can force a win if he plays correctly, a winning strategy for the general n x n Hex game, where n is any positive integer, has yet to be discovered. Chapter III investigates some basic principles of strategy and gives paired strategies for Hex games of sizes 2 x 2, 3 x 3, 4 x 4, and 5 x 5. In chapter IV some winning and losing opening moves for White are explored. And finally a winning strategy for White in a 7 x 7 Hex game is developed

Tidal disruption events onto stellar black holes in triples

Stars passing too close to a black hole can produce tidal disruption events (TDEs), when the tidal force across the star exceeds the gravitational force that binds it. TDEs have usually been discussed in relation to massive black holes that reside in the centres of galaxies or lurk in star clusters. In this paper, we investigate the possibility that triple stars hosting a stellar black hole (SBH) may be sources of TDEs. We start from a triple system made up of three main sequence (MS) stars and model the supernova (SN) kick event that led to the production of an inner binary comprised of a SBH. We evolve these triples in isolation with a high precision $N$-body code and study their TDEs as a result of Kozai-Lidov oscillations. We explore a variety of distributions of natal kicks imparted during the SN event, various maximum initial separations for the triples, and different distributions of eccentricities. We show that the main parameter that governs the properties of the SBH-MS binaries which produce a TDE in triples is the mean velocity of the natal kick distribution. Smaller $\sigma$'s lead to larger inner and outer semi-major axes of the systems that undergo a TDE, smaller SBH masses, and longer timescales. We find that the fraction of systems that produce a TDE is roughly independent of the initial conditions, while estimate a TDE rate of $7.3\times 10^{-5}-4.1 \ \mathrm{yr}^{-1}$, depending on the prescriptions adopted for the SBH natal kicks. This rate is almost comparable to the expected TDE rate for massive black holes.Comment: 12 pages, 7 figures, 1 table, accepted by MNRAS. arXiv admin note: text overlap with arXiv:1903.1051

Magnetically Driven Jets in the Kerr Metric

We compute a series of three-dimensional general relativistic magnetohydrodynamic simulations of accretion flows in the Kerr metric to investigate the properties of the unbound outflows that result. The overall strength of these outflows increases sharply with increasing black hole rotation rate, but a number of generic features are found in all cases. The mass in the outflow is concentrated in a hollow cone whose opening angle is largely determined by the effective potential for matter orbiting with angular momentum comparable to that of the innermost stable circular orbit. The dominant force accelerating the matter outward comes from the pressure of the accretion disk's corona. The principal element that shapes the outflow is therefore the centrifugal barrier preventing accreting matter from coming close to the rotation axis. Inside the centrifugal barrier, the cone contains very little matter and is dominated by electromagnetic fields that rotate at a rate tied closely to the rotation of the black hole. These fields carry an outward-going Poynting flux whose immediate energy source is the rotating spacetime of the Kerr black hole. When the spin parameter a/M of the black hole exceeds ~0.9, the energy carried to infinity by these outflows can be comparable to the nominal radiative efficiency predicted in the Novikov-Thorne model. Similarly, the expelled angular momentum can be comparable to that accreted by the black hole. Both the inner electromagnetic part and the outer matter part can contribute in significant fashion to the energy and angular momentum of the outflow.Comment: 43 pages 12 figures To Appear in the Astrophysical Journal replaced figure 3c with correct imag

Super-critical Accretion Flows around Black Holes: Two-dimensional, Radiation-pressure-dominated Disks with Photon-trapping

The quasi-steady structure of super-critical accretion flows around a black hole is studied based on the two-dimensional radiation-hydrodynamical (2D-RHD) simulations. The super-critical flow is composed of two parts: the disk region and the outflow regions above and below the disk. Within the disk region the circular motion as well as the patchy density structure are observed, which is caused by Kelvin-Helmholtz instability and probably by convection. The mass-accretion rate decreases inward, roughly in proportion to the radius, and the remaining part of the disk material leaves the disk to form outflow because of strong radiation pressure force. We confirm that photon trapping plays an important role within the disk. Thus, matter can fall onto the black hole at a rate exceeding the Eddington rate. The emission is highly anisotropic and moderately collimated so that the apparent luminosity can exceed the Eddington luminosity by a factor of a few in the face-on view. The mass-accretion rate onto the black hole increases with increase of the absorption opacity (metalicity) of the accreting matter. This implies that the black hole tends to grow up faster in the metal rich regions as in starburst galaxies or star-forming regions.Comment: 16 pages, 12 figures, accepted for publication in ApJ (Volume 628, July 20, 2005 issue

Imaging the Black Hole Silhouette of M87: Implications for Jet Formation and Black Hole Spin

The silhouette cast by the horizon of the supermassive black hole in M87 can now be resolved with the emerging millimeter very-long baseline interferometry (VLBI) capability. Despite being ~2000 times farther away than SgrA* (the supermassive black hole at the center of the Milky-Way and the primary target for horizon-scale imaging), M87's much larger black hole mass results in a horizon angular scale roughly half that of SgrA*'s, providing another practical target for direct imaging. However, unlike SgrA*, M87 exhibits a powerful radio jet, providing an opportunity to study jet formation physics on horizon scales. We employ a simple, qualitatively correct force-free jet model to explore the expected high-resolution images of M87 at wavelengths of 1.3mm and 0.87mm (230GHz and 345GHz), for a variety of jet parameters. We show that future VLBI data will be able to constrain the size of the jet footprint, the jet collimation rate, and the black hole spin. Polarization will further probe the structure of the jet's magnetic field and its effect on the emitting gas. Horizon-scale imaging of M87 and SgrA* will enable for the first time the empirical exploration of the relationship between the mass and spin of a black hole and the characteristics of the gas inflow/outflow around it.Comment: 18 pages, 7 figures, accepted by Ap