Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts

In this paper we present a model for making clean energy with a Kerr black hole. Consider a Kerr black hole with a dense plasma torus spinning around it. A toroidal electric current flows on the surface of the torus, which generates a poloidal magnetic field outside the torus. On the surface of the tours the magnetic field is parallel to the surface. The closed magnetic field lines winding around the torus compress and confine the plasma in the torus, as in the case of tokamaks. Though it is unclear if such a model is stable, we look into the consequences if the model is stable. If the magnetic field is strong enough, the baryonic contamination from the plasma in the torus is greatly suppressed by the magnetic confinement and a clean magnetosphere of electron-positron pairs is built up around the black hole. Since there are no open magnetic field lines threading the torus and no accretion, the power of the torus is zero. If some magnetic field lines threading the black hole are open and connect with loads, clean energy can be extracted from the Kerr black hole by the Blandford-Znajek mechanism. The model may be relevant to gamma-ray bursts. The energy in the Poynting flux produced by the Blandford-Znajek mechanism is converted into the kinetic energy of the electron-positron pairs in the magnetosphere around the black hole, which generates two oppositely directed jets of electron-positron pairs with super-high bulk Lorentz factors. The jets collide and interact with the interstellar medium, which may produce gamma-ray bursts and the afterglows.Comment: 14 pages, 1 figure, accepted by Ap

Extracting Energy from a Black Hole through Its Disk

When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, $ca/GM_H>0.36$ for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk ($M_H$ is the mass and $a M_H$ is the angular momentum of the black hole). This way the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from $ca/GM_H = 0.998$ to $ca/GM_H = 0.36$ by a thin Keplerian disk is $\approx 0.15 M_Hc^2$. This is larger than $\approx 0.09 M_Hc^2$ which can be extracted by the Blandford-Znajek mechanism.Comment: 8 pages, 2 figure

Multi-line detection of O_2 toward ρ Ophiuchi A

Context. Models of pure gas-phase chemistry in well-shielded regions of molecular clouds predict relatively high levels of molecular oxygen, O_2, and water, H_(2)O. These high abundances imply high cooling rates, leading to relatively short timescales for the evolution of gravitationally unstable dense cores, forming stars and planets. Contrary to expectations, the dedicated space missions SWAS and Odin typically found only very small amounts of water vapour and essentially no O_2 in the dense star-forming interstellar medium. Aims. Only toward ρOph   A did Odin detect a very weak line of O_2 at 119 GHz in a beam of size 10 arcmin. The line emission of related molecules changes on angular scales of the order of some tens of arcseconds, requiring a larger telescope aperture such as that of the Herschel Space Observatory to resolve the O2 emission and pinpoint its origin. Methods. We use the Heterodyne Instrument for the Far Infrared (HIFI) aboard Herschel to obtain high resolution O_2 spectra toward selected positions in the ρOph A   core. These data are analysed using standard techniques for O_2 excitation and compared to recent PDR-like chemical cloud models. Results. The N_J = 3_(3) − 1_(2) line at 487.2 GHz is clearly detected toward all three observed positions in the ρOph A  core. In addition, an oversampled map of the 5_(4)−3_(4) transition at 773.8 GHz reveals the detection of the line in only half of the observed area. On the basis of their ratios, the temperature of the O_2 emitting gas appears to vary quite substantially, with warm gas (≳ 50K) being adjacent to a much colder region, of temperatures lower than 30 K. Conclusions. The exploited models predict that the O_2 column densities are sensitive to the prevailing dust temperatures, but rather insensitive to the temperatures of the gas. In agreement with these models, the observationally determined O_2 column densities do not seem to depend strongly on the derived gas temperatures, but fall into the range N(O_2) = 3 to ≳ 6 × 10^(15) cm^(-2). Beam-averaged O2 abundances are about 5 × 10^(-8) relative to H_2. Combining the HIFI data with earlier Odin observations yields a source size at 119 GHz in the range of 4 to 5 arcmin, encompassing the entire ρOph A core. We speculate that one of the reasons for the generally very low detection rate of O2 is the short period of time during which O_2 molecules are reasonably abundant in molecular clouds

Extracting Energy from Accretion into Kerr Black Hole

The highest efficiency of converting rest mass into energy by accreting matter into a Kerr black hole is ~ 31% (Thorne 1974). We propose a new process in which periods of accretion from a thin disk, and the associated spin-up of the black hole, alternate with the periods of no accretion and magnetic transfer of energy from the black hole to the disk. These cycles can repeat indefinitely, at least in principle, with the black hole mass increasing by ~ 66% per cycle, and up to ~ 43% of accreted rest mass radiated away by the disk.Comment: 4 pages, 1 figur

Almost prime triples and Chen's Theorem

We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen.Comment: 22 pages; errors with numerical calculations corrected after referee report; main result somewhat improve

Magneto-Centrifugal Launching of Jets from Accretion Disks. I: Cold Axisymmetric Flows

The magneto-centrifugal model for jet formation is studied by time-dependent simulations reaching steady state in a cold gas with negligible fluid pressure, in an axisymmetric geometry, using a modification of the Zeus3D code adapted to parallel computers. The number of boundary conditions imposed at the coronal base takes into account the existence of the fast and Alfvenic critical surfaces, avoiding over-determination of the flow. The size and shape of the computational box is chosen to include these critical surfaces, reducing the influence of the outer boundary conditions. As there is a region, near the origin, where the inclination of field lines to the axis is too small to drive a centrifugal wind, we inject a thin, axial jet, expected to form electromagnetically near black holes. Acceleration and collimation appear for wide generic conditions. A reference run is shown in detail, with a wind leaving the computational volume in the axial direction with a poloidal velocity equal to 4 times the poloidal Alfven speed, collimated inside 11 degrees. Finally, the critical surfaces, fieldlines, thrust, energy, torque and mass discharge of the outgoing wind are shown for simulations with various profiles of mass and magnetic flux at the base of the corona.Comment: 27 pages, including 10 figures and 2 tables. To appear in ApJ (Dec 1999). Revised version clarifies the abstract, section 3.2.4, conclusions and appendix, adds a simulation to section 4.2, and updates the reference

Multi-physics simulation of friction stir welding process

Purpose: The Friction Stir Welding (FSW) process comprises of several highly coupled (and non-linear) physical phenomena: large plastic deformation, material flow transportation, mechanical stirring of the tool, tool-workpiece surface interaction, dynamic structural evolution, heat generation from friction and plastic deformation, etc. In this paper, an advanced Finite Element (FE) model encapsulating this complex behavior is presented and various aspects associated with the FE model such as contact modeling, material model and meshing techniques are discussed in detail. Methodology: The numerical model is continuum solid mechanics-based, fully thermomechanically coupled and has successfully simulated the friction stir welding process including plunging, dwelling and welding stages. Findings: The development of several field variables are quantified by the model: temperature, stress, strain, etc. Material movement is visualized by defining tracer particles at the locations of interest. The numerically computed material flow patterns are in very good agreement with the general findings from experiments. Value: The model is, to the best of the authors’ knowledge, the most advanced simulation of FSW published in the literature

Parametric finite-element studies on the effect of tool shape in friction stir welding

The success of the Friction Stir Welding (FSW) process, and the weld quality produced, depends significantly on the design of the welding tool. In this paper the effect of variation in various tool geometry parameters on FSW process outcomes, during the plunge stage, were investigated. Specifically the tool shoulder surface angle and the ratio of the shoulder radius to pin radius on tool reaction force, tool torque, heat generation, temperature distribution and size of the weld zone were investigated. The studies were carried out numerically using the finite element method. The welding process used AA2024 aluminium alloy plates with a thickness of 3 mm. It was found that, in plunge stage, the larger the pin radius the higher force and torque the tool experiences and the greater heat generated. It is also found that the shoulder angle has very little effect on energy dissipation as well as little effect on temperature distribution