Axisymmetric toroidal modes of general relativistic magnetized neutron star models
Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp
2014-07-20
We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.
Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs
Abdikamalov, E. B.; Ott, C. D.; Rezzolla, L.; Dessart, L.; Dimmelmeier, H.; Marek, A.; Janka, H.-T.
2010-02-15
The accretion-induced collapse (AIC) of a white dwarf may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in type Ia supernovae. In the AIC scenario, the supernova explosion energy is expected to be small and the resulting transient short-lived, making it hard to detect by electromagnetic means alone. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in axisymmetric rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, and resulting white dwarf masses, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a 'type III' signal in the literature. Despite this reduction to a single type of waveform, we show that the emitted GWs carry information that can be used to constrain the progenitor and the postbounce rotation. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Furthermore, we contrast the GW signals of AIC and rotating massive star iron core collapse and find that they can be distinguished, but only if the distance to the source is known and a detailed reconstruction of the GW time series from detector data is possible. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. The disk mass is very sensitive to progenitor mass and angular momentum
A variational principle for the axisymmetric stability of rotating relativistic stars
NASA Astrophysics Data System (ADS)
Prabhu, Kartik; Schiffrin, Joshua S.; Wald, Robert M.
2016-09-01
It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes.
Exploring Stability of General Relativistic Accretion Disks
NASA Astrophysics Data System (ADS)
Korobkin, Oleg; Abdikamalov, Ernazar; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard
2011-04-01
Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios, involving core collapse of massive stars and mergers of compact ob jects. I will present results on our recent study of the stability of such disks against runaway and non-axisymmetric instabilities, which we explore using three-dimensional hydrodynamics simulations in full general relativity. All of our models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. We will discuss the types, growth rates and pattern speeds of the unstable modes, as well as the detectability of the gravitational waves from such objects.
General Relativistic and Newtonian White Dwarfs
NASA Astrophysics Data System (ADS)
Boshkayev, K.; Rueda, J. A.; Ruffini, R.; Siutsou, I.
2015-01-01
The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of Newton's gravity and general relativity. In both cases Hartle's formalism is applied to construct the internal and external solutions to the field equations. The white dwarf (WD) matter is described by the Chandrasekhar equation of state. The region of stability of RWDs is constructed taking into account the mass-shedding limit, inverse β-decay instability, and the boundary established by the turning points of constant angular momentum J sequences which separates stable from secularly unstable configurations. We found the minimum rotation period ˜ 0.28 s in both cases and maximum rotating masses ˜ 1.534M⊙ and ˜ 1.516M⊙ for the Newtonian and general relativistic WDs, respectively. By using the turning point method we show that general relativistic WDs can indeed be axisymmetrically unstable whereas the Newtonian WDs are stable.
Axisymmetric rotating relativistic bodies: A new numerical approach for 'exact' solutions
NASA Astrophysics Data System (ADS)
Bonazzola, S.; Gourgoulhon, E.; Salgado, M.; Marck, J. A.
1993-11-01
A new set of equations and a new numerical method for computing stationary axisymmetric rapidly rotating star models within general relativity is presented. The source term of the gravitational field is not restricted to a perfect fluid one but represents the most general one, including anisotropic stresses, permitted under the assumptions of stationarity, axisymmetry and absence of meridional currents. This allows us to derive the equations governing the equilibrium of rotating neutron stars with strong magnetic fields in a self-consistent and fully relativistic way. As regards to the numerics, the improvement lies in the exact computation of the metric in the whole space outside the star, thanks to a numerial grid which extends to infinity (due to a suitable compactification of the space external to the star). The numerical integration is performed by means of an iterative procedure based on a spectral method, which provides results far more precise than previous methods, with 'evanescent' numerical errors. The code efficiency is demonstrated by considering a simple polytropic equation of state, this paper being not intended to present new astrophysical results but the equations governing more general objects than previously considered (for instance magnetized neutron stars) and the numerical method to integrate them. In that spirit, a particular emphasis is given to the evaluation of the numerical errors. A certain integral quantity is shown to be a very good indicator of the discrepancy between the numerical solution and the exact one.
On General Relativistic Uniformly Rotating White Dwarfs
NASA Astrophysics Data System (ADS)
Boshkayev, Kuantay; Rueda, Jorge A.; Ruffini, Remo; Siutsou, Ivan
2013-01-01
The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. Hartle's formalism is applied to construct the internal and external solutions to the Einstein equations. The white dwarf (WD) matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes that of Salpeter by taking into account the finite size of the nuclei, and the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion. The mass M, radius R, angular momentum J, eccentricity epsilon, and quadrupole moment Q of RWDs are calculated as a function of the central density ρ c and rotation angular velocity Ω. We construct the region of stability of RWDs (J-M plane) taking into account the mass-shedding limit, inverse β-decay instability, and the boundary established by the turning points of constant J sequences which separates stable from secularly unstable configurations. We found the minimum rotation periods ~0.3, 0.5, 0.7, and 2.2 s and maximum masses ~1.500, 1.474, 1.467, 1.202 M ⊙ for 4He, 12C, 16O, and 56Fe WDs, respectively. By using the turning-point method, we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where this occurs. We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that, by losing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum static one) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period, while super-Chandrasekhar RWDs (mass larger than maximum static one) only spin up.
ON GENERAL RELATIVISTIC UNIFORMLY ROTATING WHITE DWARFS
Boshkayev, Kuantay; Rueda, Jorge A.; Ruffini, Remo; Siutsou, Ivan E-mail: jorge.rueda@icra.it E-mail: siutsou@icranet.org
2013-01-10
The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of general relativity. Hartle's formalism is applied to construct the internal and external solutions to the Einstein equations. The white dwarf (WD) matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes that of Salpeter by taking into account the finite size of the nuclei, and the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion. The mass M, radius R, angular momentum J, eccentricity {epsilon}, and quadrupole moment Q of RWDs are calculated as a function of the central density {rho} {sub c} and rotation angular velocity {Omega}. We construct the region of stability of RWDs (J-M plane) taking into account the mass-shedding limit, inverse {beta}-decay instability, and the boundary established by the turning points of constant J sequences which separates stable from secularly unstable configurations. We found the minimum rotation periods {approx}0.3, 0.5, 0.7, and 2.2 s and maximum masses {approx}1.500, 1.474, 1.467, 1.202 M {sub Sun} for {sup 4}He, {sup 12}C, {sup 16}O, and {sup 56}Fe WDs, respectively. By using the turning-point method, we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where this occurs. We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that, by losing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum static one) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period, while super-Chandrasekhar RWDs (mass larger than maximum static one) only spin up.
Stability of general-relativistic accretion disks
Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard
2011-02-15
Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a {Gamma}-law equation of state with {Gamma}=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.
Stability of general-relativistic accretion disks
NASA Astrophysics Data System (ADS)
Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard
2011-02-01
Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a Γ-law equation of state with Γ=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.
Generalized energy principle for flute perturbations in axisymmetric mirror machines
Lansky, I.M.; Ryutov, D.D.
1993-01-20
Axial symmetry is a very desirable property of the mirror devices both for fusion and neutron source applications. The main obstacle to be circumvented in the development of such systems, is the flute instability of axisymmetric mirrors. In recent years there appeared a number of proposals, devoted to the stabilization of the flute perturbations in the framework of axisymmetric magnetic configurations, which are based on the combining of the MHD unstable central cell with various types of end-cell stabilizers. In the present paper we concentrate ourselves just on this scheme, including long solenoid with a uniform field, conjugated with the end stabilizing anchor, intended to provide MHD stability of the system as a whole. The attractive feature of such a configuration is that it allows to exploit finite larmor radius (FLR) effects for the stabilization of the flute perturbations. As is well known, FLR effects, being strong, stabilize all flute modes, except the one with azimuthal number m = 1, corresponding to the ``rigid`` displacement of the plasma column (the ``global`` mode). Consequently, in the conditions when FLR effects dominate, the anchor has to stabilize the ``global` mode only. Bearing in mind a favorable influence of FLR effects we, however, don`t restrict our paper by discussion of only ``global`` mode stability and consider a general case of an arbitrary azimuthal mode.
CoCoNuT: General relativistic hydrodynamics code with dynamical space-time evolution
NASA Astrophysics Data System (ADS)
Dimmelmeier, Harald; Novak, Jérôme; Cerdá-Durán, Pablo
2012-02-01
CoCoNuT is a general relativistic hydrodynamics code with dynamical space-time evolution. The main aim of this numerical code is the study of several astrophysical scenarios in which general relativity can play an important role, namely the collapse of rapidly rotating stellar cores and the evolution of isolated neutron stars. The code has two flavors: CoCoA, the axisymmetric (2D) magnetized version, and CoCoNuT, the 3D non-magnetized version.
Generalized magnetofluid connections in relativistic magnetohydrodynamics.
Asenjo, Felipe A; Comisso, Luca
2015-03-20
The concept of magnetic connections is extended to nonideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall, and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic connection notion to a much broader concept. PMID:25839284
Newtonian hydrodynamics with general relativistic pressure
Hwang, Jai-chan; Noh, Hyerim E-mail: hr@kasi.re.kr
2013-10-01
We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (1.1)–(1.3). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms differ from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.
General relativistic effects in atom interferometry
Dimopoulos, Savas; Hogan, Jason M.; Kasevich, Mark A.; Graham, Peter W.
2008-08-15
Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the nonrelativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this, we develop a method for calculating the phase shift in general relativity. Both the atoms and the light are treated relativistically and all coordinate dependencies are removed, thus revealing novel terms, cancellations, and new origins for previously calculated terms. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the nonlinear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose specific experiments, one currently under construction, to measure each of these effects. These experiments could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the Universe, and preferred frame and location effects.
General Relativistic Effects in Atom Interferometry
Dimopoulos, Savas; Graham, Peter W.; Hogan, Jason M.; Kasevich, Mark A.; /Stanford U., Phys. Dept.
2008-03-17
Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.
Spectral Methods in General Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
Garrison, David
2012-03-01
In this talk I discuss the use of spectral methods in improving the accuracy of a General Relativistic Magnetohydrodynamic (GRMHD) computer code. I introduce SpecCosmo, a GRMHD code developed as a Cactus arrangement at UHCL, and show simulation results using both Fourier spectral methods and finite differencing. This work demonstrates the use of spectral methods with the FFTW 3.3 Fast Fourier Transform package integrated with the Cactus Framework to perform spectral differencing using MPI.
Diffusion processes in general relativistic radiating spheres
Barreto, W.; Herrera, L.; Santos, N.O.; Universidad Central de Venezuela, Caracas; Observatorio Nacional do Brasil, Rio de Janeiro )
1989-09-01
The influence of diffusion processes on the dynamics of general relativistic radiating spheres is systematically studied by means of two examples. Differences between the streaming-out limit and the diffusion limit are exhibited, for both models, through the evolution curves of dynamical variables. In particular it is shown the Bondi mass decreases, for both models, in the diffusion limit as compared with its value at the streaming-out regime. 15 refs.
Multipatch methods in general relativistic astrophysics: Hydrodynamical flows on fixed backgrounds
Zink, Burkhard; Schnetter, Erik; Tiglio, Manuel
2008-05-15
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in x-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically symmetric or axisymmetric. In Newtonian or fixed-background relativistic approximations it is common practice to use spherical polar coordinates for computational grids; however, these coordinates have singularities and are difficult to use in fully relativistic models. We present, in this series of papers, a numerical technique which is able to use effectively spherical grids by employing multiple patches. We provide detailed instructions on how to implement such a scheme, and present a number of code tests for the fixed-background case, including an accretion torus around a black hole.
General-relativistic astrophysics. [gravitational wave astronomy
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1978-01-01
The overall relevance of general relativity to astrophysics is considered, and some of the knowledge about the ways in which general relativity should influence astrophysical systems is reviewed. Attention is focused primarily on finite-sized astrophysical systems, such as stars, globular clusters, galactic nuclei, and primordial black holes. Stages in the evolution of such systems and tools for studying the effects of relativistic gravity in these systems are examined. Gravitational-wave astronomy is discussed in detail, with emphasis placed on estimates of the strongest gravitational waves that bathe earth, present obstacles and future prospects for detection of the predicted waves, the theory of small perturbations of relativistic stars and black holes, and the gravitational waves such objects generate. Characteristics of waves produced by black-hole events in general, pregalactic black-hole events, black-hole events in galactic nuclei and quasars, black-hole events in globular clusters, the collapse of normal stars to form black holes or neutron stars, and corequakes in neutron stars are analyzed. The state of the art in gravitational-wave detection and characteristics of various types of detector are described.
A General Relativistic Magnetohydrodynamic Simulation of Jet Formation
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fishman, G. J.
2005-05-01
We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity ~0.3c) is created, as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (τS=rS/c, where rS≡2GM/c2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r=3rS. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfvén waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the lack of streaming material from an accompanying star.
A general relativistic model for free-fall absolute gravimeters
NASA Astrophysics Data System (ADS)
Tan, Yu-Jie; Shao, Cheng-Gang; Li, Jia; Hu, Zhong-Kun
2016-04-01
Although the relativistic manifestations of gravitational fields in gravimetry were first studied 40 years ago, the relativistic effects combined with free-fall absolute gravimeters have rarely been considered. In light of this, we present a general relativistic model for free-fall absolute gravimeters in a local-Fermi coordinates system, where we focus on effects related to the measuring devices: relativistic transverse Doppler effects, gravitational redshift effects and Earth’s rotation effects. Based on this model, a general relativistic expression of the measured gravity acceleration is obtained.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
General Relativistic Magnetohydrodynamic Simulations of Collapsars
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Yamada, S.; Koider, S.; Shipata, K.
2005-01-01
We have performed 2.5-dimensional general relativistic magnetohydrodynamic (MHD) simulations of collapsars including a rotating black hole. Initially, we assume that the core collapse has failed in this star. A rotating black hole of a few solar masses is inserted by hand into the calculation. The simulation results show the formation of a disklike structure and the generation of a jetlike outflow near the central black hole. The jetlike outflow propagates and accelerated mainly by the magnetic field. The total jet velocity is approximately 0.3c. When the rotation of the black hole is faster, the magnetic field is twisted strongly owing to the frame-dragging effect. The magnetic energy stored by the twisting magnetic field is directly converted to kinetic energy of the jet rather than propagating as an Alfven wave. Thus, as the rotation of the black hole becomes faster, the poloidal velocity of the jet becomes faster.
Improving general relativistic astrophysics workflows with ADIOS
NASA Astrophysics Data System (ADS)
Bode, Tanja; Slawinska, Magdalena; Logan, Jeremy; Clark, Michael; Kinsey, Matthew; Wolf, Matthew; Klasky, Scott; Laguna, Pablo
2013-04-01
There are many challenges in analyzing and visualizing data from current cutting-edge general relativistic astrophysics simulations. Many of the associated tasks are time-consuming, with large performance degradation due to the magnitude and complexity of the data. The Adaptable IO System (ADIOS) is a componentization of the IO layer that has demonstrated remarkable IO performance improvements on applications running on leadership class machines while also offering new in-memory ``staging'' operations for transforming data in situ. We have incorporated ADIOS staging technologies into our Maya numerical relativity code based on Cactus infrastructure and Carpet mesh refinement. We present results that demonstrate how ADIOS yields significant gains on IO performance while utilizing leveraged investments in ADIOS plugins for visualization tools such as VisIt.
User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.
1982-01-01
This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.
Oscillations of general relativistic superfluid neutron stars
NASA Astrophysics Data System (ADS)
Andersson, N.; Comer, G. L.; Langlois, D.
2002-11-01
We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be described by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all charged constituents (crust nuclei, protons, electrons, etc.). We use a system of equations that governs the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. The entrainment effect is explicitly included. We also take the first step towards allowing for the superfluid to be confined to a part of the star by allowing for an outer envelope composed of ordinary fluid. We derive and implement the junction conditions for the metric and matter variables at the core-envelope interface, and briefly discuss the nature of the involved phase transition. We then determine the frequencies and gravitational-wave damping times for a simple model equation of state, incorporating entrainment through an approximation scheme which extends present Newtonian results to the general relativistic regime. We investigate how the quasinormal modes of a superfluid star are affected by changes in the entrainment parameter, and unveil a series of avoided crossings between the various modes. We provide a proof that, unless the equation of state is very special, all modes of a two-fluid star must radiate gravitationally. We also discuss the future detectability of pulsations in a superfluid star and argue that it may be possible (given advances in the relevant technology) to use gravitational-wave data to constrain the parameters of superfluid neutron stars.
A generalized twistor dynamics of relativistic particles and strings
Soroka, V.A.; Sorokin, D.P.; Tkach, V.I.; Volkov, D.V. )
1992-09-30
In this paper, a generalization of relativistic particle and sting dynamics based on a notion of twistor shift and containing a fundamental length constant is considered, which results in a modification of particle (or string) interactions with background fields.
Fully relativistic multiple scattering calculations for general potentials
NASA Astrophysics Data System (ADS)
Ebert, H.; Braun, J.; Ködderitzsch, D.; Mankovsky, S.
2016-02-01
The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that require to distinguish between right- and left-hand-side solutions to the Dirac equation when setting up the electronic Green function. In addition, various technical aspects of an implementation of the relativistic KKR for general local and nonlocal potentials will be discussed.
Non-axisymmetric relativistic wind accretion with velocity gradients on to a rotating black hole
NASA Astrophysics Data System (ADS)
Cruz-Osorio, A.; Lora-Clavijo, F. D.
2016-08-01
We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients onto a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient $\\epsilon_{v}$, the black hole spin $a$, the asymptotic Mach number ${\\cal M}_{\\infty}$ and adiabatic index $\\Gamma$. We show that the flow accretion reaches a fairly stationary regime, unlike in the Newtonian case, where significant fluctuations of the mass and angular momentum accretion rates are found. On the other hand, we consider a special case where both density and velocity gradients of the fluid are taken into account. The spin of the black hole and the asymptotic Newtonian Mach number, for this case, are $a=0.98$ and ${\\cal M}_{\\infty}=1$, respectively. A kind of flip-flop behavior is found at the early times; nevertheless, the system also reaches a steady state.
Non-axisymmetric relativistic wind accretion with velocity gradients on to a rotating black hole
NASA Astrophysics Data System (ADS)
Cruz-Osorio, A.; Lora-Clavijo, F. D.
2016-08-01
We model, for the first time, the Bondi-Hoyle accretion of a fluid with velocity gradients on to a Kerr black hole, by numerically solving the fully relativistic hydrodynamics equations. Specifically, we consider a supersonic ideal gas, which has velocity gradients perpendicular to the relative motion. We measure the mass and specific angular accretion rates to illustrate whether the fluid presents unstable patterns or not. The initial parameters, we consider in this work, are the velocity gradient ɛv, the black hole spin a, the asymptotic Mach number M_{∞} and adiabatic index Γ. We show that the flow accretion reaches a fairly stationary regime, unlike in the Newtonian case, where significant fluctuations of the mass and angular momentum accretion rates are found. On the other hand, we consider a special case where both density and velocity gradients of the fluid are taken into account. The spin of the black hole and the asymptotic Newtonian Mach number, for this case, are a = 0.98 and M_{∞}=1, respectively. A kind of flip-flop behaviour is found at the early times; nevertheless, the system also reaches a steady state.
Cosmological measurements with general relativistic galaxy correlations
NASA Astrophysics Data System (ADS)
Raccanelli, Alvise; Montanari, Francesco; Bertacca, Daniele; Doré, Olivier; Durrer, Ruth
2016-05-01
We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called ``relativistic effects'', and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms, especially lensing convergence, introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. The analysis suggests a possible substantial systematic error in cosmological parameter constraints. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.
General relativistic observables for the ACES experiment
NASA Astrophysics Data System (ADS)
Turyshev, Slava G.; Yu, Nan; Toth, Viktor T.
2016-02-01
We develop a high-precision model for relativistic observables of the Atomic Clock Ensemble in Space (ACES) experiment on the International Space Station (ISS). We develop all relativistic coordinate transformations that are needed to describe the motion of ACES in Earth orbit and to compute observable quantities. We analyze the accuracy of the required model as it applies to the proper-to-coordinate time transformations, light-time equation, and spacecraft equations of motion. We consider various sources of nongravitational noise and their effects on ACES. We estimate the accuracy of orbit reconstruction that is needed to satisfy the ACES science objectives. Based on our analysis, we derive models for the relativistic observables of ACES, which also account for the contribution of atmospheric drag on the clock rate. We include the Earth's oblateness coefficient J2 and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudoinertial at the level of accuracy required by the experiment. We construct a Doppler-canceled science observable representing the gravitational redshift. We derive accuracy requirements for ISS navigation. The improved model is accurate up to <1 ps and ˜4 ×1 0-17 for time and frequency transfers, correspondingly. These limits are determined by the higher-order harmonics in Earth's gravitational potential.
NASA Technical Reports Server (NTRS)
Gnoffo, P. A.
1977-01-01
A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.
An axisymmetric charged dust distribution with NUT rotation in general relativity
NASA Astrophysics Data System (ADS)
Vargas-Rodriguez, H.; Gonzalez-Silva, R. A.; Lopez Benitez, L. I.
2010-07-01
An exact solution of the Einstein-Maxwell's field equations is presented. This solution describes an axisymmetric charged dust distribution, with NUT rotation, in the presence of an electromagnetic field of the pure magnetic type. In the comoving reference frame, there is magnetic field only, the dust's electric charges do not interact with themselves, this is due to the vanishing of the Lorentz force. A naked singularity with magnetic charge is present. The solution is of the Petrov type D and possesses four Killing vectors. This is a generalization of the Lukács solution to the case when dust is charged.
General-relativistic rotation laws in rotating fluid bodies
NASA Astrophysics Data System (ADS)
Mach, Patryk; Malec, Edward
2015-06-01
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to rederive, in the first post-Newtonian approximation, the well-known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic antidragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids self-gravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations as well as the existence of the post-Newtonian limits.
Computational cosmology: A general relativistic approach
NASA Astrophysics Data System (ADS)
Matarrese, Sabino
2016-04-01
The quality and quantity of current and forthcoming cosmological datasets call for both analytical and numerical modelling of the dynamics of nonlinear gravitational matter based on general relativity.
Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Wu, Kinwah; /Mullard Space Sci. Lab.
2007-01-05
We calculate the emission from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by general relativistic magneto-hydrodynamic simulations. We consider thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We propose that variations and drifts of the features produce certain X-ray quasi-periodic oscillations (QPOs) observed in black-hole X-ray binaries.
General relativistic magneto-hydrodynamics with the Einstein Toolkit
NASA Astrophysics Data System (ADS)
Moesta, Philipp; Mundim, Bruno; Faber, Joshua; Noble, Scott; Bode, Tanja; Haas, Roland; Loeffler, Frank; Ott, Christian; Reisswig, Christian; Schnetter, Erik
2013-04-01
The Einstein Toolkit Consortium is developing and supporting open software for relativistic astrophysics. Its aim is to provide the core computational tools that can enable new science, broaden our community, facilitate interdisciplinary research and take advantage of petascale computers and advanced cyberinfrastructure. The Einstein Toolkit currently consists of an open set of over 100 modules for the Cactus framework, primarily for computational relativity along with associated tools for simulation management and visualization. The toolkit includes solvers for vacuum spacetimes as well as relativistic magneto-hydrodynamics. This talk will present the current capabilities of the Einstein Toolkit with a particular focus on recent improvements made to the general relativistic magneto-hydrodynamics modeling and will point to information how to leverage it for future research.
Causal structure of general relativistic spacetimes
Howard, Ecaterina
2010-06-15
We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief overview of the Hawking-Penrose singularity theorems and discuss a few open problems concerning the future Cauchy development (domain of dependence), break-down criteria and energy conditions for the horizon stability. A key question is whether causality violating regions, generating a Cauchy horizon are allowed.We raise several questions concerning the invisibility and stability of closed trapped surfaces from future null infinity and derive the imprisonment conditions. We provide an up-to-date perspective of the causal boundaries and spacelike conformal boundary extensions for time oriented Lorentzian manifolds and more exotic settings.
Neoclassical transport coefficients for general axisymmetric equilibria in the banana regime
NASA Astrophysics Data System (ADS)
Angioni, C.; Sauter, O.
2000-04-01
Using the standard approach of neoclassical theory, a set of relatively simple kinetic equations has been obtained, suited for an implementation in a numerical code to compute a related set of distribution functions. The transport coefficients are then expressed by simple integrals of these functions and they can be easily computed numerically. The code CQL3D [R. W. Harvey and M. G. McCoy, in Proceedings of IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas, Montreal, 1992 (International Atomic Energy Agency, Vienna, 1993), pp. 489-526], which uses the full collision operator and considers the realistic axisymmetric configuration of the magnetic surfaces, has been modified to solve the bounce-averaged version of these equations. The coefficients have then been computed for a wide variety of equilibrium parameters, high-lighting interesting features of the influence of geometry at small aspect ratio. Differences with the most recent formulas for the ion neoclassical heat conductivity are pointed out. A set of formulas, which fit the code results, is obtained to easily evaluate all the neoclassical transport coefficients in the banana regime, at all aspect ratios, in general axisymmetric equilibria. This work extends to all the other transport coefficients, at least in the banana regime, the work of Sauter et al. [O. Sauter, C. Angioni, and Y. R. Lin-Liu, Phys. Plasmas 6, 2834 (1999)] which evaluates the neoclassical conductivity and all the bootstrap current coefficients. Formulas for arbitrary collisionality regime are proposed, obtained combining our results for the banana regime with the results of Hinton and Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)], adapted for small aspect ratio.
General Relativistic Radiative Transfer: Applications to Black-Hole Systems
NASA Technical Reports Server (NTRS)
Wu, Kinwah; Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Branduardi-Raymont, Graziella; Lee, Khee-Gan
2007-01-01
We present general relativistic radiation transfer formulations which include opacity effects due to absorption, emission and scattering explicitly. We consider a moment expansions for the transfer in the presence of scattering. The formulation is applied to calculation emissions from accretion and outflows in black-hole systems. Cases with thin accretion disks and accretion tori are considered. Effects, such as emission anisotropy, non-stationary flows and geometrical self-occultation are investigated. Polarisation transfer in curved space-time is discussed qualitatively.
Relativistic mean field model for entrainment in general relativistic superfluid neutron stars
NASA Astrophysics Data System (ADS)
Comer, G. L.; Joynt, R.
2003-07-01
General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of “relativistic”: relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro’s number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.
General relativistic models of binary neutron stars in quasiequilibrium
NASA Astrophysics Data System (ADS)
Baumgarte, T. W.; Cook, G. B.; Scheel, M. A.; Shapiro, S. L.; Teukolsky, S. A.
1998-06-01
We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft (n>~1.5). A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.
NASA Astrophysics Data System (ADS)
Dibi, S.; Drappeau, S.; Fragile, P. C.; Markoff, S.; Dexter, J.
2012-11-01
We present general relativistic magnetohydrodynamic numerical simulations of the accretion flow around the supermassive black hole in the Galactic Centre, Sagittarius A* (Sgr A*). The simulations include for the first time radiative cooling processes (synchrotron, bremsstrahlung and inverse Compton) self-consistently in the dynamics, allowing us to test the common simplification of ignoring all cooling losses in the modelling of Sgr A*. We confirm that for Sgr A*, neglecting the cooling losses is a reasonable approximation if the Galactic Centre is accreting below ˜10-8 M⊙ yr-1, i.e. M⊙<10-7M⊙ Edd . However, above this limit, we show that radiative losses should be taken into account as significant differences appear in the dynamics and the resulting spectra when comparing simulations with and without cooling. This limit implies that most nearby low-luminosity active galactic nuclei are in the regime where cooling should be taken into account. We further make a parameter study of axisymmetric gas accretion around the supermassive black hole at the Galactic Centre. This approach allows us to investigate the physics of gas accretion in general, while confronting our results with the well-studied and observed source, Sgr A*, as a test case. We confirm that the nature of the accretion flow and outflow is strongly dependent on the initial geometry of the magnetic field. For example, we find it difficult, even with very high spins, to generate powerful outflows from discs threaded with multiple, separate poloidal field loops.
A generally relativistic gauge classification of the Dirac fields
NASA Astrophysics Data System (ADS)
Fabbri, Luca
2016-04-01
We consider generally relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector. We discuss how our results are similar to those obtained by Wigner by taking into account the system of Dirac field equations. We will investigate the consequences for the dynamics and in particular we shall address the problem of getting the nonrelativistic approximation in a consistent way. We are going to comment on extensions.
Weak-field general relativistic dynamics and the Newtonian limit
NASA Astrophysics Data System (ADS)
Cooperstock, F. I.
2016-01-01
We show that the generally held view that the gravity of weak-field nonrelativistic-velocity sources being invariably almost equivalent to Newtonian gravity (NG) (the “Newtonian limit” approach) is in some instances misleading and in other cases incorrect. A particularly transparent example is provided by comparing the Newtonian and general relativistic analyses of a simple variant of van Stockum’s infinite rotating dust cylinder. We show that some very recent criticisms of our work that had been motivated by the Newtonian limit approach were incorrect and note that no specific errors in our work were found in the critique. In the process, we underline some problems that arise from inappropriate coordinate transformations. As further support for our methodology, we note that our weak-field general relativistic treatment of a model galaxy was vindicated recently by the observations of Xu et al. regarding our prediction that the Milky Way was 19-21 kpc in radius as opposed to the commonly held view that the radius was 15 kpc.
NASA Astrophysics Data System (ADS)
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
General-relativistic celestial mechanics. II. Translational equations of motion
Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX ); Soffel, M.; Xu, C. )
1992-02-15
The translational laws of motion for gravitationally interacting systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation (i.e., neglecting terms of order ({ital v}/{ital c}){sup 4} in the equations of motion), our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies.
General relativistic celestial mechanics. 2. Translational equations of motion
Damour, T.; Soffel, M.; Xu, C.
1991-10-01
The translational laws of motion for gravitationally interacting systems of N, arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses the authors' recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce global equilibrium (relativistic generalization of d'Alembert's principle). Within the post-Newtonian approximation i.e. neglecting terms of order v/c to the 4th power in the equations of motion, the authors' work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. The authors first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of the body to the post-Newtonian tidal moments (recently defined by them) felt by the body. They then give the explicit expression of these tidal moments in terms of the post-Newtonian multiple moments of the other bodies.
A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition
NASA Technical Reports Server (NTRS)
Nishikawa, K. I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fushman, G. J.
2004-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.
NASA Astrophysics Data System (ADS)
Etienne, Zachariah; Liu, Y. T.; Shapiro, S.
2007-04-01
Understanding the role general relativistic magnetohydrodynamic (GRMHD) effects play in the evolution of nascent neutron stars is a problem at the forefront of theoretical astrophysics. To this end, we performed long-term (˜10^4 M) axisymmetric simulations of differentially rotating magnetized neutron stars in the slow-rotation, weak magnetic field limit using a dynamically updated perturbative metric evolution technique. Although the perturbative metric approach yields results comparable to those obtained via a nonperturbative (BSSN) metric evolution technique, simulations performed with the perturbative metric solver require about 1/4 the computational resources at a given resolution. This computational efficiency enabled us to observe and analyze the effects of magnetic braking and the magnetorotational instability (MRI) at very high resolution. Our GRMHD simulations demonstrate that (1) MRI is not observed unless the estimated fastest-growing mode wavelength is resolved by >˜ 10 gridpoints; (2) as resolution is improved, the MRI growth rate converges, but due to the small-scale nature of MRI-induced turbulence, the maximum growth amplitude increases, but does not exhibit convergence, even at the highest resolution; and (3) independent of resolution, magnetic braking drives the star toward uniform rotation as energy is sapped from differential rotation by winding magnetic fields.
Generalized charge-screening in relativistic Thomas-Fermi model
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2014-10-01
In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, ( N s ∝ r T F 3 / r d 3 where rTF and rd are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar objects.
Cherenkov radiation from short relativistic bunches: general approach.
Baturin, S S; Kanareykin, A D
2014-11-21
In recent years new interest in Cherenkov radiation has arisen based on progress in its new applications like biomedical imaging, photonic structures, metamaterials, and beam physics. These new applications require Cherenkov radiation theory of short bunches to be extended to rather more complicated media and structures than considered originally. We present a new general approach to the analysis of Cherenkov fields and loss factors for relativistic short bunches in arbitrary slow wave guiding systems. This new formalism is obtained by considering a general integral relation that allows calculation of the fields in the vicinity of the charge. The proposed approach dramatically simplifies simulations using analytical fields near the moving source of Cherenkov radiation. PMID:25479498
Koide, Shinji
2010-01-10
To study phenomena of plasmas around rotating black holes, we have derived a set of 3+1 formalism of generalized general relativistic magnetohydrodynamic (GRMHD) equations. In particular, we investigated general relativistic phenomena with respect to the Ohm's law. We confirmed the electromotive force due to the gravitation, centrifugal force, and frame-dragging effect in plasmas near the black holes. These effects are significant only in the local small-scale phenomena compared to the scale of astrophysical objects. We discuss the possibility of magnetic reconnection, which is triggered by one of these effects in a small-scale region and influences the plasmas globally. We clarify the conditions of applicability of the generalized GRMHD, standard resistive GRMHD, and ideal GRMHD for plasmas in black hole magnetospheres.
WhiskyMHD: Numerical Code for General Relativistic Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Baiotti, Luca; Giacomazzo, Bruno; Hawke, Ian; et al.
2010-10-01
Whisky is a code to evolve the equations of general relativistic hydrodynamics (GRHD) and magnetohydrodynamics (GRMHD) in 3D Cartesian coordinates on a curved dynamical background. It was originally developed by and for members of the EU Network on Sources of Gravitational Radiation and is based on the Cactus Computational Toolkit. Whisky can also implement adaptive mesh refinement (AMR) if compiled together with Carpet. Whisky has grown from earlier codes such as GR3D and GRAstro_Hydro, but has been rewritten to take advantage of some of the latest research performed here in the EU. The motivation behind Whisky is to compute gravitational radiation waveforms for systems that involve matter. Examples would include the merger of a binary system containing a neutron star, which are expected to be reasonably common in the universe and expected to produce substantial amounts of radiation. Other possible sources are given in the projects list.
McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.
2012-04-26
Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is limited by
Generalized charge-screening in relativistic Thomas–Fermi model
Akbari-Moghanjoughi, M.
2014-10-15
In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, (N{sub s}∝r{sub TF}{sup 3}/r{sub d}{sup 3} where r{sub TF} and r{sub d} are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar
General parametrization of axisymmetric black holes in metric theories of gravity
NASA Astrophysics Data System (ADS)
Konoplya, Roman; Rezzolla, Luciano; Zhidenko, Alexander
2016-03-01
Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.
Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach
NASA Astrophysics Data System (ADS)
Gourgoulhon, Eric; Markakis, Charalampos; Uryū, Kōji; Eriguchi, Yoshiharu
2011-05-01
A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.
Multiple-event probability in general-relativistic quantum mechanics
Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo
2007-04-15
We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.
Relativistic Generalization of the Inertial and Gravitational Masses Equivalence Principle
NASA Astrophysics Data System (ADS)
Mitskievich, Nikolai V.
2008-09-01
The Newtonian approximation in the gravitational field description not necessarily involves admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field condition for gravitational field. When, e.g., a source has electromagnetic nature, one simply cannot ignore its intrinsically relativistic properties, since there cannot be invented any non-relativistic approximation which would adequately describe electromagnetic stress-energy tensor even at large distances where the fields become naturally weak. But the test particle on which gravitational field is acting, should be treated as non-relativistic (this premise is required for introduction of the Newtonian potential ΦN from the geodesic equation).
General-relativistic force-free pulsar magnetospheres
NASA Astrophysics Data System (ADS)
Pétri, J.
2016-02-01
Pulsar magnetospheres are shaped by ultrarelativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio R/rL and on frame-dragging through the spin parameter as, R is the neutron star radius and rL the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to 2 depending on the rotation rate. Moreover we retrieve the sin 2χ dependence of this luminosity, χ being the obliquity of the pulsar, as well as a braking index close to n = 3. We also show that the angular dependence of the Poynting flux scales like sin 2ϑ for the aligned rotator but like sin 4ϑ for the orthogonal rotator, ϑ being the colatitude.
A General Relativistic Magnetohydrodynamic Simulation of Jet Formation
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fishman, G. J.
2005-01-01
We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation ofjet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity approx.0.3c) is created, as shown by previous two-dimensional axi- symmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (T(sub s) = r(sub s)/c, where r(sub s = 2GM/c(sup 2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r = 3r(sub s). At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface ofthe thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfven waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the iack of streaming materiai from an accompanying star.
Axisymmetric, Nonstationary Black Hole Magnetospheres: Revisited
NASA Astrophysics Data System (ADS)
Song, Yoo Geun; Park, Seok Jae
2015-10-01
An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park & Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.
A First Approach to Hydrodynamics in General Relativistic Systems Using SPH
NASA Astrophysics Data System (ADS)
Cruz-Pérez, J. P.; González, J. A.; Montoya, E.
2010-07-01
In this work we present the Lagrangian formulation of the general relativistic ideal fluid equations. With the help of the standard Smoothed Particle Hydrodynamics (SPH) method we obtain a discretization of the motion equations. Having in mind that several of the most interesting astrophysical systems that we observe in the universe have been shaped by fluid dynamical processes, we want to use this method to study them. We present the first steps to implement such general relativistic SPH codes.
NASA Astrophysics Data System (ADS)
Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh
2016-09-01
A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.
Waves in general relativistic two-fluid plasma around a Schwarzschild black hole
NASA Astrophysics Data System (ADS)
Rahman, M. Atiqur
2012-10-01
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation.
General Relativistic MHD Models of Sgr A* and M87
NASA Astrophysics Data System (ADS)
Dexter, Jason
2011-01-01
Ongoing high resolution observations of the Galactic center black hole provide a direct probe of the structure of its accretion flow (Sgr A*) on event-horizon scales. Due to its low luminosity, this source is uniquely suitable for modeling with relativistic MHD simulations. We perform time-dependent, relativistic radiative transfer on 3D simulation data to compute images and light curves of Sgr A* at millimeter wavelengths. Fitting the images to observations allows us to constrain the parameters of the accretion flow and black hole. Simulations with misaligned angular momentum and black hole spin axes ("tilted") are also considered. Due to the precession of these accretion flows, the inferred best fit parameters should appear to change on week timescales if Sgr A* is tilted. Light curves from all simulations exhibit flaring behavior consistent with the observations. The black hole shadow, a signature of the event horizon, is visible in all best fit models and may be detected in the next 5-10 years. Preliminary results from similar models of M87 are also discussed.
Polar Cap Pair Production for an Axisymmetric Pulsar Requires General Relativity
NASA Astrophysics Data System (ADS)
Belyaev, Mikhail
2016-04-01
Using an analytical approach coupled to a condition for pair production derived from particle in cell simulations, we show that pair production by curvature photons on magnetic field lines at the polar cap is inactive if general relativity is ignored. In particular, general relativisitic frame-dragging lowers the value of the Goldreich-Julian density at the polar cap compared to its value for a flat spacetime. This leads to a region of space-like current near the surface of the neutron star where pair production is possible.However, even when general relativity is included, we show analytically that pair production on magnetic field lines is suppressed near the outer edge of the polar cap. This leads to the possibility of a ``vacuum" region of unscreened parallel electric field on open field lines near the last open field line. Such a vacuum region has indeed been observed in particle in cell simulations of the pulsar magnetosphere.Because of the generality of our analytical approach (which does not assume a dipolar surface field), our conclusions are true independent of the detailed structure of the magnetic field at the surface of the neutron star. We confirm our analytical results by comparing them to force-free simulations of a pulsar with a dipolar surface field.
Predictions of axisymmetric free turbulent shear flows using a generalized eddy-viscosity approach
NASA Technical Reports Server (NTRS)
Morgenthaler, J. H.
1973-01-01
The generalized eddy viscosity approach is described and results are presented of test cases which show that predictions obtained by this approach are adequate for most engineering applications. Because of the importance of starting computations from the injection station where experimentally determined mean and turbulence parameters are rarely available, a very simple core model applicable to simple step-type (slug) profiles was developed. Agreement between predicted and experimental mean profiles was generally almost as good for calculations made by using this model throughout the core region and the transition model for all subsequent regions as predictions made by starting from experimental profiles in the transition region. The generalized eddy-viscosity model, which was developed in part through correlation of turbulence parameters, successfully predicted turbulent shear stress, turbulent intensity, and mean velocity profiles for a 0.040-inch-diameter microjet. Therefore, successful scaling by the model was demonstrated since data used in its development was for jet areas up to 90,000 times as large as the microjet and velocities only 1/20th as high.
General relativistic magnetohydrodynamical simulations of the jet in M 87
NASA Astrophysics Data System (ADS)
Mościbrodzka, Monika; Falcke, Heino; Shiokawa, Hotaka
2016-02-01
Context. The connection between black hole, accretion disk, and radio jet can be constrained best by fitting models to observations of nearby low-luminosity galactic nuclei, in particular the well-studied sources Sgr A* and M 87. There has been considerable progress in modeling the central engine of active galactic nuclei by an accreting supermassive black hole coupled to a relativistic plasma jet. However, can a single model be applied to a range of black hole masses and accretion rates? Aims: Here we want to compare the latest three-dimensional numerical model, originally developed for Sgr A* in the center of the Milky Way, to radio observations of the much more powerful and more massive black hole in M 87. Methods: We postprocess three-dimensional GRMHD models of a jet-producing radiatively inefficient accretion flow around a spinning black hole using relativistic radiative transfer and ray-tracing to produce model spectra and images. As a key new ingredient in these models, we allow the proton-electron coupling in these simulations depend on the magnetic properties of the plasma. Results: We find that the radio emission in M 87 is described well by a combination of a two-temperature accretion flow and a hot single-temperature jet. Most of the radio emission in our simulations comes from the jet sheath. The model fits the basic observed characteristics of the M 87 radio core: it is "edge-brightened", starts subluminally, has a flat spectrum, and increases in size with wavelength. The best fit model has a mass-accretion rate of Ṁ ~ 9 × 10-3M⊙ yr-1 and a total jet power of Pj ~ 1043 erg s-1. Emission at λ = 1.3 mm is produced by the counter-jet close to the event horizon. Its characteristic crescent shape surrounding the black hole shadow could be resolved by future millimeter-wave VLBI experiments. Conclusions: The model was successfully derived from one for the supermassive black hole in the center of the Milky Way by appropriately scaling mass and
Search for general relativistic effects in table-top displacement metrology
NASA Technical Reports Server (NTRS)
Halverson, Peter G.; Diaz, Rosemary T.; Macdonald, Daniel R.
2004-01-01
As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission, were used to search for locally anisotropic space-time, with a null result at the 10 to the negative 10th power level.
Search for general relativistic effects in table-top displacement metrology
NASA Technical Reports Server (NTRS)
Halverson, Peter G.; Macdonald, Daniel R.; Diaz, Rosemary T.
2004-01-01
As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission were used to search for locally anisotropic space-time, with a null result at the 10 to the negative tenth power level.
The generalized Coulomb interactions for relativistic scalar bosons
NASA Astrophysics Data System (ADS)
Zarrinkamar, S.; Panahi, H.; Rezaei, M.
2016-07-01
Approximate analytical solutions of Duffin-Kemmer-Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song-Lin potentials via the quasi-exact analytical ansatz approach.
Sekiguchi, Yu-ichirou; Shibata, Masaru
2005-04-15
We perform axisymmetric simulations for gravitational collapse of a massive iron core to a black hole in full general relativity. The iron cores are modeled by {gamma}=4/3 equilibrium polytrope for simplicity. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme with a parametric equation of state. The Cartoon method is adopted for solving the Einstein equations. Simulations are performed for a wide variety of initial conditions changing the mass ({approx_equal}2.0-3.0M{sub {center_dot}}), the angular momentum, the rotational velocity profile of the core, and the parameters of the equations of state which are chosen so that the maximum mass of the cold spherical polytrope is {approx_equal}1.6M{sub {center_dot}}. Then, the criterion for the prompt black hole formation is clarified in terms of the mass and the angular momentum for several rotational velocity profile of the core and equations of state. It is found that (i) with the increase of the thermal energy generated by shocks, the threshold mass for the prompt black hole formation is increased by 20-40%, (ii) the rotational centrifugal force increases the threshold mass by < or approx. 25%, (iii) with the increase of the degree of differential rotation, the threshold mass is also increased, and (iv) the amplification factors shown in the results (i)-(iii) depend sensitively on the equation of state. We also find that the collapse dynamics and the structure of the shock formed at the bounce depend strongly on the stiffness of the adopted equation of state. In particular, as a new feature, a strong bipolar explosion is observed for the collapse of rapidly rotating iron cores with an equation of state which is stiff in subnuclear density and soft in supranuclear density. Gravitational waves are computed in terms of a quadrupole formula. It is also found that the waveform depends sensitively on the equations of state.
A fully general relativistic numerical simulation code for spherically symmetric matter
NASA Astrophysics Data System (ADS)
Park, Dong-Ho; Cho, Inyong; Kang, Gungwon; Lee, Hyung Mok
2013-02-01
We present a fully general relativistic open-source code that can be used for simulating a system of spherically symmetric perfect fluid matter. It is based on the Arnowitt-Deser-Misner 3+1 formalism with maximal slicing and isotropic spatial coordinates. For hydrodynamic matter High Resolution Shock Capturing (HRSC) schemes with a monotonized central-difference limiter and approximated Riemann solvers are used in the Eulerian viewpoint. The accuracy and the convergence of our numerical code are verified by performing several test problems. These include a relativistic blast wave, relativistic spherical accretion of matter into a black hole, Tolman-Oppenheimer-Volkoff (TOV) stars and Oppenheimer-Snyder (OS) dust collapses. In particular, a dynamical code test is done for the OS collapse by explicitly performing numerical coordinate transformations between our coordinate 8system and the one used for the analytic solution. Finally, some TOV star solutions are presented for the Eddington-inspired Born-Infeld gravity theory.
General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies
NASA Technical Reports Server (NTRS)
Kopeikin, Sergei
2003-01-01
The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.
Heavy meson mass-spectra by general relativistic methods (*)
Italiano, A.; Lattuada, M.; Maccarrone, G.D.; Recami, E.; Riggi, F.; Vinciguerra, D.
1984-11-01
By applying the classical methods of general relativity to elementary particles, one can get-in a natural way-the observed confinement of their constituents, avoiding any recourse to phenomenological models such as the bag model and allowing the deduction of the heavy meson (i.e., charmonium (J/psi) and bottomonium (..gamma..)) mass-spectra.
Gravity: Newtonian, Post-Newtonian, and General Relativistic
NASA Astrophysics Data System (ADS)
Will, Clifford M.
We present a pedagogical introduction to gravitational theory, with the main focus on weak gravitational fields. We begin with a thorough survey of Newtonian gravitational theory. After a brief introduction to general relativity, we develop the post-Minkowskian formulation of the field equations, which is ideally suited to studying weak-field gravity. We then discuss applications of this formulation, including post-Newtonian theory, the parametrized post-Newtonian framework, and gravitational radiation.
General relativistic effects in quantum interference of “clocks”
NASA Astrophysics Data System (ADS)
Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.
2016-06-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Fishman, Gerald J.
2006-01-01
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.
General relativistic delays in current and future VLBI
NASA Astrophysics Data System (ADS)
Soja, B.; Plank, L.; Schuh, H.
2012-12-01
The effect of gravitational time delay due to general relativity is clearly visible in VLBI measurements. While the Sun and the Earth cause gravitational delays up to some nanoseconds respectively picoseconds in geodetic VLBI observables, standard delay models also recommend the inclusion of Jupiter, the Earth's Moon and some of the other planets on the modeling side. Using the IERS Conventions model, we have calculated the gravitational time delay of standard VLBI observation constellations of the past years. The influences due to the Sun, the Earth, the Moon, Jupiter, Saturn and Venus were large enough to justify their consideration in routine VLBI data analysis (based on the accuracy of the upcoming VLBI2010 system). For VLBI data before 2002, the higher order term of the Sun should also be taken into account. Additionally, the relation between the gravitational delay of the Earth and the estimated tropospheric parameters (e.g. zenith wet delays) was investigated.
Critical rotation of general-relativistic polytropic models revisited
NASA Astrophysics Data System (ADS)
Geroyannis, V.; Karageorgopoulos, V.
2013-09-01
We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.
Confinement and hadron-hadron interactions by general relativistic methods
NASA Astrophysics Data System (ADS)
Recami, Erasmo
By postulating covariance of physical laws under global dilations, one can describe gravitational and strong interactions in a unified way. Namely, in terms of the new discrete dilational degree of freedom, our cosmos and hadrons can be regarded as finite, similar systems. And a discrete hierarchy of finite ``universes'' may be defined, which are governed by fields with strengths inversally proportional to their radii; in each universe an Equivalence Principle holds, so that the relevant field can be there geometrized. Scaled-down Einstein equations -with cosmological term- are assumed to hold inside hadrons (= strong micro-cosmoses); and they yield in a natural way classical confinement, as well as ``asymptotic freedom'', of the hadron constituents. In other words, the association of strong micro-universes of Friedmann type with hadrons (i.e., applying the methods of General Relativity to subnuclear particle physics) allows avoiding recourse to phenomenological models such as the Bag Model. Inside hadrons we have to deal with a tensorial field (= strong gravity), and hadron constituents are supposed to exchange spin-2 ``gluons''. Our approach allows us also to write down a tensorial, bi-scale field theory of hadron-hadron interactions, based on modified Einstein-type equations here proposed for strong interactions in our space. We obtain in particular: (i) the correct Yukawa behaviour of the strong scalar potential at the static limit and for r>~l fm; (ii) the value of hadron radii. As a byproduct, we derive a whole ``numerology'', connecting our gravitational cosmos with the strong micro-cosmoses (hadrons), such that it does imply no variation of G with the epoch. Finally, since a structute of the ``micro-universe'' type seems to be characteristic even of leptons, a hope for the future is including also weak interactions in our classical unification of the fundamental forces.
Relativistic model of anisotropic charged fluid sphere in general relativity
NASA Astrophysics Data System (ADS)
Pant, Neeraj; Pradhan, N.; Bansal, Rajeev K.
2016-01-01
In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353-359, 2010). Our solution is well behaved in all respects for all values of X lying in the range 0< X ≤ 0.18, α lying in the range 0 ≤ α ≤6.6, K lying in the range 0< K ≤ 6.6 and Schwarzschild compactness parameter "u" lying in the range 0< u ≤ 0.38. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X=0.088, α=0.6 and K=4.3 for which u=0.2054 and by assuming surface density ρb = 4.6888 × 10^{14} g/cm3 the mass and radius are found to be 1.51 M_{\\varTheta} and 10.90 km respectively. Assuming surface density ρb = 2 × 10^{14} g/cm3 the mass and radius for a neutron star candidate are found to be 2.313 M_{\\varTheta} and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.
Quantum interferometric visibility as a witness of general relativistic proper time.
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-01-01
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov-Bohm effect, where a particle in a flat space-time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'-a particle with evolving internal degrees of freedom-that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space-time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. PMID:22009037
Dark-matter distributions around massive black holes: A general relativistic analysis
NASA Astrophysics Data System (ADS)
Sadeghian, Laleh; Ferrer, Francesc; Will, Clifford M.
2013-09-01
The cold dark matter at the center of a galaxy will be redistributed by the presence of a massive black hole. The redistribution may be determined using an approach pioneered by Gondolo and Silk: begin with a model distribution function for the dark matter, and “grow” the black hole adiabatically, holding the adiabatic invariants of the motion constant. Unlike the approach of Gondolo and Silk, which adopted Newtonian theory together with ad hoc correction factors to mimic general relativistic effects, we carry out the calculation fully relativistically, using the exact Schwarzschild geometry of the black hole. We find that the density of dark matter generically vanishes at r=2RS, not 4RS as found by Gondolo and Silk, where RS is the Schwarzschild radius, and that the spike very close to the black hole reaches significantly higher densities. We apply the relativistic adiabatic growth framework to obtain the final dark-matter density for both cored and cusped initial distributions. Besides the implications of these results for indirect detection estimates, we show that the gravitational effects of such a dark-matter spike are significantly smaller than the relativistic effects of the black hole, including frame dragging and quadrupolar effects, for stars orbiting close to the black hole that might be candidates for testing the black-hole no-hair theorems.
General relativistic polarized radiative transfer: building a dynamics-observations interface
NASA Astrophysics Data System (ADS)
Shcherbakov, Roman V.; Huang, Lei
2011-01-01
The rising number of polarized observations of relativistic sources necessitates a correct theory for proper model fitting. The equations for general relativistic (GR) polarized radiative transfer are derived starting from the Boltzmann equation and basic ideas of general relativity. The derivation is aimed at providing a practical guide to reproducing the synchrotron part of radio and submillimetre emission from low-luminosity active galactic nuclei (LLAGNs), in particular Sgr A*, and jets. A recipe for the fast exact calculation of cyclo-synchrotron emissivities, absorptivities, Faraday rotation and conversion coefficients is given for isotropic particle distributions. The multitude of physical effects influencing simulated spectra is discussed. The application of the prescribed technique is necessary to determine the black hole spin in LLAGNs. The observations of total flux, linear and circular polarization fractions, and electric vector position angle as functions of the observed frequency could substantially constrain the absolute value and orientation of spin.
Near-critical spherical accretion by neutron stars - General relativistic treatment
NASA Technical Reports Server (NTRS)
Park, Myeong-Gu; Miller, Guy S.
1991-01-01
Time-independent spherical accretion by a neutron star is studied using general relativistic radiation hydrodynamics. Numerical integrations of the flow equations are presented. These show that when the luminosity is sufficiently close to (but below) the Eddington limit, the flow velocity increases with decreasing radius far from the neutron star, reaches a maximum at an intermediate radius, and decreases at small radii. A large fraction of the binding energy of the flow is transferred to the radiation through scattering before the flow strikes the surface of the neutron star. Following Miller's treatment of accretion at luminosites near the Eddington limit (which neglected general relativistic effects), analytic approximations for the decelerating phase of the flow's velocity profile are derived. The dependence of the solutions on the variable Eddington factor prescription chosen to close the radiation moment equations is also examined.
Relativistic Feynman-Metropolis-Teller theory for white dwarfs in general relativity
Rotondo, Michael; Rueda, Jorge A.; Ruffini, Remo; Xue Shesheng
2011-10-15
The recent formulation of the relativistic Thomas-Fermi model within the Feynman-Metropolis-Teller theory for compressed atoms is applied to the study of general relativistic white dwarf equilibrium configurations. The equation of state, which takes into account the {beta}-equilibrium, the nuclear and the Coulomb interactions between the nuclei and the surrounding electrons, is obtained as a function of the compression by considering each atom constrained in a Wigner-Seitz cell. The contribution of quantum statistics, weak, nuclear, and electromagnetic interactions is obtained by the determination of the chemical potential of the Wigner-Seitz cell. The further contribution of the general relativistic equilibrium of white dwarf matter is expressed by the simple formula {radical}(g{sub 00}){mu}{sub ws}=constant, which links the chemical potential of the Wigner-Seitz cell {mu}{sub ws} with the general relativistic gravitational potential g{sub 00} at each point of the configuration. The configuration outside each Wigner-Seitz cell is strictly neutral and therefore no global electric field is necessary to warranty the equilibrium of the white dwarf. These equations modify the ones used by Chandrasekhar by taking into due account the Coulomb interaction between the nuclei and the electrons as well as inverse {beta} decay. They also generalize the work of Salpeter by considering a unified self-consistent approach to the Coulomb interaction in each Wigner-Seitz cell. The consequences on the numerical value of the Chandrasekhar-Landau mass limit as well as on the mass-radius relation of {sup 4}He, {sup 12}C, {sup 16}O and {sup 56}Fe white dwarfs are presented. All these effects should be taken into account in processes requiring a precision knowledge of the white dwarf parameters.
Generalized Ohm's law for a background plasma in the presence of relativistic charged particles.
Sherlock, M
2010-05-21
A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically. PMID:20867035
Generalized Ohm's Law for a Background Plasma in the Presence of Relativistic Charged Particles
Sherlock, M.
2010-05-21
A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically.
NASA Astrophysics Data System (ADS)
Pétri, J.
2015-03-01
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1 formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multidomain decomposition of the simulation box belongs to the discontinuous Galerkin finite element methods. We performed several sets of simulations to look for the general relativistic force-free monopole and split monopole solutions. Results show that our code is extremely powerful in handling extended domains of hundredth of light cylinder radii rL. The code has been validated against known exact analytical monopole solutions in flat space-time. We also present semi-analytical calculations for the general relativistic vacuum monopole.
General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
NASA Astrophysics Data System (ADS)
Dionysopoulou, Kyriaki; Alic, Daniela; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-08-01
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the ℓ=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.
Exact relativistic expressions for wave refraction in a generally moving fluid.
Cavalleri, G; Tonni, E; Barbero, F
2013-04-01
The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation. PMID:23679540
NASA Astrophysics Data System (ADS)
Zhi-Yun, Wang; Pei-Jie, Chen
2016-06-01
A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.
NASA Astrophysics Data System (ADS)
Almosallami, Azzam
2011-03-01
In this paper we derived the relativistic Quantized force, where the force given as a function of frequency [1]. Where, in this paper we defined the relativistic momentum as a function of frequency equivalent to the energy held by a body, and time, and then the quantized force is given as the first derivative of the momentum with respect to time. Subsequently we introduce in section one Newton's second law as it is relativistic quantized, and in section two we introduce the relativistic quantized inertial force, and then the relativistic quantized gravitational force, and the quantized gravitational time dilation. At the end we shall generalize the Schwartzschild metric to describe the weak and strong gravitational field.
NASA Astrophysics Data System (ADS)
Koide, Shinji; Shibata, Kazunari; Kudoh, Takahiro
1999-09-01
Relativistic jets are observed in both active galactic nuclei (AGNs) and ``microquasars'' in our Galaxy. It is believed that these relativistic jets are ejected from the vicinity of black holes. To investigate the formation mechanism of these jets, we have developed a new general relativistic magnetohydrodynamic (GRMHD) code. We report on the basic methods and test calculations to check whether the code reproduces some analytical solutions, such as a standing shock and a Keplerian disk with a steady state infalling corona or with a corona in hydrostatic equilibrium. We then apply the code to the formation of relativistic MHD jets, investigating the dynamics of an accretion disk initially threaded by a uniform poloidal magnetic field in a nonrotating corona (either in a steady state infall or in hydrostatic equilibrium) around a nonrotating black hole. The numerical results show the following: as time goes on, the disk loses angular momentum as a result of magnetic braking and falls into the black hole. The infalling motion of the disk, which is faster than in the nonrelativistic case because of general relativistic effects below 3rS (rS is the Schwarzschild radius), is strongly decelerated around r=2rS by centrifugal force to form a shock inside the disk. The magnetic field is tightly twisted by the differential rotation, and plasma in the shocked region of the disk is accelerated by the JXB force to form bipolar relativistic jets. In addition, and interior to, this magnetically driven jet, we also found a gas-pressure-driven jet ejected from the shocked region by the gas-pressure force. This two-layered jet structure is formed not only in the hydrostatic corona case but also in the steady state falling corona case.
HERO - A 3D general relativistic radiative post-processor for accretion discs around black holes
NASA Astrophysics Data System (ADS)
Zhu, Yucong; Narayan, Ramesh; Sadowski, Aleksander; Psaltis, Dimitrios
2015-08-01
HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analysing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a post-processor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamic or magnetohydrodynamic simulation), the code obtains a self-consistent solution for the radiation field and for the gas temperatures using the condition of radiative equilibrium. The novel aspect of HERO is that it combines two techniques: (1) a short-characteristics (SC) solver that quickly converges to a self-consistent disc temperature and radiation field, with (2) a long-characteristics (LC) solver that provides a more accurate solution for the radiation near the photosphere and in the optically thin regions. By combining these two techniques, we gain both the computational speed of SC and the high accuracy of LC. We present tests of HERO on a range of 1D, 2D, and 3D problems in flat space and show that the results agree well with both analytical and benchmark solutions. We also test the ability of the code to handle relativistic problems in curved space. Finally, we discuss the important topic of ray defects, a major limitation of the SC method, and describe our strategy for minimizing the induced error.
NASA Astrophysics Data System (ADS)
Narayan, Ramesh; Zhu, Yucong; Psaltis, Dimitrios; Saḑowski, Aleksander
2016-03-01
We describe Hybrid Evaluator for Radiative Objects Including Comptonization (HEROIC), an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in a short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic magnetohydrodynamics simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below the photosphere in the multidimensional HEROIC solution is nearly isothermal, quite different from previous solutions based on 1D plane parallel atmospheres. The second application is to a geometrically thick radiation-dominated accretion disc accreting at 11 times the Eddington rate. Here, the multidimensional HEROIC solution shows that, for observers who are on axis and look down the polar funnel, the isotropic equivalent luminosity could be more than 10 times the Eddington limit, even though the spectrum might still look thermal and show no signs of relativistic beaming.
NASA Astrophysics Data System (ADS)
Paschalidis, Vasileios; Etienne, Zachariah B.; Shapiro, Stuart L.
2013-07-01
We perform the first general relativistic force-free simulations of neutron star magnetospheres in orbit about spinning and nonspinning black holes. We find promising precursor electromagnetic emission: typical Poynting luminosities at, e.g., an orbital separation of r=6.6RNS are LEM˜6×1042(BNS,p/1013G)2(MNS/1.4M⊙)2erg/s. The Poynting flux peaks within a broad beam of ˜40° in the azimuthal direction and within ˜60° from the orbital plane, establishing a possible lighthouse effect. Our calculations, though preliminary, preview more detailed simulations of these systems that we plan to perform in the future.
An investigation of the general relativistic (1PN) hydrodynamics in DSX scheme.
NASA Astrophysics Data System (ADS)
Dai, Yurong; Wu, Xuejun; Xu, Chongming
1999-11-01
In this paper the general relativistic (1PN) hydrodynamics is established by means of DSX scheme in both local and global coordinates. The stress-energy tensor Tμν of ordinary fluids is calculated in terms of the software Maple, then the energy equation and Euler equation are got in DSX scheme after being reduced and trimmed. All these are done in local coordinates, and the result in global coordinates can be found through the transformation law. Finally, the energy equation and Euler equation in local coordinates in the case of perfect fluids are discussed. The result in global coordinates can be found in the same way.
Caballero, O. L.; McLaughlin, G. C.; Surman, R. E-mail: olcaball@ncsu.edu E-mail: surmanr@union.edu
2012-02-01
Black hole (BH) accretion disks have been proposed as good candidates for a range of interesting nucleosynthesis, including the r-process. The presence of the BH influences the neutrino fluxes and affects the nucleosynthesis resulting from the interaction of the emitted neutrinos and hot outflowing material ejected from the disk. We study the impact of general relativistic effects on the neutrinos emitted from BH accretion disks. We present abundances obtained by considering null geodesics and energy shifts for two different disk models. We find that both the bending of the neutrino trajectories and the energy shifts have important consequences for the nucleosynthetic outcome.
Harleston, H. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Distrito Federal ); Vishniac, E.T. )
1992-06-15
The Arnowitt-Deser-Misner formalism is used to write the Einstein-Boltzmann coupled system of equations. The sources of gravitational field are represented by ordinary matter described by a perfect-fluid approximation together with a particle gas described by a phase-space distribution function obeying the general-relativistic Boltzmann transport equation. Through the use of the Liouville operator in phase space, we obtain a form of the Boltzmann equation that makes it very amenable for numerical treatment. The resulting system of equations can be used for the numerical study of either massless or massive particles interacting with ordinary matter.
THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT
Coughlin, Eric R.; Begelman, Mitchell C. E-mail: mitch@jila.colorado.edu
2014-12-20
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
The General Relativistic Equations of Radiation Hydrodynamics in the Viscous Limit
NASA Astrophysics Data System (ADS)
Coughlin, Eric R.; Begelman, Mitchell C.
2014-12-01
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
General relativistic x ray (UV) polarization rotations as a quantitative test for black holes
NASA Technical Reports Server (NTRS)
Stark, Richard F.
1989-01-01
It is now 11 years since a potentially easily observable and quantitative test for black holes using general relativistic polarization rotations was proposed (Stark and Connors 1977, and Connors and Stark 1977). General relativistic rotations of the x ray polarization plane of 10 to 100 degrees with x ray energy (between 1 and 100 keV) are predicted for black hole x ray binaries. (Classically, by symmetry, there is no rotation.) Unfortunately, x ray polarimetry has not been taken sufficiently seriously during this period, and this test has not yet been performed. A similar (though probably less clean) effect is expected in the UV for supermassive black holes in some quasars active galactic nuclei. Summarizing: (1) a quantitative test (proposed in 1977) for black holes exists; (2) x ray polarimetry of galactic x ray binaries sensitive to at least 1/2 percent between 1 keV and 100 keV is needed (polarimetry in the UV of quasars and AGN will also be of interest); and (3) proportional counters using timerise discrimination were shown in laboratory experiments able to perform x ray polarimetry and this and other methods need to be developed.
NASA Astrophysics Data System (ADS)
Silenko, Alexander J.
2015-02-01
A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition, and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.
NASA Astrophysics Data System (ADS)
Herrera, L.; Di Prisco, A.; Ibáñez, J.; Ospino, J.
2014-04-01
We carry out a general study on the collapse of axially (and reflection-)symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.
General relativistic N-body simulations in the weak field limit
NASA Astrophysics Data System (ADS)
Adamek, Julian; Daverio, David; Durrer, Ruth; Kunz, Martin
2013-11-01
We develop a formalism for general relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives to second order, and second derivatives to all orders, thus taking into account the most important nonlinear effects of Einstein gravity. It is also expected that any significant “backreaction” should appear at this order. We show that the simulation scheme is feasible in practice by implementing it for a plane-symmetric situation and running two test cases, one with only cold dark matter, and one which also includes a cosmological constant. For these plane-symmetric situations, the deviations from the usual Newtonian N-body simulations remain small and, apart from a nontrivial correction to the background, can be accurately estimated within the Newtonian framework. The correction to the background scale factor, which is a genuine backreaction effect, can be robustly obtained with our algorithm. Our numerical approach is also naturally suited for the inclusion of extra relativistic fields and thus for dark energy or modified gravity simulations.
General-relativistic celestial mechanics. I. Method and definition of reference systems
Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX, France ); Soffel, M.; Xu, C. )
1991-05-15
We present a new formalism for treating the general-relativistic celestial mechanics of systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such {ital N}-body systems ( external problem''), (ii) the local gravitational structure of each body ( internal problem''), and, (iii) the way the external and the internal problems fit together ( theory of reference systems''). This formalism uses in a complementary manner {ital N}+1 coordinate charts (or reference systems''): one global'' chart for describing the overall dynamics of the {ital N} bodies, and {ital N} local'' charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these {ital N}+1 reference systems is a systematic use of a particular exponential'' parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue.
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P.
2007-10-01
Aims:We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods: Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results: ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a
General relativistic corrections in the gamma-ray emission from pulsars
NASA Technical Reports Server (NTRS)
Gonthier, P. L.; Harding, A. K.
1994-01-01
We examine the importance of general relativistic corrections to the production of gamma rays near the surface of a neutron star. Due to the change in the magnetic dipole field in curved spacetime, the polar cap angle decreases by 30% compared to flat spacetime. However, the curved photon trajectories compensate for the decrease in the polar cap angle, and, as a result, the pulse profile of the photons emitted parallel to the field is expected to be very similar in curved spacetime and in flat spacetime. We find that the curved spacetime metric significantly increases the magnitude of the magnetic field and, therefore, the attenuation coefficients of curvature radiation gamma rays for pair production in a magnetic field can be increased by factors as large as 100. As a resutl the survival distance of 1 GeV photons for pair production is decreased by a factor of 2 for B is approximately 10(exp 12) G.
Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials
NASA Astrophysics Data System (ADS)
O. J., Oluwadare; K. E., Thylwe; K. J., Oyewumi
2016-04-01
Non-relativistic phase shifts for a generalized Yukawa potential V(r) = ‑ V0(e‑αr/r) ‑ V1(e‑2αr/r2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms. Small variations of V1 seem to have marginal effects on the effective potential and on exact phase shifts. However, as pointed out in this study, a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts. The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.
General Relativistic Ray Tracing for X-ray Reverberation and Polarimetry Studies of Black Holes
NASA Astrophysics Data System (ADS)
Hoormann, Janie; Krawczynski, Henric
2015-01-01
We present the results of General Relativistic (GR) ray tracing calculations of the X-ray emission from mass accreting stellar mass and supermassive black holes. Our study aims at exploring the X-ray reverberation and X-ray polarimetry signatures of different accretion flow geometries and different spacetime backgrounds (GR and non-GR backgrounds). We present first results derived for the well-known lamp-post model, where a point source of continuum emission illuminates an accretion disk with high energy photons which are tracked by parallel transporting the photon wave and polarization vectors. The simulation code models the reprocessing and reflection by of photons impinging on the accretion disk. We study the degeneracy of astrophysical parameters (parametrizing the geometry of the accretion disk and the location and properties of the lamppost photon source) and the parameters describing the underlying metrics. We emphasize furthermore the difference of the observational signatures for stellar mass and supermassive black holes.
General Relativistic Mini-Disk Dynamics during Black Hole Binary Inspiral
NASA Astrophysics Data System (ADS)
Bowen, Dennis
2016-01-01
During galaxy mergers, as a result of dynamical friction (stars, gas, etc.) and gravitational slingshot, the supermassive black holes (SMBHs) from each galaxy will become gravitationally bound and eventually merge due to gravitational radiation. It is expected that gas will form a circumbinary accretion disk around the SMBH binary that will persistently feed individual "mini-disks" via dense streams out to their tidal truncation radii. However, these radii are not well known during the late stages of inspiral and merger. We present general relativistic hydrodynamic simulations aimed at resolving this uncertainty and producing templates of unique electromagnetic (EM) signatures for such systems to assist in direct observational detection with currently available observatories. We place particular emphasis on the dynamics of the individual "mini-disks" where violent shocks via disk-disk and disk-stream interactions will likely produce intense EM emission.
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka; Gammie, C. F.; Dolence, J.; Noble, S. C.
2013-01-01
We perform global General Relativistic Magnetohydrodynamics (GRMHD) simulations of non-radiative, magnetized disks that are initially tilted with respect to the black hole's spin axis. We run the simulations with different size and tilt angle of the tori for 2 different resolutions. We also perform radiative transfer using Monte Carlo based code that includes synchrotron emission, absorption and Compton scattering to obtain spectral energy distribution and light curves. Similar work was done by Fragile et al. (2007) and Dexter & Fragile (2012) to model the super massive black hole SgrA* with tilted accretion disks. We compare our results of fully conservative hydrodynamic code and spectra that include X-ray, with their results.
General Relativistic Continuum Mechanics and the Post-Newtonian Equations of Motion
NASA Astrophysics Data System (ADS)
Morrill, Thomas H.
This dissertation examines aspects of general relativistic continuum mechanics. It deals with, but does not restrict itself to, perfectly elastic materials. It also emphasizes the derivation of their equations of motion, in the post-Newtonian approximation. As a basis for this study, I present a reformulation, based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. I derive a field Lagrangian describing perfect material media; show that the usual covariant conservations law (vanishing of the covariant divergence of the energy -momentum tensor) for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einsteins's field equations. In addition, I introduce a version of Mach's principle that is completely independent of metric. My version of this principle shows that the local mass density in curved space -time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. I also expand the total Lagrangian (field plus gravitational) in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. This Lagrangian fails to reproduce even the Newtonian gravitational potential unless it incorporates the post-Newtonian form of my version of Mach's principle. I derive the metric coefficients required to obtain the post-Newtonian equations of motion, as well as the post-Newtonian equations of motion for perfect continua, from the Post-Newtonian Lagrangian incorporating my version of Mach's principle. These results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law.
GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE
Ott, Christian D.; Abdikamalov, Ernazar; Moesta, Philipp; Haas, Roland; Drasco, Steve; O'Connor, Evan P.; Reisswig, Christian; Meakin, Casey A.; Schnetter, Erik
2013-05-10
We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M{sub Sun} star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M{sub Sun} progenitor was studied in 2D by Mueller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.
Evolution of Central Moments for a General-Relativistic Boltzmann Equation
NASA Astrophysics Data System (ADS)
Banach, Zbigniew; Larecki, Wieslaw
Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY) 150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau-Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.
General-relativistic Simulations of Three-dimensional Core-collapse Supernovae
NASA Astrophysics Data System (ADS)
Ott, Christian D.; Abdikamalov, Ernazar; Mösta, Philipp; Haas, Roland; Drasco, Steve; O'Connor, Evan P.; Reisswig, Christian; Meakin, Casey A.; Schnetter, Erik
2013-05-01
We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M ⊙ star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M ⊙ progenitor was studied in 2D by Müller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.
Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure
NASA Astrophysics Data System (ADS)
Baqui, P. O.; Fabris, J. C.; Piattella, O. F.
2016-04-01
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate i) the cosmological expansion, ii) linear cosmological perturbations theory and iii) stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.
Non-axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2013-08-01
A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yun; Chen, Pei-Jie; Zhang, Liang-Ying
2015-05-01
By using a generalized Langevin equation to describe the vertical oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density (PSD) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength α and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance (SR) with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a* of the black hole determine the inherent frequency of vertical oscillations in the disk, and they have significant influences on the SR phenomena in a system of black hole binaries. Project supported by the National Natural Science Foundation of China (Grant No. 11045004) and the Key Program of the Scientific Research Foundation of the Education Bureau of Hubei Province, China (Grant No. D20132603).
NASA Astrophysics Data System (ADS)
Anantua, Richard; Roger Blandford, Jonathan McKinney and Alexander Tchekhovskoy
2016-01-01
We carry out the process of "observing" simulations of active galactic nuclei (AGN) with relativistic jets (hereafter called jet/accretion disk/black hole (JAB) systems) from ray tracing between image plane and source to convolving the resulting images with a point spread function. Images are generated at arbitrary observer angle relative to the black hole spin axis by implementing spatial and temporal interpolation of conserved magnetohydrodynamic flow quantities from a time series of output datablocks from fully general relativistic 3D simulations. We also describe the evolution of simulations of JAB systems' dynamical and kinematic variables, e.g., velocity shear and momentum density, respectively, and the variation of these variables with respect to observer polar and azimuthal angles. We produce, at frequencies from radio to optical, fixed observer time intensity and polarization maps using various plasma physics motivated prescriptions for the emissivity function of physical quantities from the simulation output, and analyze the corresponding light curves. Our hypothesis is that this approach reproduces observed features of JAB systems such as superluminal bulk flow projections and quasi-periodic oscillations in the light curves more closely than extant stylized analytical models, e.g., cannonball bulk flows. Moreover, our development of user-friendly, versatile C++ routines for processing images of state-of-the-art simulations of JAB systems may afford greater flexibility for observing a wide range of sources from high power BL-Lacs to low power quasars (possibly with the same simulation) without requiring years of observation using multiple telescopes. Advantages of observing simulations instead of observing astrophysical sources directly include: the absence of a diffraction limit, panoramic views of the same object and the ability to freely track features. Light travel time effects become significant for high Lorentz factor and small angles between
A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES
You Bei; Cao Xinwu; Yuan Yefei E-mail: cxw@shao.ac.cn
2012-12-20
We calculate the structure of a standard accretion disk with a corona surrounding a massive Kerr black hole in the general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of disk-corona systems with a modified {alpha}-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor L{sub bol}/L{sub X,2-10keV} increase with the dimensionless mass accretion rate, which is qualitatively consistent with the observations of active galactic nuclei. The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter a, which leads to lower electron temperatures of the coronae for rapidly spinning black holes. The X-ray emission from the coronae surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive to the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin a, which deviates from the f{sub {nu}}{proportional_to}{nu}{sup 1/3} relation expected by the standard thin disk model.
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka
The goal of the series of studies in this thesis is to understand the black hole accretion process and predict its observational properties. The highly non-linear process involves a turbulent magnetized plasma in a general relativistic regime, thus making it hard to study analytically. We use numerical simulations, specifically general relativistic magnetohydrodynamics (GRMHD), to construct a realistic dynamical and radiation model of accretion disks. Our simulations are for black holes in low luminous regimes that probably possesses a hot and thick accretion disk. Flows in this regime are called radiatively inefficient accretion flows (RIAF). The most plausible mechanism for transporting angular momentum is turbulence induced by magnetorotational instability (MRI). The RIAF model has been used to model the supermassive black hole at the center of our Milky Way galaxy, Sagittarius A* (Sgr A*). Owing to its proximity, rich observational data of Sgr A* is available to compare with the simulation results. We focus mainly on four topics. First, we analyse numerical convergence of 3D GRMHD global disk simulations. Convergence is one of the essential factors in deciding quantitative outcomes of the simulations. We analyzed dimensionless shell-averaged quantities such as plasma beta, the azimuthal correlation length (angle) of fluid variables, and spectra of the source for four different resolutions. We found that all the variables converged with the highest resolution (384x384x256 in radial, poloidal, and azimuthal directions) except the magnetic field correlation length. It probably requires another factor of 2 in resolution to achieve convergence. Second, we studied the effect of equation of state on dynamics of GRMHD simulation and radiative transfer. Temperature of RIAF gas is high, and all the electrons are relativistic, but not the ions. In addition, the dynamical time scale of the accretion disk is shorter than the collisional time scale of electrons and ions
Zhang Yongpeng; Liu Guozhi; Yang Zhanfeng; Shao Hao; Xiao Renzhen; Xing Qingzi; Zhong Huaqiang; Lin Yuzheng
2009-04-15
In this paper, the Child-Langmuir law and Langmuir-Blodgett law are generalized to the relativistic regime by a simple method. Two classical laws suitable for the nonrelativistic regime are modified to simple approximate expressions applicable for calculating the space-charge-limited currents of one-dimensional steady-state planar diodes and coaxial diodes under the relativistic regime. The simple approximate expressions, extending the Child-Langmuir law and Langmuir-Blodgett law to fit the full range of voltage, have small relative errors less than 1% for one-dimensional planar diodes and less than 5% for coaxial diodes.
NASA Astrophysics Data System (ADS)
Geroyannis, Vassilis; Tzelati, Eleftheria
In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\\sim 10 \\, \\mathrm{km}$ and mass between $\\sim 1.4$ and $3.2$ solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava
2015-10-01
We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity—whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity.
General relativistic, nonstandard model for the dark sector of the Universe
NASA Astrophysics Data System (ADS)
Stichel, P. C.; Zakrzewski, W. J.
2015-01-01
We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial energy flow. In an approximation valid at sub-Hubble scales we find that the present-day cosmic acceleration is not attributed to any kind of negative pressure but it is due to a dynamically determined negative energy density. This property turns out to be equivalent to a time-dependent spatial curvature. The obtained cosmological equations, at sub-Hubble scales, agree with those of the nonrelativistic model but they are given a new physical interpretation. Furthermore, we have derived the self-consistent equation to be satisfied by the nonrelativistic gravitational potential produced by a galactic halo in our model from a weak-field limit of a generalized Tolman-Oppenheimer-Volkoff equation.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-02-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
NASA Astrophysics Data System (ADS)
Pfefferlé, D.; Graves, J. P.; Cooper, W. A.
2015-05-01
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).
Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de
2012-09-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Marek, Andreas
2012-09-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M ⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
The General Relativistic Instability Supernova of a Supermassive Population III Star
NASA Astrophysics Data System (ADS)
Chen, Ke-Jung; Heger, Alexander; Woosley, Stan; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.
2014-08-01
The formation of supermassive Population III stars with masses gsim10,000 M ⊙ in primeval galaxies in strong ultraviolet backgrounds at z ~ 15 may be the most viable pathway to the formation of supermassive black holes by z ~ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M ⊙ can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 1055 erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z <~ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.
High-order fully general-relativistic hydrodynamics: new approaches and tests
NASA Astrophysics Data System (ADS)
Radice, David; Rezzolla, Luciano; Galeazzi, Filippo
2014-04-01
We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars (Radice et al 2014 Mon. Not. R. Astron. Soc. 437 L46-L50). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late-inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or more.
The general relativistic instability supernova of a supermassive population III star
Chen, Ke-Jung; Woosley, Stan; Heger, Alexander; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.
2014-08-01
The formation of supermassive Population III stars with masses ≳10,000 M{sub ☉} in primeval galaxies in strong ultraviolet backgrounds at z ∼ 15 may be the most viable pathway to the formation of supermassive black holes by z ∼ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M{sub ☉} can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 10{sup 55} erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z ≲ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.
Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies
NASA Astrophysics Data System (ADS)
Emmanoulopoulos, D.
2015-03-01
Many theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.
Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime
NASA Astrophysics Data System (ADS)
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-04-01
General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.
NASA Astrophysics Data System (ADS)
Sofuoğlu, Değer; Mutuş, Haşim
2014-12-01
By adopting a metric based approach and making use of -gravity extended tetrad equations, we have considered three spatially homogeneous metrics in order to investigate the existence of simultaneously rotating and expanding solutions of the -gravity field equations with shear-free perfect fluids as sources. We have shown that the Gödel type expanding universe, as well as a rotating Bianchi-type II spacetime allow no such solutions of the field equations of this modified gravity. On the other hand, we have found that there exist two types of models in which a shear-free Bianchi-type IX universe can expand and rotate at the same time. The matter content of this universe is described by a perfect fluid having positive or negative pressure, depending on the type of model and on the cosmological constant; in the particular case of a vanishing cosmological constant we have found that the universe is filled with a pure radiation. Whatsoever the cases, the universe exhibits always coasting anisotropic expansions along three spatial directions evolving like a flat Milne universe, and has a vorticity inversely proportional to cosmic time. A further result is that, due to the nonvanishing of the gravito-magnetic part of the Weyl tensor, this model allows for gravitational waves. Our solution constitutes one more example giving support to that in -gravity there is no counterpart of the general relativistic shear-free conjecture.
NASA Astrophysics Data System (ADS)
Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.
2016-08-01
We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.
General-relativistic approach to the nonlinear evolution of collisionless matter
Matarrese, S.; Pantano, O. ); Saez, D. )
1993-02-15
A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian form at different times, can be traced back to the Eulerian picture by solving supplementary first-order differential equations for the relative position vectors of neighboring fluid elements. Similarly to the Zel'dovich approximation, in our approach the evolution of each fluid element is completely determined by the local initial conditions and can be independently followed up to the time when it enters a multistream region. Unlike the Zel'dovich approximation, however, our approach is correct also in three dimensions (except for the possible role of gravitational waves). The accuracy of our numerical procedure is tested by integrating the nonlinear evolution of a spherical perturbation in an otherwise spatially flat Friedmann-Robertson-Walker universe and comparing the results with the exact Tolman-Bondi solution for the same initial profile. An exact solution for the planar symmetric case is also given, which turns out to be locally identical to the Zel'dovich solution.
NASA Astrophysics Data System (ADS)
Evans, C. R., II
A method is presented which allows fully self-consistent numerical simulation of asymptotically flat axisymmetric nonrotating general relativistic systems. These techniques have been developed to model and understand resulting relativistic effects in gravitational core collapse and gravitational radiation generation. Both vacuum (Brill) spacetimes and matter-filled configurations can be treated. The (3 + 1) decomposition of Arnowitt, Deser and Misner is used to write general relativity in a dynamical form. The conformal approach, including the transverse-traceless decomposition of extrinsic curvature due to York, is used to solve the initial value problem. In addition, these techniques are extended to provide a fully constrained evolution scheme. Several new boundary conditions, applied at large but finite radius, are derived for the elliptic constraint equations. This method uses a simplifying three-gauge, placing the metric in quasi-isotropic form.
NASA Astrophysics Data System (ADS)
Lestrade, J.-F.
1981-07-01
Analytical formulas are presented for relativistic perturbations of planetary orbits in the generalized three-parameter Schwarzschild metric, and a semianalytic Newtonian solution combined with the present relativistic corrections for the orbital motion of Mercury is compared with results of numerical integrations. The Lagrangian corresponding to the generalized three-parameter Schwarzschild metric in the first post-Newtonian approximation is used to construct a first-order analytical solution for the post-Newtonian corrections to the Newtonian solutions for the orbital motions of the planets in terms of the osculating orbital elements. Comparisons of the Newtonian semianalytical solution of Bretagnon (1980) corrected by the present formulas with the numerical solutions of Oesterwinter and Cohen (1972) and the DE 102 solution of Newhall (1980) are then used to propose new integration constants for the orbit of Mercury fit to the respective numerical orbits.
Relativistic fluid dynamics. Proceedings.
NASA Astrophysics Data System (ADS)
Anile, A. M.; Choquet-Bruhat, Y.
Contents: 1. Covariant theory of conductivity in ideal fluid or solid media (B. Carter). 2. Hamiltonian techniques for relativistic fluid dynamics and stability theory (D. D. Holm). 3. Covariant fluid mechanics and thermodynamics: an introduction (W. Israel). 4. Relativistic plasmas (H. Weitzner). 5. An improved relativistic warm plasma model (A. M. Anile, S. Pennisi). 6. Relativistic extended thermodynamics II (I. Müller). 7. Relativistic extended thermodynamics: general assumptions and mathematical procedure (T. Ruggeri). 8. Relativistic hydrodynamics and heavy ion reactions (D. Strottman). 9. Some problems in relativistic hydrodynamics (C. G. van Weert).
NASA Astrophysics Data System (ADS)
Roedig, C.; Zanotti, O.; Alic, D.
2012-10-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic (GR) hydrodynamics coupled to an optically thick radiation field in two existing GR-(magneto)hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in most astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several simple 1D tests, we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in one spatial dimension, we compute a luminosity versus accretion rate diagram for the set-up of spherical accretion on to a Schwarzschild black hole and find good agreement with previous work which included more radiation processes than we currently have available. Lastly, we revisit the supersonic Bondi-Hoyle-Lyttleton (BHL) accretion in two dimensions where we can now present simulations of realistic temperatures, down to T ˜ 106 K or less. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching γeff ˜ 4/3; (ii) accretion rates two orders of magnitude lower than without radiation pressure, but still super-Eddington; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as ηBHL˜10-2; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of
Finite axisymmetric charged dust disks in conformastatic spacetimes
NASA Astrophysics Data System (ADS)
González, Guillermo A.; Gutiérrez-Piñeres, Antonio C.; Ospina, Paolo A.
2008-09-01
An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by González and Reina [G. A. González and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).MNRAA40035-871110.1111/j.1365-2966.2006.10819.x], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.
Finite axisymmetric charged dust disks in conformastatic spacetimes
Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Ospina, Paolo A.
2008-09-15
An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonzalez and Reina [G. A. Gonzalez and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.
Stability of axisymmetric liquid bridges
NASA Astrophysics Data System (ADS)
Fel, Leonid G.; Rubinstein, Boris Y.
2015-12-01
Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.
Discretizations of axisymmetric systems
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg
2002-11-01
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.
GPU-based four-dimensional general-relativistic ray tracing
NASA Astrophysics Data System (ADS)
Kuchelmeister, Daniel; Müller, Thomas; Ament, Marco; Wunner, Günter; Weiskopf, Daniel
2012-10-01
This paper presents a new general-relativistic ray tracer that enables image synthesis on an interactive basis by exploiting the performance of graphics processing units (GPUs). The application is capable of visualizing the distortion of the stellar background as well as trajectories of moving astronomical objects orbiting a compact mass. Its source code includes metric definitions for the Schwarzschild and Kerr spacetimes that can be easily extended to other metric definitions, relying on its object-oriented design. The basic functionality features a scene description interface based on the scripting language Lua, real-time image output, and the ability to edit almost every parameter at runtime. The ray tracing code itself is implemented for parallel execution on the GPU using NVidia's Compute Unified Device Architecture (CUDA), which leads to performance improvement of an order of magnitude compared to a single CPU and makes the application competitive with small CPU cluster architectures. Program summary Program title: GpuRay4D Catalog identifier: AEMV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 73649 No. of bytes in distributed program, including test data, etc.: 1334251 Distribution format: tar.gz Programming language: C++, CUDA. Computer: Linux platforms with a NVidia CUDA enabled GPU (Compute Capability 1.3 or higher), C++ compiler, NVCC (The CUDA Compiler Driver). Operating system: Linux. RAM: 2 GB Classification: 1.5. External routines: OpenGL Utility Toolkit development files, NVidia CUDA Toolkit 3.2, Lua5.2 Nature of problem: Ray tracing in four-dimensional Lorentzian spacetimes. Solution method: Numerical integration of light rays, GPU-based parallel programming using CUDA, 3D
Relativistic and non-relativistic magnetohydrodynamic flows around compact stars
NASA Astrophysics Data System (ADS)
Mobarry, Clark Matthew
A set of theoretical tools are developed for studying the magnetized accretion disks and astrophysical jets in active galaxies. A general theory is developed for the steady axisymmetric flow of an ideal general-relativistic fluid around a Schwarzschild black hole. The theory leads to a second-order partial differential equation, a Grad-Shafranov equation, for the magnetic flux function psi(R, theta). The magnetic surface functions of the Grad-Shafranov method are shown to be the Lagrange multipliers of an energy principle. Thus, the magnetic surface functions are not arbitrary functions, but must be chosen consistent with physically stable equilibria. From the energy principle, a numerical artificial friction method is developed to solve the general relativistic Grad-Shafranov equation with fluid flow. This method is suited for the internal boundaries between elliptic and hyperbolic behavior present in magnetospheres with fluid flow. The friction method is shown to be compatible with a theory for the slow dissipative evolution of a nearly ideal MagnetoHydroDynamic (MHD) fluid. A virial theorem is derived from the basic equations of general relativistic MHD. It is used to obtain an upper bound on the total energy in the electromagnetic field in terms of the total gravitational binding energy between the black hole and the matter (and energy) outside it. An analysis is made of the motion of a charged test particle in the electromagnetic field of a magnetized accretion disk surrounding a black hole. The results are consistent with stable orbits close to the event horizon. A semi-analytical model is developed for the evolution and dissipation of narrow magnetized jets from an active galaxy. This model exhibits the acceleration and expansion of the jets with increasing axial distance from the central object.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas
2014-06-01
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M ⊙, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, langErang, of \\bar{\
Galaxies, Axisymmetric Systems and Relativity
NASA Astrophysics Data System (ADS)
MacCallum, M. A. H.
2011-06-01
List of contributors; Preface; Prof. W. B. Bonnor: a biological sketch; Part I. Galaxies and Cosmology: 1. The origin of large scale cosmic structure B. J. T. Jones and P. L. Palmer; 2. The problem of origin of the primordial pertubations and the modern cosmology V. N. Lukash and I. D. Novikov; 3. The automorphism group and field equations for Bianchi universes W. L. Rogue and G. F. R. Ellis; 4. New perspectives on galaxy formation J. Silk; Part II. Axisymmetric Systems: 5. On exact radiative solutions representing finite sources J. Bicak; 6. Proof of a generalized Geroch conjecture I. Hauser and F. J. Ernst; 7. Limits of the double Kerr solution C. Hoenselaers; 8. Non-inheritance of static symmetry by Maxwell fields M. A. H. MacCallum and N. Van den Bergh; 9. Stationary axisymmetric electrovacuum fields in general relativity G. Neugebauer and D. Kramer; 10. An almost conformal approach to axial symmetry Z. Perjes; 11. Conformally stationary axisymmetric space-times J. Winicour; Part III. Relativity: 12. A family of conformally flat space-times having the same curvature tensor in a given co-ordinate frame C. D. Collinson; 13. On the Bell-Szekeres solution for colliding electromagnetic waves J. B. Griffiths; 14. A remark on the Hauser metric A. Held; 15. Numerical relativity by power series R. Penrose; 16. Projective relativity and the equation of motion E. Schmutzer; 17. On generalized equations of goedesic deviation B. F. Schutz; 18. Lobatchevski plane gravitational waves S. T. C. Siklos; 19. Perfect fluid and vacuum solutions of Einstein's field equations with flat 3-dimensional slices H. Stephani and Th. Wolf; 20. Self-similar solutions of Einstein's equations J. Wainwright.
General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka; Krolik, Julian H.; Cheng, Roseanne M.; Piran, Tsvi; Noble, Scott C.
2015-05-01
We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the subsequent debris motion, we track the evolution of such a system until ≃ 80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly bound debris dissipate orbital energy, but only enough to make its characteristic radius comparable to the semimajor axis of the most bound material, not the tidal radius as previously envisioned. The outer shocks are caused by post-Newtonian relativistic effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is both non-monotonic and slow, requiring several to 10 times the orbital period of the most tightly bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accumulation time. Deflection by shocks does, however, cause some mass to lose both angular momentum and energy, permitting it to move inward even before most of the mass is accumulated into the accretion flow. Although the accretion rate still rises sharply and then decays roughly as a power law, its maximum is ≃ 0.1× the previous expectation, and the timescale of the peak is ≃ 5× longer than previously predicted. The geometric mean of the black hole mass and stellar mass inferred from a measured event timescale is therefore ≃ 0.2× the value given by classical theory.
Sørensen, Lasse K; Olsen, Jeppe; Fleig, Timo
2011-06-01
A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented. PMID:21663339
NASA Astrophysics Data System (ADS)
Bagayoko, Diola
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
A general relativistic approach to the Navarro Frenk White galactic halos
NASA Astrophysics Data System (ADS)
Matos, Tonatiuh; Núñez, Darío; Sussman, Roberto A.
2004-11-01
Although galactic dark matter halos are basically Newtonian structures, the study of their interplay with large-scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, makes it necessary to obtain adequate relativistic descriptions for these self-gravitating systems. With this purpose in mind, we construct a post-Newtonian fluid framework for the 'Navarro Frenk White' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo centre, the extrapolation of the fitting formula leads to a spherically averaged 'universal' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical 'cut-off' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an 'ideal gas' type of equation of state, where mass-density is the dominant rest-mass contribution to matter-energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of statistical mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter q of Tsallis' formalism.
General relativistic considerations of the field shedding model of fast radio bursts
NASA Astrophysics Data System (ADS)
Punsly, Brian; Bini, Donato
2016-06-01
Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.
General Relativistic Magnetohydrodynamic Simulations of Jet Formation with a Thin Keplerian Disk
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Gerald, J. Fishman
2006-01-01
We have performed several simulations of black hole systems (non-rotating, black hole spin parameter a = 0.0 and rapidly rotating, a = 0.95) with a geometrically thin Keplerian disk using the newly developed RAISHIN code. The simulation results show the formation of jets driven by the Lorentz force and the gas pressure gradient. The jets have mildly relativistic speed (greater than or equal to 0.4 c). The matter is continuously supplied from the accretion disk and the jet propagates outward until each applicable terminal simulation time (non-rotating: t/tau S = 275 and rotating: t/tau S = 200, tau s equivalent to r(sub s/c). It appears that a rotating black hole creates an additional, faster, and more collimated inner outflow (greater than or equal to 0.5 c) formed and accelerated by the twisted magnetic field resulting from frame-dragging in the black hole ergosphere. This new result indicates that jet kinematic structure depends on black hole rotation.
NASA Astrophysics Data System (ADS)
Sun, Qiming; Xiao, Yunlong; Liu, Wenjian
2012-11-01
The previously proposed exact two-component (X2C) relativistic theory of nuclear magnetic resonance (NMR) parameters [Q. Sun, W. Liu, Y. Xiao, and L. Cheng, J. Chem. Phys. 131, 081101 (2009), 10.1063/1.3216471] is reformulated to accommodate two schemes for kinetic balance, five schemes for magnetic balance, and three schemes for decoupling in a unified manner, at both matrix and operator levels. In addition, three definitions of spin magnetization are considered in the coupled-perturbed Kohn-Sham equation. Apart from its simplicity, the most salient feature of X2C-NMR lies in that its diamagnetic and paramagnetic terms agree individually with the corresponding four-component counterparts for any finite basis. For practical applications, five approximate schemes for the first order coupling matrix X10 and four approximate schemes for the treatment of two-electron integrals are introduced, which render the computations of X2C-NMR very much the same as those of approximate two-component approaches.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
Teraki, Yuto; Takahara, Fumio
2014-05-20
Using a numerical method, we examine the radiation spectra from relativistic electrons moving in Langmuir turbulence, which are expected to exist in high energy astrophysical objects. The spectral shape is characterized by the spatial scale λ, field strength σ, and frequency of the Langmuir waves, and in terms of frequency they are represented by ω{sub 0} = 2πc/λ, ω{sub st} = eσ/mc, and ω{sub p}, respectively. We normalize ω{sub st} and ω {sub p} by ω{sub 0} as a ≡ ω{sub st}/ω{sub 0} and b ≡ ω{sub p}/ω{sub 0}, and examine the spectral shape in the a–b plane. An earlier study based on the diffusive radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is γ{sup 2}ω{sub p} and that the low frequency spectrum behaves as F {sub ω}∝ω{sup 1} for b > 1 irrespective of a. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence by superposing Fourier modes, injecting monoenergetic electrons, solving the equation of motion, and calculating the radiation spectra using a Lienard-Wiechert potential. We find different features from the DRL theory for a > b > 1. The peak frequency turns out to be γ{sup 2}ω{sub st}, which is higher than the γ{sup 2}ω{sub p} predicted by the DRL theory, and the spectral index of the low frequency region is not 1 but 1/3. This is because the typical deflection angle of electrons is larger than the angle of the beaming cone ∼1/γ. We call the radiation for this case 'wiggler radiation in Langmuir turbulence'.
NASA Astrophysics Data System (ADS)
Mitra, Abhas
2011-11-01
Hoyle & Folwler (1963a,b) suggested that quasars may contain Radiation Pressure Supported Stars (RPSS), which are quasi-Newtonian (surface redshitf z ≪ 1) and supermassive. This proposal however did not work and one of the reasons was that such quasi-Newtonian PRSSs are unstable to gravitational contraction to become extremely general relativistic RPSSs. And since trapped surfaces are not allowed, (Mitra 2009a) these relativistic RPSSs are bound to hover around their instantaneous "Schwarzschild Radius" Rs = 2GM/c2. In view of the fact that they have z ≫ 1, they appear as "Black Holes" (BH) to distant observers. However since, they are always radiating, in a strict sense, they are always contracting. During such extreme compatification, RPSSs are likely to acquire extremely large magnetic field due to magnetic flux freezing, and hence they have strong magnetosphere around them by which they may arrest the accretion disk surrounding them at "Alfven Radius", Ra ≫ Rs. In contrast, for an accreting Schwarzschild black hole, one expects the inner edge of the accretion disk to be at Ri = 3Rs. Consequently, such ultramagnetized RPSSs have been nick named as Magnetospheric Eternally Collapsing Objects" (MECOs). Microlensing studies of several quasar structures have shown that indeed Ri ˜ 35Rs rather that R1 = 3Rs, and which confirms that quasars harbor MECOs rather than true black holes (Schild et al. 2006, 2008, Lovegrove et al. 2011). Further the recent proof that the true BHs have M = 0 confirms that the BH candidates are not true BHs (Mitra 2004a,b; 2009b). Here we highlight the facts (i) outflows from quasars and (ii) their ability to recycle cosmic matter for having new stars and galaxies are best understood by realizing that they contain MECOs rather than true BHs.
Axisymmetric multiwormholes revisited
NASA Astrophysics Data System (ADS)
Clément, Gérard
2016-06-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Magneto-hydrodynamically stable axisymmetric mirrorsa)
NASA Astrophysics Data System (ADS)
Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.
2011-09-01
Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.
A confirmation of the general relativistic prediction of the Lense-Thirring effect.
Ciufolini, I; Pavlis, E C
2004-10-21
An important early prediction of Einstein's general relativity was the advance of the perihelion of Mercury's orbit, whose measurement provided one of the classical tests of Einstein's theory. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system and to an Earth-orbiting satellite. General relativity also predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it, which will affect the orbit of a satellite. This Lense-Thirring effect has hitherto not been detected with high accuracy, but its detection with an error of about 1 per cent is the main goal of Gravity Probe B--an ongoing space mission using orbiting gyroscopes. Here we report a measurement of the Lense-Thirring effect on two Earth satellites: it is 99 +/- 5 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total +/- 10 per cent uncertainty to include underestimated and unknown sources of error. PMID:15496915
The field lines of an axisymmetric magnetic field
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.
The Effective-One-Body Approach to the General Relativistic Two Body Problem
NASA Astrophysics Data System (ADS)
Damour, Thibault; Nagar, Alessandro
The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.
NASA Astrophysics Data System (ADS)
Sospedra-Alfonso, Reinel; Agueh, Martial; Illner, Reinhard
2012-09-01
We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Seehafer (Commun Math Sci 6:749-769, 2008) following the work in Pallard (Int Mat Res Not 57191:1-31, 2006). Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transversal component of the electric field. These estimates are crucial in the references cited above. Instead, we exploit the formulation of the RVD system in terms of the generalized space and momentum variables. By doing so, we produce a simple a priori estimate on the transversal component of the electric field. We widen the functional space required for the Cauchy datum to extend the solution globally in time, and we improve decay estimates given in Seehafer (2008) on the electromagnetic field and its space derivatives. Our method extends the constructive proof presented in Rein (Handbook of differential equations: evolutionary equations, vol 3. Elsevier, Amsterdam, 2007) to solve the Cauchy problem for the Vlasov-Poisson system with a small initial datum.
Schumaker, B.L.
1985-01-01
This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit.
NASA Astrophysics Data System (ADS)
Lucchesi, David M.; Peron, Roberto
2014-04-01
The aim of this paper is to extend, clarify, and deepen the results of our previous work [D. M. Lucchesi and R. Peron, Phys. Rev. Lett. 105, 231103 (2010)], related to the precise measurement of LAGEOS (LAser GEOdynamics Satellite) II pericenter shift. A 13-year time span of LAGEOS satellites' laser tracking data has been considered, obtaining a very precise orbit and correspondingly residuals time series from which to extract the relevant signals. A thorough description is provided of the data analysis strategy and the dynamical models employed, along with a detailed discussion of the known sources of error in the experiment, both statistical and systematic. From this analysis, a confirmation of the predictions of Einstein's general relativity, as well as strong bounds on alternative theories of gravitation, clearly emerge. In particular, taking conservatively into account the stricter error bound due to systematic effects, general relativity has been confirmed in the Earth's field at the 98% level (meaning the measurement of a suitable combination of β and γ PPN parameters in weak-field conditions). This bound has been used to constrain possible deviations from the inverse-square law parameterized by a Yukawa-like new long range interaction with strength |α|≲1×10-10 at a characteristic range λ ≃1 Earth radius, a possible nonsymmetric gravitation theory with the interaction parameter C⊕LAGEOS II≲(9 × 10-2 km)4, and a possible spacetime torsion with a characteristic parameter combination |2t2+t3|≲7×10-2. Conversely, if we consider the results obtained from our best fit of the LAGEOS II orbit, the constraints in fundamental physics improve by at least 2 orders of magnitude.
NASA Astrophysics Data System (ADS)
Hees, A.; Bertone, S.; Le Poncin-Lafitte, C.
2014-10-01
Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the time transfer function formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the time transfer functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the time transfer function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral that is easily computable numerically. We also provide the derivatives of the time transfer function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the Juno mission in the Jovian system.
NASA Astrophysics Data System (ADS)
Mitra, Abhas
2013-04-01
It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.
The motion of axisymmetric satellite with drag and radiation pressure
NASA Astrophysics Data System (ADS)
Elshaboury, S. M.; Mostafa, A.
2014-08-01
The axisymmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. The energy-like and Laplace-like invariants of motion have been derived for a general drag force function of the polar angle, and the Laplace-like invariant is used to find the orbit equation in the case of a spherical satellite. Then using the small parameter, the orbit of the satellite is determined for an axisymmetric satellite.
NASA Astrophysics Data System (ADS)
Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P.
2015-12-01
The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%.
NASA Astrophysics Data System (ADS)
Koide, Shinji; Shibata, Kazunari; Kudoh, Takahiro
1998-03-01
The radio observations have revealed the compelling evidence of the existence of relativistic jets not only from active galactic nuclei but also from ``microquasars'' in our Galaxy. In the cores of these objects, it is believed that a black hole exists and that violent phenomena occur in the black hole magnetosphere, forming the relativistic jets. To simulate the jet formation in the magnetosphere, we have newly developed the general relativistic magnetohydrodynamic code. Using the code, we present a model of these relativistic jets, in which magnetic fields penetrating the accretion disk around a black hole play a fundamental role of inducing nonsteady accretion and ejection of plasmas. According to our simulations, a jet is ejected from a close vicinity to a black hole (inside 3rS, where rS is the Schwarzschild radius) at a maximum speed of ~90% of the light velocity (i.e., a Lorentz factor of ~2). The jet has a two-layered shell structure consisting of a fast gas pressure-driven jet in the inner part and a slow magnetically driven jet in the outer part, both of which are collimated by the global poloidal magnetic field penetrating the disk. The former jet is a result of a strong pressure increase due to shock formation in the disk through fast accretion flow (``advection-dominated disk'') inside 3rS, which has never been seen in the nonrelativistic calculations.
Attitude stability criteria of axisymmetric solar sail
NASA Astrophysics Data System (ADS)
Hu, Xiaosai; Gong, Shengping; Li, Junfeng
2014-07-01
Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.
NASA Astrophysics Data System (ADS)
Kovács, Z.; Harko, T.
2011-11-01
We present a full general relativistic numerical code for estimating the energy-momentum deposition rate (EMDR) from neutrino pair annihilation (?). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour-flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino-antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino-antineutrino pair annihilation around compact stellar objects, as measured at infinity.
Müller, Bernhard; Janka, Hans-Thomas E-mail: bjmuellr@mpa-garching.mpg.de
2014-06-10
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M {sub ☉}, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, (E), of ν-bar {sub e} and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M ≳ 10 M {sub ☉} as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of 〈E{sub ν-bar{sub e}}〉 with the proto-neutron star (PNS) mass, which holds in time as well as for different progenitors. Convection inside the PNS affects the neutrino emission on the 10%-20% level, and accretion continuing beyond the onset of the explosion prevents the abrupt drop of the neutrino luminosities seen in artificially exploded 1D models. We demonstrate that a wavelet-based time-frequency analysis of SN neutrino signals in IceCube will offer sensitive diagnostics for the SN core dynamics up to at least ∼10 kpc distance. Strong, narrow-band signal modulations indicate quasi-periodic shock sloshing motions due to the standing accretion shock instability (SASI), and the frequency evolution of such 'SASI neutrino chirps' reveals shock expansion or contraction. The onset of the explosion is accompanied by a shift of the modulation frequency below 40-50 Hz, and post-explosion, episodic accretion downflows will be signaled by activity intervals stretching over an extended frequency range in the wavelet spectrogram.
NASA Astrophysics Data System (ADS)
Harikae, Seiji; Kotake, Kei; Takiwaki, Tomoya; Sekiguchi, Yu-ichiro
2010-09-01
Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation (ν + {\\bar{ν}} → e^{-} + e^{+}) in the vicinity of an accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic (GR) neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. We employ the Fehlberg (4,5) adaptive integrator in the Runge-Kutta method to perform the numerical integration accurately. For the neutrino opacity, the charged-current β-processes, which are dominant in the vicinity of the accretion tori, are taken into account. The numerical accuracy of the developed code is certified by several tests in which we show comparisons with the corresponding analytical solutions. In order to solve the energy-dependent ray-tracing transport, we propose that an adaptive-mesh-refinement approach, which we take for the two radiation angles (θ, phi) and the neutrino energy, is useful in reducing the computational cost significantly. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the GR effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percent. After the accretion disk settles into a stationary state (typically later than ~9 s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest that the neutrino pair annihilation is potentially as important as the conventional magnetohydrodynamic mechanism for igniting the GRB
NASA Astrophysics Data System (ADS)
Takahashi, Hiroyuki R.; Ohsuga, Ken; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-07-01
Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk (≳ {10}7 {{K}}) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is ≳ {10}9 {{K}} and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is ˜ 30{r}{{g}} for \\dot{M}˜ {L}{{Edd}}/{c}2, where {r}{{g}},\\dot{M},{L}{Edd},c are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to ˜ 10{r}{{g}} with increasing mass accretion rate \\dot{M}˜ 100{L}{{Edd}}/{c}2, which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of \\dot{M}≲ 100{L}{{Edd}}/{c}2. Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.
NASA Astrophysics Data System (ADS)
Takahashi, Hiroyuki R.; Ohsuga, Ken; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-07-01
Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk (≳ {10}7 {{K}}) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is ≳ {10}9 {{K}} and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is ∼ 30{r}{{g}} for \\dot{M}∼ {L}{{Edd}}/{c}2, where {r}{{g}},\\dot{M},{L}{Edd},c are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to ∼ 10{r}{{g}} with increasing mass accretion rate \\dot{M}∼ 100{L}{{Edd}}/{c}2, which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of \\dot{M}≲ 100{L}{{Edd}}/{c}2. Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.
Evans, C.R. II
1984-01-01
A method is presented that allows fully self-consistent numerical simulation of asymptotically flat axisymmetric nonrotating general relativistic systems. These techniques were developed to model and understand resulting relativistic effects in gravitational core collapse and gravitational radiation generation. Both vacuum (Brill) spacetimes and matter-filled configurations can be treated. The author uses the (3 + 1) composition of Arnowitt, Deser, and Misner to write general relativity in a dynamical form. The conformal approach, including the transverse-traceless decomposition of extrinsic curvature due to York, is used to solve the initial-value problem. In addition, these techniques are extended to provide a fully constrained evolution scheme. Several new boundary conditions, applied at large but finite radius, are derived for the elliptic constraint equations. The method uses a simplifying three-gauge, placing the metric in quasi-isotropic form. The resulting three-metric contains only two components that must be solved. One, the conformal factor, is fixed by the Hamiltonian constraint. The second has nice radiative features and is related in the weak-field limit to the usual transverse-traceless gravitational wave amplitude. The time slicing is determined by implementation of the maximal slicing condition.
Wright, B.L.; Alrick, K.R.; Fritz, J.N.
1994-05-01
Axisymmetric magnetic (ASM) gauges are useful diagnostic tools in the study of the conversion of energy from underground explosions to distant seismic signals. Requiring no external power, they measure the strength (particle velocity) of the emerging shock wave under conditions that would destroy most instrumentation. Shock pins are included with each gauge to determine the angle of the shock front. For the Non-Proliferation Experiment, two ASM gauges were installed in the ANFO mixture to monitor the detonation wave and 10 were grouted into boreholes at various ranges in the surrounding rock (10 to 64 m from the center of explosion). These gauges were of a standard 3.8-inch-diameter design. In addition, two unique Jumbo ASM gauges (3-ft by 3-ft in cross section) were grouted to the wall of a drift at a range of 65 m. We discuss issues encountered in data analysis, present the results of our measurements, and compare these results with those of model simulations of the experiment.
NASA Astrophysics Data System (ADS)
Shaghaghian, M.
2016-02-01
We examine a thick accretion disc in the presence of external gravity and intrinsic dipolar magnetic field due to a non-rotating central object. In this paper, we generalize the Newtonian theory of stationary axisymmetric resistive tori of Tripathy, Prasanna & Das by including the fully general relativistic features. If we are to obtain the steady state configuration, we have to take into account the finite resistivity for the magnetofluid in order to avoid the piling up of the field lines anywhere in the accretion discs. The efficient value of conductivity must be much smaller than the classical conductivity to be astrophysically interesting. The accreting plasma in the presence of an external dipole magnetic field gives rise to a current in the azimuthal direction. The azimuthal current produced due to the motion of the magnetofluid modifies the magnetic field structure inside the disc and generates a poloidal magnetic field for the disc. The solutions we have found show that the radial inflow, pressure and density distributions are strongly modified by the electrical conductivity both in relativistic and Newtonian regimes. However, the range of conductivity coefficient is different for both regimes, as well as that of the angular momentum parameter and the radius of the innermost stable circular orbit. Furthermore, it is shown that the azimuthal velocity of the disc which is not dependent on conductivity is sub-Keplerian in all radial distances for both regimes. Owing to the presence of pressure gradient and magnetic forces. This work may also be important for the general relativistic computational magnetohydrodynamics that suffers from the lack of exact analytic solutions that are needed to test computer codes.
Axisymmetric Coanda-assisted vectoring
NASA Astrophysics Data System (ADS)
Allen, Dustin; Smith, Barton L.
2009-01-01
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.
Ermler, Walter V.; Tilson, Jeffrey L.
2012-12-15
A procedure for structuring generally contracted valence-core/valence basis sets of Gaussian-type functions for use with relativistic effective core potentials (gcv-c/v-RECP basis sets) is presented. Large valence basis sets are enhanced using a compact basis set derived for outer core electrons in the presence of small-core RECPs. When core electrons are represented by relativistic effective core potentials (RECPs), and appropriate levels of theory, these basis sets are shown to provide accurate representations of atomic and molecular valence and outer-core electrons. Core/valence polarization and correlation effects can be calculated using these basis sets through standard methods for treating electron correlation. Calculations of energies and spectra for Ru, Os, Ir, In and Cs are reported. Spectroscopic constants for RuO2+, OsO2+, Cs2 and InH are calculated and compared with experiment.
Magneto-hydrodynamically stable axisymmetric mirrors
NASA Astrophysics Data System (ADS)
Ryutov, Dmitri
2010-11-01
The achievement of high beta (60%) plasma with near classical confinement in a linear axisymmetric magnetic configuration has sparked interest in the Gas Dynamic Trap concept. The significance of these results is that they can be projected directly to a neutron source for materials testing. The possibility of axisymmetric mirrors (AM) being magneto-hydrodynamically (MHD) stable is also of interest from a general physics standpoint (as it seemingly contradicts to well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a brief summary of classical results (in particular of the Rosenbluth-Longmire theory and of the energy principle as applied to AM) several approaches towards achieving MHD stabilization of the AM will be considered: 1) Employing the favorable field-line curvature in the end tanks; 2) Using the line-tying effect; 3) Setting the plasma in a slow or fast differential rotation; 4) Imposing a divertor configuration on the solenoidal magnetic field; 5) Controlling the plasma dynamics by the ponderomotive force; 6) Other techniques. Several of these approaches go beyond pure MHD and require accounting for finite Larmor radius effects and trapped particle modes. Some illuminative theoretical approaches for understanding axisymmetric mirror stability will be described. Wherever possible comparison of theoretical and experimental results on AM will be provided. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors will be discussed and the constraints on the plasma parameters will be formulated. Prepared by LLNL under Contract DE-AC52-07NA27344.
Axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2012-06-01
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect.
NASA Astrophysics Data System (ADS)
Valente, Giovanni; Owen Weatherall, James
2014-11-01
Relativity theory is often taken to include, or to imply, a prohibition on superluminal propagation of causal processes. Yet, what exactly the prohibition on superluminal propagation amounts to and how one should deal with its possible violation have remained open philosophical problems, both in the context of the metaphysics of causation and the foundations of physics. In particular, recent work in philosophy of physics has focused on the causal structure of spacetime in relativity theory and on how this causal structure manifests itself in our most fundamental theories of matter. These topics were the subject of a workshop on "Relativistic Causality in Quantum Field Theory and General Relativity" that we organized (along with John Earman) at the Center for Philosophy of Science in Pittsburgh on April 5-7, 2013. The present Special Issue comprises contributions by speakers in that workshop as well as several other experts exploring different aspects of relativistic causality. We are grateful to the journal for hosting this Special Issue, to the journal's managing editor, Femke Kuiling, for her help and support in putting the issue together, and to the authors and the referees for their excellent work.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald
2010-07-01
We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the "ray-by-ray plus" approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in
Mueller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald E-mail: thj@mpa-garching.mpg.d
2010-07-15
We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the 'ray-by-ray plus' approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in
NASA Astrophysics Data System (ADS)
Papasotiriou, P. J.; Geroyannis, V. S.
We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.
NASA Astrophysics Data System (ADS)
Kolesnikov, E. K.; Manuilov, A. S.
2016-04-01
The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker-Planck kinetic equation.
Relativistic viscoelastic fluid mechanics
Fukuma, Masafumi; Sakatani, Yuho
2011-08-15
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
REVIEW ARTICLE: Control of non-axisymmetric toroidal plasmas
NASA Astrophysics Data System (ADS)
Boozer, Allen H.
2010-10-01
The control of non-axisymmetric toroidal plasmas, stellarators, has a different character than the control of tokamaks for two reasons. Non-axisymmetric magnetic fields (1) can provide an arbitrarily large fraction of the poloidal magnetic field and (2) can strongly center the plasma in the chamber making it impossible to lose position control. The focus of stellarator design is on plasmas that are stable without feedback, need little or no change in the external magnetic field as the plasma evolves, and require no external power to maintain the desired magnetic configuration. The physics of non-axisymmetric fields is the same whether in a tokamak or a stellarator and whether introduced intentionally or accidentally. Fundamental physics indicates that plasma shape, which is controlled by the distribution of the external magnetic field that is normal to the plasma surface, is the primary control for fusion plasmas. The importance of non-axisymmetric control is set by the importance of toroidal plasma physics. Informed decisions on the development strategy of tokamaks, as well as magnetic fusion in general, require an understanding of the capabilities and difficulties of plasma control at various levels of non-axisymmetric shaping.
Stationary axisymmetric fields in a teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Saez, D.
1984-12-01
The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.
NASA Astrophysics Data System (ADS)
Stefańska, Patrycja
2016-02-01
We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997), 10.1088/0953-4075/30/4/007; J. Phys. B 30, 2747 (1997), 10.1088/0953-4075/30/11/023], We derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.
Axisymmetric Vortices with Swirl
NASA Astrophysics Data System (ADS)
Elcrat, A.
2007-11-01
This talk is concerned with finding solutions of the Euler equations by solving elliptic boundary value problems for the Bragg-Hawthorne equation L u= -urr -(1/r)ur - = r^2f (u) + h(u). Theoretical results have been given for previously (Elcrat and Miller, Differential and Integral Equations 16(4) 2003, 949-968) for problems with swirl and general classes of profile functions f, h by iterating Lu(n+1)= rf(u)n)) + h(u(n)), and showing u(n) converges montonically to a solution. The solutions obtained depend on the initial guess, which can be thought of as prescribing level sets of the vortex. When a computational program was attempted these monotone iterations turned out to be numerically unstable, and a stable computation was acheived by fixing the moment of the cross section of a vortex in the merideanal plane. (This generalizes previous computational results in Elcrat, Fornberg and Miller, JFM 433 2001, (315-328) We obtain famillies of vortices related to vortex rings with swirl, Moffatt's generalization of Hill's vortex and tubes of vorticity with swirl wrapped around the symmetry axis. The vortices are embedded in either an irrotational flow or a flow with shear, and we deal with the transition form no swirl in the vortex to flow with only swirl, a Beltrami flow.
The Formation of Relativistic Jets from Kerr Black Holes
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Richardson, G.; Preece, R.; Hardee, P.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Fishman, G. J.
2003-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamics (GRMHD) simulation for Schwarzschild and Kerr black holes with a free falling corona and thin accretion disk. The initial simulation results with a Schwarzschild metric show that a jet is created as in the previous axisymmetric simulations with mirror symmetry at the equator. However, the time to form the jet is slightly longer than in the 2-D axisymmetric simulation. We expect that the dynamics of jet formation are modified due to the additional freedom in the azimuth dimension without axisymmetry with respect to the Z axis and reflection symmetry respect to the equatorial plane. The jet which is initially formed due to the twisted magnetic fields and shocks becomes a wind at the later time. The wind flows out with a much wider angle than the initial jet. The twisted magnetic fields at the earlier time were untwisted and less pinched. The accretion disk became thicker than the initial condition. Further simulations with initial perturbations will provide insights for accretion dynamics with instabilities such as magneto-rotational instability (MRI) and accretion-eject instability (AEI). These instabilities may contribute to variabilities observed in microquasars and AGN jets.
Rotating and binary relativistic stars with magnetic field
NASA Astrophysics Data System (ADS)
Markakis, Charalampos
We develop a geometrical treatment of general relativistic magnetohydrodynamics for perfectly conducting fluids in Einstein--Maxwell--Euler spacetimes. The theory is applied to describe a neutron star that is rotating or is orbiting a black hole or another neutron star. Under the hypotheses of stationarity and axisymmetry, we obtain the equations governing magnetohydrodynamic equilibria of rotating neutron stars with poloidal, toroidal or mixed magnetic fields. Under the hypothesis of an approximate helical symmetry, we obtain the first law of thermodynamics governing magnetized equilibria of double neutron star or black hole - neutron star systems in close circular orbits. The first law is written as a relation between the change in the asymptotic Noether charge deltaQ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetofluid. In an attempt to provide a better theoretical understanding of the methods used to construct models of isolated rotating stars and corotating or irrotational binaries and their unexplained convergence properties, we analytically examine the behavior of different iterative schemes near a static solution. We find the spectrum of the linearized iteration operator and show for self-consistent field methods that iterative instability corresponds to unstable modes of this operator. On the other hand, we show that the success of iteratively stable methods is due to (quasi-)nilpotency of this operator. Finally, we examine the integrability of motion of test particles in a stationary axisymmetric gravitational field. We use a direct approach to seek nontrivial constants of motion polynomial in the momenta---in addition to energy and angular momentum about the symmetry axis. We establish the existence and uniqueness of quadratic constants and the nonexistence of quartic constants for stationary axisymmetric Newtonian potentials with equatorial symmetry
Experiments in axisymmetric supersonic jets
NASA Astrophysics Data System (ADS)
Moore, Cyrille Dennis
An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric
Kallay, Mihaly; Nataraj, H. S.; Sahoo, B. K.; Das, B. P.; Visscher, Lucas
2011-03-15
We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the black-body radiation shift of the Al{sup +} clock has been estimated precisely. The computed shift relative to the frequency of the 3s{sup 2} {sup 1}S{sub 0}{sup e}{yields}3s3p {sup 3}P{sub 0}{sup o} clock transition given by (-3.66{+-}0.60)x10{sup -18} calls for an improvement over the recent measurement with a reported result of (-9{+-}3)x10{sup -18}[Phys. Rev. Lett. 104, 070802 (2010)].
Shi Changsheng; Li Xiangdong E-mail: lixd@nju.edu.c
2010-05-10
We suggest a possible explanation for the high frequency quasi-periodic oscillations (QPOs) in black hole (BH) low-mass X-ray binaries. By solving the perturbation general relativistic magnetohydrodynamic equations, we find two stable modes of the Alfven wave in the accretion disks with toroidal magnetic fields. We suggest that these two modes may lead to the double high frequency QPOs if they are produced in the transition region between the inner advection-dominated accretion flow and the outer thin disk. This model naturally accounts for the 3:2 relation for the upper and lower frequencies of the QPOs, and the relation between the BH mass and QPO frequency.
NASA Astrophysics Data System (ADS)
Baiotti, Luca; Shibata, Masaru; Yamamoto, Tetsuro
2010-09-01
We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the whisky code and the sacra code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular, in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.
Axisymmetric supersonic flow in rotating impellers
NASA Technical Reports Server (NTRS)
Goldstein, Arthur W
1952-01-01
General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.
A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields
NASA Astrophysics Data System (ADS)
Jiang, J.; Wang, J. X.
2007-05-01
More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric α2-Ω dynamo model is derived to explore the characteristics of the axisymmetric (m = 0) and the first non-axisymmetric (m = 1) modes and to provide a theoretical basis with which to explain the `active longitude', `flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the α2-Ω and the α-Ω models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.
ACCELERATION AND COLLIMATION OF RELATIVISTIC MAGNETOHYDRODYNAMIC DISK WINDS
Porth, Oliver; Fendt, Christian E-mail: fendt@mpia.d
2010-02-01
We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 x 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied-an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically-implying three relativistically distinct regimes in the flow-an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface-similar to the spine-sheath structure currently
Local stability of axisymmetric plumes
NASA Astrophysics Data System (ADS)
R. v. K., Chakravarthy; Lesshafft, Lutz; Huerre, Patrick
2014-11-01
A linear stability analysis of a forced plume with non-zero momentum at the inlet is performed for Pr = 1 , Re = 100 and Ri near 1. The steady base flow is obtained as a laminar solution of the steady Navier Stokes equations. The base flow asymptotes to a self-similar solution as it evolves downstream. In the non-self-similar regime close to the inlet, both axisymmetric mode (m = 0) and the helical mode (m = 1) are convectively unstable at sufficiently low Richardson number. In the self-similar regime, only the helical mode is absolutely unstable and the axisymmetric mode is stable. Higher helical modes (m >= 2) are seen to be convectively unstable very close to the inlet and become stable as the flow evolves downstream. The transition from convective to absolute instability makes the flow a good candidate for observing steep nonlinear global modes associated with buoyancy. This work is supported by a PhD scholarship from Ecole polytechnique.
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1977-01-01
The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.
Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures
Cremaschini, Claudio; Stuchlík, Zdeněk
2014-04-15
The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.
Simulations of Relativistic Extragalactic Jets
NASA Astrophysics Data System (ADS)
Hughes, P. A.; Duncan, G. C.
1994-05-01
We present results for 2-D, axisymmetric simulations of flows with Lorentz factors ~ 5 -- 10, typical of values inferred for superluminal BL Lacs and QSOs. The simulations were performed with a numerical hydrodynamic code that admits relativistic flow speed. We exploit the property that the relativistic Euler equations for mass, momentum and total energy densities in the laboratory frame have the same form as the nonrelativistic equations, to solve for laboratory frame variables using a conventional Godunov-type scheme with approximate Riemann solver: the HLLE method. The relativistic nature of the flow is incorporated by performing a Lorentz transformation at every step, at each cell center or cell boundary where pressure, sound speed or velocity are required. Determination of the velocity in this manner is a robust algebraic procedure within which we can ensure that v
NASA Astrophysics Data System (ADS)
Haba, Z.
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed. PMID:19391727
The r-process in black hole-neutron star mergers based on a fully general-relativistic simulation
NASA Astrophysics Data System (ADS)
Nishimura, N.; Wanajo, S.; Sekiguchi, Y.; Kiuchi, K.; Kyutoku, K.; Shibata, M.
2016-01-01
We investigate the black hole-neutron star binary merger in the contest of the r-process nucleosynthesis. Employing a hydrodynamical model simulated in the framework of full general relativity, we perform nuclear reaction network calculations. The extremely neutron-rich matter with the total mass 0.01 M⊙ is ejected, in which a strong r-process with fission cycling proceeds due to the high neutron number density. We discuss relevant astrophysical issues such as the origin of r-process elements as well as the r-process powered electromagnetic transients.
Post-Newtonian reference ellipsoid for relativistic geodesy
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena
2016-02-01
We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to
Reintjes, Moritz; Temple, Blake
2015-01-01
We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C0,1 to C1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C1,1, cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein–Euler equations remains open. PMID:27547092
Relativistic radiation transport in dispersive media
Kichenassamy, S.; Krikorian, R.A.
1985-10-15
A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.
The Case for General Relativistic Effects in the Fe K(alpha) Profile of an Active Galaxy
NASA Technical Reports Server (NTRS)
Turner, T. J.; Mushotzky, R.; Yaqoob, T.; George, I. M.; Snowden, S. L.; Netzer, H.; Kraemer, S. B.; Nandra, K.; Chelouche, D.; White, Nicholas E. (Technical Monitor)
2002-01-01
We present results from a simultaneous Chandra HETG (High Energy Transmission Grating) and XMM (X-ray Multi-mirror Mission)-Newton observation of NGC 3516. We find evidence for several narrow components of Fe K(alpha) along with a broad line. We consider the possibility that the lines arise in a blob of material ejected from the nucleus with velocity of approximately 0.25c. We also consider an origin in a neutral accretion disk, suffering enhanced illumination at 35 and 175 R(sub g), perhaps due to magnetic reconnection. The presence of these narrow features indicates there is no Comptonizing region along the line-of-sight to the nucleus. This in turn is compelling support for the hypothesis that broad Fe K(alpha) components are, in general, produced by strong gravity.
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Banik, Prabir
2015-07-01
In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central
NASA Astrophysics Data System (ADS)
Flury, J.
2016-06-01
Quantum metrology enables new applications in geodesy, including relativistic geodesy. The recent progress in optical atomic clocks and in long-distance frequency transfer by optical fiber together pave the way for using measurements of the gravitational frequency redshift for geodesy. The remote comparison of frequencies generated by calibrated clocks will allow for a purely relativistic determination of differences in gravitational potential and height between stations on Earth surface (chronometric leveling). The long-term perspective is to tie potential and height differences to atomic standards in order to overcome the weaknesses and inhomogeneity of height systems determined by classical spirit leveling. Complementarily, gravity measurements with atom interferometric setups, and satellite gravimetry with space borne laser interferometers allow for new sensitivities in the measurement of the Earth's gravity field.
Allen, M.A.; Azuma, O.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Hoag, H.A.; Koontz, R.F.
1989-03-01
Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs.
NASA Astrophysics Data System (ADS)
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1990-01-01
A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.
MAGNETIC ENERGY BUILDUP FOR RELATIVISTIC MAGNETAR GIANT FLARES
Yu Cong
2011-09-01
Motivated by coronal mass ejection studies, we construct general relativistic models of a magnetar magnetosphere endowed with strong magnetic fields. The equilibrium states of the stationary, axisymmetric magnetic fields in the magnetar magnetosphere are obtained as solutions of the Grad-Shafranov equation in a Schwarzschild spacetime. To understand the magnetic energy buildup in the magnetar magnetosphere, a generalized magnetic virial theorem in the Schwarzschild metric is newly derived. We carefully address the question whether the magnetar magnetospheric magnetic field can build up sufficient magnetic energy to account for the work required to open up the magnetic field during magnetar giant flares. We point out the importance of the Aly-Sturrock constraint, which has been widely studied in solar corona mass ejections, as a reference state in understanding magnetar energy storage processes. We examine how the magnetic field can possess enough energy to overcome the Aly-Sturrock energy constraint and open up. In particular, general relativistic (GR) effects on the Aly-Sturrock energy constraint in the Schwarzschild spacetime are carefully investigated. It is found that, for magnetar outbursts, the Aly-Sturrock constraint is more stringent, i.e., the Aly-Sturrock energy threshold is enhanced due to the GR effects. In addition, neutron stars with greater mass have a higher Aly-Sturrock energy threshold and are more difficult to erupt. This indicates that magnetars are probably not neutron stars with extreme mass. For a typical neutron star with mass of 1-2 M{sub sun}, we further explore the cross-field current effects, caused by the mass loading, on the possibility of stored magnetic field energy exceeding the Aly-Sturrock threshold.
Relativistic Bernstein waves in a degenerate plasma
Ali, Muddasir; Hussain, Azhar; Murtaza, G.
2011-09-15
Bernstein mode for a relativistic degenerate electron plasma is investigated. Using relativistic Vlasov-Maxwell equations, a general expression for the conductivity tensor is derived and then employing Fermi-Dirac distribution function a generalized dispersion relation for the Bernstein mode is obtained. Two limiting cases, i.e., non-relativistic and ultra-relativistic are discussed. The dispersion relations obtained are also graphically presented for some specific values of the parameters depicting how the propagation characteristics of Bernstein waves as well as the Upper Hybrid oscillations are modified with the increase in plasma number density.
Radiation from Axisymmetric Waveguide Fed Horns
NASA Technical Reports Server (NTRS)
Chinn, G. C.; Hoppe, D. J.; Epp, L. W.
1995-01-01
Return losses and radiation patterns for axisymmetric waveguide fed horns are calculated with the finite element method (FEM) in conjunction with the method of moments (MoM) and the mode matching technique (MM).
NASA Astrophysics Data System (ADS)
Uryū, Kōji; Tsokaros, Antonios; Galeazzi, Filippo; Hotta, Hideya; Sugimura, Misa; Taniguchi, Keisuke; Yoshida, Shin'ichirou
2016-02-01
We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.
Four motional invariants in axisymmetric tori equilibria
A ring gren, O.; Moiseenko, V.E.
2006-05-15
In addition to the standard set ({epsilon},{mu},p{sub {phi}}) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I{sub r}. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I{sub r}=
The inviscid stability of supersonic flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Duck, Peter W.
1990-01-01
The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).
Transition and mixing in axisymmetric jets and vortex rings
NASA Technical Reports Server (NTRS)
Allen, G. A., Jr.; Cantwell, B. J.
1986-01-01
A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.
Axisymmetric MHD Instabilities in Solar/Stellar Tachoclines
NASA Astrophysics Data System (ADS)
Dikpati, Mausumi; Gilman, Peter A.; Cally, Paul S.; Miesch, Mark S.
2009-02-01
Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.
Cremaschini, Claudio; Kovář, Jiří; Slaný, Petr; Stuchlík, Zdeněk; Karas, Vladimír
2013-11-01
The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.
Oscillations of rapidly rotating relativistic stars
Gaertig, Erich; Kokkotas, Kostas D.
2008-09-15
Nonaxisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility of studying the complete problem by including space-time perturbations. Our study includes both axisymmetric and nonaxisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulas for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.
NASA Technical Reports Server (NTRS)
Lerche, I.; Low, B. C.
1980-01-01
The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation. PMID:22463331
Dissipation in Relativistic Pair-Plasma Reconnection
NASA Technical Reports Server (NTRS)
Hesse, Michael; Zenitani, Seiji
2007-01-01
We present an investigation of the relativistic dissipation in magnetic reconnection. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. We analyze a set of numerical simulations, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For anti-parallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
Dissipation in relativistic pair-plasma reconnection
Hesse, Michael; Zenitani, Seiji
2007-11-15
An investigation into the relativistic dissipation in magnetic reconnection is presented. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. A set of numerical simulations is analyzed, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For antiparallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
Relativistic electrons associated with solar flares.
NASA Technical Reports Server (NTRS)
Sakurai, K.
1972-01-01
Solar flares which produce relativistic electrons generally occur within sunspot groups which are active in the emission of meter type I noise storms. It is suggested that relativistic electrons in solar flares are accelerated from the keV-energy electrons responsible for the type I noise storms. The relationship between flare developments and the ejection of keV-electrons is briefly considered.
Constants of motion in stationary axisymmetric gravitational fields
NASA Astrophysics Data System (ADS)
Markakis, C.
2014-07-01
The motion of test particles in stationary axisymmetric gravitational fields is generally non-integrable unless a non-trivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant in Kerr-de Sitter space-time is the only example known to date. Proposed astrophysical tests of the black hole no-hair theorem have often involved integrable gravitational fields more general than the Kerr family, but the existence of such fields has been a matter of debate. To elucidate this problem, we treat its Newtonian analogue by systematically searching for non-trivial constants of motion polynomial in the momenta and obtain two theorems. First, solving a set of quadratic integrability conditions, we establish the existence and uniqueness of the family of stationary axisymmetric potentials admitting a quadratic constant. As in Kerr-de Sitter space-time, the mass moments of this class satisfy a `no-hair' recursion relation M2l +2 = a2M2l, and the constant is Noether related to a second-order Killing-Stäckel tensor. Second, solving a new set of quartic integrability conditions, we establish non-existence of quartic constants. Remarkably, a subset of these conditions is satisfied when the mass moments obey a generalized `no-hair' recursion relation M2l +4 = (a2 + b2)M2l +2 - a2b2M2l. The full set of quartic integrability conditions, however, cannot be satisfied non-trivially by any stationary axisymmetric vacuum potential.
Supersonic quasi-axisymmetric vortex breakdown
NASA Technical Reports Server (NTRS)
Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.
1991-01-01
An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.
Quasi-static axisymmetric eversion hemispherical domes made of elastomers
NASA Astrophysics Data System (ADS)
Kabrits, Sergey A.; Kolpak, Eugeny P.
2016-06-01
The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.
Marginally stable circular orbits in stationary axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Beheshti, Shabnam; Gasperín, Edgar
2016-07-01
We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.
Cremaschini, Claudio; Stuchlík, Zdeněk; Tessarotto, Massimo
2013-05-15
The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.
The relativistic Doppler broadening of the line absorption profile
NASA Astrophysics Data System (ADS)
Kichenassamy, S.; Krikorian, R.; Nikogosian, A.
1982-06-01
The classical results of Doppler broadening of the line absorption profile are generalized to a relativistic gas in thermal equilibrium by taking into account the relativistic variance of the volume absorption coefficients of the gas, as derived by L. H. Thomas. This variance produces a small correction, even in the non-relativistic approximation.
NASA Astrophysics Data System (ADS)
Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo
2015-05-01
The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.