Torus System Research Articles

Long-term Monte Carlo-based neutrino-radiation hydrodynamics simulations for a black hole-torus system

We present our new general relativistic Monte Carlo (MC)-based neutrino radiation hydrodynamics code designed to solve axisymmetric systems with several improvements. The main improvements are as follows: (i) the development of an extended version of the implicit MC method for multispecies radiation fields; (ii) modeling of neutrino pair process rates based on a new numerically efficient and asymptotically correct fitting function for the kernel function; (iii) the implementation of new numerical limiters on the radiation-matter interaction to ensure a stable and physically correct evolution of the system. We apply our code to a black hole (BH)-torus system with a BH mass of 3M⊙, BH dimensionless spin of 0.8, and a torus mass of 0.1M⊙, which mimics a postmerger remnant of a binary neutron star merger in the case that the massive neutron star collapses to a BH within a short timescale (∼10 ms). We follow the evolution of the BH-torus system up to more than 1 s with our MC-based radiation viscous-hydrodynamics code that dynamically takes into account nonthermal pair annihilation. We find that the system evolution and the various key quantities, such as neutrino luminosity, ejecta mass, torus Ye, and pair annihilation luminosity, are broadly in agreement with the results of the previous studies. We also find that the νeν¯e pair annihilation can launch a relativistic outflow for a timescale of ∼0.1 s, and it can be energetic enough to explain some of short-hard gamma-ray bursts and the precursors. Finally, we calculate the indicators of the fast flavor instability directly from the obtained neutrino distribution functions, which indicate that the instability can occur particularly near the equatorial region of the torus. Published by the American Physical Society 2025

Self-rotation-eversion of an anisotropic-friction-surface torus

Recent experiments have revealed a new end-to-end ribbon spiral structure capable of demonstrating two interconnected periodic zero-energy-mode self-rotation-eversion in reaction to constant temperature or constant light sources, yet its fabrication is challenging due to its intricate nature. Differently, this paper develops a light-fueled self-rotating and everting liquid crystal elastomer torus on an isotropic frictional plane, by imparting anisotropic frictional properties to the surface of the torus. Based on a mature dynamic liquid crystal elastomer model, we constructed the theoretical model of the torus system. The torus is capable of absorbing the illumination energy to counteract damping dissipation and produce zero-energy-mode self-eversion-rotation. Theoretical findings demonstrate that the angular velocity of self-eversion is influenced by light intensity, light penetration depth, gravitational acceleration and anisotropic friction surface. Moreover, there is a proportional relationship between the self-rotation and self-eversion angular velocities, which is determined by the anisotropic frictional surface. The detailed criterion for the self-rotation direction is also established. Theoretical findings exhibit several similar phenomena to experimental observations. This paper proposes a new simple strategy that utilizes anisotropic friction surface to control self-eversion-rotation, which has guiding significance for the application of soft robots, active devices, and energy harvesters.

IMPLEMENTATION OF MULTI-FOLDED TORUS ATTRACTORS VIA A PIECEWISE SYSTEM WITH A PIECEWISE LINEAR ODD FUNCTION

Among the family of multi-scroll chaotic attractors, we have the multi-folded torus chaotic attractor. Concerns were raised among applied scientists on how to control, merge, split or modify the whole or parts of these multi-folded torus attractors in their implementation processes while conserving the same circuit diagram and the same system of differential equations. In this paper, we strive to address these concerns by using the piecewise process, that is, applying to the modified multi-folded torus system, the piecewise derivative made of the fractal-fractional and classical derivatives. A modified piecewise linear odd function is also used in the process. The modified model is first solved numerically thanks to the wavelet method and numerical simulations are performed. The results show the progressive transformation of the initial multi-folded torus attractors into stretched or reduced multi-folded torus attractors. However, the chaotic state of the system is preserved by the piecewise modification.

The disk–torus system in active galactic nuclei: possible evidence of highly spinning black holes

We study the ratio R between the luminosity of the torus and that of the accretion disk, inferred from the relativistic model KERRBB for a sample of approximately 2000 luminosity-selected radio-quiet Type I active galactic nuclei from the Sloan Digital Sky Survey catalog. We find a mean ratio R ≈ 0.8 and a considerable number of sources with R ≳ 1. Our statistical analysis regarding the distribution of the observed ratios suggests that the largest values might be linked to strong relativistic effects due to a large black hole spin (a > 0.8), despite the radio-quiet nature of the sources. The mean value of R sets a constraint on the average torus aperture angle (in the range 30° < θT < 70°) and, for about one-third of the sources, the spin must be a > 0.7. Moreover, our results suggest that the strength of the disk radiation (i.e., the Eddington ratio) could shape the torus geometry and the relative luminosity ratio R. Given the importance of the involved uncertainties on this statistical investigation, an extensive analysis and discussion have been made to assess the robustness of our results.

A Global Numerical Model of the Prompt Emission in Short Gamma-ray Bursts

Abstract We present the first global model of prompt emission from a short gamma-ray burst (GRB) that consistently describes the evolution of the central black hole (BH) torus system, the propagation of the jet through multicomponent merger ejecta, the transition into free expansion, and the photospheric emission from the relativistic jet. To this end, we perform a special relativistic neutrino-hydrodynamics simulation of a viscous BH-torus system, which is formed about 500 ms after the merger and is surrounded by dynamical ejecta as well as neutron star winds, along with a jet that is injected in the vicinity of the central BH. In a postprocessing step, we compute the photospheric emission using a relativistic Monte Carlo radiative transfer code. It is found that the wind from the torus leaves a strong imprint on the jet as well as on the emission, causing narrow collimation and rapid time variability. The dependence of the emission on viewing angle gives rise to correlations among the spectral peak energy, E p , isotropic energy, E iso, and peak luminosity, L p , which may provide natural explanations for the Amati and Yonetoku relations. We also find that the degree of polarization is small for emission from the jet core (≲2%), while it tends to increase with viewing angle outside the core and can become as high as ∼10%–40% for energies larger than the peak energy. Finally, the comparison of our model with GRB 170817A strongly disfavors the photospheric emission scenario and therefore supports alternative scenarios, such as cocoon shock breakout.

Multimessenger Parameter Estimation of GW170817: From Jet Structure to the Hubble Constant

Abstract The electromagnetic radiation that followed the neutron star merger event GW170817 revealed that gamma-ray burst afterglows from jets misaligned with our line of sight exhibit a light curve with slowly rising flux. The slope of the rising light curve depends sensitively on the angle of the observer with respect to the jet axis, which is likely to be perpendicular to the merger plane of the neutron star binary. Therefore, the afterglow emission can be used to constrain the inclination of the merging system. Here, we calculate the gamma-ray burst afterglow emission based on the realistic jet structure derived from general-relativistic magnetohydrodynamical simulations of a black hole torus system for the central engine of the gamma-ray burst. Combined with gravitational wave parameter estimation, we fit the multi-epoch afterglow emission of GW170817. We show that with such a jet model, the observing angle can be tightly constrained by multimessenger observations. The best fit observing angle of GW170817 is θ v = 0.38 ± 0.02 rad. With such a constraint, we can break the degeneracy between inclination angle and luminosity distance in gravitational wave parameter estimation, and substantially increase the precision with which the Hubble constant is constrained by the standard siren method. Our estimation of the distance is D L = 43.4 ± 1 Mpc and the Hubble constant constraint is 69.5 ± 4 km s−1 Mpc−1. As a result, multimessenger observations of short-duration gamma-ray bursts, combined with a good theoretical understanding of the jet structure, can be powerful probes of cosmological parameters.

Parameter estimation of butyl rubber aided with dynamic mechanical analysis for numerical modelling of an air-inflated torus and experimental validation using 3D-laser Doppler vibrometer

Over the few decades, there has been an exponential growth in the application of inflated torus system in the field of space deployable antenna design, solar propulsion, and aerodynamic deceleration system. However, such a system is inherently susceptible to mechanical vibration and hence requires precise modal analysis to produce stable inflatable structures. This paper summarizes all the necessary steps to be followed for dynamic analysis of inflatable structures. With this objective, a butyl rubber-based inflated torus system with dynamic material properties has been considered in this work. On performing mechanical tests of the rubber sample, properties like Prony series parameters, complex modulus, and damping values were obtained. Using laser Doppler vibrometry, the modal behavior of a butyl rubber-based air-inflated torus with free–free boundary condition was studied. The results achieved from experimental modal analysis and simulation involving fluid–structure interaction were found to be in close proximity. It is envisaged that the test template integrated with numerical validation can lay the foundation for designing complex inflatable torus structures.

An Explosion is Triggered by the Late Collapse of the Compact Remnant from a Neutron Star Merger

Abstract It is known that a binary neutron star (BNS) merger produces a hypermassive neutron star. The lifetime of this compact remnant depends on the total mass and the equation of state. The collapse of this compact remnant to a black hole torus system is expected to give rise to a powerful jet and a short gamma-ray burst. Nevertheless, if the collapse is delayed half a second or so, the surrounding matter would already be accreted and/or expelled, hence no significant torus is formed. However, the collapse itself gives rise to a quasi-isotropic magnetized fireball. This magnetic bomb dissipates much of its energy due to magnetic reconnection and produces the prompt emission. The energy range of such an explosion depends on the initial magnetic field strength and the amplification of the magnetic energy during merger. We briefly estimate the physical parameters at the time of collapse. We discuss the production of a quasi-isotropic magnetized fireball and its subsequent interaction with the ejected matter during merger as the outcome of the coalescence of a BNS system. We further suggest the radial stratification of the outflow, following the quasi-normal modes of the black hole.

Cooling Timescale of Dust Tori in Dying Active Galactic Nuclei

Abstract We estimate the dust torus cooling timescale once the active galactic nucleus (AGN) is quenched. In a clumpy torus system, once the incoming photons are suppressed, the cooling timescale of one clump from T dust = 1000 K to several 10 K is less than 10 years, indicating that the dust torus cooling time is mainly governed by the light crossing time of the torus from the central engine. After considering the light crossing time of the torus, the AGN torus emission at 12 μm becomes over two orders of magnitude fainter within 100 years after the quenching. We also propose that those “dying” AGNs could be found using the AGN indicators with a different physical scale R such as 12 μm band luminosity tracing AGN torus (R ∼ 10 pc) and the optical [O iii]λ5007 emission line tracing narrow line regions (R = 102–4 pc).

Quantum Bound States on Some Hyperbolic Surfaces

The aim of this work is to highlight results of energy eigenstates on some noncompact finite hyperbolic surfaces. Such systems are known to exhibit both continuous and discrete spectra and are dependent on the subgroups of the modular group that underlie these surfaces. We study explicitly the cases of Maass cusp forms on the singly punctured two-torus and the triply punctured two-sphere for their eigenvalues. The eigenvalues for the torus system are doubly degenerate while for the sphere case, the eigenvalues are nondegenerate. We also note that the lowest eigenvalue of the sphere system is larger than that of the torus system.

A computer model of the ionic wind in the unipolar approximation with the boundary condition on the ion flow variation rate

A new simplified model of the ionic wind in air is presented. An expression for the electron flow variation rate at the outer boundary of the corona sheath is obtained. It is shown that, in order to simulate the ionic wind in the case of the negative polarity of the high voltage electrode, not only negative ions but also electrons should be taken into account in the external zone. The proposed and the traditional computer models of the ionic wind in the point–torus system are compared.

General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars

We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed at assessing the modifications introduced by resistive effects on the dynamics of the binary after the merger and through to collapse, we have carried out a close comparison with an equivalent simulation performed within the traditional ideal magnetohydrodynamic approximation. We have found that there are many similarities between the two evolutions but also one important difference: the survival time of the hyper massive neutron star increases in a RMHD simulation. This difference is due to a less efficient magnetic-braking mechanism in the resistive regime, in which matter can move across magnetic-field lines, thus reducing the outward transport of angular momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried here have been performed at higher resolutions and with a different grid structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732, L6 (2011)], but confirm the formation of a low-density funnel with an ordered magnetic field produced by the black hole--torus system. In both regimes the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Reconnection processes or neutrino annihilation occurring in the funnel, none of which we model, could potentially increase the internal energy in the funnel and launch a relativistic outflow, which, however, is not produced in these simulations.

Spherical-shell accretion onto the black hole–torus system

The general relativistic hydrodynamical simulation of the spherical-shell accretion onto the stable torus around non-rotating and rotating black holes isotropically falling from a finite distance are constructed for the first time. This type of accretion might be used to explain the dynamics of the torus. The accreted matter sonically, supersonically or highly supersonically interacts with a torus and forms a newly developed dynamical structure. This spherical-shell changes the angular momentum of the torus and mediates torus instabilities which cause the termination of the torus. The impact of the rest-mass density of the perturbation is also studied which found that the high density perturbation destroys the torus in a few dynamical times. It is also found that the dumping time of the matter is much larger for the torus around a rotating black hole. On the other hand, the Papaloizou–Pringle instability from the spherical-shell accretion appears to be much more softer than the former perturbations which are called the Bondi–Hoyle accretion and accretion of the bulk of gas. The Papaloizou–Pringle instability is damped in a short time scale immediately after their formation.

The dynamical evolution of the black hole–torus system perturbed by a Bondi–Hoyle accretion

The existence of the black hole (BH)–torus system has been given a considerable attention to explain the variability of X-ray and Gamma-ray (γ-ray) data. The perturbation of this system by a Bondi–Hoyle accretion leads to an instability which might be used to understand the dynamics of X-ray binaries and γ-ray burst (GRB). The instability is of a Papaloizou–Pringle type and the fastest growing mode of this instability corresponds to m = 1. In this paper, we put forward a scenario in which the stable BH–torus system is perturbed by a matter which is coming from red giants due to the stellar winds. We model the perturbed BH–torus system to find out how the dynamics of the system changes depending on the rest-mass density of the initial perturbation and to estimate the maximum rest-mass density of the perturbation, ρp, which creates a quasi-periodic oscillation without having a shock cone around the BH for fixed ρc (ρc is the maximum rest-mass density of the initial stable torus). We have found that the perturbation with a rest-mass density, ρp < 100ρ atm (ρatm is the rest-mass density of the atmosphere), for any Mach number is the best model for the formation of the oscillating torus around the BH. Otherwise, the shock cone appears in the downstream region of the accreted domain. It is also found that the instability is observed while ρp < 100ρ atm .

Accurate evolutions of unequal-mass neutron-star binaries: properties of the torus and short GRB engines

We present new results from accurate and fully general-relativistic simulations of the coalescence of unmagnetized binary neutron stars with various mass ratios. The evolution of the stars is followed through the inspiral phase, the merger, and the prompt collapse to a black hole, up until the appearance of a thick accretion disc, which is studied as it enters and remains in a regime of quasi-steady accretion. Although a simple ideal-fluid equation of state with Γ = 2 is used, this work presents a systematic study within a fully general-relativistic framework of the properties of the resulting black-hole–torus system produced by the merger of unequal-mass binaries. More specifically, we show that (1) the mass of the torus increases considerably with the mass asymmetry, and equal-mass binaries do not produce significant tori if they have a total baryonic mass Mtot ≳ 3.7 M⊙; (2) tori with masses Mtor ∼ 0.2 M⊙ are measured for binaries with Mtot ∼ 3.4 M⊙ and mass ratios q ∼ 0.75–0.85; (3) the mass of the torus can be estimated by the simple expression , involving the maximum mass for the binaries and coefficients constrained from the simulations, and suggesting that the tori can have masses as large as for Mtot ∼ 2.8 M⊙ and q ∼ 0.75–0.85; (4) using a novel technique to analyze the evolution of the tori, we find no evidence for the onset of non-axisymmetric instabilities and that very little, if any, of their mass is unbound; (5) finally, for all the binaries considered, we compute the complete gravitational waveforms and the recoils imparted to the black holes, discussing the prospects of the detection of these sources for a number of present and future detectors.

Essential Surfaces in Graph Link Exteriors

AbstractAn irreducible graph manifold M contains an essential torus if it is not a special Seifert manifold. WhetherM contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits M into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors.

Quantum mechanics of the doubled torus

We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce the number of degrees of freedom to the correct physical number. We consider this system from the point of view of constrained Hamiltonian dynamics. In this case the constraints are second class, and we can quantize on the constrained surface using Dirac brackets. We perform the quantization for a simple T-fold background and compare to results for the conventional non-doubled torus system. Finally, we formulate a consistent supersymmetric version of the doubled torus system, including supersymmetric constraints.

Improved tokamak concept focusing on easy maintenance

Maintainability improvement on tokamak fusion reactor may prove to be a critical path in order to launch the fusion energy into commercial use. The more the development of tokamak device progresses from an experimental reactor to a commercial reactor, the more important the maintenance issue becomes. The maintenance difficulty of tokamak system is due to its configuration complexity, enormous electromagnetic loads and material radioactivation. In order to mitigate the difficulty, a very low activation material of SiC/SiC composite and a torus configuration with high aspect ratio of eight are introduced. The torus system is radially divided into equal sectors and each sector forms an assembly unit. All the piping and feeder systems are extracted to the spacious torus central region. The new concept is called `DREAM' tokamak reactor, which stands for DRastically EAsy Maintenance. The maximum toroidal field strength of 20 T and the plasma major and minor radii of 16 m and 2 m lead to high fusion power of 5.5 GW under the moderate physics constraints such as a `non-reversed shear profile' with the MHD safety factor of 3, Troyon factor of 3 for the beta limit and the energy confinement time enhancement factor of 2.

Large turbomolecular pumps for fusion research and high-energy physics

Progress in high-energy physics and nuclear fusion research requires among other things an ultra-cleàn, hydrocarbon-free vacuum environment. The use of large turbomolecular pumps as roughing and high vacuum pumping systems for particle accelerators and for the torus and diagnostic system of plasma fusion experiments is described. Special emphasis is given to the behaviour of such pumps under the specific conditions of these experiments. The impact of tritium and a radioactive environment and the presence of strong magnetic fields requires the use of selected materials within the pump. The necessary modifications of a standard turbomolecular pump are described in detail. Such a modified turbomolecular pump is capable of pumping tritium and to withstand a radiation dose of 10 8 rad.

Equilibrium of the Plasma Column in the Torus System with Multipole Configuration

The system consisted of the self-field. of a plasma and the external magnetic field, “Tokamak”, is treated. The MED equilibrium equation is computed by the approximate method. The current of a plasma is replaced by the ring current on the magnetic axis. The current distribution of a plasma is as to be uniform.Using this solution, we investigate the equilibrium in the shell-less multipole system by way of example. The gradient of the vertical magnetic field shows a focusing property, which is the same as the strong focusing accelerator, in the horizontal direction.