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Representations of some quantum tori Lie subalgebras

In this paper, we define the q-analog Virasoro-like Lie subalgebras in x{sub {infinity}}=a{sub {infinity}}(b{sub {infinity}}, c{sub {infinity}}, d{sub {infinity}}). The embedding formulas into x{sub {infinity}} are introduced. Irreducible highest weight representations of A(tilde sign){sub q}, B(tilde sign){sub q}, and C(tilde sign){sub q}-series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the A(tilde sign){sub q}, B(tilde sign){sub q}, C(tilde sign){sub q}, and D(tilde sign){sub q}-series of the q-analog Virasoro-like Lie algebras.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Curvature and geometric modules of noncommutative spheres and tori

When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tori, Klein bottles, and modulo 8 parity/time-reversal anomalies of 2+1d staggered fermions

We study the symmetries of lattice staggered fermions in 2+1d. Using the symmetries, we can place the system on any sheared torus or Klein bottle. These different backgrounds provide diagnostics of various ’t Hooft anomalies associated with the crystalline symmetries. We then compare the lattice model to its continuum limit. The symmetries of the lattice system are mapped in a nontrivial way to the symmetries of the continuum theories. Using this map, we match the ’t Hooft anomalies on the lattice and the continuum. Along the way, we develop a general formalism to study Hamiltonian lattice models on nontrivial, compact, flat spaces.

Algorithms and Theoretical Developments↗

Modelling jets, tori and flares in pulsar wind nebulae

In this contribution we review the recent progress in the modelling of Pulsar Wind Nebulae (PWN). We start with a brief overview of the relevant physical processes in the magnetosphere, the wind-zone and the inflated nebula bubble. Radiative signatures and particle transport processes obtained from 3D simulations of PWN are discussed in the context of optical and X-ray observations. We then proceed to consider particle acceleration in PWN and elaborate on what can be learned about the particle acceleration from the dynamical structures called GwispsG observed in the Crab nebula. We also discuss recent observational and theoretical results of gamma-ray flares and the inner knot of the Crab nebula, which had been proposed as the emission site of the flares. Here, we extend the discussion to GeV flares from binary systems in which the pulsar wind interacts with the stellar wind from a companion star. The chapter concludes with a discussion of solved and unsolved problems posed by PWN.

79 ASTRONOMY AND ASTROPHYSICS↗

Toroidal Alfvén mode instability driven by plasma current in low-density Ohmic plasmas of the spherical tori

Due to intrinsically low magnetic fields, at low density the drift speed of the current-carrying electrons in spherical tokamaks can exceed fraction of the Alfvén speed sufficient for the excitation of the Alfvén gap modes. A particular case of the toroidal mode, observed during minor disruptions in Ohmic shots on SUNIST [Liu et al., Phys. Plasmas 23, 120706 (2016)], is considered in the present communication. Due to the negligible effect of the electron pressure gradient, the growth rate scales linearly with the drift speed, with slope inversely proportional to electron thermal velocity. In the absence of continuum damping, the threshold value of the drift speed for TAE excitation is independent of electron temperature.

Marchenko, V. S. (ORCID:0000000261480533)↗

An X-ray spectral model for clumpy tori in active galactic nuclei

We construct an X-ray spectral model for the clumpy torus in an active galactic nucleus (AGN) using Geant4, which includes the physical processes of the photoelectric effect, Compton scattering, Rayleigh scattering, γ conversion, fluorescence line, and Auger process. Since the electrons in the torus are expected to be bounded instead of free, the deviation of the scattering cross section from the Klein-Nishina cross section has also been included, which changes the X-ray spectra by up to 25% below 10 keV. We have investigated the effect of the clumpiness parameters on the reflection spectra and the strength of the fluorescent line Fe Kα. The volume filling factor of the clouds in the clumpy torus only slightly influences the reflection spectra, however, the total column density and the number of clouds along the line of sight significantly change the shapes and amplitudes of the reflection spectra. The effect of column density is similar to the case of a smooth torus, while a small number of clouds along the line of sight will smooth out the anisotropy of the reflection spectra and the fluorescent line Fe Kα. The smoothing effect is mild in the low column density case (N {sub H} = 10{sup 23} cm{sup –2}), whereas it is much more evident in the high column density case (N {sub H} = 10{sup 25} cm{sup –2}). Our model provides a quantitative tool for the spectral analysis of the clumpy torus. We suggest that the joint fits of the broad band spectral energy distributions of AGNs (from X-ray to infrared) should better constrain the structure of the torus.

79 ASTRONOMY AND ASTROPHYSICS↗

Formation of dark matter tori around supermassive black holes via the eccentric Kozai-Lidov mechanism

We explore the effects of long-term secular perturbations on the distribution of dark matter particles around supermassive black hole (BH) binaries. We show that in the hierarchical (in separation) three-body problem, one of the BHs and a dark matter particle form an inner binary. Gravitational perturbations from the BH companion, on a much wider orbit, can cause the dark matter particle to reach extremely high eccentricities and even get accreted onto the BH by what is known as the eccentric Kozai-Lidov (EKL) mechanism. We show that this may produce a torus-like configuration for the dark matter distribution around the less massive member of the BH binary. We first consider an intermediate BH (IMBH) in the vicinity of our galactic center, which may be a relic of a past minor merger. We show that if the IMBH is close enough (i.e., near the stellar disk) the EKL mechanism is very efficient in exciting the eccentricity of dark matter particles in near-polar configurations to extremely high values where they are accreted by the IMBH. We show that this mechanism is even more effective if the central BH grows in mass, where we have assumed adiabatic growth. Because near-polar configurations are disrupted, a torus-like shape is formed. We also show that this behavior is also likely to be relevant for supermassive BH binaries. We suggest that if the BHs are spinning, the accreted dark matter particles may linger in the ergosphere, and thereby generate self-annihilations and produce an indirect signature of potential interest.

79 ASTRONOMY AND ASTROPHYSICS↗

TRANSIT OF EXOMOON PLASMA TORI: NEW DIAGNOSIS

In the solar system, moons largely exceed planets in number. The Kepler database has been shown to be sensitive to exomoon detection down to the mass of Mars, but the first search has been unsuccessful. Here, we use a particles-in-cell code to predict the transit of the plasma torus produced by a satellite. Despite the small size of a moon, the spatial extent of its plasma torus can be large enough to produce substantial transit absorptions. The model is used for the interpretation of Hubble Space Telescope early ingress absorptions apparently observed during the WASP-12 b and HD 189733 b UV transits for which no consistent explanation exists. For HD 189733 b an exomoon transiting ∼16 R{sub p} ahead of the planet and loading ∼10{sup 29} C II ions s{sup –1} into space is required to explain the tentative early ingress absorption observed for C II. For WASP-12b, a moon transiting ∼6 R{sub p} ahead from the planet and ejecting ∼10{sup 28} Mg II ions per second is required to explain the NUV early ingress absorption feature. Interestingly, both HD 189733 b and WASP-12b predicted satellites are outside the Hill sphere of their planets, an indication that the moons, if present, were not formed in situ but probably captured later. Finally, our simulations show a strong electromagnetic coupling between the polar regions of planets and the orbital position of the moons, an expected outcome of the unipolar induction DC circuit model. Future observations should test our predictions with a potential opportunity to unambiguously detect the first exomoon plasma torus.

79 ASTRONOMY AND ASTROPHYSICS↗

AN X-RAY SPECTRAL MODEL OF REPROCESSING BY SMOOTH AND CLUMPY MOLECULAR TORI IN ACTIVE GALACTIC NUCLEI WITH THE MONACO FRAMEWORK

We construct an X-ray spectral model of reprocessing by a torus in an active galactic nucleus (AGN) with the Monte Carlo simulation framework MONACO. Two torus geometries of smooth and clumpy cases are considered and compared. In order to reproduce a Compton shoulder accurately, MONACO includes not only free electron scattering but also bound electron scattering. Raman and Rayleigh scattering are also treated, and scattering cross sections dependent on chemical states of hydrogen and helium are included. Doppler broadening by turbulence velocity can be implemented. Our model gives results consistent with other available models, such as MYTorus, except for differences due to different physical parameters and assumptions. We studied the dependence on torus parameters for a Compton shoulder, and found that a intensity ratio of a Compton shoulder to the line core mainly depends on column density, inclination angle, and metal abundance. For instance, an increase of metal abundance makes a Compton shoulder relatively weak. Also, the shape of a Compton shoulder depends on the column density. Furthermore, these dependences become different between smooth and clumpy cases. Then, we discuss the possibility of ASTRO-H/SXS spectroscopy of Compton shoulders in AGN reflection spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

Geometrically Thick Obscuration by Radiation-driven Outflow from Magnetized Tori of Active Galactic Nuclei

Near-Eddington radiation from active galactic nuclei (AGNs) has significant dynamical influence on the surrounding dusty gas, plausibly furnishing AGNs with geometrically thick obscuration. We investigate this paradigm with radiative magnetohydrodynamics simulations. The simulations solve the magnetohydrodynamics equations simultaneously with the infrared (IR) and ultraviolet (UV) radiative transfer (RT) equations; no approximate closure is used for RT. We find that our torus, when given a suitable sub-Keplerian angular momentum profile, spontaneously evolves toward a state in which its opening angle, density distribution, and flow pattern change only slowly. This “steady” state lasts for as long as there is gas resupply toward the inner edge. The torus is best described as a midplane inflow and a high-latitude outflow. The outflow is launched from the torus inner edge by UV radiation and expands in solid angle as it ascends; IR radiation continues to drive the wide-angle outflow outside the central hole. The dusty outflow obscures the central source in soft X-rays, the IR, and the UV over three-quarters of solid angle, and each decade in column density covers roughly equal solid angle around the central source; these obscuration properties are similar to what observations imply.

79 ASTRONOMY AND ASTROPHYSICS↗

Cooling Timescale of Dust Tori in Dying Active Galactic Nuclei

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 {sub 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 μ m 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 μ m band luminosity tracing AGN torus ( R ∼ 10 pc) and the optical [O iii] λ 5007 emission line tracing narrow line regions ( R = 10{sup 2–4} pc).

79 ASTRONOMY AND ASTROPHYSICS↗