Numerical studies of baroclinic instability at small Richardson number

Baroclinic instability at small Richardson number consists of competition between symmetric (Solberg) modes, zonal (Eady) modes, and possibly other modes whose orientation is neither symmetric nor zonal. In FY-84, a study of the fully nonlinear development and energetics of the symmetric modes was completed. The nonlinear effects were quite strong and, in some senses, unexpected. Secondly, a study of the dependency of the energetics of the symmetric modes upon the physical parameters was completed

A preliminary study of numerical simulation of thermosolutal convection of interest to crystal growth

Calculations were performed with computer models using three types of finite difference methods of thermosolutal convection: horizontal heating of a container filled with a stably stratified solution, finger convection in a container, and finger convection in a horizontally infinite channel. The importance of including thermosolutal convection in models of crystal growth is emphasized, and the difficulties in doing so are demonstrated. It is pointed out that these difficulties, due primarily to the fine structure of the convection, may be partly overcome by the use of fine grids and implicit time stepping methods

X-ray reverberation in NLS1

Reverberation from scattering material around the black hole in active galactic nuclei is expected to produce a characteristic signature in a Fourier analysis of the time delays between directly-viewed continuum emission and the scattered light. Narrow-line Seyfert 1 galaxies (NLS1) are highly variable at X-ray energies, and are ideal candidates for the detection of X-ray reverberation. We show new analysis of a small sample of NLS1 that clearly shows the expected time-delay signature, providing strong evidence for the existence of a high covering fraction of scattering and absorbing material a few tens to hundreds of gravitational radii from the black hole. We also show that an alternative interpretation of time delays in the NLS1 1H0707-495, as arising about one gravitational radius from the black hole, is strongly disfavoured in an analysis of the energy-dependence of the time delays.Comment: Published online in Proceedings of Science, "Narrow-line Seyfert 1 Galaxies and their place in the Universe", held in Milan, Italy April 4-6, 201

The hard X-ray spectrum of NGC 1365: scattered light, not black hole spin

Active Galactic Nuclei (AGN) show excess X-ray emission above 10 keV compared with extrapolation of spectra from lower energies. Risaliti et al. have recently attempted to model the hard X-ray excess in the type 1.8 AGN NGC 1365, concluding that the hard excess most likely arises from Compton-scattered reflection of X-rays from an inner accretion disk close to the black hole. Their analysis disfavored a model in which the hard excess arises from a high column density of circumnuclear gas partially covering a primary X-ray source, despite such components being required in the NGC 1365 data below 10 keV. Using a Monte Carlo radiative transfer approach, we demonstrate that this conclusion is invalidated by (i) use of slab absorption models, which have unrealistic transmission spectra for partial covering gas, (ii) neglect of the effect of Compton scattering on transmitted spectra and (iii) inadequate modeling of the spectrum of scattered X-rays. The scattered spectrum is geometry dependent and, for high global covering factors, may dominate above 10 keV. We further show that, in models of circumnuclear gas, the suppression of the observed hard X-ray flux by reprocessing may be no larger than required by the `light bending' model invoked for inner disk reflection, and the expected emission line strengths lie within the observed range. We conclude that the time-invariant `red wing' in AGN X-ray spectra is probably caused by continuum transmitted through and scattered from circumnuclear gas, not by highly redshifted line emission, and that measurement of black hole spin is not possible.Comment: Revised version, accepted for publication by Ap.J. Letter

Laboratory studies of baroclinic instability at small Richardson number

As part of the support program for the Atmospheric General Circulation Experiment, laboratory studies of baroclinic and other convective instabilities were performed for a thin layer of fluid between thermally conducting horizontal discs. There were three types of modes identified. The first has a spiral-arm appearance, and exists for large enough horizontal thermal forcing, weak enough static stability, and large enough rotation. The source of this wave is shown to be the Eady mode of instability. The second mode is due to convective instability in the thermal boundary layers which exist due to the thermally conducting horizontal boundaries. Finally, for strong enough negative static stability, thermal convection of the Benard type appears. The most significant result is that the symmetric (Solberg) mode was not found, even though the infinite-plane theory predicts this mode under certain experimental conditions

X-ray Signatures of Circumnuclear Gas in AGN

X-ray spectra of AGN are complex. X-ray absorption and emission features trace gas covering a wide range of column densities and ionization states. High resolution spectra show the absorbing gas to be outflowing, perhaps in the form of an accretion disk wind. The absorbing complex shapes the form of the X-ray spectrum while X-ray reverberation and absorption changes explain the spectral and timing behaviour of AGN. We discuss recent progress, highlighting some new results and reviewing the implications that can be drawn from the data.Comment: Proceedings of the conference "Suzaku 2011, Exploring the X-ray Universe: Suzaku and Beyond

Geometry and General Relativity in the Groupoid Model with a Finite Structure Group

In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation groupoid $\Gamma$ determined by the action of the Lorentz group on the frame bundle $(E, \pi_M, M)$ over space-time $M$. In the present work, we construct a simplified version of the gravitational sector of this model in which the Lorentz group is replaced by a finite group $G$ and the frame bundle is trivial $E=M\times G$. The model is fully computable. We define the Einstein-Hilbert action, with the help of which we derive the generalized vacuum Einstein equations. When the equations are projected to space-time (giving the "general relativistic limit"), the extra terms that appear due to our generalization can be interpreted as "matter terms", as in Kaluza-Klein-type models. To illustrate this effect we further simplify the metric matrix to a block diagonal form, compute for it the generalized Einstein equations and find two of their "Friedmann-like" solutions for the special case when $G =\mathbb{Z}_2$. One of them gives the flat Minkowski space-time (which, however, is not static), another, a hyperbolic, linearly expanding universe.Comment: 32 page

Models of q-algebra representations: Matrix elements of the q-oscillator algebra

This article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. This ``local'' approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ``group operator'' (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the Bargmann–Segal Hilbert space of entire functions