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.
A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). CFHTLenS comprises 154 sq deg of multicolour optical data
from the CFHT Legacy Survey, with lensing measurements being made in the i band to a depth i(AB)<24.7, for galaxies with signal-to-noise ratio greater than about 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The method creates pixel-based models of the varying point spread function (PSF) in individual image exposures. It fits PSF-convolved two-component (disk plus bulge) models, to measure the ellipticity of each galaxy, with bayesian marginalisation over model nuisance parameters of galaxy position, size, brightness and bulge fraction. The method allows optimal joint measurement of multiple, dithered image exposures, taking into account imaging distortion and the alignment of the multiple measurements. We discuss the effects of noise bias on the likelihood distribution of galaxy ellipticity. Two sets of image simulations that mirror the observed properties of CFHTLenS have been created, to establish the methods accuracy and to derive an empirical correction for the effects of noise bias.
We give sufficient conditions for F-injectivity to deform. We show these conditions are met in two common geometrically interesting setting, namely when the special fiber has isolated CM-locus or is F-split.
Let k be an arbitrary field (of arbitrary characteristic) and let X = [x_{i,j}] be a generic m x n matrix of variables. Denote by I_2(X) the ideal in k[X] = k[x_{i,j}: i = 1, ..., m; j = 1, ..., n] generated by the 2 x 2 minors of X. We give a recurs
ive formulation for the lengths of the k[X]-module k[X]/(I_2(X) + (x_{1,1}^q,..., x_{m,n}^q)) as q varies over all positive integers using Grobner basis. This is a generalized Hilbert-Kunz function, and our formulation proves that it is a polynomial function in q. We give closed forms for the cases when m is at most 2, %as well as the closed forms for some other special length functions. We apply our method to give closed forms for these Hilbert-Kunz functions for cases $m le 2$.
The ring of classic Witt vectors is a fundamental object in mixed characteristic commutative algebra which has many applications in number theory. There is a significant generalization due to Dress and Siebeneicher which for any profinite group G pro
duces a ring valued functor W_G, where the classic Witt vectors are recovered as the example G = Z_p. This article explores the structure of the image of this functor where G is the pro-2 group formed by taking the inverse limit of 2-power dihedral groups, and the image of W_G is taken on a field of characteristic 2.
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. Narr
ow-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.
The narrow-line Seyfert 1 galaxy 1H0707-495 has previously been identified as showing time lags between flux variations in the soft- (0.3-1 keV) and medium-energy (1-4 keV) X-ray bands that oscillate between positive and negative values as a function
of the frequency of the mode of variation. Here we measure and analyse the lags also between a harder X-ray band (4-7.5 keV) and the soft and medium bands, using existing XMM-Newton data, and demonstrate that the entire spectrum of lags, considering both the full energy range, 0.3-7.5 keV, and the full frequency range, 10^-5 < nu < 10^-2 Hz, are inconsistent with previous claims of arising as reverberation associated with the inner accretion disk. Instead we demonstrate that a simple reverberation model, in which scattering or reflection is present in all X-ray bands, explains the full set of lags without requiring any ad hoc explanation for the time lag sign changes. The range of time delays required to explain the observed lags extends up to about 1800 s in the hard band. The results are consistent with reverberation caused by scattering of X-rays passing through an absorbing medium whose opacity decreases with increasing energy and that partially-covers the source. A high covering factor of absorbing and scattering circumnuclear material is inferred.
