Symmetry-preserving discrete schemes for some heat transfer equations

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modeling helps to retain qualitative properties of the differential equations in their difference counterparts.Comment: 21 pages, 4 ps figure

A heat transfer with a source: the complete set of invariant difference schemes

In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where a few invariant models for heat transfer equations were presented.Comment: arxiv version is already officia

Active galaxy unification in the era of X-ray polarimetry

Active Galactic Nuclei (AGN), Seyfert galaxies and quasars, are powered by luminous accretion and often accompanied by winds which are powerful enough to affect the AGN mass budget, and whose observational appearance bears an imprint of processes which are happening within the central parsec around the black hole (BH). One example of such a wind is the partially ionized gas responsible for X-ray and UV absorption ('warm absorbers'). Here we show that such gas will have a distinct signature when viewed in polarized X-rays. Observations of such polarization can test models for the geometry of the flow, and the gas responsible for launching and collimating it. We present calculations which show that the polarization depends on the hydrodynamics of the flow, the quantum mechanics of resonance line scattering and the transfer of polarized X-ray light in the highly ionized moving gas. The results emphasize the three dimensional nature of the wind for modeling spectra. We show that the polarization in the 0.1-10 keV energy range is dominated by the effects of resonance lines. We predict a $5-25$ X-ray polarization signature of type-2 objects in this energy range. These results are general to flows which originate from a cold torus-like structure, located $\sim 1$pc from the BH, which wraps the BH and is ultimately responsible for the apparent dichotomy between type 1 and type 2 AGNs. Such signals will be detectable by future dedicated X-ray polarimetry space missions, such as the NASA Gravity and Extreme Magnetism SMEX, GEMS.Comment: 13 pages, 4 figures, ApJ Letters accepted for publicatio

AGN Torus Threaded by Large Scale Magnetic Field

Large scale magnetic eld can be easily dragged from galactic scales towards AGN alongwith accreting gas. There, it can contribute to both the formation of AGN "torus" and help to remove angular momentum from the gas which fuels AGN accretion disk. Howeverthe dynamics of such gas is also strongly inuenced by the radiative feedback from theinner accretion disk. Here we present results from the three-dimensional simulations ofpc-scale accretion which is exposed to intense X-ray heating

An axisymmetric, hydrodynamical model for the torus wind in AGN

We report on time-dependent axisymmetric simulations of an X-ray excited flow from a parsec-scale, rotating, cold torus around an active galactic nucleus. Our simulations account for radiative heating and cooling and radiation pressure force. The simulations follow the development of a broad bi-conical outflow induced mainly by X-ray heating. We compute synthetic spectra predicted by our simulations. The wind characteristics and the spectra support the hypothesis that a rotationally supported torus can serve as the source of a wind which is responsible for the warm absorber gas observed in the X-ray spectra of many Seyfert galaxies.Comment: ApJ Letters, accepted for publicatio

An axisymmetric hydrodynamical model for the torus wind in AGN. III: Spectra from 3D radiation transfer calculations

We calculate a series of synthetic X-ray spectra from outflows originating from the obscuring torus in active galactic nuclei (AGN). Such modeling includes 2.5D hydrodynamical simulations of an X-ray excited torus wind, including the effects of X-ray heating, ionization, and radiation pressure. 3D radiation transfer calculations are performed in the 3D Sobolev approximation. Synthetic X-ray line spectra and individual profiles of several strong lines are shown at different inclination angles, observing times, and for different characteristics of the torus. Our calculations show that rich synthetic warm absorber spectra from 3D modeling are typically observed at a larger range of inclinations than was previously inferred from simple analysis of the transmitted spectra. In general, our results are supportive of warm absorber models based on the hypothesis of an "X-ray excited funnel flow" and are consistent with characteristics of such flows inferred from observations of warm absorbers from Seyfert 1 galaxies.Comment: 31 pages, 10 figure

Lie point symmetries of difference equations and lattices

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations