Quantum Integrals of Motion for the Heisenberg Spin Chain

An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferrromagnetic and antiferromagnetic sectors are briefly discussed.Comment: 10 pages Report #: LAVAL-PHY-94-2

The evolution of active galactic nuclei and their spins

Massive black holes (MBHs) in contrast to stellar mass black holes are expected to substantially change their properties over their lifetime. MBH masses increase by several order of magnitude over the Hubble time, as illustrated by Soltan's argument. MBH spins also must evolve through the series of accretion and mergers events that grow the MBH's masses. We present a simple model that traces the joint evolution of MBH masses and spins across cosmic time. Our model includes MBH-MBH mergers, merger-driven gas accretion, stochastic fueling of MBHs through molecular cloud capture, and a basic implementation of accretion of recycled gas. This approach aims at improving the modeling of low-redshift MBHs and AGN, whose properties can be more easily estimated observationally. Despite the simplicity of the model, it captures well the global evolution of the MBH population from z\sim6 to today. Under our assumptions, we find that the typical spin and radiative efficiency of MBHs decrease with cosmic time because of the higher incidence of stochastic processes in gas-rich galaxies and MBH-MBH mergers in gas-poor galaxies. At z=0 the spin distribution in gas-poor galaxies peaks at spins 0.4-0.8, and it is not strongly mass dependent. MBHs in gas-rich galaxies have a more complex evolution, with low-mass MBHs at low redshift having low spins, and spins increasing at larger masses and redshifts. We also find that at z>1 MBH spins are on average highest in high luminosity AGN, while at lower redshifts these differences disappear.Comment: ApJ, in pres

Limits on thickness and efficiency of Polish doughnuts in application to the ULX sources

Polish doughnuts (PDs) are geometrically thick disks that rotate with super-Keplerian velocities in their innermost parts, and whose long and narrow funnels along rotation axes collimate the emerging radiation into beams. In this paper we construct an extremal family of PDs that maximize both geometrical thickness and radiative efficiency. We then derive upper limits for these quantities and subsequently for the related ability to collimate radiation. PDs with such extreme properties may explain the observed properties of the ultraluminous X-ray sources without the need for the black hole masses to exceed ~ 10 solar masses. However, we show that strong advective cooling, which is expected to be one of the dominant cooling mechanisms in accretion flows with super-Eddington accretion rates, tends to reduce the geometrical thickness and luminosity of PDs substantially. We also show that the beamed radiation emerging from the PD funnels corresponds to "isotropic" luminosities that linearly scale with the mass accretion rate, and do not obey the familiar and well-known logarithmic relation.Comment: 7 pages, 8 figure

Are Quasar Jets Matter or Poynting Flux Dominated?

If quasar jets are accelerated by magnetic fields but terminate as matter dominated, where and how does the transition occur between the Poynting-dominated and matter-dominated regimes? To address this question, we study constraints which are imposed on the jet structure by observations at different spatial scales. We demonstrate that observational data are consistent with a scenario where the acceleration of a jet occurs within 10^{3-4} R_g. In this picture, the non-thermal flares -- important defining attributes of the blazar phenomenon - are produced by strong shocks formed in the region where the jet inertia becomes dominated by matter. Such shocks may be formed due to collisions between the portions of a jet accelerated to different velocities, and the acceleration differentiation is very likely to be related to global MHD instabilities.Comment: to appear in "Astrophysical Sources of High Energy Particles and Radiation", AIP Proceedings Series, eds. T. Bulik, G. Madejski, and B. Rudak (20-24 June 2005, Torun, Poland

Relativistic slim disks with vertical structure

We report on a scheme for incorporating vertical radiative energy transport into a fully relativistic, Kerr-metric model of optically thick, advective, transonic alpha disks. Our code couples the radial and vertical equations of the accretion disk. The flux was computed in the diffusion approximation, and convection is included in the mixing-length approximation. We present the detailed structure of this "two-dimensional" slim-disk model for alpha=0.01. We then calculated the emergent spectra integrated over the disk surface. The values of surface density, radial velocity, and the photospheric height for these models differ by 20%-30% from those obtained in the polytropic, height-averaged slim disk model considered previously. However, the emission profiles and the resulting spectra are quite similar for both types of models. The effective optical depth of the slim disk becomes lower than unity for high values of the alpha parameter and for high accretion rates.Comment: 15 pages, 18 figures (2 new), A&A in pres

No observational proof of the black-hole event-horizon

Recently, several ways of obtaining observational proof of the existence of black-hole horizons have been proposed. We argue here that such proof is fundamentally impossible: observations can provide arguments, sometimes very strong ones, in favour of the existence of the event horizon, but they cannot prove it. This applies also to future observations, which will trace very accurately the details of the spacetime metric of a body suspected of being a black hole.Comment: 4 pages, no figures, submitted to A&A Letter

Hyperbolic generalized triangle groups, property (T) and finite simple quotients

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan\u27s property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Kazhdan groups possess finite simple quotient groups of arbitrarily large rank; they constitute the first-known specimens combining those properties. All the hyperbolic groups we consider are non-positively curved k-fold generalized triangle groups, that is, groups that possess a simplicial action on a CAT(0) triangle complex, which is sharply transitive on the set of triangles, and such that edge-stabilizers are cyclic of order k