Particle Acceleration in Advection-Dominated Accretion Disks with Shocks: Green's Function Energy Distribution

The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally-supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.Comment: Published in Ap

Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U_(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur

Far-Infrared Spectral Energy Distributions and Photometric Redshifts of Dusty Galaxies

We infer the large-scale source parameters of dusty galaxies from their observed spectral energy distributions (SEDs) using the analytic radiative transfer methodology presented in Chakrabarti & McKee (2005). For local ultra-luminous infrared galaxies (ULIRGs), we show that the millimeter to far-infrared (FIR) SEDs can be well fit using the standard dust opacity index of 2 when self-consistent radiative transfer solutions are employed, indicating that the cold dust in local ULIRGs can be described by a single grain model. We develop a method for determining photometric redshifts of ULIRGs and sub-mm galaxies from the millimeter-FIR SED; the resulting value of $1+z$ is typically accurate to about 10%. As such, it is comparable to the accuracy of near-IR photometric redshifts and provides a complementary means of deriving redshifts from far-IR data, such as that from the upcoming $\it{Herschel Space Observatory}$. Since our analytic radiative transfer solution is developed for homogeneous, spherically symmetric, centrally heated, dusty sources, it is relevant for infrared bright galaxies that are primarily powered by compact sources of luminosity that are embedded in a dusty envelope. We discuss how deviations from spherical symmetry may affect the applicability of our solution, and we contrast our self-consistent analytic solution with standard approximations to demonstrate the main differences.Comment: 37 pages, 14 Figures, 3 Tables, submitted to ApJ. submitted to Ap

Satellite observations of thought experiments close to a black hole

Since black holes are `black', methods of their identification must necessarily be indirect. Due to very special boundary condition on the horizon, the advective flow behaves in a particular way, which includes formation of centrifugal pressure dominated boundary layer or CENBOL where much of the infall energy is released and outflows are generated. The observational aspects of black holes must depend on the steady and time-dependent properties of this boundary layer. Several observational results are written down in this review which seem to support the predictions of thought experiments based on this advective accretion/outflow model. In future, when gravitational waves are detected, some other predictions of this model could be tested as well.Comment: Published in Classical and Quantum Gravity, v. 17, No. 12, p. 2427, 200

Decompositions of Triangle-Dense Graphs

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, radius 2 subgraphs. This result quantifies the extent to which triangle-dense graphs resemble unions of cliques. We also show that our algorithm recovers planted clusterings in approximation-stable k-median instances.Comment: 20 pages. Version 1->2: Minor edits. 2->3: Strengthened {\S}3.5, removed appendi

Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.Comment: Revtex4, 10 pages including 10 figures; corrected a sign error in Eq. 32; this is the final published versio

Particle Acceleration and the Production of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

Relativistic outflows (jets) of matter are commonly observed from systems containing black holes. The strongest outflows occur in the radio-loud systems, in which the accretion disk is likely to have an advection-dominated structure. In these systems, it is clear that the binding energy of the accreting gas is emitted primarily in the form of particles rather than radiation. However, no comprehensive model for the disk structure and the associated outflows has yet been produced. In particular, none of the existing models establishes a direct physical connection between the presence of the outflows and the action of a microphysical acceleration mechanism operating in the disk. In this paper we explore the possibility that the relativistic protons powering the jet are accelerated at a standing, centrifugally-supported shock in the underlying accretion disk via the first-order Fermi mechanism. The theoretical analysis employed here parallels the early studies of cosmic-ray acceleration in supernova shock waves, and the particle acceleration and disk structure are treated in a coupled, self-consistent manner based on a rigorous mathematical approach. We find that first-order Fermi acceleration at standing shocks in advection-dominated disks proves to be a very efficient means for accelerating the jet particles. Using physical parameters appropriate for M87 and SgrA*, we verify that the jet kinetic luminosities computed using our model agree with estimates based on observations of the sources.Comment: accepted for publication in the Astrophysical Journa

Finite energy/action solutions of p1p_1 Yang-Mills equations on p2p_2 Schwarzschild and deSitter backgrounds for dimension d≥4d \ge 4

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by $p_1$, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by $p_2$. In this paper, we study the classical equations of the $p_1 = 1,2$ YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter,anti-deSitter) of the $p_2=1,2,3$ EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When $p_1=p_2$ self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the non-self-dual solutions.Comment: LaTeX, 25 pages, 2 figures, new title, minor change

Temperature Effects on the Kinetics of Ferrocene and Cobaltocenium in Methyltriphenylphosphonium Bromide Based Deep Eutectic Solvents

The oxidation of ferrocene (Fc/Fc+) and reduction of cobaltocenium (Cc+/Cc) under different temperatures has been studied by cyclic voltammetry and double potential step chronoamperometry in deep eutectic solvents (DESs) consisting of methyltriphenylphosphonium bromide salt with tri-ethylene glycol, glycerol or ethylene glycol as hydrogen bond donors. The temperature dependence of the measured physical properties of DESs (such as viscosity and conductivity) is discussed in detail. The kinetics of the redox couples are studied using cyclic voltammetry, and the standard heterogeneous electron transfer rate constant, k0 is found to be of the order of 10−5 to 10−4 cms−1 at different temperatures. The diffusion coefficient, D, of Fc and Cc+ is determined to lie between 8.28 × 10−10 to 6.65 × 10−9 cm2 s−1. These results show that both k0 and D increase with temperature in the studied DESs. In addition, better kinetic parameters for the DES with ethylene glycol as hydrogen bond donor means that this could be evaluated favorably as both solvents and electrolytes for redox flow cells

Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses

Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that bond-dilution enables the numerical treatment of larger lattices, and that the subsequent combination of such data at various bond densities into a finite-size scaling Ansatz produces more robust scaling behavior. In the present study we test the potential of such a procedure, in particular, to obtain the stiffness exponent for the hierarchical Migdal-Kadanoff lattice. Critical exponents for this model are known with great accuracy and any simulations can be executed to very large lattice sizes at almost any bond density, effecting a insightful comparison that highlights the advantages -- as well as the weaknesses -- of this method. These insights are applied to the Edwards-Anderson model in $d=3$ with Gaussian bonds.Comment: corrected version, 10 pages, RevTex4, 12 ps-figures included; related papers available a http://www.physics.emory.edu/faculty/boettcher