Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.Comment: 17 pages, 10 figures, uses RevTeX

Integrable vortex-type equations on the two-sphere

We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential, we reduce the instanton equations on S^2xSigma to vortex-type equations on the sphere S^2. It is shown that when the scalar curvature of the manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can be obtained as compatibility conditions of two linear equations (Lax pair) which are written down explicitly. Thus, the standard methods of integrable systems can be applied for constructing their solutions. However, even if the scalar curvature of S^2xSigma does not vanish, the vortex equations are well defined and have solutions for any values of the topological charge N. We show that any solution to the vortex equations on S^2 with a fixed topological charge N corresponds to a Yang-Mills instanton on S^2xSigma of charge (g-1)N.Comment: 14 pages; v2: clarifying comments added, published versio

Casimir Force at a Knife's Edge

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.Comment: 5 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no changes to results); v4: fix similar factor in Eq. (16) (again no changes to results

One-zone models for spheroidal galaxies with a central supermassive black-hole. Self-regulated Bondi accretion

By means of a one-zone evolutionary model, we study the co-evolution of supermassive black holes and their host galaxies, as a function of the accretion radiative efficiency, dark matter content, and cosmological infall of gas. In particular, the radiation feedback is computed by using the self-regulated Bondi accretion. The models are characterized by strong oscillations when the galaxy is in the AGN state with a high accretion luminosity. We found that these one-zone models are able to reproduce two important phases of galaxy evolution, namely an obscured-cold phase when the bulk of star formation and black hole accretion occur, and the following quiescent hot phase in which accretion remains highly sub-Eddington. A Compton-thick phase is also found in almost all models, associated with the cold phase. An exploration of the parameter space reveals that the closest agreement with the present-day Magorrian relation is obtained, independently of the dark matter halo mass, for galaxies with a low-mass seed black hole, and the accretion radiative efficiency ~0.1.Comment: Accepted for publication in A&A, 12 pages, 5 figure

A multifrequency study of giant radio sources-II. Spectral ageing analysis of the lobes of selected sources

Multifrequency observations with the GMRT and the VLA are used to determine the spectral breaks in consecutive strips along the lobes of a sample of selected giant radio sources (GRSs) in order to estimate their spectral ages. The maximum spectral ages estimated for the detected radio emission in the lobes of our sources range from $\sim$6 to 36 Myr with a median value of $\sim$20 Myr using the classical equipartition fields. Using the magnetic field estimates from the Beck & Krause formalism the spectral ages range from $\sim$5 to 38 Myr with a median value of $\sim$22 Myr. These ages are significantly older than smaller sources. In all but one source (J1313+6937) the spectral age gradually increases with distance from the hotspot regions, confirming that acceleration of the particles mainly occurs in the hotspots. Most of the GRSs do not exhibit zero spectral ages in the hotspots, as is the case in earlier studies of smaller sources. This is likely to be largely due to contamination by more extended emission due to relatively modest resolutions. The injection spectral indices range from $\sim$0.55 to 0.88 with a median value of $\sim$0.6. We discuss these values in the light of theoretical expectations, and show that the injection spectral index appears to be correlated with luminosity and/or redshift as well as with linear size.Comment: 12 Pages, 13 Figures, 9 Tables, Accepted for publication in MNRA

Lambda Polarization in Polarized Proton-Proton Collisions at RHIC

We discuss Lambda polarization in semi-inclusive proton-proton collisions, with one of the protons longitudinally polarized. The hyperfine interaction responsible for the $\Delta$-$N$ and $\Sigma$-$\Lambda$ mass splittings gives rise to flavor asymmetric fragmentation functions and to sizable polarized non-strange fragmentation functions. We predict large positive Lambda polarization in polarized proton-proton collisions at large rapidities of the produced Lambda, while other models, based on SU(3) flavor symmetric fragmentation functions, predict zero or negative Lambda polarization. The effect of $\Sigma^0$ and $\Sigma^*$ decays is also discussed. Forthcoming experiments at RHIC will be able to differentiate between these predictions.Comment: 18 pages, 5 figure

Canonical Particle Acceleration in FRI Radio Galaxies

Matched resolution multi-frequency VLA observations of four radio galaxies are used to derive the asymptotic low energy slope of the relativistic electron distribution. Where available, low energy slopes are also determined for other sources in the literature. They provide information on the acceleration physics independent of radiative and other losses, which confuse measurements of the synchrotron spectra in most radio, optical and X-ray studies. We find a narrow range of inferred low energy electron energy slopes, n(E)=const*E^-2.1 for the currently small sample of lower luminosity sources classified as FRI (not classical doubles). This distribution is close to, but apparently inconsistent with, the test particle limit of n(E)=const*E^-2.0 expected from strong diffusive shock acceleration in the non-relativistic limit. Relativistic shocks or those modified by the back-pressure of efficiently accelerated cosmic rays are two alternatives to produce somewhat steeper spectra. We note for further study the possiblity of acceleration through shocks, turbulence or shear in the flaring/brightening regions in FRI jets as they move away from the nucleus. Jets on pc scales and the collimated jets and hot spots of FRII (classical double) sources would be governed by different acceleration sites and mechanisms; they appear to show a much wider range of spectra than for FRI sources.Comment: 16 figures, including 5 color. Accepted to Astrophysical Journa

Structure and Production of Lambda Baryons

We discuss the quark parton structure of the $\Lambda$ baryon and the fragmentation of quarks into $\Lambda$ baryons. We show that the hyperfine interaction, responsible for the $\Delta$-$N$ and $\Sigma^0$-$\Lambda$ mass splittings, leads not only to sizeable SU(3) and SU(6) symmetry breaking in the quark distributions of the $\Lambda$, but also to significant polarized non-strange quark distributions. The same arguments suggest flavor asymmetric quark fragmentation functions and non-zero polarized non-strange quark fragmentation functions. The calculated fragmentation functions give a good description of all measured observables. We predict significant positive $\Lambda$ polarization in semi-inclusive DIS experiments while models based on SU(3) flavor symmetry predict zero or negative $\Lambda$ polarization. Our approach also provides a natural explanation for the dependence of the maximum of the $\xi=\ln(1/z)$ spectrum on the mass of the particles produced in $e^+e^-$ annihilation.Comment: 24 pages, 9 figures, minor change

The spectra and energies of classical double radio lobes

We compare two temporal properties of classical double radio sources: i) radiative lifetimes of synchrotron-emitting particles and ii) dynamical source ages. We discuss how these can be quite discrepant from one another, rendering use of the traditional spectral ageing method inappropriate: we contend that spectral ages give meaningful estimates of dynamical ages only when these ages are << 10^7 years. In juxtaposing the fleeting radiative lifetimes with source ages which are significantly longer, a refinement of the paradigm for radio source evolution is required. The changing spectra along lobes are explained, not predominantly by synchrotron ageing but, by gentle gradients in a magnetic field mediated by a low-gamma matrix which illuminates an energy-distribution of particles, controlled largely by classical synchrotron loss in the high magnetic field of the hotspot. The energy in the particles is an order of magnitude higher than that inferred from the minimum-energy estimate, implying that the jet-power is of the same order as the accretion luminosity produced by the quasar central engine. This refined paradigm points to a resolution of the findings of Rudnick et al (1994) and Katz-Stone & Rudnick (1994) that both the Jaffe-Perola and Kardashev-Pacholczyk model spectra are invariably poor descriptions of the curved spectral shape of lobe emission, and indeed that for Cygnus A all regions of the lobes are characterised by a `universal spectrum'. [abridged]Comment: LaTeX, 4 figures. To appear in A