Free analysis and planar algebras

We study 2-cabled analogs of Voiculescu's trace and free Gibbs states on Jones planar algebras. These states are traces on a tower of graded algebras associated to a Jones planar algebra. Among our results is that, with a suitable definition, finiteness of free Fisher information for planar algebra traces implies that the associated tower of von Neumann algebras consists of factors, and that the standard invariant of the associated inclusion is exactly the original planar algebra. We also give conditions that imply that the associated von Neumann algebras are non-$\Gamma$ non-$L^2$ rigid factors

Reflected Iron Line From a Source Above a Kerr Black Hole Accretion Disc

In this paper we present a fully relativistic approach to modelling both the continuum emission and the reflected fluorescent iron line from a primary X-ray source near a Kerr black hole. The X-ray source is located above an accretion disc orbiting around the black hole. The source is assumed to be a static point source located on an arbitrary position above the disc, on or off the axis of rotation. We carry out Monte Carlo simulations in order to estimate the iron line spectrum as well as its equivalent width. Because of the gravitational lensing effect, an enhancement of the iron line is expected when the primary source is located close to the central black hole. We find that for a source located on the axis of rotation the enhancement is relatively modest. An observer at inclination 30 degrees would measure an equivalent width of ~300eV in the extreme case of a maximally rotating black hole and a source located at height 1.5 gravitational radius from the centre. This corresponds to an equivalent width enhancement factor of about 2 compared to the classical value where no lensing effect comes into play. However, when allowing the source to be located off the axis of rotation, much stronger enhancement can be obtained. In the extreme case of a maximally rotating black hole and a source located just above the approaching side of the disc, an observer at inclination 30d egrees could measure an equivalent width as high as ~1.5 keV (i.e. ~10 times the classical value). We also find that observers located at high inclination angles observe a stronger line than observers at low inclination angles.Comment: 11 pages, 13 figures. Submitted to Monthly Notices of the Royal Astronomical Society (MNRAS

Molecular Hydrogen Emission Lines in Far Ultraviolet Spectroscopic Explorer Observations of Mira B

We present new Far Ultraviolet Spectroscopic Explorer (FUSE) observations of Mira A's wind-accreting companion star, Mira B. We find that the strongest lines in the FUSE spectrum are H2 lines fluoresced by H I Lyman-alpha. A previously analyzed Hubble Space Telescope (HST) spectrum also shows numerous Lyman-alpha fluoresced H2 lines. The HST lines are all Lyman band lines, while the FUSE H2 lines are mostly Werner band lines, many of them never before identified in an astrophysical spectrum. We combine the FUSE and HST data to refine estimates of the physical properties of the emitting H2 gas. We find that the emission can be reproduced by an H2 layer with a temperature and column density of T=3900 K and log N(H2)=17.1, respectively. Another similarity between the HST and FUSE data, besides the prevalence of H2 emission, is the surprising weakness of the continuum and high temperature emission lines, suggesting that accretion onto Mira B has weakened dramatically. The UV fluxes observed by HST on 1999 August 2 were previously reported to be over an order of magnitude lower than those observed by HST and the International Ultraviolet Explorer (IUE) from 1979--1995. Analysis of the FUSE data reveals that Mira B was still in a similarly low state on 2001 November 22.Comment: 23 pages, 6 figures; AASTEX v5.0 plus EPSF extensions in mkfig.sty; accepted by Ap

Structural response to O*-O' and magnetic transitions in orthorhombic perovskites

We present a temperature dependent single crystal x-ray diffraction study of twinned orthorhombic perovskites La1-xCaxMnO3, for x=0.16 and x=0.25. These data show the evolution of the crystal structure from the ferromagnetic insulating state to the ferromagnetic metallic state. The data are modelled in space group Pnma with twin relations based on a distribution of the b axis over three perpendicular cubic axes. The twin model allows full structure determination in the presence of up to six twin fractions using the single crystal x-ray diffraction data.Comment: 13 pages, including 13 figures and 2 table

Magnetic Stress at the Marginally Stable Orbit: Altered Disk Structure, Radiation, and Black Hole Spin Evolution

Magnetic connections to the plunging region can exert stresses on the inner edge of an accretion disk around a black hole. We recompute the relativistic corrections to the thin-disk dynamics equations when these stresses take the form of a time-steady torque on the inner edge of the disk. The additional dissipation associated with these stresses is concentrated relatively close outside the marginally stable orbit, scaling as r to the -7/2 at large radius. As a result of these additional stresses: spin-up of the central black hole is retarded; the maximum spin-equilibrium accretion efficiency is 36%, and occurs at a/M=0.94; the disk spectrum is extended toward higher frequencies; line profiles (such as Fe K-alpha) are broadened if the line emissivity scales with local flux; limb-brightening, especially at the higher frequencies, is enhanced; and the returning radiation fraction is substantially increased, up to 58%. This last effect creates possible explanations for both synchronized continuum fluctuations in AGN, and polarization rises shortward of the Lyman edge in quasars. We show that no matter what additional stresses occur, when a/M < 0.36, the second law of black hole dynamics sets an absolute upper bound on the accretion efficiency.Comment: 11 pages, 15 figures, accepted for publication in the Astrophysical Journa

Suppression of Magnetic Phase Separation in Epitaxial SrCoOx Films

Using pulsed laser deposition and a unique fast quenching method, we have prepared SrCoOx epitaxial films on SiTiO3 substrates. As electrochemical oxidation increases the oxygen content from x = 2.75 to 3.0, the films tend to favor the discrete magnetic phases seen in bulk samples for the homologous series SrCoO(3-n/8) (n = 0, 1, 2). Unlike bulk samples, 200nm thick films remain single phase throughout the oxidation cycle. 300 nm films can show two simultaneous phases during deoxidation. These results are attributed to finite thickness effects and imply the formation of ordered regions larger than approximately 300 nm.Comment: The following article has been submitted to Applied Physics Letters. After it is published, it will be found at http://apl.aip.or

Logarithmic Moduli Spaces for Surfaces of Class VII

In this paper we describe logarithmic moduli spaces of pairs (S,D) consisting of minimal surfaces S of class VII with positive second Betti number b_2 together with reduced divisors D of b_2 rational curves. The special case of Enoki surfaces has already been considered by Dloussky and Kohler. We use normal forms for the action of the fundamental group of the complement of D and for the associated holomorphic contraction germ from (C^2,0) to (C^2,0).Comment: Minor correction of the dimension of the moduli spac

Superconductivity in CoSr2(Y1-xCax)Cu2O7+d

The roles of aliovalent Ca(II)-for-Y(III) substitution and high-pressure-oxygen annealing in the process of "superconducterizing" the Co-based layered copper oxide, CoSr2(Y1-xCax)Cu2O7+d (Co-1212), were investigated. The as-air-synthesized samples up to x = 0.4 were found essentially oxygen stoichiometric (-0.03 <= d <= 0.00). These samples, however, were not superconductive, suggesting that the holes created by the divalent-for-trivalent cation substitution are trapped on Co in the charge reservoir. Ultra-high-pressure heat treatment carried out at 5 GPa and 500C for 30 min in the presence of Ag2O2 as an excess oxygen source induced bulk superconductivity in these samples. The highest Tc was obtained for the high-oxygen-pressure treated x = 0.3 sample at ~40 K.Comment: 16 pages, 6 figures, submitted to Solid State Communication