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

An extended scheme for fitting X-ray data with accretion disk spectra in the strong gravity regime

Accreting black holes are believed to emit X-rays which then mediate information about strong gravity in the vicinity of the emission region. We report on a set of new routines for the Xspec package for analysing X-ray spectra of black-hole accretion disks. The new computational tool significantly extends the capabilities of the currently available fitting procedures that include the effects of strong gravity, and allows one to systematically explore the constraints on more model parameters than previously possible (for example black-hole angular momentum). Moreover, axial symmetry of the disk intrinsic emissivity is not assumed, although it can be imposed to speed up the computations. The new routines can be used also as a stand-alone and flexible code with the capability of handling time-resolved spectra in the regime of strong gravity. We have used the new code to analyse the mean X-ray spectrum from the long XMM--Newton 2001 campaign of the Seyfert 1 galaxy MCG--6-30-15. Consistent with previous findings, we obtained a good fit to the broad Fe K line profile for a radial line intrinsic emissivity law in the disk which is not a simple power law, and for near maximal value of black hole angular momentum. However, equally good fits can be obtained also for small values of the black hole angular momentum. The code has been developed with the aim of allowing precise modelling of relativistic effects. Although we find that current data cannot constrain the parameters of black-hole/accretion disk system well, the approach allows, for a given source or situation, detailed investigations of what features of the data future studies should be focused on in order to achieve the goal of uniquely isolating the parameters of such systems.Comment: Accepted for publication in ApJ S

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

Microwave background anisotropies and non-linear structures II. Numerical computations

A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent and we investigate the subsequent evolution of the density field. Photon paths are also calculated, allowing a detailed consideration of gravitational lensing effects and microwave background anisotropies induced by the cluster. We apply the method to modelling high-redshift clusters and, in particular, we consider the reported microwave decrement observed towards the quasar pair PC1643+4631 A&B. We also consider the effect on the primordial microwave background power spectrum due to gravitational lensing by a population of massive high-redshift clusters.Comment: 15 pages, 23 figures; Monthly Notices of the Royal Astronomical Society (MNRAS), in pres

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

The lack of variability of the iron line in MCG-6-30-15: general relativistic effects

The spectrum and variability of the Seyfert galaxy MCG-6-30-15 can be decomposed into two apparently disconnected components: a highly variable power law and an almost constant component which contains a broad and strong iron line. We explore a possible explanation of the puzzling lack of variability of the iron line, by assuming that the variations of the power law component are due to changes in the height of the primary source in the near vicinity of a rotating black hole. Due to the bending of light in the strong field of the central black hole, the apparent brightness of the power-law component can vary by about a factor 4 according to its position, while the total iron line flux variability is less than 20 percent. This behaviour is obtained if the primary source is located within 3-4 gravitational radii ($r_{\rm g}$) from the rotation axis with a variable height of between $\sim$ 3 and 8 $r_{\rm g}$. These results revive the possibility that future X-ray observations of MCG-6-30-15 can map out the strong gravity regime of accreting black holes.Comment: accepted for publication in MNRAS Letter