A. Lasenby

Efficient computation of CMB anisotropies in closed FRW models

We implement the efficient line-of-sight method to calculate the anisotropy and polarization of the cosmic microwave background for scalar and tensor modes in almost Friedmann-Robertson-Walker models with positive spatial curvature. We present new results for the polarization power spectra in such models.

A Deep Submillimeter Survey of the Galactic Center

We present first results from a submillimeter continuum survey of the Galactic center central molecular zone (CMZ), made with the Submillimeter Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. SCUBAs scan-map mode has allowed us to make extremely wide field maps of thermal dust emission with unprecedented speed and sensitivity. We also discuss some issues related to the elimination of artifacts in scan-map data. Our simultaneous 850/450 μm maps have a total size of approximately 28 × 05 (400 × 75 pc) elongated along the Galactic plane. They cover the Sagittarius A region, including Sgr A*, the circumnuclear disk, and the 20 and 50 km s-1 clouds; the area around the Pistol; Sgr B2, the brightest feature on the maps; and at their Galactic western and eastern edges the Sgr C and Sgr D regions. There are many striking features such as filaments and shell-like structures as well as point sources such as Sgr A* itself. The total mass in the CMZ is greater than that revealed in previous optically thin molecular line maps by a factor of ~3, and new details are revealed on scales down to 0.33 pc across this 400 pc-wide region.

Gravity, gauge theories and geometric algebra

A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the position and orientation of the matter fields. In this manner all properties of the background spacetime are removed from physics and what remains are a set of ‘intrinsic’ relations between physical fields. For a wide range of phenomena, including all present experimental tests, the theory reproduces the predictions of general relativity. Differences do emerge, however, through the first–order nature of the equations and the global properties of the gauge fields and through the relationship with quantum theory. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle and consistency with the minimal coupling procedure selects an action which is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin–torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time–dependent, spherically symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology and to the formation and properties of black holes. Insistence on finding global solutions, together with the first–order nature of the equations, leads to a new understanding of the role played by time reversal. This alters the physical picture of the properties of a horizon around a black hole. The existence of global solutions enables one to discuss the properties of field lines inside the horizon due to a point charge held outside it. The Dirac equation is studied in a black hole background and provides a quick (though ultimately unsound) derivation of the Hawking temperature. Some applications to cosmology are also discussed and a study of the Dirac equation in a cosmological background reveals that the only models consistent with homogeneity are spatially flat. It is emphasized throughout that the description of gravity in terms of gauge fields, rather than spacetime geometry, leads to many simple and powerful physical insights. The language of ‘geometric algebra’ best expresses the physical and mathematical content of the theory and is employed throughout. Methods for translating the equations into other languages (tensor and spinor calculus) are given in appendices.

Simultaneous Planck, Swift, and Fermi observations of X-ray and γ-ray selected blazars

We present simultaneous Planck, Swift, Fermi, and ground-based data for 105 blazars belonging to three samples with flux limits in the soft X-ray, hard X-ray, and -ray bands, and we compare our results to those of a companion paper presenting simultaneous Planck and multi-frequency observations of 104 radio-loud northern active galactic nuclei selected at radio frequencies. While we confirm several previous results, our unique data set has allowed us to demonstrate that the selection method strongly influences the results, producing biases that cannot be ignored. Almost all the BL Lac objects have been detected by Fermi Large Area Telescope (LAT), whereas 30 to 40% of the flat-spectrum radio quasars (FSRQs) in the radio, soft X-ray, and hard X-ray selected samples are still below the -ray detection limit even after integrating 27 months of Fermi-LAT data. The radio to sub-millimetre spectral slope of blazars is quite flat, withh i 0 up to about 70 GHz, above which it steepens toh i 0:65. BL Lacs have significantly flatter spectra than FSRQs at higher frequencies. The distribution of the rest-frame synchrotron peak frequency ( S ) in the spectral energy distribution (SED) of FSRQs is the same in all the blazar samples withh S i = 10 13:1 0:1 Hz, while the mean inverse-Compton peak frequency,h IC i, ranges from 10 21 to 10 22 Hz. The distributions of S and of IC of BL Lacs are much broader and are shifted to higher energies than those of FSRQs; their shapes strongly depend on the selection method. The Compton dominance of blazars ranges from less than 0.2 to nearly 100, with only FSRQs reaching values larger than about 3. Its distribution is broad and depends strongly on the selection method, with -ray selected blazars peaking at 7 or more, and radio-selected blazars at values close to 1, thus implying that the common assumption that the blazar power budget is largely dominated by high-energy emission is a selection e ect. A comparison of our multi-frequency data with theoretical predictions shows that simple homogeneous SSC models cannot explain the simultaneous SEDs of most of the -ray detected blazars in all samples. The SED of the blazars that were not detected by Fermi-LAT may instead be consistent with SSC emission. Our data challenge the correlation between bolometric luminosity and S predicted by the blazar sequence.

Relativistic Corrections to the Sunyaev-Zeldovich Effect

We present an extension of the Kompaneets equation which allows relativistic effects to be included to any desired order. Using this, we are able to obtain simple analytic forms for the spectral changes due to the Sunyaev-Zeldovich effect in hot clusters, correct to first and second order in the expansion parameter θe = kBTe/mc2. These analytic forms agree with previous numerical calculations of the effect based upon the multiple scattering formalism and are expected to be very accurate over all regions of the cosmic microwave background spectrum for kBTe up to ~10 keV. Our results confirm previous conclusions that the result of including relativistic corrections in the Sunyaev-Zeldovich effect is a small reduction in the amplitude of the effect over the majority of the spectrum: specifically, we find ΔT/T = -2y(1 - 17/10θe + 123/40θ2e) (correct to second order) in the Rayleigh-Jeans region, where y is the usual Comptonization parameter. For a typical cluster temperature of 8 keV, this amounts to a correction downward to the value of the Hubble constant derived using combined X-ray and Rayleigh-Jeans Sunyaev-Zeldovich information by about 5%.

The profile and equivalent width of the X-ray iron emission line from a disc around a Kerr black hole

Recent X-ray observations have shown broad, skewed iron line emission from Seyfert 1 galaxies which is explained by the emission being fluorescence on a disk close to a black hole. During one interval, the line in MCG--6-30-15 was so broad and redshifted that a Kerr black hole is implied. We are therefore studying the effects of the Kerr metric on the line profile, and extending the work by Laor and Kojima which dealt only with extreme values of the spin parameter. Here we report that the spin parameter of the black hole in MCG--6-30-15 is high (a/M>0.94), and invert the line profile to obtain the disk emissivity profile, which approximates a power-law. Continuum radiation returning to the disk because of the Kerr metric does not enhance the equivalent width of the line seen above 3 keV by more than about 20 per cent if the continuum source corotates with the disk.

New Geometric Methods for Computer Vision: An Application toStructure and Motion Estimation

We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the three-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is not a system designed specifically for the task in hand, but rather a framework for all mathematical physics. Central to the power of this approach is the way in which the formalism deals with rotations; for example, if we have two arbitrary sets of vectors, known to be related via a 3D rotation, the rotation is easily recoverable if the vectors are given. Extracting the rotation by conventional means is not as straightforward. The calculus associated with geometric algebra is particularly powerful, enabling one, in a very natural way, to take derivatives with respect to any multivector (general element of the algebra). What this means in practice is that we can minimize with respect to rotors representing rotations, vectors representing translations, or any other relevant geometric quantity. This has important implications for many of the least-squares problems in computer vision where one attempts to find optimal rotations, translations etc., given observed vector quantities. We will illustrate this by analysing the problem of estimating motion from a pair of images, looking particularly at the more difficult case in which we have available only 2D information and no information on range. While this problem has already been much discussed in the literature, we believe the present formulation to be the only one in which least-squares estimates of the motion and structure are derived simultaneously using analytic derivatives.

High-sensitivity measurements of the cosmic microwave background power spectrum with the extended Very Small Array

We present deep Ka-band (ν ≈ 33 GHz) observations of the cosmic microwave background (CMB) made with the extended Very Small Array (VSA). This configuration produces a naturally weighted synthesized FWHM beamwidth of ∼11 arcmin, which covers anrange of 300 to 1500. On these scales, foreground extragalactic sources can be a major source of contamination to the CMB anisotropy. This problem has been alleviated by identifying sources at 15 GHz with the Ryle Telescope and then monitoring these sources at 33 GHz using a single-baseline interferometer collocated with the VSA. Sources with flux densities20 mJy at 33 GHz are subtracted from the data. In addition, we calculate a statistical correction for the small residual contribution from weaker sources that are below the detection limit of the survey. The CMB power spectrum corrected for Galactic foregrounds and extragalactic point sources is presented. A totalrange of 150-1500 is achieved by combining the complete extended array data with earlier VSA data in a compact configuration. Our resolution of �� ≈ 60 allows the first three acoustic peaks to be clearly delineated. This is achieved by using mosaiced observations in seven regions covering a total area of 82 deg 2 . There is good agreement with the Wilkinson Microwave Anisotropy Probe (WMAP) data up to � = 700 where WMAP data run out of resolution. For highervalues out to � = 1500, the agreement in power spectrum amplitudes with other experiments is also very good despite differences in frequency and observing technique.

Cross-Correlation of Tenerife Data with Galactic Templates-Evidence for Spinning Dust?

The recent discovery of dust-correlated diffuse microwave emission has prompted two rival explanations: free-free emission and spinning dust grains. We present new detections of this component at 10 and 15 GHz by the switched-beam Tenerife experiment. The data show a turnover in the spectrum and thereby support the spinning dust hypothesis. We also present a significant detection of synchrotron radiation at 10 GHz, which is useful for normalizing foreground contamination of cosmic microwave background experiments at high galactic latitudes.

A high-significance detection of non-Gaussianity in the Wilkinson Microwave Anisotropy Probe 1-yr data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.