Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200

Displacement- and Timing-Noise Free Gravitational-Wave Detection

Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus realizable by shot-noise-limited laser interferometry. This is possible due to two reasons: first, gravitational waves and displacement disturbances contribute to light propagation times in different manners; second, for an N-detector system, the number of signal channels is of the order O(N^2), while the total number of timing- and displacement-noise channels is of the order O(N).Comment: 4 pages, 3 figures; mistake correcte

Shape Reconstruction and Weak Lensing Measurement with Interferometers: A Shapelet Approach

We present a new approach for image reconstruction and weak lensing measurements with interferometers. Based on the shapelet formalism presented in Refregier (2001), object images are decomposed into orthonormal Hermite basis functions. The shapelet coefficients of a collection of sources are simultaneously fit on the uv plane, the Fourier transform of the sky brightness distribution observed by interferometers. The resulting chi-square fit is linear in its parameters and can thus be performed efficiently by simple matrix multiplications. We show how the complex effects of bandwidth smearing, time averaging and non-coplanarity of the array can be easily and fully corrected for in our method. Optimal image reconstruction, co-addition, astrometry, and photometry can all be achieved using weighted sums of the derived coefficients. As an example we consider the observing conditions of the FIRST radio survey (Becker et al. 1995; White et al. 1997). We find that our method accurately recovers the shapes of simulated images even for the sparse uv sampling of this snapshot survey. Using one of the FIRST pointings, we find our method compares well with CLEAN, the commonly used method for interferometric imaging. Our method has the advantage of being linear in the fit parameters, of fitting all sources simultaneously, and of providing the full covariance matrix of the coefficients, which allows us to quantify the errors and cross-talk in image shapes. It is therefore well-suited for quantitative shape measurements which require high-precision. In particular, we show how our method can be combined with the results of Refregier & Bacon (2001) to provide an accurate measurement of weak lensing from interferometric data.Comment: 9 pages, 5 figures. To appear in ApJ; minor changes to match accepted versio

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2-16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2-16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R ⊙, the major axis scattering angle is ~0.7" at λ=6 cm and it varies with heliocentric distance as R -1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to λ=20 cm, has a value 20±7 at 5R⊙ and varies with heliocentric distance as R -3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8-3.4 for scales sizes between 2-35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R⊙ and 4 km at 13R ⊙. These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum

A Wide Field, Low Frequency Radio Survey of the Field of M31: I. Construction and Statistical Analysis of the Source Catalog

We present here the results of a 325 MHz radio survey of M31, conducted with the A-configuration of the Very Large Array. The survey covered an area of 7.6 deg$^2$, and a total of 405 radio sources between \la6\arcsec and 170\arcsec in extent were mapped with a resolution of 6\arcsec and a 1$\sigma$ sensitivity of $\sim$0.6 \mjyb. For each source, its morphological class, major axis $\theta_M$, minor axis $\theta_m$, position angle $\theta_{PA}$, peak flux $I$, integrated flux density $S$, spectral index $\alpha$ and spectral curvature parameter $\phi$ were calculated. A comparison of the flux and radial distribution -- both in the plane of the sky and in the plane of M31 -- of these sources with those of the XMM--LSS and WENSS radio surveys revealed that a vast majority of sources detected are background radio galaxies. As a result of this analysis, we expect that only a few sources are intrinsic to M31. These sources are identified and discussed in an accompanying paper.Comment: 29 pages with 4 tables and 10 figures (JPEGs), accepted for publication in ApJS. Full-resolution images available on reques

On the Enhanced Interstellar Scattering Toward B1849+005

(Abridged) This paper reports new Very Large Array (VLA) and Very Long Baseline Array (VLBA) observations of the extragalactic source B1849+005 at frequencies between 0.33 and 15 GHz and the re-analysis of archival VLA observations at 0.33, 1.5, and 4.9 GHz. The structure of this source is complex but interstellar scattering dominates the structure of the central component at least to 15 GHz. An analysis of the phase structure functions of the interferometric visibilities shows the density fluctuations along this line of sight to be anisotropic (axial ratio = 1.3) with a frequency-independent position angle, and having an inner scale of roughly a few hundred kilometers. The anisotropies occur on length scales of order 10^{15} cm (D/5 kpc), which within the context of certain magnetohydrodynamic turbulence theories indicates the length scale on which the kinetic and magnetic energy densities are comparable. A conservative upper limit on the velocity of the scattering material is 1800 km/s. In the 0.33 GHz field of view, there are a number of other sources that might also be heavily scattered. Both B1849+005 and PSR B1849+00 are highly scattered, and they are separated by only 13'. If the lines of sight are affected by the same ``clump'' of scattering material, it must be at least 2.3 kpc distant. However, a detailed attempt to account for the scattering observables toward these sources does not produce a self-consistent set of parameters for such a clump. A clump of H\alpha emission, possibly associated with the H II region G33.418-0.004, lies between these two lines of sight, but it seems unable to account for all of the required excess scattering.Comment: 23 pages, LaTeX2e AASTeX, 13 figures in 14 PostScript files, accepted for publication in Ap

A multiple-beam CLEAN for imaging intra-day variable radio sources

The CLEAN algorithm, widely used in radio interferometry for the deconvolution of radio images, performs well only if the raw radio image (dirty image) is, to good approximation, a simple convolution between the instrumental point-spread function (dirty beam) and the true distribution of emission across the sky. An important case in which this approximation breaks down is during frequency synthesis if the observing bandwidth is wide enough for variations in the spectrum of the sky to become significant. The convolution assumption also breaks down, in any situation but snapshot observations, if sources in the field vary significantly in flux density over the duration of the observation. Such time-variation can even be instrumental in nature, for example due to jitter or rotation of the primary beam pattern on the sky during an observation. An algorithm already exists for dealing with the spectral variation encountered in wide-band frequency synthesis interferometry. This algorithm is an extension of CLEAN in which, at each iteration, a set of N `dirty beams' are fitted and subtracted in parallel, instead of just a single dirty beam as in standard CLEAN. In the wide-band algorithm the beams are obtained by expanding a nominal source spectrum in a Taylor series, each term of the series generating one of the beams. In the present paper this algorithm is extended to images which contain sources which vary over both frequency and time. Different expansion schemes (or bases) on the time and frequency axes are compared, and issues such as Gibbs ringing and non-orthogonality are discussed. It is shown that practical considerations make it often desirable to orthogonalize the set of beams before commencing the cleaning. This is easily accomplished via a Gram-Schmidt technique.Comment: 9 pages, 7 figures. Accepted for publication in A&

Influence of symmetry and Coulomb-correlation effects on the optical properties of nitride quantum dots

The electronic and optical properties of self-assembled InN/GaN quantum dots (QDs) are investigated by means of a tight-binding model combined with configuration interaction calculations. Tight-binding single particle wave functions are used as a basis for computing Coulomb and dipole matrix elements. Within this framework, we analyze multi-exciton emission spectra for two different sizes of a lens-shaped InN/GaN QD with wurtzite crystal structure. The impact of the symmetry of the involved electron and hole one-particle states on the optical spectra is discussed in detail. Furthermore we show how the characteristic features of the spectra can be interpreted using a simplified Hamiltonian which provides analytical results for the interacting multi-exciton complexes. We predict a vanishing exciton and biexciton ground state emission for small lens-shaped InN/GaN QDs. For larger systems we report a bright ground state emission but with drastically reduced oscillator strengths caused by the quantum confined Stark effect.Comment: 15 pages, 17 figure

Development of a unified tensor calculus for the exceptional Lie algebras

The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad is now well-known. This paper uses it to embark on the development of a unified tensor calculus for the exceptional Lie algebras. It deals explicitly with all the tensors that arise at the n=2 stage, obtaining a large body of systematic information about their properties and identities satisfied by them. Some results at the n=3 level are obtained, including a simple derivation of the the dimension and Casimir eigenvalue data for all the constituents of ad^3. This is vital input data for treating the set of all tensors that enter the picture at the n=3 level, following a path already known to be viable for a_1. The special way in which the Lie algebra d_4 conforms to its place in the family F alongside the exceptional Lie algebras is described.Comment: 27 pages, LaTeX 2