Sérsiclets – a matched filter extension of Shapelets for weak lensing studies

The precision study of dark matter using weak lensing by large-scale structure is strongly constrained by the accuracy with which one can measure galaxy shapes. Several methods have been devised but none has demonstrated the ability to reach the level of precision required by future weak lensing surveys. In this paper, we explore new avenues to the existing 'Shapelets' approach, combining a priori knowledge of the galaxy profile with the power of orthogonal basis function decomposition. This paper discusses the new issues raised by this matched filter approach and proposes promising alternatives to shape measurement techniques. In particular, it appears that the use of a matched filter (e.g. Sérsic profile) restricted to elliptical radial fitting functions resolves several well-known Shapelet issues.     

Bayesian galaxy shape measurement for weak lensing surveys – I. Methodology and a fast-fitting algorithm

The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP).     

Background–source separation in astronomical images with Bayesian probability theory – I. The method

A probabilistic technique for the joint estimation of background and sources with the aim of detecting faint and extended celestial objects is described. Bayesian probability theory is applied to gain insight into the co-existence of background and sources through a probabilistic two-component mixture model, which provides consistent uncertainties of background and sources. A multiresolution analysis is used for revealing faint and extended objects in the frame of the Bayesian mixture model. All the revealed sources are parametrized automatically providing source position, net counts, morphological parameters and their errors.
We demonstrate the capability of our method by applying it to three simulated data sets characterized by different background and source intensities. The results of employing two different prior knowledge on the source signal distribution are shown. The probabilistic method allows for the detection of bright and faint sources independently of their morphology and the kind of background. The results from our analysis of the three simulated data sets are compared with other source detection methods. Additionally, the technique is applied to ROSAT All-Sky Survey data.     

Weak gravitational shear and flexion with polar shapelets

We derive expressions, in terms of 'polar shapelets', for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide a natural representation, in which both shear and flexion transformations are compact. Through this tool, we understand progress in several weak lensing methods. We then exploit various symmetries of shapelets to construct a range of shear estimators with useful properties. Through an analogous investigation, we also explore several flexion estimators. In particular, some of the estimators can be measured simultaneously and independently for every galaxy, and will provide unique checks for systematics in future weak lensing analyses. Using simulated images from the Shear TEsting Programme, we show that we can recover input shears with no significant bias. A complete software package to parametrize astronomical images in terms of polar shapelets, and to perform a full weak lensing analysis, is available on the Internet.     

Deconvolution of ASCA X-ray data – I. Spectral-imaging method

In this paper we describe a self-contained method for performing the spectral-imaging deconvolution of X-ray data on clusters of galaxies observed by the ASCA satellite. Spatially resolved spectral studies of data from this satellite require such a correction, because its optics redistribute photons over regions that are of comparable size to the angular scales of interest in clusters. This scattering is a function not only of spatial position but also of energy. To perform a correction for these effects we employ maximum-likelihood deconvolution of the image (within energy bands of 1 keV) to determine the spatial redistribution, followed by a Monte Carlo energy reassignment of photon energies with position to determine the spectral redistribution. We present tests on simulated cluster data, convolved with the various instrumental characteristics and the X-ray background, which show that our methodology can successfully recover a variety of intrinsic temperature profiles in typical observational circumstances. In Paper II (this issue) we shall apply our spectral-imaging deconvolution procedure to a large sample of galaxy clusters to determine temperature profiles.     

Direct observation of cosmic strings via their strong gravitational lensing effect – I. Predictions for high-resolution imaging surveys

We use present theoretical estimates for the density of long cosmic strings to predict the number of strong gravitational lensing events in astronomical imaging surveys as a function of the angular resolution and survey area. We show that angular resolution is the single most important factor, and that interesting limits on the dimensionless string tension   G μ/ c ²  can be obtained by existing and planned surveys. At the resolution of the Hubble Space Telescope ( HST ) (0.14 arcsec), it is sufficient to survey of the order of a few square degrees – well within reach of the current HST archive – to probe the regime   G μ/ c ²∼ 10⁻⁷  . If lensing by cosmic strings is not detected, such a survey would improve the limit on the string tension by a factor of two over that available from the cosmic microwave background. Future high resolution imaging surveys, covering a few hundred square degrees or more, either from space in the optical or from large-format radio telescopes on the ground, would be able to further lower this limit to   G μ/ c ²∼ 10⁻⁸  . These limits will not be improved significantly by increasing the solid angle of the survey.     

Real-time difference imaging analysis of MOA Galactic bulge observations during 2000

We describe observations carried out by the MOA group of the Galactic bulge during 2000 that were designed to detect efficiently gravitational microlensing of faint stars in which the magnification is high and/or of short duration. These events are particularly useful for studies of extrasolar planets and faint stars. Approximately 17 deg² were monitored at a sampling rate of up to six times per night. The images were analysed in real time using a difference imaging technique. 20 microlensing candidates were detected, of which eight were alerted to the microlensing community whilst in progress. Approximately half of the candidates had high magnifications (≳10), at least one had very high magnification (≳50), and one exhibited a clear parallax effect. The details of these events are reported here, together with details of the on-line difference imaging technique. Some nova-like events were also observed and these are described, together with one asteroid.     

The SuperCOSMOS Sky Survey – II. Image detection, parametrization, classification and photometry

In this, the second in a series of three papers concerning the SuperCOSMOS Sky Survey, we describe the methods for image detection, parametrization, classification and photometry. We demonstrate the internal and external accuracy of our object parameters. Using examples from the first release of data, the South Galactic Cap survey, we show that our image detection completeness is close to 100 per cent to within ∼1.5 mag of the nominal plate limits. We show that for the B _J survey data, the image classification is externally > 99 per cent reliable to B _J∼19.5 . Internally, the image classification is reliable at a level of > 90 per cent to B _J∼21 , R ∼19 . The photometric accuracy of our data is typically ∼0.3 mag with respect to external data for m >15 . Internally, the relative photometric accuracy in restricted position and magnitude ranges can be as accurate as ∼5 per cent for well-exposed stellar images. Colours are externally accurate to σ _{B − R , R − I} ∼0.07 at B _J∼16.5 , rising to σ _{B − R , R − I} ∼0.16 at B _J∼20 .     

Using galaxy redshift surveys to detect gravitationally lensed quasars

Gravitationally lensed quasars can be discovered as a by-product of galaxy redshift surveys. Lenses discovered spectroscopically in this way should require less observational effort per event than those found in dedicated lens surveys. Further, the lens galaxies should be relatively nearby, facilitating a number of detailed observations that are impossible for the more common high-redshift lenses. This is epitomized by the wide range of results that have been obtained from Q 2237+0305, which was discovered as part of the Center for Astrophysics redshift survey, and remains the only quasar lens discovered in this way. The likelihood of this survey yielding a lens is calculated to be ∼0.03, which is an order of magnitude larger than previous estimates due to two effects. First, the quasar images themselves increase the observed flux of the lens, so that lens galaxies up to a magnitude fainter than the nominal survey limit must be included in the calculation. Secondly, it is possible for lensed quasars with extremely faint deflectors to enter the survey due to the extended morphology of the multiple images. Extrapolating these results to future surveys, the 2 degree Field galaxy redshift survey should contain between 10 and 50 lenses and the Sloan Digital Sky Survey should yield between 50 and 300 lenses, depending on the cosmological model and the observing conditions.     

Data analysis of continuous gravitational wave: Fourier transform – I

We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for a 1-d observation time and our analysis is applicable for an arbitrary location of detector and source. We have taken into account the effects arising due to the rotational as well as orbital motions of the Earth.     

The Chang–Refsdal lens revisited

This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang–Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the four images, as well as moment sums of their signed magnifications. The image topographies and equations of the caustics and critical curves are also studied. We derive the fully analytic expressions for pre-caustics, which are the loci of non-critical points that map to the caustics under the lens mapping. They constitute boundaries of the region in the image domain that maps on to the interior of the caustics. The areas under the critical curves, caustics and pre-caustics are all evaluated, which enables us to calculate the mean magnification of the source within the caustics. Additionally, the exact analytic expression for the magnification distribution for the source in the triangular caustics is derived, as well as a useful approximate expression. Finally, we find that the Chang–Refsdal lens with additional convergence greater than unity (the 'overfocusing case') can exhibit third-order critical behaviour, if the 'reduced shear' is exactly equal to     , and that the number of images for N -point masses with non-zero constant shear cannot be greater than  5 N − 1  .     

Far-infrared detection limits – I. Sky confusion due to Galactic cirrus

Fluctuations in the brightness of the background radiation can lead to confusion with real point sources. This type of confusion with background emission is relevant when making infrared (IR) observations with relatively large beam sizes, since the amount of fluctuation tends to increase with the angular scale. To quantitively assess the effect of the background emission on the detection of point sources for current and future far-IR observations by space-borne missions such as Spitzer , ASTRO-F , Herschel and Space Infrared Telescope for Cosmology and Astrophysics ( SPICA ), we have extended the Galactic emission map to a higher level of angular resolution than that of the currently available data. Using this high-resolution map, we estimate the sky confusion noise owing to the emission from interstellar dust clouds or cirrus, based on fluctuation analysis and detailed photometry over realistically simulated images. We find that the confusion noise derived by simple fluctuation analysis agrees well with the results from realistic simulations. Although sky confusion noise becomes dominant in long wavelength bands  (>100 μm)  with 60–90 cm aperture missions, it is expected to be two orders of magnitude lower for the next generation of space missions (with larger aperture sizes) such as Herschel and SPICA .     

A fuzzy logic‐based algorithm for cosmic‐ray hit rejection from single images

An algorithm for cosmic‐ray rejection from single images is presented. The algorithm is based on modeling human perception using fuzzy logic. The proposed algorithm is specifically designed to reject multiple‐pixel cosmic ray hits that are larger than some of the point spread functions of the true astronomical sources. Experiments show that the algorithm can accurately reject ∼97.5% of the cosmic rays hits, while mistakenly rejecting 0.02% of the true astronomical sources. The major advantage of the presented algorithm is its computational efficiency. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)