Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

The Dark UNiverse Explorer (DUNE): Proposal to ESA's Cosmic Vision

The Dark UNiverse Explorer (DUNE) is a wide-field space imager whose primary goal is the study of dark energy and dark matter with unprecedented precision. For this purpose, DUNE is optimised for the measurement of weak gravitational lensing but will also provide complementary measurements of baryonic accoustic oscillations, cluster counts and the Integrated Sachs Wolfe effect. Immediate auxiliary goals concern the evolution of galaxies, to be studied with unequalled statistical power, the detailed structure of the Milky Way and nearby galaxies, and the demographics of Earth-mass planets. DUNE is an Medium-class mission which makes use of readily available components, heritage from other missions, and synergy with ground based facilities to minimise cost and risks. The payload consists of a 1.2m telescope with a combined visible/NIR field-of-view of 1 deg^2. DUNE will carry out an all-sky survey, ranging from 550 to 1600nm, in one visible and three NIR bands which will form a unique legacy for astronomy. DUNE will yield major advances in a broad range of fields in astrophysics including fundamental cosmology, galaxy evolution, and extrasolar planet search. DUNE was recently selected by ESA as one of the mission concepts to be studied in its Cosmic Vision programme.Comment: Accepted in Experimental Astronom

Subaru Suprime-Cam Weak Lensing Survey over 33 deg^2

Under the currently popular CDM model, mass plays the major role in evolution of large scale structure of the universe. In order to examine the paradigm based on observations, it ould be ideal to use purely mass selected object catalog. Weak lensing surveys enable a blind search of cluster scale objects, and thus could provide such catalogs. We are working on a weak lensing survey using Subaru Prime Focus Camera (Suprime-Cam). In this note, we introduce our survey strategy, and the status as well as the performance of Suprime-Cam as a weak lensing surveyor

Modal decomposition of astronomical images with application to shapelets

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis functions, which may be linearly dependent, non-orthogonal and incomplete. It is shown that such circumstances may result even from the digitisation of continuous basis functions that are orthogonal and complete. In particular, digitised shapelet basis functions are investigated and are shown to suffer from such difficulties. As a result the standard method of performing shapelet analysis produces unnecessarily inaccurate decompositions. The optimal method presented here is shown to yield more accurate decompositions in all cases.Comment: 12 pages, 17 figures, submitted to MNRA

Effect of Gravitational Lensing on Measurements of the Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect of a cluster of galaxies is usually measured after background radio sources are removed from the cluster field. Gravitational lensing by the cluster potential leads to a systematic deficit in the residual intensity of unresolved sources behind the cluster core relative to a control field far from the cluster center. As a result, the measured decrement in the Rayleigh-Jeans temperature of the cosmic microwave background is overestimated. We calculate the associated systematic bias which is inevitably introduced into measurements of the Hubble constant using the SZ effect. For the cluster A2218, we find that observations at 15 GHz with a beam radius of 0'.4 and a source removal threshold of 100 microJy underestimate the Hubble constant by 6-10%. If the profile of the gas pressure declines more steeply with radius than that of the dark matter density, then the ratio of lensing to SZ decrements increases towards the outer part of the cluster.Comment: 11 pages, 3 figures, submitted to ApJ

Gravitational Lensing of the X-Ray Background by Clusters of Galaxies

Gravitational lensing by clusters of galaxies affects the cosmic X-ray background (XRB) by altering the observed density and flux distribution of background X-ray sources. At faint detection flux thresholds, the resolved X-ray sources appear brighter and diluted, while the unresolved component of the XRB appears dimmer and more anisotropic, due to lensing. The diffuse X-ray intensity in the outer halos of clusters might be lower than the sky-averaged XRB, after the subtraction of resolved sources. Detection of the lensing signal with a wide-field X-ray telescope could probe the mass distribution of a cluster out to its virialization boundary. In particular, we show that the lensing signature imprinted on the resolved component of the XRB by the cluster A1689, should be difficult but possible to detect out to 8' at the 2-4 sigma level, after 10^6 seconds of observation with the forthcoming AXAF satellite. The lensing signal is fairly insensitive to the lens redshift in the range 0.1<z<0.6. The amplitude of the lensing signal is however sensitive to the faint end slope of the number-flux relation for unresolved X-ray sources, and can thus help constrain models of the XRB. A search for X-ray arcs or arclets could identify the fraction of all faint sources which originate from extended emission of distant galaxies. The probability for a 3 sigma detection of an arclet which is stretched by a factor of about 3 after a 10^6 seconds observation of A1689 with AXAF, is roughly comparable to the fraction of all background X-ray sources that have an intrinsic size of order 1''.Comment: 41 LaTeX pages, 11 postscript figures, 1 table, in AASTeX v4.0 format. To appear in ApJ, April 1, 1997, Vol. 47