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Register a new userElliptical Weighted HOLICs for Weak Lensing Shear Measurement part3:Random Count Noise Effect for Images Moments in Weak Lensing Analysis
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This is the third paper on the improvements of systematic errors in our weak lensing analysis using an elliptical weight function, called E-HOLICs. In the previous papers we have succeeded in avoiding error which depends on ellipticity of background image. In this paper, we investigate the systematic error which depends on signal to noise ratio of background image. We find that the origin of the error is the random count noise which comes from Poisson noise of sky counts. Random count noise makes additional moments and centroid shift error, and those 1st orders are canceled in averaging, but 2nd orders are not canceled. We derived the equations which corrects these effects in measuring moments and ellipticity of the image and test their validity using simulation image. We find that the systematic error becomes less than 1% in the measured ellipticity for objects with $S/N>3$.
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This paper extends the method introduced in Rivi et al. (2016b) to measure galaxy ellipticities in the visibility domain for radio weak lensing surveys. In that paper we focused on the development and testing of the method for the simple case of individual galaxies located at the phase centre, and proposed to extend it to the realistic case of many sources in the field of view by isolating visibilities of each source with a faceting technique. In this second paper we present a detailed algorithm for source extraction in the visibility domain and show its effectiveness as a function of the source number density by running simulations of SKA1-MID observations in the band 950-1150 MHz and comparing original and measured values of galaxies ellipticities. Shear measurements from a realistic population of 10^4 galaxies randomly located in a field of view of 1 deg^2 (i.e. the source density expected for the current radio weak lensing survey proposal with SKA1) are also performed. At SNR >= 10, the multiplicative bias is only a factor 1.5 worse than what found when analysing individual sources, and is still comparable to the bias values reported for similar measurement methods at optical wavelengths. The additive bias is unchanged from the case of individual sources, but is significantly larger than typically found in optical surveys. This bias depends on the shape of the uv coverage and we suggest that a uv-plane weighting scheme to produce a more isotropic shape could reduce and control additive bias.
Highly precise weak lensing shear measurement is required for statistical weak gravitational lensing analysis such as cosmic shear measurement to achieve severe constraint on the cosmological parameters. For this purpose, the accurate shape measurement of background galaxies is absolutely important in which any systematic error in the measurement should be carefully corrected. One of the main systematic error comes from photon noise which is Poisson noise of flux from the atmosphere(noise bias). We investigate how the photon noise makes a systematic error in shear measurement within the framework of ERA method we developed in earlier papers and gives a practical correction method. The method is tested by simulations with real galaxy images with various conditions and it is confirmed that it can correct $80 sim 90%$ of the noise bias except for galaxies with very low signal to noise ratio.
We present weak lensing shear catalogues for 139 square degrees of data taken during the Science Verification (SV) time for the new Dark Energy Camera (DECam) being used for the Dark Energy Survey (DES). We describe our object selection, point spread function estimation and shear measurement procedures using two independent shear pipelines, IM3SHAPE and NGMIX, which produce catalogues of 2.12 million and 3.44 million galaxies respectively. We detail a set of null tests for the shear measurements and find that they pass the requirements for systematic errors at the level necessary for weak lensing science applications using the SV data. We also discuss some of the planned algorithmic improvements that will be necessary to produce sufficiently accurate shear catalogues for the full 5-year DES, which is expected to cover 5000 square degrees.
Metacalibration is a recently introduced method to accurately measure weak gravitational lensing shear using only the available imaging data, without need for prior information about galaxy properties or calibration from simulations. The method involves distorting the image with a small known shear, and calculating the response of a shear estimator to that applied shear. The method was shown to be accurate in moderate sized simulations with galaxy images that had relatively high signal-to-noise ratios, and without significant selection effects. In this work we introduce a formalism to correct for both shear response and selection biases. We also observe that, for images with relatively low signal-to-noise ratios, the correlated noise that arises during the metacalibration process results in significant bias, for which we develop a simple empirical correction. To test this formalism, we created large image simulations based on both parametric models and real galaxy images, including tests with realistic point-spread functions. We varied the point-spread function ellipticity at the five percent level. In each simulation we applied a small, few percent shear to the galaxy images. We introduced additional challenges that arise in real data, such as detection thresholds, stellar contamination, and missing data. We applied cuts on the measured galaxy properties to induce significant selection effects. Using our formalism, we recovered the input shear with an accuracy better than a part in a thousand in all cases.
We have developed a method for measuring higher-order weak lensing distortions of faint background galaxies, namely the weak gravitational flexion, by fully extending the Kaiser, Squires & Broadhurst method to include higher-order lensing image characteristics (HOLICs) introduced by Okura, Umetsu, & Futamase. We take into account explicitly the weight function in calculations of noisy shape moments and the effect of higher-order PSF anisotropy, as well as isotropic PSF smearing. Our HOLICs formalism allows accurate measurements of flexion from practical observational data in the presence of non-circular, anisotropic PSF. We test our method using mock observations of simulated galaxy images and actual, ground-based Subaru observations of the massive galaxy cluster A1689 ($z=0.183$). From the high-precision measurements of spin-1 first flexion, we obtain a high-resolution mass map in the central region of A1689. The reconstructed mass map shows a bimodal feature in the central $4times 4$ region of the cluster. The major, pronounced peak is associated with the brightest cluster galaxy and central cluster members, while the secondary mass peak is associated with a local concentration of bright galaxies. The refined, high-resolution mass map of A1689 demonstrates the power of the generalized weak lensing analysis techniques for quantitative and accurate measurements of the weak gravitational lensing signal.
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