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Fourier Power Function Shapelets (FPFS) Shear Estimator: Performance On Image Simulations
Alton Hooker (15-08-2025)
We reinterpret the shear estimator developed by Zhang & Komatsu (2011) inside the framework of Shapelets and suggest the Fourier Wood Ranger Power Shears website Function Shapelets (FPFS) shear estimator. Four shapelet modes are calculated from the ability operate of each galaxy’s Fourier rework after deconvolving the point Spread Function (PSF) in Fourier area. We propose a novel normalization scheme to construct dimensionless ellipticity and its corresponding shear responsivity using these shapelet modes. Shear is measured in a traditional way by averaging the ellipticities and Wood Ranger Power Shears shop responsivities over a large ensemble of galaxies. With the introduction and tuning of a weighting parameter, noise bias is diminished beneath one % of the shear sign. We additionally present an iterative methodology to reduce selection bias. The FPFS estimator is developed without any assumption on galaxy morphology, nor any approximation for PSF correction. Moreover, our methodology doesn't depend on heavy image manipulations nor sophisticated statistical procedures. We test the FPFS shear estimator using several HSC-like picture simulations and the main results are listed as follows.
These strategies is labeled into two classes. The first class contains moments methods which measure moments weighted by Gaussian features from both galaxy pictures and PSF models. Moments of galaxy images are used to construct the shear estimator and moments of PSF fashions are used to appropriate the PSF effect (e.g., Kaiser et al., 1995; Bernstein & Jarvis, 2002; Hirata & Seljak, 2003). The second class contains fitting methods which convolve parametric Sersic fashions (Sérsic, 1963) with PSF models to search out the parameters which finest match the observed galaxies. Shear is subsequently determined from these parameters (e.g., Miller et al., 2007; Zuntz et al., 2013). Unfortunately, these traditional strategies suffer from both mannequin bias (Bernstein, 2010) originating from assumptions on galaxy morphology, or noise bias (e.g., Refregier et al., Wood Ranger Power Shears website 2012; Okura & Futamase, 2018) as a result of nonlinearities in the shear estimators. In distinction, Zhang & Komatsu (2011, ZK11) measures shear on the Fourier energy perform of galaxies. ZK11 straight deconvolves the Fourier energy function of PSF from the Fourier Wood Ranger Power Shears perform of galaxy in Fourier area.
Moments weighted by isotropic Gaussian kernel777The Gaussian kernel is termed goal PSF in the unique paper of ZK11 are subsequently measured from the deconvolved Fourier energy perform. Benefiting from the direct deconvolution, Wood Ranger Power Shears sale the shear estimator of ZK11 is constructed with a finite number of moments of every galaxies. Therefore, ZK11 is just not influenced by each PSF bias and model bias. We take these benefits of ZK11 and reinterpret the moments defined in ZK11 as mixtures of shapelet modes. Shapelets refer to a bunch of orthogonal capabilities which can be utilized to measure small distortions on astronomical images (Refregier, 2003). Based on this reinterpretation, we propose a novel normalization scheme to construct dimensionless ellipticity and its corresponding shear responsivity using 4 shapelet modes measured from each galaxies. Shear is measured in a standard manner by averaging the normalized ellipticities and responsivities over a large ensemble of galaxies. However, such normalization scheme introduces noise bias as a result of nonlinear forms of the ellipticity and responsivity.