Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling

Abstract

LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. We quantified the scientific performance through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images; realistic clustering with a mean surface number density of 250 arcmin${}^{-2}$ ($I_{\mathrm{E}}<29.5$) for galaxies, and 6 arcmin${}^{-2}$ ($I_{\mathrm{E}}<26$) for stars; and a diffraction-limited chromatic PSF with a full width at half maximum of $0{.}^{\prime \prime }2$ and spatial variation across the field of view. LensMC measured objects with a density of 90 arcmin${}^{-2}$ ($I_{\mathrm{E}}<26.5$) in 4500 deg${}^2$. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We found measurement multiplicative and additive biases of $m_1=(-3.6\pm 0.2)\times 10^{-3}$, $m_2=(-4.3\pm 0.2)\times 10^{-3}$, $c_1=(-1.78\pm 0.03)\times 10^{-4}$, $c_2=(0.09\pm 0.03)\times 10^{-4}$; a large detection bias with a multiplicative component of $1.2\times 10^{-2}$ and an additive component of $-3\times 10^{-4}$; and a measurement PSF leakage of ${\alpha }_1=(-9\pm 3)\times 10^{-4}$ and ${\alpha }_2=(2\pm 3)\times 10^{-4}$. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies ($-5\times 10^{-3}$). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at https://gitlab.com/gcongedo/LensMC

28 pages, 18 figures, and 2 tables

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