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

LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling to deal with convolution by a point spread function 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. The scientific performance is quantified 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 (IE<29.5) for galaxies, and 6 arcmin−2 (IE<26) for stars; and a diffraction-limited chromatic point spread function with a full width at half maximum of 0.′′2 and spatial variation across the field of view. Objects are measured with a density of 90 arcmin−2 (IE<26.5) in 4500 deg2. The total shear bias is broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We find: measurement multiplicative and additive biases of m1=(−3.6±0.2)×10−3, m2=(−4.3±0.2)×10−3, c1=(−1.78±0.03)×10−4, c2=(0.09±0.03)×10−4; a large detection bias with a multiplicative component of 1.2×10−2 and an additive component of −3×10−4; and a measurement PSF leakage of α1=(−9±3)×10−4 and α2=(2±3)×10−4. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies (−5×10−3). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at gitlab.com/gcongedo/LensMC.