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 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 arcmin2 (IE < 29.5) for galaxies, and 6 arcmin2 (IE < 26) for stars, and a diffraction-limited chromatic PSF with a full width at half maximum of 02.22 and spatial variation across the field of view. LENSMC measured objects with a density of 90 arcmin2 (IE < 26.5) in 4500 deg2. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed in future work). We found measurement multiplicative and additive biases of m1 = (3.6 ± 0.2) A- 103, m2 = (4.3 ± 0.2) A- 103, c1 = (1.78 ± 0.03) A- 104, and c2 = (0.09 ± 0.03) A- 104; a large detection bias with a multiplicative component of 1.2 A- 102 and an additive component of 3 A- 104; and a measurement PSF leakage of α1 = (9 ± 3) A- 104 and α2 = (2 ± 3) A- 104. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies (5 A- 103). Although significant, model bias will be straightforward to calibrate given its weak sensitivity on galaxy morphology parameters. LENSMC is publicly available at gitlab.com/gcongedo/LensMC.