# Euclid Preparation IV. Impact of undetected galaxies on weak-lensing shear measurements

## TL;DR

This study investigates how undetected faint galaxies affect weak-lensing shear measurements and emphasizes the need to include their clustering in simulations to meet Euclid survey accuracy requirements.

## Contribution

It demonstrates the significance of faint galaxy clustering on shear bias and proposes methods to incorporate this effect into calibration simulations.

## Key findings

- Faint galaxies cause a shear bias of a few times 10^{-3} with uniform distribution.
- Clustering of faint galaxies increases bias to about 10^{-2}.
- Magnification effects are negligible for shear bias.

## Abstract

In modern weak-lensing surveys, the common approach to correct for residual systematic biases in the shear is to calibrate shape measurement algorithms using simulations. These simulations must fully capture the complexity of the observations to avoid introducing any additional bias. In this paper we study the importance of faint galaxies below the observational detection limit of a survey. We simulate simplified Euclid VIS images including and excluding this faint population, and measure the shift in the multiplicative shear bias between the two sets of simulations. We measure the shear with three different algorithms: a moment-based approach, model fitting, and machine learning. We find that for all methods, a spatially uniform random distribution of faint galaxies introduces a shear multiplicative bias of the order of a few times $10^{-3}$. This value increases to the order of $10^{-2}$ when including the clustering of the faint galaxies, as measured in the Hubble Space Telescope Ultra-Deep Field. The magnification of the faint background galaxies due to the brighter galaxies along the line of sight is found to have a negligible impact on the multiplicative bias. We conclude that the undetected galaxies must be included in the calibration simulations with proper clustering properties down to magnitude 28 in order to reach a residual uncertainty on the multiplicative shear bias calibration of a few times $10^{-4}$, in line with the $2\times10^{-3}$ total accuracy budget required by the scientific objectives of the Euclid survey. We propose two complementary methods for including faint galaxy clustering in the calibration simulations.