On the shear estimation bias induced by the spatial variation of colour across galaxy profiles

The spatial variation of the colour of a galaxy may introduce a bias in the measurement of its shape if the point spread function (PSF) profile depends on wavelength. We study how this bias depends on the properties of the PSF and the galaxies themselves. The bias depends on the scales used to estimate the shape, which may be used to optimize methods to reduce the bias. Here, we develop a general approach to quantify the bias. Although applicable to any weak lensing survey, we focus on the implications for the ESA Euclid mission. Based on our study of synthetic galaxies, we find that the bias is a few times 10(-3) for a typical galaxy observed by Euclid. Consequently, it cannot be neglected and needs to be accounted for. We demonstrate how one can do so using spatially resolved observations of galaxies in two filters. We show that Hubble Space Telescope (HST) observations in the F606W and F814W filters allow us to model and reduce the bias by an order of magnitude, sufficient to meet Euclid's scientific requirements. The precision of the correction is ultimately determined by the number of galaxies for which spatially resolved observations in at least two filters are available. We use results from the Millennium simulation to demonstrate that archival HST data will be sufficient for the tomographic cosmic shear analysis with the Euclid data set.