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The spatial variation of the colour of a galaxy may introduce a bias in themeasurement of its shape if the PSF profile depends on wavelength. We study howthis bias depends on the properties of the PSF and the galaxies themselves. Thebias depends on the scales used to estimate the shape, which may be used tooptimise methods to reduce the bias. Here we develop a general approach toquantify the bias. Although applicable to any weak lensing survey, we focus onthe implications for the ESA Euclid mission.  Based on our study of synthetic galaxies we find that the bias is a few times10^-3 for a typical galaxy observed by Euclid. Consequently, it cannot beneglected and needs to be accounted for. We demonstrate how one can do so usingspatially resolved observations of galaxies in two filters. We show that HSTobservations in the F606W and F814W filters allow us to model and reduce thebias by an order of magnitude, sufficient to meet Euclid's scientificrequirements. The precision of the correction is ultimately determined by thenumber of galaxies for which spatially-resolved observations in at least twofilters are available. We use results from the Millennium Simulation todemonstrate that archival HST data will be sufficient for the tomographiccosmic shear analysis with the Euclid dataset.

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