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

Abstract

The spatial variation of the colour of a galaxy may introduce a bias in the measurement of its shape if the 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 optimise 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 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 dataset.

The impact of cosmic variance on simulating weak lensing surveys

“…Unfortunately, we cannot directly test the strength of any colour gradient variations with environment using COSMOS data, due to the fact that there is only single-band coverage in much of its area. We note that our findings may seem to be at odds with the conclusions in Semboloni et al (2013) based on synthetic galaxy models that the existing area of HST coverage with 2 bands is sufficient for calibration of colour gradients 3 . This is particularly striking given that, as shown there, the dominant galaxy sample with 2-band coverage is the AEGIS dataset, which has substantially smaller area than COS-MOS, and therefore should exhibit a stronger influence of cosmic variance.…”

“…However, it is important to bear in mind that the method proposed in Semboloni et al (2013) involves determining not just a redshift-dependent correction but also a type-dependent colour gradient correction, which could partially mitigate the effects of the environment dependence seen here. Moreover, the colour gradient effect is higher order than the intrinsic ellipticity distribution, and thus may be less susceptible to systematics due to the environmental effects considered here.…”

Scientific Synergy between LSST and Euclid

“…Finally, a joint pixel-level measurement would be more robust against the problem of objects blending together (see, e.g., Section 2.1), which is beneficial for LSST because of the wider PSF. Also, this could account for color variations within galaxies, which needs to be accounted for with Euclid due to the single VIS filter for shape measurements (Voigt et al 2012;Semboloni et al 2013).…”

Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise

“…In addition, galaxies are not intrinsically circular such that their ellipticities are noisy estimators of the cosmic distortion. Current theoretical work consequently focuses on sources of bias in shape measurements, such as pixel-noise bias, shape-noise bias, underfitting bias, colour gradients, or several selection biases (Hirata & Seljak 2003;Hirata et al 2004;Mandelbaum et al 2005;Melchior et al 2010;Viola et al 2011;Melchior & Viola 2012;Kacprzak et al 2012;Massey et al 2013;Semboloni et al 2013).…”