Origins of weak lensing systematics, and requirements on future instrumentation (or knowledge of instrumentation)

Abstract

The first half of this paper explores the origin of systematic biases in the measurement of weak gravitational lensing. Compared to previous work, we expand the investigation of PSF instability and fold in for the first time the effects of non-idealities in electronic imaging detectors and imperfect galaxy shape measurement algorithms. Together, these now explain the additive A( ) and multiplicative M( ) systematics typically reported in current lensing measurements. We find that overall performance is driven by a product of a telescope/camera's absolute performance, and our knowledge about its performance.The second half of this paper propagates any residual shear measurement biases through to their effect on cosmological parameter constraints. Fully exploiting the statistical power of Stage IV weak lensing surveys will require additive biases A < ∼ 1.8× 10 −12 and multiplicative biases M < ∼ 4.0 × 10 −3 . These can be allocated between individual budgets in hardware, calibration data and software, using results from the first half of the paper.If instrumentation is stable and well-calibrated, we find extant shear measurement software from GREAT10 already meet requirements on galaxies detected at S/N=40. Averaging over a population of galaxies with a realistic distribution of sizes, it also meets requirements for a 2D cosmic shear analysis from space. If used on fainter galaxies or for 3D cosmic shear tomography, existing algorithms would need calibration on simulations to avoid introducing bias at a level similar to the statistical error. Requirements on hardware and calibration data are discussed in more detail in a companion paper. Our analysis is intentionally general, but is specifically being used to drive the hardware and ground segment performance budget for the design of the European Space Agency's recently-selected Euclid mission.

On scale-dependent cosmic shear systematic effects

“…a number density of 30 galaxies per square arcminute (this is the number for which shapes can be measured, not the actual number density down to the limiting magnitude), with a number density distribution n(z) given in Taylor et al (2006), and a photometric redshift probability distribution that is assumed to be Gaussian with a standard deviation of σ (z) = 0.05(1 + z) (the photometric redshifts will be derived from onboard near-infrared filters and overlapping ground-based optical imaging). These characteristics are described in Laureijs et al (2011), and are the same as those used in Massey et al (2013). We assume that a field of view is 0.5 deg 2 , covered by a 6 × 6 array of detectors, that are assumed to be four-side buttable (i.e.…”

“…In Massey et al (2013) and Cropper et al (2013), the multiplicative and additive terms were linked to systematic changes in convolutive effects on the image (e.g. PSF effects and other effects that occur in the optics), non-convolutive effects (e.g.…”

“…The remaining terms, which still convolve C , are then treated as diagonal, and hence -dependent multiplicative biases. The terms m 3 and m 4 in Cropper et al (2013) only refer to errors not biases, but as stated in Massey et al (2013) they '[Ignore] a bias term in M proportional to the square of one already present (therefore negligible if the bias is small)', so these convert to C terms, despite no bias being referred to. The constants a i and m i can be derived from galaxy and instrumental properties, and have values, taken from Cropper et al (2013), of: a 1 = 0.1, a 2 = 0.74, a 3 = 0.001, a 4 = 0.0042, a 5 = 0.001, and m 1 = 1.20, m 2 = 0.34, m 3 = 0.18, m 4 = 0.015, m 5 = 1.20.…”

“…The blue dots show the range of biases found when taking 1000 realizations of the Guassian functional form described in Section 3.1. The green dots show the upper limit of the biases caused by realizations of a binned functional form in -mode (repeating the analysis of Massey et al 2013). The survey parameters are described in Section 2.3. σ 2 sys ≤ 10 −7 does ensure that dark energy biases are below bias/ error = 1 (or the revised requirement of 0.31 used in Massey et al 2014), but that a more thorough functional search, including power spectra with spike-like functional features can produce biases that are an order of magnitude larger.…”

“…Those studies that have included some scale dependence have made an assumption that all systematic effects have scale-dependent functional behaviour that mimics a cosmological signal, the requirement used being an integral over all scales used in the analysis. This was the approach taken in Massey et al (2013) and Cropper et al (2013) that propagated requirements on systematic effects through to the performance on cosmological parameters.…”