TY - JOUR

T1 - Noise bias in weak lensing shape measurements

AU - Refregier, Alexandre

AU - Kacprzak, Tomasz

AU - Amara, Adam

AU - Bridle, Sarah

AU - Rowe, Barnaby

PY - 2012/9/21

Y1 - 2012/9/21

N2 - Weak lensing experiments are a powerful probe into cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper, we investigate noise bias, a systematic error that arises from second-order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general maximum-likelihood estimators in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modelled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic six-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematic requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper.

AB - Weak lensing experiments are a powerful probe into cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper, we investigate noise bias, a systematic error that arises from second-order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general maximum-likelihood estimators in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modelled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic six-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematic requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper.

KW - Cosmology: observations

KW - Dark energy

KW - Dark matter

KW - Gravitational lensing: weak

KW - Methods: statistical

KW - Techniques: image processing

UR - http://www.scopus.com/inward/record.url?scp=84865608882&partnerID=8YFLogxK

UR - https://academic.oup.com/mnras/issue/425/3

U2 - 10.1111/j.1365-2966.2012.21483.x

DO - 10.1111/j.1365-2966.2012.21483.x

M3 - Article

AN - SCOPUS:84865608882

SN - 0035-8711

VL - 425

SP - 1951

EP - 1957

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 3

ER -