## Abstract

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.

Original language | English |
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Pages (from-to) | 1951-1957 |

Number of pages | 7 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 425 |

Issue number | 3 |

DOIs | |

Publication status | Published - 21 Sep 2012 |

## Keywords

- Cosmology: observations
- Dark energy
- Dark matter
- Gravitational lensing: weak
- Methods: statistical
- Techniques: image processing