Means of confusion: how pixel noise affects shear estimates for weak
  gravitational lensing
  Weak-lensing shear estimates show a troublesome dependence on the apparent
brightness of the galaxies used to measure the ellipticity: In several studies,
the amplitude of the inferred shear falls sharply with decreasing source
significance. This dependence limits the overall ability of upcoming large
weak-lensing surveys to constrain cosmological parameters.
  We seek to provide a concise overview of the impact of pixel noise on
weak-lensing measurements, covering the entire path from noisy images to shear
estimates. We show that there are at least three distinct layers, where pixel
noise not only obscures but biases the outcome of the measurements: 1) the
propagation of pixel noise to the non-linear observable ellipticity; 2) the
response of the shape-measurement methods to limited amount of information
extractable from noisy images; and 3) the reaction of shear estimation
statistics to the presence of noise and outliers in the measured ellipticities.
  We identify and discuss several fundamental problems and show that each of
them is able to introduce biases in the range of a few tenths to a few percent
for galaxies with typical significance levels. Furthermore, all of these biases
do not only depend on the brightness of galaxies but also on their ellipticity,
with more elliptical galaxies often being harder to measure correctly. We also
discuss existing possibilities to mitigate and novel ideas to avoid the biases
induced by pixel noise. We present a new shear estimator that shows a more
robust performance for noisy ellipticity samples. Finally, we release the
open-source python code to predict and efficiently sample from the noisy
ellipticity distribution and the shear estimators used in this work at
https://github.com/pmelchior/epsnoise
