S\'{e}rsic galaxy models in weak lensing shape measurement: model bias,
  noise bias and their interaction
  Cosmic shear is a powerful probe of cosmological parameters, but its
potential can be fully utilised only if galaxy shapes are measured with great
accuracy. Two major effects have been identified which are likely to account
for most of the bias for maximum likelihood methods in recent shear measurement
challenges. Model bias occurs when the true galaxy shape is not well
represented by the fitted model. Noise bias occurs due to the non-linear
relationship between image pixels and galaxy shape. In this paper we
investigate the potential interplay between these two effects when an imperfect
model is used in the presence of high noise. We present analytical expressions
for this bias, which depends on the residual difference between the model and
real data. They can lead to biases not accounted for in previous calibration
schemes. By measuring the model bias, noise bias and their interaction, we
provide a complete statistical framework for measuring galaxy shapes with model
fitting methods from GRavitational lEnsing Accuracy Testing (GREAT) like
images. We demonstrate the noise and model interaction bias using a simple toy
model, which indicates that this effect can potentially be significant. Using
real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify
the strength of the model bias, noise bias and their interaction. We find that
the interaction term is often a similar size to the model bias term, and is
smaller than the requirements of the current and shortly upcoming galaxy
surveys.
