Quantifying galaxy shapes: Sersiclets and beyond
  Parametrising galaxy morphologies is a challenging task, e.g., in shear
measurements of weak lensing or investigations of galaxy evolution. The huge
variety of morphologies requires an approach that is highly flexible, e.g.,
accounting for azimuthal structure. We revisit the method of sersiclets, where
galaxy morphologies are decomposed into basis functions based on the Sersic
profile. This approach is justified by the fact that the Sersic profile is the
first-order Taylor expansion of any real light profile. We show that sersiclets
overcome the modelling failures of shapelets. However, sersiclets implicate an
unphysical relation between the steepness of the light profile and the spatial
scale of azimuthal structures, which is not obeyed by real galaxy morphologies
and can therefore give rise to modelling failures. Moreover, we demonstrate
that sersiclets are prone to undersampling, which restricts sersiclet modelling
to highly resolved galaxy images. Analysing data from the Great08 challenge, we
demonstrate that sersiclets should not be used in weak-lensing studies. We
conclude that although the sersiclet approach appears very promising at first
glance, it suffers from conceptual and practical problems that severly limit
its usefulness. The Sersic profile can be enhanced by higher-order terms in the
Taylor expansion, which can drastically improve model reconstructions of galaxy
images. If orthonormalised, these higher-order profiles can overcome the
problems of sersiclets while preserving their mathematical justification.
