Parametrising arbitrary galaxy morphologies: potentials and pitfalls
  We demonstrate that morphological observables (e.g. steepness of the radial
light profile, ellipticity, asymmetry) are intertwined and cannot be measured
independently of each other. We present strong arguments in favour of
model-based parametrisation schemes, namely reliability assessment,
disentanglement of morphological observables, and PSF modelling. Furthermore,
we demonstrate that estimates of the concentration and Sersic index obtained
from the Zurich Structure & Morphology catalogue are in excellent agreement
with theoretical predictions. We also demonstrate that the incautious use of
the concentration index for classification purposes can cause a severe loss of
the discriminative information contained in a given data sample. Moreover, we
show that, for poorly resolved galaxies, concentration index and M_20 suffer
from strong discontinuities, i.e. similar morphologies are not necessarily
mapped to neighbouring points in the parameter space. This limits the
reliability of these parameters for classification purposes. Two-dimensional
Sersic profiles accounting for centroid and ellipticity are identified as the
currently most reliable parametrisation scheme in the regime of intermediate
signal-to-noise ratios and resolutions, where asymmetries and substructures do
not play an important role. We argue that basis functions provide good
parametrisation schemes in the regimes of high signal-to-noise ratios and
resolutions. Concerning Sersic profiles, we show that scale radii cannot be
compared directly for profiles of different Sersic indices. Furthermore, we
show that parameter spaces are typically highly nonlinear. This implies that
significant caution is required when distance-based classificaton methods are
used.
