Characterising the optical properties of galaxy clusters with GMPhoRCC
  We introduce the Gaussian Mixture full Photometric Red sequence Cluster
Characteriser (GMPhoRCC), an algorithm for determining the redshift and
richness of a galaxy cluster candidate. By using data from a multi-band sky
survey with photometric redshifts, a red sequence colour magnitude relation
(CMR) is isolated and modelled and used to characterise the optical properties
of the candidate. GMPhoRCC provides significant advantages over existing
methods including, treatment of multi-modal distributions, variable width full
CMR red sequence, richness extrapolation and quality control in order to
algorithmically identify catastrophic failures. We present redshift comparisons
for clusters from the GMBCG, NORAS, REFLEX and XCS catalogues, where the
GMPhoRCC estimates are in excellent agreement with spectra, showing accurate,
unbiased results with low scatter ($\sigma_{\delta z / (1+z)} \sim 0.014$). We
conclude with the evaluation of GMPhoRCC performance using empirical Sloan
Digital Sky Survey (SDSS) like mock galaxy clusters. GMPhoRCC is shown to
produce highly pure characterisations with very low probabilities ($<1\%$) of
spurious, clean characterisations. In addition GMPhoRCC is shown to demonstrate
high rates of completeness with respect to recovering redshift, richness and
correctly identifying the BCG.
