Direct Minkowski Functional analysis of large redshift surveys: a new high-speed code tested on the LRG SDSS-DR7 catalogue

As deeper galaxy catalogues are soon to come, it becomes even more important to measure large-scale fluctuations in the catalogues with robust statistics that cover all moments of the galaxy distribution. In this paper we reinforce a direct analysis of galaxy data by employing the Germ-Grain method to calculate the family of Minkowski Functionals. We introduce a new code, suitable for the analysis of large data sets without smoothing and without the construction of excursion sets. We provide new tools to measure correlation properties, putting emphasis on explicitly isolating non-Gaussian correlations with the help of integral--geometric relations. As a first application we present the analysis of large-scale fluctuations in the LRG sample of SDSS DR7 data. We find significant (more than 2-sigma) deviations from the simulated mock catalogues on samples as large as $500h^{-1}$Mpc and $700h^{-1}$Mpc, respectively, and we investigate possible sources of these deviations.