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Clusters of galaxies are believed to be at the intersections of cosmologicalfilaments and to grow by accreting matter from these filaments. Such continuousinfall has major consequences not only on clusters but also on the physics ofcluster galaxies. Faint galaxies are particularly interesting as they are verysensitive to environmental effects, and may have a different behaviour fromthat of bright galaxies. The aim of this paper is to sample the Coma clusterbuilding history, based on the analysis of galaxy luminosity functions and redsequences in the Color Magnitude Relation down to faint magnitudes, which areprivileged tools for this purpose. The present analysis is based on deep(R~24), wide (~0.5 deg2) multiband (BVRI Vega system) images of the Comacluster obtained with the CFH12K camera at the CFHT. We have derived LFs andCMRs in twenty 10x10 arcmin2 regions and in larger regions. In all photometricbands, we found steeply rising LFs in the north-northeast half of the cluster(due to early type galaxies at bright magnitudes and due to late type galaxiesat the faint end), and much flatter LFs in the south-southwest region. Althoughthe fine behaviour of the CMR RS is different in these two regions, a goodagreement is found in general between the RS computed for faint and for brightgalaxies. All these results can be interpreted consistently in the framework ofthe building up process previously proposed. The Northern Coma area is arelatively quiescent region while the southern area experiences severalinfalls.

Spatial variations of the optical galaxy luminosity functions and red sequences in the Coma cluster: clues to its assembly history