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We have analyzed the galaxy number density and luminosity density profiles ofrich clusters of galaxies from redshifts z=0 to z=0.5. We show that theluminosity profile computed with bright galaxies is significantly cusped in thecenter of the clusters, whatever the redshift. This is in agreement with thedark matter profiles predicted by numerical simulations. The galaxy numberdensity profile for the bright galaxies is fitted equally well with a coremodel or a cusped model. In contrast, the luminosity and the galaxy numberdensity profiles of the fainter galaxies are significantly better fitted by acore rather than a cusp model. We did not detect any statistically significantdifferent fits when applied to data in range from z=0 to z=0.5. The differencein profile between faint and bright galaxies may be due to the rapid (relativeto the age of the universe at z=0 versus z=0.5) destruction of the faintgalaxies by tidal forces and merging events in the denser central regions ofthe clusters. This process could erase the cusp by turning faint galaxies intodiffuse light. In this case, the galaxies (with a cusp visible in the brightgalaxy number density and mainly in luminosity profiles) would trace the totalmass distribution.Comment: 8 pages, 3 figures, accepted in A&

Central matter distributions in rich clusters of galaxies from ${z\sim{0}}$ to ${z\sim {0.5}}$