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| - Central matter distributions in rich clusters of galaxies from ${z\sim{0}}$ to ${z\sim {0.5}}$
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| - We have analyzed the galaxy number density and luminosity density profiles of rich clusters of galaxies from redshifts $z\sim0$ to $z\sim0.5$. We show that the luminosity profile computed with bright galaxies $(M_R < -21)$ is significantly cusped in the center of the clusters, whatever the redshift. This is in agreement with the dark matter profiles predicted by numerical simulations. The galaxy number density profile for the bright galaxies is fitted equally well with a core model or a cusped model. In contrast, the luminosity and the galaxy number density profiles of the fainter galaxies are significantly better fitted by a core model. We did not detect any statistically significant different fits when applied to data in the range from $z\sim0$ to $z\sim0.5$. The difference in profile between faint and bright galaxies may be due to the rapid (relative to the age of the universe at $z=0$ versus $z=0.5$) destruction of the faint galaxies by tidal forces and merging events in the denser central regions of the clusters. This process could erase the cusp by turning faint galaxies into diffuse light. In this case, the galaxies (with a cusp visible in the bright galaxy number density and mainly in luminosity profiles) would trace the total mass distribution.
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