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Deep CCD photometry and positions for a new sample of $\simeq 250$ dwarfelliptical (dE) galaxies in the Coma cluster core are analyzed. A significantcolor gradient is detected in their projected radial distribution, given by$\Delta (B$--$R)/\Delta (\log R_{\rm cc}) = -0.08\pm0.02$ mag. Calibratingthese dE galaxies against Galactic globular clusters yields a correspondingmetallicity gradient which goes as $Z \propto R_{\rm cc}^{-0.29}$. Simulationsreveal that this gradient in the projected radial distribution corresponds to atrue (three-dimensional) radial color gradient which goes as $\Delta(B$--$R)/\Delta (\log r) \simeq -0.20$ mag, or $Z \propto r^{-0.69}$, over thesame radial range. If this radial gradient is a primordial one, it isconsistent with a model in which the intracluster gas exerted a significantconfinement pressure, impeding the outflow of supernovae-driven metal-rich gasfrom the young dE galaxies.

A Constraint on the Formation of Dwarf Elliptical Galaxies in the Dense Coma Cluster Core