Deprojection of luminosity functions of galaxies in the Coma cluster

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Abstract
We use a simple analytic model to deproject 2-d luminosity functions (LF) of galaxies in the Coma cluster measured by Beijersbergen et al. 2002. We demonstrate that the shapes of the LFs change after deprojection. It is therefore essential to correct LFs for projection effects. The deprojected LFs of the central area have best-fitting Schechter parameters of M^{*}_U=-18.31^{+0.08}_{-0.08} and \alpha_U=-1.27^{+0.018}_{-0.018}, M^{*}_B=-19.79^{+0.14}_{-0.15} and \alpha_B=-1.44^{+0.016}_{-0.016} and M^{*}_r=-21.77^{+0.20}_{-0.28} and \alpha_r=-1.27^{+0.012}_{-0.012}. The corrections are not significant enough to change the previously observed trend of increasing faint end slopes with increasing distance to the cluster center. The weighted U, B, and r band slopes of the deprojected LFs show a slightly weaker steepening with increasing projected cluster radius.

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