1997A&A...321..713J

Deep (B_T<21.5) overall and type-specific luminosity functions (LFs) are presented for the galaxies populating the central region of the Centaurus cluster. Assuming the "same distance" hypothesis for the spatial distribution of the two Centaurus velocity components Cen30 and Cen45, these LFs are discussed and compared with those found in the two nearby clusters in Virgo and Fornax. Although the three overall LFs have similar appearance in general, clear variations exist due to differences in the mixtures of Hubble types. The Schechter parameters M^*_BT and α are used for a quantitative discussion of the LFs. We present new evidence against their universality. Both parameters change from one cluster to the other and depend for a single cluster on the cut-off in absolute magnitude. In contrast to the overall LF, previously derived shapes of the type-specific LFs (Sandage et al. 1985b) could be fully confirmed. Bright galaxies of type E, S0, and spiral have bell-shaped, Gaussian-like LFs, whereas the LF of early-type dwarfs (dE&dS0) rises exponentially with decreasing luminosity. These results strongly support the idea that the shapes of the type-specific LFs are invariant at least among clusters and have a physical origin. Furthermore, statistical evidence is given for a skewness towards the faint end in the LF of E galaxies. The LF of the Im&BCD's is disturbed by the magnitude completeness limit of our survey and is not well defined. As an application of the close similarity in form we used the type-specific LFs of S0's, spirals and dE&dS0's in the Centaurus and the Virgo clusters as distance indicators. The results are consistent and give a mean relative distance modulus of {DELTA}(m-M)⁰_Cen–Virgo=1.63(±0.14).