We present a photometric study of the early-type dwarf galaxy population of the Centaurus cluster, aiming at investigating the galaxy luminosity function (LF) and galaxy scaling relations down to the regime of galaxies with M_V~-10 mag. On deep VLT/FORS1 V- and I-band images of the central part of the cluster, we identify cluster dwarf-galaxy candidates using both morphological and surface brightness selection criteria. Photometric and structural parameters of the candidates are derived from analysis of their surface brightness profiles. Fundamental scaling relations, such as the colour-magnitude and the magnitude-surface brightness relation, are used to distinguish the cluster from the background. We find a flat LF with a slope of alpha = -1.14 pm 0.12 for M_V>-14 mag, when fitting a power law to the completeness-corrected galaxy number counts. When plotting the central surface brightness of a Sersic model vs. the galaxy magnitude, we find a continuous relation for magnitudes -20<M_V<-10 mag, with only the brightest core galaxies deviating from this relation, in agreement with previous studies of other clusters. In a size-luminosity diagram of early-type galaxies from a range of environments, we observe that R_eff slowly decreases with decreasing luminosity for -21<M_V<-13 mag and decreases more rapidly at fainter magnitudes. This trend continues to the ultra-faint Local Group dwarf galaxies (M_V~-4 mag). The continuous central surface brightness vs. absolute magnitude relation and the smooth relation in the size-luminosity diagram over a wide range of magnitudes are consistent with the interpretation of dwarf galaxies and more massive elliptical galaxies being one family of objects with gradually changing structural properties. The most massive core galaxies and the rare cE galaxies are the only exceptions.
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