In order to study the mechanism of the formation of cD galaxies, we search for possible dependencies between the K-band luminosity of cD galaxies and the parameters of their host clusters which we select to have a dominant cD galaxy, corresponding to a cluster morphology of Bautz-Morgan type I (BM I). As a comparison sample we use cD galaxies in clusters where they are not dominant, which we define here as non-BM I (NBMI) type clusters. We find that for 71 BM I clusters the absolute K-band luminosity of cD galaxies depends on the cluster richness, but less strongly on the cluster velocity dispersion. Meanwhile, for 35 NBMI clusters the correlation between cD luminosity and cluster richness is weaker, and is absent between cD luminosity and velocity dispersion. In addition, we find that the luminosity of the cD galaxy hosted in BM I clusters tends to increase with the cD's peculiar velocity with respect to the cluster mean velocity. In contrast, for NBMI clusters the cD luminosity decreases with increasing peculiar velocity. Also, the X-ray luminosity of BM I clusters depends on the cluster velocity dispersion, while in NBMI clusters such a correlation is absent. These findings favour the cannibalism scenario for the formation of cD galaxies. We suggest that cD galaxies in clusters of BM I type were formed and evolved preferentially in one and the same cluster. In contrast, cD galaxies in NBMI-type clusters were either originally formed in clusters that later merged with groups or clusters to form the current cluster, or are now in the process of merging.Key words: galaxies: clusters: general -galaxies: elliptical and lenticular, cD -galaxies: formation.
I N T RO D U C T I O NThe formation mechanism of the brightest cluster galaxies (BCGs) is an important problem of modern astronomy (e.g. Garijo, Athanassoula & Garcia-Gómez 1997;Jordán et al. 2004;Lin & Mohr 2004;Tutukov, Dryumov & Dryumova 2007;von der Linden et al. 2007;Hansen et al. 2009). Some of the BCGs are cD galaxies (Matthews, Morgan & Schmidt 1964) which are characterized by an extended 'envelope' or halo. The physical properties of these unique objects were reviewed, for example, by Tonry (1987), Kormendy & Djorgovski (1989), Schombert (1992) 1 and Jordán et al. (2004). According to one of the proposed scenarios, BCGs are formed in cluster cooling flows, when the gas density has grown enough to cool and condense, leading to star formation in the cluster core (Silk 1976;Cowie & Binney 1977;Fabian 1994). In this scenario there should be colour gradients of the optical haloes in the sense that the latter should become redder with increasing radius. However, such gradients have not been found (Andreon et al. 1992). Also, E-mail: hrant@inaoep.mx (HMT); heinz@astro.ugto.mx (HA) 1 cf. also http://ned.ipac.caltech.edu/level5/March07/Schombert/frames.html the finding that the X-ray gas does not cool significantly below a threshold temperature of kT ≈ 1-2 keV (Kaastra et al. 2001;Peterson et al. 2001;Tamura et al. 2001) puts this possibility of cD format...