The specific frequencies of ultra-compact dwarf galaxies

Context. One formation channel discussed for ultra-compact dwarf galaxies (UCDs) is that of massive star clusters, and the other main scenario is that of tidally transformed dwarf galaxies. Aims. We aim at quantifying the specific frequency of UCDs in a range of environments and at relating this to the frequency of star clusters and potential progenitor dwarf galaxies. Are the frequencies of UCDs consistent with being the bright tail of the globular cluster luminosity function (GCLF)? Methods. We propose a definition for the specific frequency of UCDs, S-N,S-UCD = N(UCD)10(0.4(MV,host MV,0))c(w). The parameter M-V,M-0 is the zero point of the definition, chosen such that the specific frequency of UCDs is the same as those of globular clusters, S-N,S-GC, if UCDs follow a simple extrapolation of the GCLF. Considering UCDs as compact stellar systems with M-V < -10.25 mag (mass above similar to 2 x 10(6) M-circle dot), it is M-V,M-0 = -20 mag. The parameter c(w) is a correction term to take the dependence of the GCLF width sigma on the host galaxy luminosity into account. We apply our definition of S-N,S-UCD to results of spectroscopic UCD searches in the Fornax, Hydra, and Centaurus galaxy clusters, two Hickson compact groups, and the Local Group. This includes a large database of 180 confirmed UCDs in Fornax. Results. We find that the specific frequencies derived for UCDs match those of GCs very well, to within 10-50%. The ratio S-N,S-UCD/S-N,S-GC is 1.00 +/- 0.44 for the four environments Fornax, Hydra, Centaurus, and Local Group, which have S-N,S-GC values. This good match also holds for individual giant galaxies in Fornax and in the Fornax intracluster-space. The error ranges of the derived UCD specific frequencies in the various environments then imply that not more than similar to 50% of UCDs were formed from dwarf galaxies. We show that such a scenario would require greater than or similar to 90% of primordial dwarfs in galaxy cluster centers (< 100 kpc) to have been stripped of their stars. Conclusions. We conclude that the number counts of UCDs are fully consistent with them being the bright tail of the GC population. From a statistical point of view there is no need to invoke an additional formation channel.