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Ultra-compact dwarf galaxies (UCDs) share many properties with globularclusters (GCs) and are found in similar environments. A large sample of UCDsand GCs around NGC 1399, the central giant elliptical of the Fornax galaxycluster, is used to infer their formation history and also that of NGC 1399. Weassumed that all GCs and UCDs in our sample are star clusters (SCs) and usedthem as tracers of past star formation activities. After correcting our GC/UCDsample for mass loss, we interpreted their overall mass function to be asuperposition of SC populations that formed coevally during different times.The SC masses of each population were distributed according to the embeddedcluster mass function (ECMF), a pure power law with the slope $-\beta$ and astellar upper mass limit, $M_{\mathrm{max}}$, which depended on the starformation rate (SFR). We decomposed the observed GC/UCD mass function intoindividual SC populations and converted $M_{\mathrm{max}}$ of each SCpopulation to an SFR. The overall distribution of SFRs reveals how the GC/UCDsample formed. Considering the age of the GCs/UCDs and the present stellar massof NGC 1399, we found that the formation of the GCs/UCDs can be well explainedfor $\beta<2.3$. This agrees very well with the observation in young SCs where$\beta\approx2.0$ is usually found. Even if taking into account that some ofthe most massive objects might not be genuine SCs and applying differentcorrections for the mass loss, the outcome is not influenced much. We foundpeak SFRs between approximately 300 and 3000 $M_{\odot}\mathrm{yr}^{-1}$, whichmatches the SFRs observed in massive high-$z$ sub-mm galaxies and an SFRestimate inferred from NGC 1399 based on "downsizing", i.e. more massivegalaxies must have formed over shorter times. Our results suggest that NGC 1399and its GC/UCD system formed in an early, short, and intense starburst.

Distribution of star formation rates during the rapid assembly of NGC 1399 as deduced from its globular cluster system