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