How many explosions does one need? -- Quantifying supernovae in globular
  clusters from iron abundance spreads
  Many globular clusters (GCs) are known to host multiple populations
distinguishable by their light-element content. Less common are GCs displaying
iron abundance spreads which are seen as evidence for enrichment through core
collapse supernovae (SNe). We present a simple analytical method to estimate
the number of SNe required to have occurred in a GC from its metallicity and
iron abundance spread. We then use this result to estimate how long star
formation (SF) lasted to build the GC. We apply our method to up-to-date
measurements and find that, assuming the correctness of these measurements,
multiple SNe (up to $10^5$) are required in most GCs with iron abundance
spreads. The number of SNe events which contributed to the enrichment of the
GCs studied here is typically a factor of 10 less than the expected number of
SNe in a canonical initial mass function (IMF). This indicates that gas
expulsion from the forming GC occurred after the first 10 per cent of SNe
exploded. We compute that for the GCs typically SF ends after only a few Myr
(extending up to $\approx 30 ~\rm Myr$ in a few cases). We also discuss
possible improvements of this method and especially its sensitivity to the
error of iron abundance measurements of individual stars of a GC. The method
presented here can quickly give an estimate for the number of SNe required to
explain the iron abundance spread in a GC without the requirement of any
hydrodynamical simulations.
