How many explosions does one need? -- Quantifying supernovae in globular clusters from iron abundance spreads

TL;DR

This paper introduces an analytical method to estimate the number of supernovae events in globular clusters based on their iron abundance spread, providing insights into star formation duration and gas expulsion timing.

Contribution

It presents a simple, non-hydrodynamical approach to quantify supernovae in GCs from metallicity data, improving understanding of their formation history.

Findings

Most GCs with iron spreads require up to 10^5 SNe.

The number of SNe is about 10 times less than expected from a canonical IMF.

Star formation typically ends within a few Myr, up to 30 Myr in some cases.

Abstract

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.