The minimum metallicity of globular clusters and its physical origin – implications for the galaxy mass–metallicity relation and observations of proto-globular clusters at high redshift

In the local Universe, globular clusters (GCs) with metallicities [Fe/H] < −2.5 are extremely rare. In this Letter, the close connection between GC formation and galaxy evolution is used to show that this GC metallicity ‘floor’ results from the galaxy mass–metallicity relation of ultra low-luminosity galaxies (ULLGs) at high redshift, where the most metal-poor GCs must have formed. Galaxies with metallicities [Fe/H] ≲ −2.5 have too low masses to form GCs with initial masses Mi ≳ 105 M⊙ needed to survive for a Hubble time. This translates the galaxy mass–metallicity relation into a maximum initial cluster mass–metallicity relation for [Fe/H] ≲ −1.8, which naturally leads to the observed colour–magnitude relation of metal-poor GCs at z = 0 (the ‘blue tilt’). Its strength traces the slope of the gas phase mass–metallicity relation of ULLGs. Based on the observed blue tilt of GCs in the Virgo and Fornax Clusters, the galaxy mass–metallicity relation is predicted to have a slope of α = 0.4 ± 0.1 for 105 ≲ M⋆/M⊙ ≲ 107 at z ≳ 2. The GC metallicity floor implies a minimum host galaxy mass and a maximum redshift for GC formation. Any proto-GCs that may be detected at z > 9 are most likely to end up in galaxies presently more massive than the Milky Way, whereas GCs in low-mass galaxies such as the Fornax dSph (M⋆ ≈ 4 × 107 M⊙) formed at z ≲ 3.