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Globular cluster (GC) systems of massive galaxies often show a bimodal colourdistribution. This has been interpreted as a metallicity bimodality, created bya two-stage galaxy formation where the red, metal-rich GCs were formed in theparent halo and the blue metal-poor GCs were accreted. This interpretation,however, crucially depends on the assumption that GCs are exclusively oldstellar systems with a linear colour-metallicity relation (CZR). The shape ofthe CZR and range of GC ages are currently under debate, because their studyrequires high quality spectra to derive reliable stellar population properties.We determined metallicities with full spectral fitting from a sample of 187 GCswith high spectral signal-to-noise ratio in 23 galaxies of the Fornax clusterthat were observed as part of the Fornax 3D project. The derived CZR from thissample is non-linear and can be described by a piecewise linear function with abreak point at ($g - z$) $\sim$ 1.1 mag. The less massive galaxies in oursample ($M_\ast < 10^{10} M_\odot$) appear to have slightly younger GCs, butthe shape of the CZR is insensitive to the GC ages. Although the least massivegalaxies lack red, metal-rich GCs, a non-linear CZR is found irrespective ofthe galaxy mass, even in the most massive galaxies ($M_\ast \geq 10^{11}M_\odot$). Our CZR predicts narrow unimodal GC metallicity distributions forlow mass and broad unimodal distributions for very massive galaxies, dominatedby a metal-poor and metal-rich peak, respectively, and bimodal distributionsfor galaxies with intermediate masses (10$^{10}$ $\leq$ $M_\ast < 10^{11}M_\odot$) as a consequence of the relative fraction of red and blue GCs. Thediverse metallicity distributions challenge the simple differentiation of GCpopulations solely based on their colour.

The Fornax 3D project: Non-linear colour-metallicity relation of globular clusters