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tokens: origin. Our findings from this Section for the radial metallicity distribution of red and blue GCs in massive ETGs are summarized in a schematic way in Fig. 2 . This representative diagram shows the same radial metallicity gradient for the red (metal-rich) GCs and the blue (metal-poor) GCs, only offset by 1 dex in metallicity. We have argued that the stellar metallicity gradient is similar to that of the red GCs. At some large effective radius (8 R e in the diagram), the blue GC metallicity gradient gives way to an outer halo gradient that is flat, i.e. constant metallicity. We refer the reader to fig. 1 of Forbes et al. ( 2011 ) and fig. 10 of Faifer et al. ( 2011 ) for real-world examples of our schematic plot, which show not only the mean gradients but also the individual GC data points. Figure 2. Schematic representation of globular cluster metallicity gradients as described in Section 3 . The diagram shows the metallicity gradient of the metal-rich GCs in red. This gradient is similar to that of the stellar metallicity gradient. Approximately 1 dex lower in metallicity, the metallicity gradients for the metal-poor GCs are shown in blue. At several effective radii ( R e ), this radial gradient may give way to a constant metallicity for metal-poor GCs to large radius. 4 COMPARISON WITH MAGNETICUM SIMULATIONS Although a number of simulations have modelled the formation of GCs in a hierarchical cosmology (e.g. Bekki et al 2008 ; Muratov Gnedin 2010 ; Li Gnedin 2014 ; Kruijssen 2015 ; Choksi et al. 2018 ) with reasonable success in reproducing bimodal metallicity distributions and some global scaling relations, none have predicted the radial colour or metallicity profiles for GC subpopulations (although see Pfeffer et al. 2018 , for a first step in modelling the spatial distribution of GC systems in Milky Way-like galaxies). However, simulations of the stars in massive ETGs are available and, as noted above, GC metallicity gradients tend to be similar to those of their host galaxy stellar metallicity profiles. Thus, it is useful to investigate simulated stellar gradients as a proxy for GC gradients. The Magneticum hydrodynamical cosmological simulation suite (Dolag et al., in prep.) produces in its highest resolution ( and as every gas particle can spawn up to four stellar particles) massive ETGs with properties that successfully reproduce observations (e.g. Teklu et al. 2015 , for stellar-mass–angular-momentum properties; Remus et al. 2017 , for mass–size relations at different redshifts and dark matter properties; Teklu et al. 2017 , for satellite fractions and the morphology–density relation; Schulze et al. 2018 , for kinematic properties). The simulation adopts a WMAP7 (Komatsu et al. 2011 ) ΛCDM cosmology with σ 8 = 0.809, h = 0.704, , Ω M = 0.272, and Ω B = 0.0451, and an initial slope for the power spectrum of n s = 0.963 (see Hirschmann et al. 2014 ; Teklu et al. 2015 , for more simulation details; Dolag, Mevius Remus 2017 , for