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Recent spatially-resolved observations of massive early-type galaxies (ETGs)have uncovered evidence for radial gradients of the stellar initial massfunction (IMF), ranging from super-Salpeter IMFs in the centre to MilkyWay-like beyond the half-light radius, $r_e$. We compare these findings withour new cosmological, hydrodynamical simulations based on the EAGLE model thatself-consistently vary the IMF on a per-particle basis such that it becomeseither bottom-heavy (LoM-50) or top-heavy (HiM-50) in high-pressureenvironments. These simulations were calibrated to reproduce inferred IMFvariations such that the IMF becomes "heavier" due to either excess dwarf starsor stellar remnants, respectively, in galaxies with increasing stellar velocitydispersion. In agreement with observations, both simulations produce negativeradial IMF gradients, transitioning from high to low excess mass-to-light ratio(MLE) at around $r_e$. We find negative metallicity radial gradients for bothsimulations, but positive and flat [Mg/Fe] gradients in LoM-50 and HiM-50,respectively. Measured in radial bins, the MLE increases strongly with localmetallicity for both simulations, in agreement with observations. However, thelocal MLE increases and decreases with local [Mg/Fe] in LoM-50 and HiM-50,respectively. These qualitative differences can be used to break degeneraciesin the manner with which the IMF varies in these high-mass ETGs. At $z=2$, wefind that the MLE has a higher and lower normalization for bottom- andtop-heavy IMF variations, respectively. We speculate that a hybrid of our LoMand HiM models may be able to reconcile observed IMF diagnostics instar-forming galaxies and ETGs.

Calibrated, cosmological hydrodynamical simulations with variable IMFs III: Spatially-resolved properties and evolution