First results from the IllustrisTNG simulations: A tale of two elements
  -- chemical evolution of magnesium and europium
  The distribution of elements in galaxies provides a wealth of information
about their production sites and their subsequent mixing into the interstellar
medium. Here we investigate the distribution of elements within stars in the
IllustrisTNG simulations. In particular, we analyze the abundance ratios of
magnesium and europium in Milky Way-like galaxies from the TNG100 simulation
(stellar masses ${\log} (M_\star / {\rm M}_\odot) \sim 9.7 - 11.2$). As
abundances of magnesium and europium for individual stars in the Milky Way are
observed across a variety of spatial locations and metallicities, comparison
with the stellar abundances in our more than $850$ Milky Way-like galaxies
provides stringent constraints on our chemical evolutionary methods. To this
end we use the magnesium to iron ratio as a proxy for the effects of our SNII
and SNIa metal return prescription, and a means to compare our simulated
abundances to a wide variety of galactic observations. The europium to iron
ratio tracks the rare ejecta from neutron star -- neutron star mergers, the
assumed primary site of europium production in our models, which in turn is a
sensitive probe of the effects of metal diffusion within the gas in our
simulations. We find that europium abundances in Milky Way-like galaxies show
no correlation with assembly history, present day galactic properties, and
average galactic stellar population age. In general, we reproduce the europium
to iron spread at low metallicities observed in the Milky Way, with the level
of enhancement being sensitive to gas properties during redshifts $z \approx
2-4$. We show that while the overall normalization of [Eu/Fe] is susceptible to
resolution and post-processing assumptions, the relatively large spread of
[Eu/Fe] at low [Fe/H] when compared to that at high [Fe/H] is very robust.
