We use cosmological, magnetohydrodynamical simulations of Milky Way-mass galaxies from the Auriga project to study their enrichment with rapid neutron capture (r-process) elements. We implement a variety of enrichment models from both binary neutron star mergers and rare core-collapse supernovae. We focus on the abundances of (extremely) metal-poor stars, most of which were formed during the first ~Gyr of the Universe in external galaxies and later accreted onto the main galaxy. We find that the majority of metal-poor stars are r-process enriched in all our enrichment models. Neutron star merger models result in a median r-process abundance ratio which increases with metallicity, whereas the median trend in rare core-collapse supernova models is approximately flat. The scatter in r-process abundance increases for models with longer delay times or lower rates of r-process producing events. Our results are nearly perfectly converged, in part due to the mixing of gas between mesh cells in the simulations. Additionally, different Milky Way-mass galaxies show only small variation in their respective r-process abundance ratios. Current (sparse and potentially biased) observations of metal-poor stars in the Milky Way seem to prefer rare core-collapse supernovae over neutron star mergers as the dominant source of r-process elements at low metallicity, but we discuss possible caveats to our models. Dwarf galaxies which experience a single r-process event early in their history show highly enhanced r-process abundances at low metallicity, which is seen both in observations and in our simulations. We also find that the elements produced in a single event are mixed with ~10^8 Msun of gas relatively quickly, distributing the r-process elements over a large region.
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