  The role of compact binary mergers as the main production site of r-process
elements is investigated by combining stellar abundances of Eu observed in the
Milky Way, galactic chemical evolution (GCE) simulations, binary population
synthesis models, and Advanced LIGO gravitational wave measurements. We
compiled and reviewed seven recent GCE studies to extract the frequency of
neutron star - neutron star (NS-NS) mergers that is needed in order to
reproduce the observed [Eu/Fe] vs [Fe/H] relationship. We used our simple
chemical evolution code to explore the impact of different analytical
delay-time distribution (DTD) functions for NS-NS mergers. We then combined our
metallicity-dependent population synthesis models with our chemical evolution
code to bring their predictions, for both NS-NS mergers and black hole -
neutron star mergers, into a GCE context. Finally, we convolved our results
with the cosmic star formation history to provide a direct comparison with
current and upcoming Advanced LIGO measurements. When assuming that NS-NS
mergers are the exclusive r-process sites, and that the ejected r-process mass
per merger event is 0.01 Msun, the number of NS-NS mergers needed in GCE
studies is about 10 times larger than what is predicted by standard population
synthesis models. These two distinct fields can only be consistent with each
other when assuming optimistic rates, massive NS-NS merger ejecta, and low Fe
yields for massive stars. Population synthesis models and GCE simulations are
in agreement with the current upper limit (O1) established by Advanced LIGO
during their first run of observations. Upcoming measurements will provide
important constraints on the actual local NS-NS merger rate, will provide
insights on the plausibility of the GCE requirement, and will help to define
whether or not compact binary mergers can be the dominant source of r-process
elements in the Universe.
