Pinning down neutron star merger rates and populations with observations

Astronomical observations of neutron stars and time-domain transients yield quantitative insight into the rates and population properties of neutron-star mergers over cosmic time. The first neutron-star merger observed in gravitational waves, GW170817, established the connection between neutron stars in compact binaries, gamma-ray bursts, kilonovae, and heavy element ($r$-process) nucleosynthesis. It revolutionized our understanding of matter at supra-nuclear densities, and has remained a key player in joint inference of neutron-star properties alongside radio and x-ray pulsar observations. While no comparable multi-messenger event has yet been discovered, continued astronomical observations will all these individual messengers are providing updated insights on the rate and delay times of neutron-star merger events, the masses and spins of component stars, and the matter properties that define the merger dynamics and the launch of associated outflows. In this talk, I will outline how current astronomical observations constrain the contribution of neutron-star mergers to r-process nucleosynthesis, including the latest gravitational-wave survey results alongside a wide array of additinal constraints on the astrophysics of neutron stars. I will then review how, when neutron-ster merger contribution models are compared to the stellar spectra of Milky Way disk stars, astronomical observations are revealing the need for additional channels of heavy-element production to fully account for the $r$-process element enrichment observed in our galaxy.