The diverse outcomes of binary white dwarf mergers and connections to Galactic LISA sources

In the coming decade, the millihertz gravitational wave observatory LISA will provide the best constraints yet on the tens of thousands of close white dwarf binaries in the Milky Way, yielding unprecedented insights into the most abundant class of compact object binaries. Following inspiral via gravitational wave emission, interacting white dwarf binary pairs can lead to a multitude of outcomes, including AM Canum Venaticorum (AM CVn) binaries, R Coronae Borealis stars, young, rapidly-spinning single white dwarfs, (millisecond) magnetars, and a variety of explosive transients, most notably Type Ia supernovae. Current and future electromagnetic observations of these various outcomes coupled with the forthcoming flood of data from LISA place us on the precipice of a significant advance in our understanding of the long-term fate of white dwarf binaries. In this paper, we present a suite of mock catalogs of the Milky Way's white dwarf merger history, created using the population synthesis code $\texttt{COSMIC}$. We summarize the various merger outcomes expected (based upon varying white dwarf masses and chemical compositions) and explore ways the rates of these outcomes may vary with model uncertainties pertaining to binary evolution. We publicly release these merger catalogs as a tool for facilitating connections between gravitational wave science and white dwarf binary astrophysics.