Characterizing accreting double white dwarf binaries with the Laser Interferometer Space Antenna and Gaia

We demonstrate a method to fully characterize mass-transferring double white dwarf (DWD) systems with a helium-rich (He) WD donor based on the mass--radius relationship for He WDs. Using a simulated Galactic population of DWDs, we show that donor and accretor masses can be inferred for up to $\sim\, 60$ systems observed by both Laser Interferometer Space Antenna (LISA) and Gaia. Half of these systems will have mass constraints $Δ\,M_{\rm{D}}\lesssim0.2M_{\odot}$ and $Δ\,M_{\rm{A}}\lesssim2.3\,M_{\odot}$. We also show how the orbital frequency evolution due to astrophysical processes and gravitational radiation can be decoupled from the total orbital frequency evolution for up to $\sim 50$ of these systems.