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 $\mathrm{\Delta }{M}_{\mathrm{D}}\lesssim 0.2M_{\odot }$ and $\mathrm{\Delta }{M}_{\mathrm{A}}\lesssim 2.3M_{\odot }$. 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.