Electromagnetic characterization of the LISA verification binary ZTF J0526$+$5934

Abstract: We present an analysis of new and archival data to the 20.506-minute LISA verification binary J052610.42$+$593445.32 (J0526$+$5934). Our joint spectroscopic and photometric analysis finds that the binary contains an unseen $M_1=0.89\pm0.11~{\rm M_\odot}$ CO-core white dwarf primary with an $M_2=0.38\pm0.07~{\rm M_\odot}$ post-core-burning subdwarf, or low-mass white dwarf, companion. Given the short orbital period and relatively large total binary mass, we find that LISA will detect this binary with signal-to-noise ratio $44$ after 4 years of observations. J0526$+$5934 is expected to merge within $1.8\pm0.3~{\rm Myr}$ and likely result in a ${\rm D}^6$ scenario Type Ia supernova or form a He-rich star which will evolve into a massive single white dwarf.