Orbital Decay in a 20 Minute Orbital Period Detached Binary with a Hydrogen Poor Low Mass White Dwarf

We report the discovery of a detached double white dwarf binary with an orbital period of $\approx20.6\,\rm minutes$, PTF J053332.05+020911.6. The visible object in this binary, PTF J0533+0209B, is a $\approx 0.17\,M_\odot$ mass white dwarf with a helium-dominated atmosphere containing traces of hydrogen (DBA). This object exhibits ellipsoidal variations due to tidal deformation, and is the visible component in a single-lined spectroscopic binary with a velocity semi-amplitude of $K_B=618.7\pm6.9 \, \rm km \, s^{-1}$. We have detected significant orbital decay due to the emission of gravitational radiation, and we expect that the Laser Interferometer Space Antenna (LISA) will detect this system with a signal to noise of $8.4^{+4.2}_{-3.0}$ after four years of operation. Because this system already has a well determined orbital period, radial velocity semi-amplitude, temperature, atmospheric composition, surface gravity, and orbital decay rate, a LISA signal will help fully constrain the properties of this system by providing a direct measurement of its inclination. Thus, this binary demonstrates the synergy between electromagnetic and gravitational radiation for constraining the physical properties of an astrophysical object.