V407 Vul: a triple star system with an AM CVn detectable by gravitational wave observatories

The AM CVn class includes mass transferring, ultra-compact double white dwarf binaries with orbital periods on the timescale of minutes. A long-standing puzzle is that none of the roughly fifty ultra-compact, "verification binaries" which are easily detectable in the millihertz gravitational wave regime reside in a triple star configuration. Much evidence has hinted at V407 Vul being an inspiraling, double white dwarf AM CVn with an orbital period of 569s. Yet, a decisive confirmation has proved challenging since a main sequence star dominates its visible spectrum. We present a clear confirmation of the triple star nature of the source by detecting a significant astrometric wobble of the photocentre on the 569s orbital period of the binary. The AM CVn and the main sequence components are gravitationally bound with a spatial separation of roughly 0.03-0.04'', equating to an orbital separation of approximately 120AU. A total of 23 years of orbital timing constrained the orbital decay of the AM CVn as being precise to the 1% level, critical in understanding if this class of binary survives through a period minimum or coalesce. New Hubble Space Telescope ultra-violet imaging and spectroscopic data allowed the isolated detection of the AM CVn at shorter wavelengths, revealing an approximately 58000 K accretor white dwarf, while placing a firm distance constraint of 3510+140-110 pc. At this distance, we predict that the Laser Interferometer Space Antenna (LISA) will detect V407 Vul with a 28.4+-9.2 signal-to-noise ratio in a 4yr mission time, making it the first verification binary with an outer tertiary, or "verification triple", detectable for millihertz gravitational wave observatories.