  We report the discovery of pulsations in the extremely low mass (ELM), likely
helium-core white dwarf GD 278 via ground- and space-based photometry. GD 278
was observed by the Transiting Exoplanet Survey Satellite (TESS) in Sector 18
at a 2-min cadence for roughly 24 d. The TESS data reveal at least 19
significant periodicities between 2447-6729 s, one of which is the longest
pulsation period ever detected in a white dwarf. Previous spectroscopy found
that this white dwarf is in a 4.61 hr orbit with an unseen >0.4 solar-mass
companion and has Teff = 9230 +/- 100 K and log(g) = 6.627 +/- 0.056, which
corresponds to a mass of 0.191 +/- 0.013 solar mass. Patterns in the TESS
pulsation frequencies from rotational splittings appear to reveal a stellar
rotation period of roughly 10 hr, making GD 278 the first ELM white dwarf with
a measured rotation rate. The patterns inform our mode identification for
asteroseismic fits, which unfortunately do not reveal a global best-fit
solution. Asteroseismology reveals two main solutions roughly consistent with
the spectroscopic parameters of this ELM white dwarf, but with vastly different
hydrogen-layer masses; future seismic fits could be further improved by using
the stellar parallax. GD 278 is now the tenth known pulsating ELM white dwarf;
it is only the fifth known to be in a short-period binary, but is the first
with extended, space-based photometry.
