The evolutionary history of GD1400, a white dwarf-brown dwarf binary

GD1400AB was one of the first known white dwarf$+$brown dwarf binaries, and is the only one of these systems where the white dwarf is a ZZ Ceti pulsator. Here we present both radial velocity measurements and time series photometry, analysing both the white dwarf pulsations and the effects of irradiation on the brown dwarf. We find the brightness temperatures of 1760$/pm$10 K for the night side and 1860$/pm$10 K for the day side indicate the brown dwarf is hotter than spectra have previously suggested, although brightness temperatures calculated using a larger radius for the brown dwarf are consistent with previously determined spectral types. We also discuss the likely evolutionary pathway of this binary, and put its common envelope phase into context with the other known systems.