Evidence for a substellar secondary in the magnetic cataclysmic binary   EF Eridani
  Low-state spectrophotometry of the short-period polar EF Eridani (Porb=81 min) found the system at V=18.0 with no trace of the companion (Wheatley and Ramsay 1998). We show that the lack of such spectral features implies that the companion to the white dwarf in EF Eri has a spectral type later than M9 and is either a transition object at the brink of hydrogen burning or a brown dwarf. The optical low state spectrum indicates a temperature of the white dwarf of Teff=9500+-500K. This is one of the coldest white dwarfs in cataclysmic variables, implying a cooling age t_cool>=10e9 yrs or accretional heating at a rate as given by gravitational radiation. The large age of the system excludes a warm brown dwarf as companion. EF Eri has either just passed through the period minimum of cataclysmic variable stars or has started mass transfer from an old brown dwarf secondary. 
K. Beuermann, P. Wheatley, G. Ramsay, F. Euchner, B.T. Gaensicke