Evidence for a substellar secondary in the magnetic cataclysmic binary EF Eridani

Low-state spectrophotometry of the short-period polar EF Eridani (P-orb= 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 t han M9 and is either a transition object at the brink of hydrogen burning o r a brown dwarf. The optical low state spectrum indicates a temperature of the white dwarf of T-eff= 9500 +/- 500 K. This is one of the coldest white dwarfs in cataclysmic variables, implying a cooling age t(cool) greater tha n or equal to 10(9) yrs or accretional heating at a rate as given by gravit ational 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 c ataclysmic variable stars or has started mass transfer from an old brown dw arf secondary.