X-Shooting EF Eridani: further evidence for a massive white dwarf and a sub-stellar secondary

High resolution spectral observations of the polar EF Eridani obtained in a low state with X-Shooter revealed narrow emission lines from the irradiated secondary. The lines were most prominent in the near-IR CaII-triplet, the more intensive H alpha line had additional emission likely originating from an accretion stream. The lines with a radial velocity amplitude, K(2)(') = 385 +/- 4 km s(-1), serve as tracer of the otherwise unseen companion. The mass function implies a massive white dwarf with M(wd) > 0.65 M(circle dot) at 3 sigma confidence, and a short distance to the binary, d similar to 111 pc (<145 pc at 3 sigma confidence). The spectral energy distribution from the UV to the IR together with the high mass ratio gives further strong evidence of EF Eri being a post period- minimum object with M(2) < 0.06 M(circle dot).