  The binary star HD 45166 has been observed since 1922 but its orbital period
has not yet been found. It is considered a peculiar Wolf-Rayet star, and its
assigned classification varied along the years. High-resolution spectroscopic
observations show that the spectrum, in emission and in absorption, is quite
rich. The emission lines have great diversity of widths and profiles. The
Hydrogen and Helium lines are systematically broader than the CNO lines.
Assuming that HD 45166 is a double-line spectroscopic binary, it presents an
orbital period of P = 1.596 days, with an eccentricity of e = 0.18. In
addition, a search for periodicity using standard techniques reveals that the
emission lines present at least two other periods, of 5 hours and of 15 hours.
The secondary star has a spectral type of B7 V and, therefore, should have a
mass of about 4.8 solar masses. Given the radial velocity amplitudes, we
determined the mass of the hot (primary) star as being 4.2 solar masses and the
inclination angle of the system, i = 0.77 degr. As the eccentricity of the
orbit is non zero, the Roche lobes increase and decrease as a function of the
orbital phase. At periastron, the secondary star fills its Roche lobe. The
distance to the star has been re-determined as d = 1.3 kpc and a color excess
of E(B-V)=0.155 has been derived. This implies an absolute B magnitude of -0.6
for the primary star and -0.7 for the B7 star. We suggest that the discrete
absorption components (DACs) observed in the ultraviolet with a periodicity
similar to the orbital period may be induced by periastron events.
