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The enigmatic object HD 45166 is a qWR star in a binary system with anorbital period of 1.596 day, and presents a rich emission-line spectrum inaddition to absorption lines from the companion star (B7 V). As the systeminclination is very small (i=0.77 +- 0.09 deg), HD 45166 is an ideal laboratoryfor wind-structure studies. The goal of the present paper is to determine thefundamental stellar and wind parameters of the qWR star. A radiative transfermodel for the wind and photosphere of the qWR star was calculated using thenon-LTE code CMFGEN. The wind asymmetry was also analyzed using arecently-developed version of CMFGEN to compute the emerging spectrum intwo-dimensional geometry. The temporal-variance spectrum (TVS) was calculatedfor studying the line-profile variations. Abundances, stellar and windparameters of the qWR star were obtained. The qWR star has an effectivetemperature of Teff=50000 +- 2000 K, a luminosity of log(L/Lsun)=3.75 +- 0.08,and a corresponding photospheric radius of Rphot=1.00 Rsun. The star ishelium-rich (N(H)/N(He) = 2.0), while the CNO abundances are anomalous whencompared either to solar values, to planetary nebulae, or to WR stars. Themass-loss rate is Mdot = 2.2 . 10^{-7} Msun/yr, and the wind terminal velocityis vinf=425 km/s. The comparison between the observed line profiles and modelscomputed under different latitude-dependent wind densities strongly suggeststhe presence of an oblate wind density enhancement, with a density contrast ofat least 8:1 from equator to pole. If a high velocity polar wind is present(~1200 km/s), the minimum density contrast is reduced to 4:1. The windparameters determined are unusual when compared to O-type stars or to typicalWR stars. (abridged)

The qWR star HD 45166. II. Fundamental stellar parameters and evidence of a latitude-dependent wind