B[e] supergiants are luminous, massive post-main sequence stars exhibiting non-spherical winds, forbidden lines, and hot dust in a disc-like structure. The physical properties of their rich and complex circumstellar environment (CSE) are not well und
erstood, partly because these CSE cannot be easily resolved at the large distances found for B[e] supergiants (typically $ga 1$~kpc). From mid-IR spectro-interferometric observations obtained with VLTI/MIDI we seek to resolve and study the CSE of the Galactic B[e] supergiant CPD-57degr,2874. For a physical interpretation of the observables (visibilities and spectrum) we use our ray-tracing radiative transfer code (FRACS), which is optimised for thermal spectro-interferometric observations. Thanks to the short computing time required by FRACS ($<10$~s per monochromatic model), best-fit parameters and uncertainties for several physical quantities of CPD-57degr,2874 were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, and disc inclination. The analysis of VLTI/MIDI data with FRACS allowed one of the first direct determinations of physical parameters of the dusty CSE of a B[e] supergiant based on interferometric data and using a full model-fitting approach. In a larger context, the study of B[e] supergiants is important for a deeper understanding of the complex structure and evolution of hot, massive stars.
Context: As is the case of several other Be stars, Achernar is surrounded by an envelope, recently detected by near-IR interferometry. Aims: We search for the signature of circumstellar emission at distances of a few stellar radii from Achernar, in
the thermal IR domain. Methods: We obtained interferometric observations on three VLTI baselines in the N band (8-13 mic), using the MIDI instrument. Results: From the measured visibilities, we derive the angular extension and flux contribution of the N band circumstellar emission in the polar direction of Achernar. The interferometrically resolved polar envelope contributes 13.4 +/- 2.5 % of the photospheric flux in the N band, with a full width at half maximum of 9.9 +/- 2.3 mas (~ 6 Rstar). This flux contribution is in good agreement with the photometric IR excess of 10-20% measured by fitting the spectral energy distribution. Due to our limited azimuth coverage, we can only establish an upper limit of 5-10% for the equatorial envelope. We compare the observed properties of the envelope with an existing model of this star computed with the SIMECA code. Conclusions: The observed extended emission in the thermal IR along the polar direction of Achernar is well reproduced by the existing SIMECA model. Already detected at 2.2mic, this polar envelope is most probably an observational signature of the fast wind ejected by the hot polar caps of the star.
