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Resolving the dusty circumstellar environment of the A[e] supergiant HD 62623 with the VLTI/MIDI

B[e] stars are hot stars surrounded by circumstellar gas and dust responsible for the presence of emission lines and IR-excess in their spectra. How dust can be formed in this highly illuminated and diluted environment remains an open issue. HD 62623 is one of the very few A-type supergiants showing the B[e] phenomenon. We obtained nine calibrated visibility measurements using the VLTI/MIDI instrument in SCI-PHOT mode and PRISM spectral dispersion mode with projected baselines ranging from 13 to 71 m and with various position angles. We used geometrical models and physical modeling with a radiative transfer code to analyze these data. The dusty circumstellar environment of HD 62623 is partially resolved by the VLTI/MIDI even with the shortest baselines. The environment is flattened and can be separated into two components: a compact one whose extension grows from 17 mas at 8 microns to 30 mas at 9.6 microns and stays almost constant up to 13 microns, and a more extended one that is over-resolved even with the shortest baselines. Using the radiative transfer code MC3D, we managed to model HD 62623's circumstellar environment as a dusty disk with an inner radius of 3.85+-0.6 AU, an inclination angle of 60+-10 deg, and a mass of 2x10^-7Mo. It is the first time that the dusty disk inner rim of a supergiant star exhibiting the B[e] phenomenon is significantly constrained. The inner gaseous envelope likely contributes up to 20% to the total N band flux and acts like a reprocessing disk. Finally, the hypothesis of a stellar wind deceleration by the companion's gravitational effects remains the most probable case since the bi-stability mechanism does not seem to be efficient for this star.