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Gaia and sigma Orionis from 20 Msol to 3 MJup: the most complete and precise Initial Mass Function with a parallax determination?

The sigma Orionis cluster is to date the star-forming region with the largest number of confirmed brown dwarfs and substellar objects below the deuterium burning mass limit. The most massive star, sigma Ori Aa, just in the cluster centre, is the \sim20Msol-mass O9.5V star that illuminates the Horsehead Nebula, while the least massive object yet reported, S Ori 70, is only around 3 MJup. In the middle, there is a continuum of stars and substellar objects of all types (including magnetically active B2Vp stars, Herbig-Haro objects, FU Ori stars or T Tauri brown dwarfs) that makes the cluster a cornerstone in the study of the initial mass function, disc presence, X-ray emission or accretion at all mass domains. However, the derived masses strongly depend on the actual heliocentric distance to the cluster. Gaia will solve the dilemma.