The eclipsing binary V578 Mon in the Rosette nebula: age and distance to NGC 2244 using Fourier disentangled component spectra

V578 Mon is a member of the young stellar cluster NGC 2244 which is embedde d in the Rosette nebula. It is a double-lined binary, consisting of two ear ly-B type components which eclipse each other partially during their 2.4084 8-day orbit. A novel technique of Fourier disentangling is applied to disen tangle the spectrum of the binary into the spectra of its components, allow ing a direct spectroscopic temperature determination for each component. To gether with an analysis of the light curve, the spectral disentangling proc ess allows us to derive the orbital and fundamental stellar parameters. The hotter star (T-eff = 30 000 K) has a mass of 14.5 M. and a radius of 5.2 R .. The cooler one (T-eff = 26 400 K) has a mass of 10.3 Mg and a radius of 4.3 R.. Both stars are well inside their critical Roche lobe and move in an eccentric orbit (e=0.087) which has a semi-major axis of 22 R. and is seen at an inclination of 72.6 degrees. The rotation of both stars is synchroni zed with the orbital motion. The systemic velocity of 34.9 km s(-1) confirm s that the binary belongs to NGC 2244. The age of the binary, and hence of NGC 2244, is (2.3+/- 0.2) 10(6) years. From the fundamental stellar paramet ers and the interstellar absorption, the distance to the cluster is derived to be 1.39 +/- 0.1 kpc, i.e. slightly lower than that found from photometr ic studies. Its age and space velocity indicate that NGC 2244 is formed in the galactic plane. The high accuracy obtained (e.g. probable errors of 0.5 % for the masses, 1-1.5% for the radii, despite the lack of total eclipses, and 1.5% for the temperatures) is a direct consequence of the spectral dis entangling technique, which as a by-product delivers very accurate radial v elocities for all orbital phases.