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 embedded in the Rosette nebula. It is a double-lined binary, consisting of two early-B type components which eclipse each other partially during their 2.40848-day orbit. A novel technique of Fourier disentangling is applied to disentangle the spectrum of the binary into the spectra of its components, allowing a direct spectroscopic temperature determination for each component. Together with an analysis of the light curve, the spectral disentangling process 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_sun and a radius of 5.2 R_sun . The cooler one (T_eff = 26 400 K) has a mass of 10.3 M_sun and a radius of 4.3 R_sun . 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_sun and is seen at an inclination of 72.6degr . The rotation of both stars is synchronized with the orbital motion. The systemic velocity of 34.9 km s^-1 ,confirms that the binary belongs to NGC 2244. The age of the binary, and hence of NGC 2244, is (2.3±0.2) 10⁶ years. From the fundamental stellar parameters 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 photometric 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^m -1.5% for the radii, despite the lack of total eclipses, and 1.5% for the temperatures) is a direct consequence of the spectral disentangling technique, which as a by-product delivers very accurate radial velocities for all orbital phases. Based on observations obtained at the European Southern Observatory (ESO), La Silla, Chile Table 5 is only available in electronic form at the CDS via anonymous ftp to 130.79.128.5 or at http://cdsweb.u-strasbg.fr