Stellar population of the Rosette Nebula and NGC 2244: application of the probabilistic random forest

(Abridged) In this work, we study the 2.8x2.6 deg2 region in the emblematic Rosette Nebula, centred at the young cluster NGC 2244, with the aim of constructing the most reliable candidate member list to date, determining various structural and kinematic parameters, and learning about the past and the future of the region. Starting from a catalogue containing optical to mid-infrared photometry, as well as positions and proper motions from Gaia EDR3, we apply the Probabilistic Random Forest algorithm and derive membership probability for each source. Based on the list of almost 3000 probable members, of which about a third are concentrated within the radius of 20' from the centre of NGC 2244, we identify various clustered sources and stellar concentrations, and estimate the average distance of 1489+-37 pc (entire region), 1440+-32 pc (NGC 2244) and 1525+-36 pc (NGC 2237). The masses, extinction, and ages are derived by SED fitting, and the internal dynamic is assessed via proper motions relative to the mean proper motion of NGC 2244. NGC 2244 is showing a clear expansion pattern, with an expansion velocity that increases with radius. Its IMF is well represented by two power laws (dN/dM\propto M^{-\alpha}), with slopes \alpha = 1.05+-0.02 for the mass range 0.2 - 1.5 MSun, and \alpha = 2.3+-0.3 for the mass range 1.5 - 20 MSun, in agreement with other star forming regions. The mean age of the region is ~2 Myr. We find evidence for the difference in ages between NGC 2244 and the region associated with the molecular cloud, which appears slightly younger. The velocity dispersion of NGC 2244 is well above the virial velocity dispersion derived from the total mass (1000+-70 MSun) and half-mass radius (3.4+-0.2 pc). From the comparison to other clusters and to numerical simulations, we conclude that NGC 2244 may be unbound, and possibly even formed in a super-virial state.