2006A&A...460...83B

Structural and dynamical parameters of faint open clusters are probed with quality 2MASS-photometry and analytical procedures developed for bright clusters. We derive fundamental parameters of the faint open clusters Lynga2, BH63, Lynga12 and King20, the last three of which have no prior determinations. We also focus on the structure and dynamical state of these clusters. J, H and K_s 2MASS photometry with errors smaller than 0.2mag are used to build CMDs, radial density profiles, colour-colour diagrams, luminosity and mass functions. Colour-magnitude filters are used to isolate probable member stars. Field-star decontamination is applied to Lynga2, Lynga12 and King20. Reddening values are in the range 0.22≤E(B-V)≤1.9, with BH63 the most reddened object. Ages of Lynga2, King20, Lynga12 and BH63 are ≃90, ≃200, ≃560 and ≃700Myr, respectively. The radial density distributions of Lynga12 and King20 are well-represented by King profiles. Lynga2 and BH63 are very small with core and limiting radii of ≃0.12pc and ≃1.5pc. Yet, they fit in the small-radii tail of the open cluster size distribution. Lynga12 and King20 have R_core≃0.43pc and R_lim≃3.9pc. Lynga2 and Lynga12 are inside the Solar circle. Total stellar masses (extrapolating the MFs to stars with 0.08M_☉) range from ≃340M_☉ (BH63) to ≃2300M_☉ (Lynga12). Observed masses are ∼1/4 of these values. In all clusters the core mass function is flatter than the halo's. Faint open clusters can be probed with 2MASS when associated with colour-magnitude filters and field-star decontamination. BH63 appears to be in an advanced dynamical state, both in the core and halo. To a lesser degree the same applies to King20. Marginal evidence of dynamical evolution is present in the cores of Lynga2 and Lynga12.