Faint open clusters with 2MASS: BH 63, Lyngå 2, Lyngå 12 and King 20

Context. Structural and dynamical parameters of faint open clusters are probed with quality 2MASS-photometry and analytical procedures developed for bright clusters. Aims. We derive fundamental parameters of the faint open clusters Lynga 2, BH 63, Lynga 12 and King 20, the last three of which have no prior determinations. We also focus on the structure and dynamical state of these clusters. Methods. J , H and K s 2MASS photometry with errors smaller than 0.2 mag 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 Lynga 2, Lynga 12 and King 20. Results. Reddening values are in the range 0.22≤E(B-V)≤1.9, with BH 63 the most reddened object. Ages of Lynga 2, King 20, Lynga 12 and BH 63 are ≈ 90, ≈ 200, ≈ 560 and ≈ 700 Myr, respectively. The radial density distributions of Lynga 12 and King 20 are well-represented by King profiles. Lynga 2 and BH 63 are very small with core and limiting radii of ≈ 0.12 pc and ≈ 1.5 pc. Yet, they fit in the small-radii tail of the open cluster size distribution. Lynga 12 and King 20 have R core pc and R lim pc. Lynga 2 and Lynga 12 are inside the Solar circle. Total stellar masses (extrapolating the MFs to stars with 0.08 M_) range from ≈ 340 M_ (BH 63) to ≈ 2300 M_ (Lynga 12). Observed masses are ~$1/4$ of these values. In all clusters the core mass function is flatter than the halo's. Conclusions. Faint open clusters can be probed with 2MASS when associated with colour-magnitude filters and field-star decontamination. BH 63 appears to be in an advanced dynamical state, both in the core and halo. To a lesser degree the same applies to King 20. Marginal evidence of dynamical evolution is present in the cores of Lynga 2 and Lynga 12.