SIMBAD references

The combination of several mass-decreasing processes may critically affect the structure of open clusters (OCs), to the point that most dissolve into the field in a time-scale shorter than ~1Gyr. Therefore, as is observed, old OCs should be sparse within the Galaxy. These mass-decreasing processes can only be quantifiably examined given the derivation of the fundamental parameters, age, distance and mass, for a sample of old OCs. In this paper we focus on four candidate old star clusters, namely, LK1, LK10, FSR1521 and FSR1555. The first two clusters, discovered by Le Duigou & Knödlseder, are projected towards the Cygnus association, whilst the remaining two have been detected in the fourth quadrant as cluster candidates from stellar overdensities by Froebrich, Scholz & Raftery. To analyse the target clusters we construct near-infrared colour-magnitude diagrams (CMDs) and derive stellar radial density profiles (RDPs). The CMDs are constructed using Two Micron All-Sky Survey (2MASS) J, H and K_sbands, and the intrinsic morphologies of the target OCs within these diagrams are revealed by applying a field-star decontamination algorithm. Fundamental parameters are estimated with Padova isochrones built for the 2MASS filters. We derive extinctions to the objects within the range 3.4 ≤ A_V≤ 8.9, which makes them suitable for the near-infrared analysis, ages within 1.0-2.0Gyr, and distances from the Sun within 1.4-4.5kpc. These distances, in conjunction with the positions in the sky, place the present four OCs close to the solar circle (≲0.6kpc). For LK10 our photometry reaches a depth ∼3mag below the main-sequence turn off, from which we derive a relatively steep mass function slope (χ = 2.4±0.4) when compared to the Salpeter value (χ = 1.35). LK10 is a rather massive old OC, with a mass within 1360 ≤ m (M_☉) ≤ 4400, for stars in the observed magnitude range and the extrapolation to 0.08M_☉, respectively. The mass estimated in the restricted magnitude range for the remaining, more distant OCs is within 260 ≤ m (M_☉) ≤ 380. However, similarity with the CMD morphology and red clump of LK10 suggests that they may be as massive as LK10. The RDPs are well represented by a King-like function, except LK10, which has a central cusp suggesting post-core collapse. Structurally, LK1, FSR1521 and FSR1555 are similar to a sample of nearby OCs of comparable age.