Investigating the age and structure of the infrared old open clusters   LK1, LK10, FSR1521 and FSR1555
  (Abridged) - 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 $\approx1$ Gyr. In this paper we focus on 4 candidate old star clusters, namely, LK 1, LK 10, FSR 1521, and FSR 1555. 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 2MASS \jj, \hh, and \ks bands, 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 $3.4\le\aV\le8.9$, which makes them suitable for the near-infrared analysis, ages within $1.0 - 2.0$ Gyr, and distances from the Sun within $1.4 - 4.5$ kpc. These distances, in conjunction with the positions in the sky, place the present 4 OCs close to the solar circle ($\la0.6$ kpc). For LK 10 our photometry reaches a depth $\approx3$ mags below the main sequence turn off, from which we derive a relatively steep mass function slope ($\chi=2.4\pm0.4$) when compared to the Salpeter value ($\chi=1.35$). LK 10 is a rather massive old OC, with a mass within $1360\le m(\ms)\le4400$, for stars in the observed magnitude range and the extrapolation to $0.08 \ms$, respectively. The mass estimated in the restricted magnitude range for the remaining, more distant OCs is within $260\le m(\ms)\le380$. However, similarity with the CMD morphology and red clump of LK 10 suggests that they may be as massive as LK 10. 
Charles Bonatto and Eduardo Bica