## Methods for improving open cluster fundamental parameters applied to M 52 and NGC 3960

### Abstract

Aims.We derive accurate parameters related to the CMD, structure and dynamical state of M 52 and NGC 3960, whose fields are affected by differential reddening. Previous works estimated their ages in the ranges $35{-}135$ Myr and $0.5{-}1.0$ Gyr, respectively. Methods.J, H and Ks 2MASS photometry with errors <0.2 mag is used to build CMDs, radial density profiles, luminosity and mass functions, and correct for differential reddening. Field-star decontamination is applied to uncover the cluster's intrinsic CMD morphology, and colour–magnitude filters are used to isolate stars with high probability of being cluster members. Results.The differential-reddening corrected radial density profile of M 52 follows King's law with core and limiting radii of $R_{\rm core} =0.91 \pm$ 0.14 pc and $R_{\rm lim} =8.0$ ± 1.0 pc. NGC 3960 presents an excess of the stellar density over King's profile ($R_{\rm core} = 0.62$ ± 0.11 pc and $R_{\rm lim} =6.0$ ± 0.8 pc) at the center. The tidal radii of M 52 and NGC 3960 are $R_{\rm tidal}=13.1$ ± 2.2 pc and $R_{\rm tidal}=10.7$ ± 3.7 pc. Cluster ages of M 52 and NGC 3960 derived with Padova isochrones are constrained to 60 ± 10 Myr and 1.1 ± 0.1 Gyr. In M 52 the core MF ($\chi_{\rm core}=0.89 \pm$ 0.12) is flatter than the halo's ($\chi_{\rm halo}=1.65$ ± 0.12). In NGC 3960 they are $\chi_{\rm core}=-0.74$ ± 0.35 and $\chi_{\rm halo}=1.26$ ± 0.26. The mass locked up in MS/evolved stars in M 52 is ~1200 $M_\odot$, and the total mass (extrapolated to 0.08$M_\odot$) is ~3800 $M_\odot$. The total mass in NGC 3960 is ~1300 $M_\odot$. Conclusions.Compared to open clusters in different dynamical states studied with similar methods, the core and overall parameters of M 52 are consistent with an open cluster more massive than 1000 $M_\odot$ and ~60 Myr old, with some mass segregation in the inner region. The core of NGC 3960 is in an advanced dynamical state with strong mass segregation in the core/halo region, while the somewhat flat overall MF ($\chi\approx 1.07$) suggests low-mass star evaporation. The excess stellar density in the core may suggest post-core collapse. The dynamical evolution of NGC 3960 may have been accelerated by the tidal Galactic field, since it lies ≈0.5 kpc inside the Solar circle

Topics: Galaxy: open clusters and associations: individual: M 52, Galaxy: structure, Galaxy: open clusters and associations: individual: NGC 3960
Publisher: EDP Sciences
DOI identifier: 10.1051/0004-6361:20065315/pdf
OAI identifier: oai:edpsciences.org:dkey/10.1051/0004-6361:20065315