Mass function and dynamical study of the open clusters Berkeley 24 and Czernik 27

We present a $UBVI$ photometric study of the open clusters Berkeley 24 (Be 24) and Czernik 27 (Cz 27). The radii of the clusters are determined as 2\farcm7 and 2\farcm3 for Be 24 and Cz 27, respectively. We use the Gaia Data Release 2 (GDR2) catalogue to estimate the mean proper motions for the clusters. We found the mean proper motion of Be 24 as $0.35\pm0.06$ mas yr$^{-1}$ and $1.20\pm0.08$ mas yr$^{-1}$ in right ascension and declination for Be 24 and $-0.52\pm0.05$ mas yr$^{-1}$ and $-1.30\pm0.05$ mas yr$^{-1}$ for Cz 27. We used probable cluster members selected from proper motion data for the estimation of fundamental parameters. We infer reddenings $E(B-V)$ = $0.45\pm0.05$ mag and $0.15\pm0.05$ mag for the two clusters. Analysis of extinction curves towards the two clusters show that both have normal interstellar extinction laws in the optical as well as in the near-IR band. From the ultraviolet excess measurement, we derive metallicities of [Fe/H]= $-0.025\pm0.01$ dex and $-0.042\pm0.01$ dex for the clusters Be 24 and Cz 27, respectively. The distances, as determined from main sequence fitting, are $4.4\pm0.5$ kpc and $5.6\pm0.2$ kpc. The comparison of observed CMDs with $Z=0.01$ isochrones, leads to an age of $2.0\pm0.2$ Gyr and $0.6\pm0.1$ Gyr for Be 24 and Cz 27, respectively. In addition to this, we have also studied the mass function and dynamical state of these two clusters for the first time using probable cluster members. The mass function is derived after including the corrections for data incompleteness and field star contamination. Our analysis shows that both clusters are now dynamically relaxedComment: 16 pages including 8 tables. 22 figures. Accepted by MNRA

Astrometric and photometric study of NGC 6067, NGC 2506, and IC 4651 open clusters based on wide-field ground and Gaia DR2 data

We present an analysis of three southern open star clusters NGC 6067, NGC 2506, and IC 4651 using wide-field photometric and Gaia DR2 astrometric data. They are poorly studied clusters. We took advantage of the synergy between Gaia DR2 high precision astrometric measurements and ground-based wide-field photometry to isolate cluster members and further study these clusters. We identify the cluster members using proper motions, parallax and colour\u2013magnitude diagrams. Mean proper motion of the clusters in \u3bc\u3b1cos\u3b4 and \u3bc\u3b4 is estimated as 121.90 \ub1 0.01 and 122.57 \ub1 0.01 mas yr 121 for NGC 6067, 122.57 \ub1 0.01, and 3.92 \ub1 0.01 mas yr 121 for NGC 2506 and 122.41 \ub1 0.01 and 125.05 \ub1 0.02 mas yr 121 for IC 4651. Distances are estimated as 3.01 \ub1 0.87, 3.88 \ub1 0.42, and 1.00 \ub1 0.08 kpc for the clusters NGC 6067, NGC 2506, and IC 4651, respectively, using parallaxes taken from Gaia DR2 catalogue. Galactic orbits are determined for these clusters using Galactic potential models. We find that these clusters have circular orbits. Cluster radii are determined as 10 arcmin for NGC 6067, 12 arcmin for NGC 2506, and 11 arcmin for IC 4651. Ages of the clusters estimated by isochrones fitting are 66 \ub1 8 Myr, 2.09 \ub1 0.14 Gyr, and 1.59 \ub1 0.14 Gyr for NGC 6067, NGC 2506, and IC 4651, respectively. Mass function slope for the entire region of cluster NGC 2506 is found to be comparable with the Salpeter value in the mass range of 0.77\u20131.54 M. The mass function analysis shows that the slope becomes flat when one goes from halo to core region in all the three clusters. A comparison of dynamical age with cluster\u2019s age indicates that NGC 2506 and IC 4651 are dynamically relaxed clusters