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-magnitude diagrams. Mean proper motion of the clusters in RA and DEC is
estimated as -1.90 \pm 0.01 and -2.57 \pm 0.01 mas/yr for NGC 6067, -2.57 \pm
0.01 and 3.92 \pm 0.01 mas/yr for NGC 2506 and -2.41 \pm 0.01 and -5.05 \pm
0.02 mas/yr for IC 4651. Distances are estimated as 3.01 \pm 0.87, 3.88 \pm
0.42 and 1.00 \pm 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 \pm 8 Myr, 2.09 \pm 0.14 Gyr
and 1.59 \pm 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 0.77 - 1.54 Solar mass.
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's age indicates that NGC 2506 and IC 4651 are dynamically relaxed
clusters.
