A comprehensive photometric study of dynamically evolved small van den Bergh-Hagen open clusters

We present results from Johnson $UBV$, Kron-Cousins $RI$ and Washington $CT_1T_2$ photometries for seven van den Bergh-Hagen (vdBH) open clusters, namely, vdBH\,1, 10, 31, 72, 87, 92, and 118. The high-quality, multi-band photometric data sets were used to trace the cluster stellar density radial profiles and to build colour-magnitude diagrams (CMDs) and colour-colour (CC) diagrams from which we estimated their structural parameters and fundamental astrophysical properties. The clusters in our sample cover a wide age range, from $\sim$ 60 Myr up to 2.8 Gyr, are of relatively small size ($\sim$ 1 $-$ 6 pc) and are placed at distances from the Sun which vary between 1.8 and 6.3 kpc, respectively. We also estimated lower limits for the cluster present-day masses as well as half-mass relaxation times ($t_r$). The resulting values in combination with the structural parameter values suggest that the studied clusters are in advanced stages of their internal dynamical evolution (age/$t_r$ $\sim$ 20 $-$ 320), possibly in the typical phase of those tidally filled with mass segregation in their core regions. Compared to open clusters in the solar neighbourhood, the seven vdBH clusters are within more massive ($\sim$ 80 $-$ 380$M_\odot$), with higher concentration parameter values ($c$ $\sim$ 0.75$-$1.15) and dynamically evolved ones.