In order to study the relation between the core and corona in
galactic star clusters, the spatial structure of 38 rich open star clusters has
been studied using radial density profiles derived from the photometric data of
the Digital Sky Survey. The shape of the radial density profile indicates
that the corona, most probably, is the outer region around the cluster. It can
exist from the very beginning of the cluster formation and dynamical
evolution is not the reason for its occurrence. The study does not find any
relation between cluster size and age but indicates that the clusters with
galacto-centric distances > 9.5 kpc have larger sizes. Further, we find that
the average value of the core radius is 1.3 ± 0.7 pc and that of annular width
of the corona is 5.6 ± 1.9 pc, while average values of densities of cluster
members in the core and corona are 15.4 ± 9.9 star/pc2 and 1.6 ± 0.99
star/pc2 respectively. Average field star contaminations in the core and
corona are ~35% and 80% respectively. In spite of smaller densities
in the coronal region, it contains ~75% of the cluster members due to
its larger area in comparison to the core region. This clearly demonstrates
the importance of the coronal region in studies dealing with the entire stellar
contents of open star clusters as well as their dynamical evolution. In contrast
to the cluster cores, the structure of coronal regions differs significantly
from one cluster to other.