Study of open clusters within 1.8 kpc and understanding the Galactic structure

Context. Significant progress has been made in recent years to understand the formation and evolution of our Galaxy, but we still lack a complete understanding of the Galaxy and its structure. Aims. Using an almost complete sample of Galactic open star clusters within 1.8 kpc, we aim to understand the general properties of the open cluster system in the Galaxy and probe the Galactic structure. Methods. We first extracted 1241 open clusters within 1.8 kpc of the Sun from the Milky Way Star Clusters (MWSC) catalog. Considering it an almost complete sample of clusters within this distance, we performed a comprehensive statistical analysis of various cluster parameters such as spatial position, age, size, mass, and extinction. Results. We find an average cluster scale height of z(h) = 60 +/- 2 pc for clusters younger than 700 Myr, which increases to 64 +/- 2 pc when we include all the clusters. The z(h) is found to be strongly dependent on R-GC and age, and on an average, z(h) is more than twice as large as in the outer region than in the inner region of the solar circle, except for the youngest population of clusters. The solar off set is found to be 6.2 +/- 1.1 pc above the formal Galactic plane. We derive a local mass density of rho(0) = 0.090 +/- 0.005 M-circle dot/pc(3) and estimate a negligibly small amount of dark matter in the solar neighborhood. The reddening in the direction of clusters suggests a strong correlation with their vertical distance from the Galactic plane with a respective slope of dE(B - V)/dz = 0.40 +/- 0.04 and 0.42 +/- 0.05 mag /kpc below and above the Galactic plane. We observe a linear mass-radius and mass-age relations in the open clusters and derive the slopes of dR/d(log M) = 2.08 +/- 0.10 and d(log M)/d(log T) = 0.36 +/- 0.05, respectively. Conclusions. The dependence of the spatial distribution of clusters on their age points to a complex interplay between cluster formation and survivability within the Galaxy. The geometrical characteristics of a significant number of clusters enabled us to understand large-scale spatial properties of the cluster systems within the Galaxy. The structural and physical parameters of clusters allowed us to check mutual correlations between the individual parameters.