Updated fundamental parameters of the old open cluster NGC 188 based on $Gaia$-EDR3

Abstract

This paper revisits fundamental properties of the old open cluster NGC 188 based on more reliable cluster members in $Gaia$-EDR3. The DBSCAN clustering algorithm is used to identify cluster members in a normalized 5D parametric space. We obtain 1212 core members and 183 border members down to $G\sim 21$ mag within 60 arcmin of the cluster center. These 5D cluster members enable us to estimate more precise fundamental parameters for the cluster. The distance of NGC 188 is determined to be 1847 ± 6 pc using a Monte-Carlo simulation method. The lower limit of the cluster radius is estimated to be $R_{cl}\sim 34$ arcmin (18.2 pc). We find that NGC 188 has a core radius of $R_{c}= 4.5 \pm 0.1$ arcmin (2.4 ± 0.1 pc) and a tidal radius of $R_{t}= 56.3 \pm 8.8$ arcmin (30.2 ± 4.7 pc), respectively. The concentration parameter of the cluster is determined to be $\log(R_{t}/R_{c}) \sim 1.1$, indicating that NGC 188 has formed a dense core and an extended halo due to dynamical evolution. We confirm that the halo of the cluster is slightly asymmetrical. We also investigate the Galactic orbit of the cluster based on the obtained distance and kinematics. We determine a low orbit eccentricity ($e\sim 0.053$) and a high maximum distance from the Galactic plane ($Z_{\max}\sim 873$ pc). The orbit parameters indicate that NGC 188 is a typical thick-disk cluster located well outside the solar circle.