New Non-Parametric Approach to Determine Proper Motion of Star Clusters

Abstract: The bulk motion of star clusters can be determined after careful membership analysis using parametric or non-parametric approaches. This study aims to implement non-parametric membership analysis based on Binned Kernel Density Estimator which accounts measurements errors (simply called BKDE-e) and to determine the average proper motion of each cluster. This method is applied to 178 selected star clusters with angular diameter less than 20 arc minutes. Proper motion data from UCAC4 are used for membership determination. Non-parametric analysis using BKDE-e successfully determined the average proper motion of 129 clusters, with good accuracy. Compared to COCD and NCOVOCC, there are 79 clusters with less than $3\sigma$ difference. Moreover, we are able to analyse distribution of the member stars in vector point diagram which is not always normal distribution.