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

TL;DR

This paper introduces a non-parametric method using Binned Kernel Density Estimator with measurement error correction to accurately determine the proper motion of star clusters, enabling analysis of star distributions beyond normal assumptions.

Contribution

It presents a novel non-parametric approach (BKDE-e) for membership analysis and proper motion determination of star clusters, improving accuracy and distribution analysis capabilities.

Findings

Successfully determined proper motions for 129 clusters with good accuracy.

79 clusters showed less than 3σ difference compared to existing catalogs.

Enabled analysis of star distribution in vector point diagrams beyond normal distribution assumptions.

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.