The Implementation of Binned Kernel Density Estimation to Determine Open Clusters' Proper Motions: Validation of the Method

TL;DR

This paper introduces BKDE-e, a non-parametric method for determining open cluster memberships using proper motions that incorporates measurement errors, showing improved accuracy over traditional KDE in simulations and real data applications.

Contribution

The paper proposes BKDE-e, an error-aware non-parametric method for stellar membership determination, enhancing accuracy and robustness over existing KDE approaches.

Findings

BKDE-e reduces misclassification by a factor of two compared to KDE.

Median accuracy of BKDE-e is about 93%, comparable to parametric methods.

Application to UCAC4 data yields consistent proper motion estimates for NGC 2682.

Abstract

Stellar membership determination of an open cluster is an important process to do before further analysis. Basically, there are two classes of membership determination method: parametric and non-parametric. In this study, an alternative of non-parametric method based on Binned Kernel Density Estimation that accounts measurements errors (simply called BKDE-e) is proposed. This method is applied upon proper motions data to determine cluster's membership kinematically and estimate the average proper motions of the cluster. Monte Carlo simulations show that the average proper motions determination using this proposed method is statistically more accurate than ordinary Kernel Density Estimator (KDE). By including measurement errors in the calculation, the mode location from the resulting density estimate is less sensitive to non-physical or stochastic fluctuation as compared to ordinary KDE that excludes measurement errors. For the typical mean measurement error of 7 mas/yr, BKDE-e suppresses the potential of miscalculation by a factor of two compared to KDE. With median accuracy of about 93%, BKDE-e method has comparable accuracy with respect to parametric method (modified Sanders algorithm). Application to real data from The Fourth USNO CCD Astrograph Catalog (UCAC4), especially to NGC 2682 is also performed. The mode of member stars distribution on Vector Point Diagram is located at $\mu_{\alpha}\cos\delta=-9.94\pm0.85$ mas/yr and $\mu_{\delta}=-4.92\pm0.88$ mas/yr. Although the BKDE-e performance does not overtake parametric approach, it serves a new view of doing membership analysis, expandable to astrometric and photometric data or even in binary cluster search.