An Application of The Markov Chain Monte Carlo (MCMC) Method to Open Cluster Membership Determination

Abstract

The determination of membership in open clusters will be more difficult than determination membership of the globular clusters. This is due to the location of open clusters which located on the galactic disk. From that location, when observing open clusters, it will be observed foreground and background stars also. Determination of membership in cluster could be done by calculating the probability of a star becoming a cluster member. We used double elliptic bivariate Gaussian function to represent the population of cluster and field stars in the region. The function has eleven parameters and solved by using Markov Chain Monte Carlo (MCMC). The Metropolis-Hastings algorithm is used in this works to obtain the probability of open cluster membership. We used astrometric data from GAIA Data Release 2 for two open clusters which their membership are to be determined i.e. IC 1590 and NGC 2262. Our result is nearly in accordance with the MWSC II catalogue. After the cluster membership is obtained, the physical parameters of the two clusters using isochrones fitting from [1] are the distance(pc) 2200 and 2366, reddening(mag) 0.728 and 0.830, distance modulus(mag) 12.210 and 12.438 also log age 6.895 and 8.995, respectively for IC 1590 and NGC 2262.