Fitting isochrones to open cluster photometric data

Abstract

We present a new technique to fit color-magnitude diagrams of open clusters based on the cross-entropy global optimization algorithm. The method uses theoretical isochrones available in the literature and maximizes a weighted likelihood function based on distances measured in the color-magnitude space. The weights are obtained through a non parametric technique that takes into account the star distance to the observed center of the cluster, observed magnitude uncertainties, the stellar density profile of the cluster among others. The parameters determined simultaneously are distance, reddening, age and metallicity. The method takes binary fraction into account and uses a Monte-Carlo approach to obtain uncertainties on the determined parameters for the cluster by running the fitting algorithm many times with a re-sampled data set through a bootstrapping procedure. We present results for 9 well studied open clusters, based on 15 distinct data sets, and show that the results are consistent with previous studies. The method is shown to be reliable and free of the subjectivity of most previous visual isochrone fitting techniques.

Radial velocities and metallicities from infrared Ca II triplet spectroscopy of open clusters

“…Similar values have been obtained by other investigations in this cluster (Kaluzny & Mazur 1991;Dutra & Bica 2000;Tadross 2001;Tadross et al 2002;Lata et al 2002;Salaris et al 2004;Paunzen & Netopil 2006;Maciejewski & Niedzielski 2007;Maciejewski et al 2008;Paunzen et al 2010;Monteiro et al 2010).…”

Proper motions of the optically visible open clusters based on the UCAC4 catalog

“…We refer the reader to the A79, page 2 of 8 papers of Rubinstein (1997), Rubinstein (1999), and Kroese & Rubinstein (2006) for their very complete discussion of the technique and the series of papers of our group (Monteiro et al 2010;Monteiro & Dias 2011;Dias et al 2012;and Oliveira et al 2013) for an application of the method to the determine fundamental parameters of open clusters. The main goal of the CE continuous multi-extremal optimization method is to find a set of parameters for which the model provides the best description of the data as per maximum likelihood definition.…”

“…We adopted 10 −3 as the value of the tolerance for convergence. For more details, see the description of these parameters in Monteiro et al (2010). An advantage of this fitting procedure is that it allows the determination of the errors on the parameters through a MonteCarlo technique.…”

ASteCA: Automated Stellar Cluster Analysis

“…This can be seen for example in the series of articles by Kerber et al (Kerber et al 2002;Kerber & Santiago 2005) where an estimate of the density of field stars in the cluster region is used to implement a field star removal process together with a cluster CMD modeling strategy that selects the best observed vs. artificial fit via a statistical tool; the white dwarf based Bayesian CMD inversion technique developed in von Hippel et al (2006) expanded and coupled with a basic field star cleaning process in van Dyk et al (2009); the synthetic cluster fitting method introduced in Monteiro et al (2010;MDC10, further developed in the articles Dias et al 2012;Oliveira et al 2013), which includes a likelihood-based decontamination algorithm; the work by Pavani et al (2011) where CMD density-based membership probabilities are given to stars within the cluster region to later apply a very basic isochrone fitting process that makes use of stars close to a given isochrone in CMD space; and the articles by Alves et al (2012) and Dias et al (2014), who employ the same membership probability assignment method used in Pavani et al (2011) coupled with a slightly improved isochrone fitting algorithm based on the one developed by MDC10, but applied to a Hess diagram of the CMD instead of the full CMD. In Buckner & Froebrich (2013) the membership assignment method presented in Froebrich et al (2010), a variation of the Bonatto & Bica (2007) algorithm, is used in conjunction with the Besançon model of the galaxy 16 to derive distances to OCs, based on foreground stars density estimations.…”