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Fitting Isochrones to Open Cluster Photometric Data

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Fitting Isochrones to Open Cluster Photometric Data A&A 539, A125 (2012) Astronomy DOI: 10.1051/0004-6361/201118206 & c ESO 2012 Astrophysics Fitting isochrones to open cluster photometric data II. Nonparametric open cluster membership likelihood estimation and its application in optical and 2MASS near-IR data W. S. Dias, H. Monteiro, T. C. Caetano, and A. F. Oliveira UNIFEI, DFQ – Instituto de Ciências Exatas, Universidade Federal de Itajubá, Itajubá MG, Brazil e-mail: [email protected] Received 4 October 2011 / Accepted 9 December 2011 ABSTRACT Aims. Open clusters are essential tools for understanding Galactic structure, as well as stellar evolution, because they are distributed over the whole Galactic plane, and because their ages, distances, and reddening can be determined. The values of derived cluster fundamental parameters can vary greatly because of the often subjective nature of both the isochrone fitting technique and member star selection. To minimize the subjectivity in the selection of stars and to improve the fitting procedure, our group has developed a nonparametric method that estimates the membership likelihood for apparent cluster stars. Methods. The cluster member selection method is based on the star position relative to the cluster center, the density of stars in the color–magnitude diagram (which can be multidimensional), the photometric errors, and the limiting magnitude of observations. We use this method, together with the global optimization tool developed in our previous articles, to fit theoretical isochrones to open cluster photometric data, making use of UBV and 2MASS data sets. Results. Using this likelihood estimation as a weight in the fitting procedure, we show that the method is robust in that it assigns low weights to most contaminating stars and high weights to the stars that are likely cluster members. Our results show that the fundamental parameters determined using 2MASS data agree with those from UBV data when both are determined from the global optimization fitting method, however, the analysis of the open cluster Dias 6 indicates that a revision of the determined parameters might be required for some cases. Key words. open clusters and associations: general 1. Introduction One of the main reasons for the lack of determined param- eters, besides the lack of observational data, is the presence Open clusters are essential tools for understanding the structure of field contaminating stars that make it difficult to identify and dynamics of our Galaxy, as well as in providing constraints true members in a cluster. The effect translates to open clus- to star formation history in the disk. Our group focuses on this ter features being less evident in the color–magnitude diagram subject using open clusters to determine the velocity of the spiral (CMD), so it affects the determination of the fundamental para- arms and the location of the corotation radius based on observa- meters obtained through the usual main sequence fitting method tional data (see details in Dias & Lépine 2005) and the connec- (MSF). tion between features of the metallicity gradient in the Galactic Proper motion data is used to (statistically) distinguish be- disk and the spiral structure (Lépine et al. 2011). This research tween members and nonmembers (see the works of our group requires well-determined ages, distances and spatial velocities e.g. Dias et al. 2006; and the recent method proposed by Sánchez that allow spatial integration of the cluster orbits backwards in et al. 2010, discussing the dependence of the membership prob- time to determine where they were born. Clearly with more ac- abilities obtained from kinematical variables on the radius of curate determination of cluster membership it is also possible to the field of view around open clusters and references therein), better determine distances, ages, and velocities (proper motion but the efficiency is still constrained by the limiting magni- and radial velocity). tude and the errors, especially for faint stars. The lack of in- The open clusters provide the possibility of determining their formation on the photometric standard system associated with distance, age and metallicity. Even though about two thousand the precise proper motion data limits more efficient analysis of open clusters are known, only about 60% have determined fun- the CMDs and consequently accurate fundamental parameter damental parameters1. determination. Very schematically, from the photometric point of view, one can find different approaches to decontaminating the field Figures 3–30 are available in electronic form at stars: http://www.aanda.org 1 Information obtained from the version 3.1 of the New catalogue of – through statistical comparison of star samples taken from the optically visible open clusters and candidates (Dias et al. 2002), avail- cluster region and offset field (see Carraro & Costa 2007,and able electronically at www.astro.iag.usp.br/~wilton references therein; and Bonatto & Bica 2007); Article published by EDP Sciences A125, page 1 of 21 A&A 539, A125 (2012) – CMDs ploted using only stars within the determined cluster 2. Estimating membership likelihood limits (Vázquez et al. 2010, 2008;Tadross2008); – considering photometric membership estimates based on the In Paper I we introduced schemes to filter out contaminat- position of the star in the CMDs and color–color diagram ing field stars, trying to eliminate the majority of the non- (Clariá & Lapasset 1986; and recently Piatti et al. 2010); cluster members in the most efficient manner and then assign- – CMD cut in strips 1 mag wide, and then the color–color dia- ing weights to the remaining stars based on characteristics such gram analyzed for the stars contained in each strip (Carraro as distance to the center of the cluster, among others. This was et al. 2010, and references therein). done to improve the accuracy and precision of the fitting method, which is directly related to how well the cluster stars used in the fit are defined. In this work we adopt a new approach to substi- Basically, analysis of the CMDs is preceded by a decontamina- tute the filtering and weighing procedure by using a nonparamet- tion process of the field stars, where stars that do not match a ric estimation of membership likelihood. The objective here is defined criterion are not considered members of the cluster and to maximize contrast of cluster stars in relation to the field stars, are not used in the fits. giving some estimate of membership likelihood, instead of only Our recent work has emphasized two main points in de- decontaming and removing outliers. The nonparametric weight- termining the fundamental parameters of open clusters: 1) the ing scheme we developed takes the observational data available subjectivity in the isochrone fitting and 2) the apparent require- for the open cluster to be studied and computes the membership ment of U band photometric data. To derive the fundamen- likelihood for each star in the field based on the following: tal parameters of open clusters, the main sequence “fitting” in most works until today has been done mostly with subjective visual fitting. We have already addressed the subjectivity of – the magnitude limit of observations; the (visual) isochrone fitting in Monteiro et al. (2010, hereafter – density profile of stars as a function of radius distance from Paper I), so we refer the reader to that work for more detailed the center of the cluster; discussion. – density of stars in magnitude space. The U band photometry allows for a better determination of the color excess and therefore leads to a more accurate de- termination of the distance modulus via MSF. The color excess The magnitude limit of observation is taken based on the V filter. toward the cluster is determined based on the observed photo- A histogram of the observed V magnitudes is constructed and − metric data, typically by visual fitting isochrones to the (B V) the weight is set zero for stars fainter than the histogram peak. − vs. (U B) diagram, as in Paper I and in this paper. However, we This procedures effectively disregards in the analysis stars that investigated the possibility of determining open cluster param- are intrinsically bright but at greater distances. eters from only BVRI photometry in Monteiro & Dias (2011), where we show that it is in fact possible with reasonable pre- A density profile is obtained for remaining stars as a func- cision and accuracy. The positive results in Monteiro & Dias tion of distance to the cluster center using a Gaussian kernel. (2011) lead us to the question of whether it is possible to de- The width of the kernel can be supplied by the user or estimated termine accurate and precise fundamental parameters of open based on the distribution of distances of the stars among them- clusters using only 2MASS near-IR data. selves. The procedure calculates for each star its distance to all other stars, and the average and standard deviation of the dis- Accurate distances and ages require knowing the stars that tances is obtained after repeating for all stars in the sample. The belong to the cluster. Membership likelihood is important for σ ff standard deviation is used as the width ( )oftheGaussianker- untangling the features (e.g. main sequence, turn-o , and giant nel if this is not supplied by the user. branch) of the cluster in the CMDs from field stars for posterior physical parameters determination via MSF, either by visual fit From the density distribution obtained previously the proce- or automated fitting routines. dure determines the center of the cluster in the observed field. In this context we present a nonparametric method that es- This can be done in two ways: 1) finding the peak of the density timates the likelihood values of stars observed in a cluster field distribution and 2) calculating the average X and Y position in based on their limiting magnitude of observation, position rela- the field, weighted by the density distribution.
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