v.1, n.1, p.2-18, 2018. The use of artificial intelligence in the search for structural parameters of clusters of young stars A. Hetem1, S. E. Matsuda Sampa1, J. L. Lima Berretta1 1Federal University of ABC ABSTRACT Due to the huge amount of data available to the astrophysicists nowadays it is imperative to use state of the art tools in the many processes involving data reduction, data traformation and generation of high level indicators in order to advance to the physical analysis. With the rise of huge parallel computer resources, it is possible to concatenate the many Artificial Inteligence tools necessary to model the astrophysical data. We present a realization of this idea applied to a real case of astrophysical study: the analysis of a large sample of clusters of young stars in order to investigate the inherent properties of clustering and dynamic evolution of stellar components. To achieve the statistical parameter Q measured for each cluster, it is necessary to pass the original star data set through a series of processes, each one with its own characteriscits, needs and behaviour. So, we present a set of results obtained by the proposed method and some perspectives of future work in this path. Keywords: artificial inteligence; genetic algorithm; cross-entropy; physical-mathematical model; young star cluster. INTRODUCTION Clusters of young stars In our galaxy it is possible to find some groups of stars that move as an unity, when compared to the other stars. In the studies of stellar evolution, the open clusters are very important objects because their members (stars) are of similar chemical composition and same age. Other properties as distance, metallicity and extinction can be easily determined than for isolated stars. Figures 1 and 2 presents examples of such object. When a survey of the characteristics and dimensions of groups of young stars is made, a broad spectrum of values and qualities is observed [1]. Such groups can be found both in the form of large associations of young stars and compact concentrations of protostars embedded in regions of star formation. Taking into account the actual models and processes of stellar formation [2], it is evident the need to investigate the natural connection between these various stellar group scales. Most likely, all stellar formation processes must be connected, despite the scales involved. 2 v.1, n.1, p.2-18, 2018. Figure 1. NGC 265: an example of open cluster in the constelation of Tucana. One can see the almost spherical aglomeration of stars in the center of the picture. (Image Credit: [3]) Figure 2. Mel 111, also known as Coma star cluster: an open star cluster in the constalation of Coma Berenices. (Image Credit: [4]) 3 v.1, n.1, p.2-18, 2018. In previous works [5]; [6] a large sample of groups of young stars was investigated in order to investigate the inherent properties of the stellar components. In these studies, special attention was given to the statistical pa- rameter Q [7], measured for stellar groups, and their possible correlations with the fractal dimension estimated for the projected clouds [8]. The conclusions of these studies show that more than 50% of the studied sample has substructures (or subgroups) that, once analyzed from a statistical and geometric point of view, tend to reproduce simulations of artificial star distributions [9]. An increasing number of publications in recent years have shown that this subject is of great interest, both in the studies of galaxy star groups and in nearby gala- xies [10]. As a consequence, fractal-statistical analysis tools have evolved and allowed new interpretations and modeling [11][12][13]. METHODOLOGY This work was accomplished through the amalgamation of several known methodologies, including: mem- bership and kinematic determination from proper motion, age and mass from colour-magnitude diagrams and theoretical evolutive models, validation with previous results, fractal analysis and dynamic evolution parame- ters and correlation of obtained clusters properties. Fig. 3 presents a pictorial explanation of the sequence of data acquisition, calculus and manipulation and each step is explained in the following subsections. Selected objects The main data relates to the stars belonging to each target cluster. Position, proper motion and parallaxe (and respective uncertainties) were obtained from GAIA DR2 [13]. Magnitudes JHK were obtained from 2MASS catalogue [14]. All the selected young clusters have intermediate distances of d > 2 kpc and similar angular sizes (R < 20 arcmin) for most of the objects. Table 1 presents the fields extracted via SQL queries from the GAIA DR2 archive, including the 2MASS JHK magnitudes cross referenced by the search on-line tool. Table 2 lists the young star clusters analyzed in the present work. Cluster membership determination The extracted data about a given cluster consists of the stars belonging to that cluster contaminated by back- ground stars. We applied artificial inteligence to choose from the obtained data those stars that belong to the cluster, apart of the field stars. A reliable way to evaluate the star membership with relation to a cluster or not is to consider their own motions, that is radial velocities and/or parallaxes velocities. Cluster stars move- ments stablish the velocity components the center of mass due to the gravitational bounding of their members. An usual reference on this subject is [15], who proposed a method for identifying cluster stars by their own movements modelled in a maximum probability frame. The cross entropy (CE) technique was first introduced by [16] and later modified by the same author [17] to deal with discrete combinatorial and continuous multiextremal optimization problems. The CE method has as objective the estimating of probabilities of rare events in complex stochastic networks. It is asymptotic 4 v.1, n.1, p.2-18, 2018. Figure 3. Methods fluxogram: 1) Membership and kinematic properties from proper motion data by using a Bayesian distribution model whose parameters are obtained by cross-entropy and/or genetic algorithms. 2) Age and mass from JHK unreddened magnitudes and theoretical evolutive models. 3) Method validation by comparing with previous results. 4) Fractal analysis and dynamic evolution parameters. 5) Correlation of clusters properties (age, mass, crossing time, tidal radius, fractal parameters, etc). Table 1. Fields extracted from GAIA DR2 catalog. GAIA DR2 description field Gaia2 Unique source designation ext_source_id 2MASS Catalogue source identifier ra [deg] Right ascension ra_error [mas] Standard error of ra dec [deg] Declination dec_error [mas] Standard error of dec parallax [mas] Parallax parallax_error [mas] Standard error of parallax pmra [mas/yr] Proper motion in ra direction pmra_error [mas/yr] Standard error of proper motion in ra direction pmdec [mas/yr] Proper motion in dec direction pmdec_error [mas/yr] Standard error of proper motion in dec direction Qflag Photometric quality flag j_m [mag] Default J-band magnitude h_m [mag] Default H-band magnitude ks_m [mag] Default Ks-band magnitude 5 v.1, n.1, p.2-18, 2018. Table 2. Sample analysed in the present work with information from the literature. Non evident columns are: NT is the number of star members; n is the density (stars per square parsec); R is the radius of the cluster; and rc is the radius of core. cluster NT age d n R rc (Myr) (pc) pc−2 (pc) (pc) Berkeley 86 78 3 1600 1.5 4 Collinder 205 114 3 1900 1.5 4.9 0.3 Hogg 10 21 2 2300 0.9 2.7 0.46 Hogg 22 28 3 1700 1.5 2.5 1.9 Lynga 14 10 5 1000 4.6 0.8 0.22 Markarian 38 23 3 1600 2.5 1.7 0.13 NGC 2244 292 3 1600 1.8 7.1 NGC 2264 337 3 740 3.4 5.6 NGC 2302 17 9 1600 1.6 1.9 0.54 NGC 2362 96 4 1400 8 2 0.26 NGC 2367 32 3 2200 1.4 2.7 0.34 NGC 2645 71 5 1900 2.3 3.2 0.22 NGC 2659 200 4 2000 2.2 5.3 1.93 NGC 3572 50 3 2000 1.9 5.3 0.16 NGC 3590 19 8 1700 1.1 3.7 0.29 NGC 5606 54 5 2400 1 4 0.51 NGC 6178 38 2 1400 0.8 2.7 0.3 NGC 6530 75 1 1300 0.7 5 NGC 6604 58 3 1700 1.9 2.5 0.5 NGC 6613 66 4 1600 3 2.8 0.12 Ruprecht 79 71 3 2700 1.9 3.1 2.2 Stock 13 16 3 2000 1.9 3.3 0.11 Stock 16 82 2 2000 0.8 5.4 1.2 Trumpler 18 144 3 2800 0.6 3 0.38 Trumpler 28 9 2 1100 1.2 4.7 0.84 Observation: A parsec (symbol pc) corresponds to 3.26156 lightyears or 3.0857 × 1016 m. convergent, as demonstrated in works of [18], and efficient in solving continuous multi-extremal optimization problems [19]. [20] presents an extended list of applications of CE method and its formalism. Cross-Entropy method In this work, we applied the global optimization technique based on the CE global optimization procedure to fit the observed distribution of proper motions and to obtain the probability of a given star belonging or not to the cluster. Being a stochastic method, the CE technique behavior is similar to simple general adaptive method for estimating optimal parameters values and does not need an implementation of priory deep knowledge of the model. The iterative CE method consists of some steps, as follows. Initially the first generation is stablished as sets of parameters randomly chosen based on some pre-defined criteria, which depends on the problem being analyzed.