Insight into Binary Star Formation via Modelling Visual Binaries Datasets © Oleg Malkov © Dmitry Chulkov © Dana Kovaleva © Alexey Sytov © Alexander Tutukov © Lev Yungelson Institute of Astronomy, Russian Academy of Sciences, Moscow, Russia [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] © Yikdem Gebrehiwot Entoto Observatory and Research Center, Addis Ababa, Ethiopia Mekelle University, College of Natural and Computational Sciences, Mekelle, Ethiopia [email protected] © Nikolay Skvortsov Institute of Informatics Problems, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia [email protected] © Solomon Belay Tessema Ethiopian Space Science and Technology Institute, Entoto Observatory and Research Center Astronomy and Astrophysics, Addis Ababa, Ethiopia tessemabelay@gmail com Abstract. We describe the project aimed at finding initial distributions of binary stars over masses of components, mass ratios of them, semi-major axes and eccentricities of orbit, and also pairing scenarios by means of Monte-Carlo modeling of the sample of about 1000 visual binaries of luminosity class V with Gaia DR1 TGAS trigonometric parallax larger than 2 mas, limited by 2 200 arcsec, 9.5 , 11.5 , 4 , which can be considered as free of observational incompletness effects. We present some 1 2 preliminary results which allow already to reject initial distributions of≤ binaries≤ over semi-major ≤ axes of the≤ orbits more∆ ≤steep than . Keywords: binary stars,−1 5 stellar formation, modeling ∝ which, combined, we will call “the birth function” 1 Introduction (henceforth, BF). Most important, BF is, first, a benchmark for the Majority of stars accessible for detailed observational theories of star formation and, second, the base for the study appear to be binary ones. Interaction between estimates of the number of objects in the models of binary star components in the course of their evolution different stellar populations and model rates of various results in a rich variety of astrophysical phenomena and events, e. g., supernovae explosions etc. objects. Study of the structure and evolution of binary In the present study, we assume that BF is defined by stars is one of the most actively developing fields of the three fundamental functions describing distribution of modern astrophysics. stars over initial mass of primary component , mass Among fundamental problems aimed by these studies ratio of components , and semi-major axes of orbits 1 is the one of initial distributions of binary stars over their [25]. It was suggested by Vereshchagin et al. (1988) [35] main parameters: that BF for visual binaries has the form • mass of the primary component , • mass ratio of components = , . 1 d d d log d (1) • and semi-major axis of component orbits, 3 −2 5 −2 5 −1 2 1 1 1 ⁄ where M ∝ and are ∙expressed ∙ in solar units. As a “minor” characteristics, we consider eccentricity of 1 Proceedings of the XX International Conference orbits . The aim of the current paper is presentation of “Data Analytics and Management in Data Intensive preliminary results of the assessment of BF by means of Domains” (DAMDID/RCDL’2018), Moscow, Russia, October 9-12, 2018 98 comparison of results of Monte-Carlo model of the local the short summary of the used pairing functions. population of field visual binaries with their observed Masses of the of components or total masses of the sample. binaries were drawn randomly from Salpeter [32] or We probe, for a given type of stars, whether the Kroupa [21] initial mass functions (IMF), separation synthetic dataset differs significantly due to the change was drawn from one of the following distributions: of initial fundamental distributions, and how the change , . , , and eccentricity was distributed of every distribution affects it. For this purpose, we assuming−1 −1 following5 −2 options: (i) all orbits are circular, (ii)∝ compare synthetic populations for different pairing eccentricities∝ obey∝ thermal distribution ( ) = 2 , and functions and particular sets of fundamental functions. (iii) equiprobable distribution ( ) = 1. We adopt We attempt to find whether certain initial distributions or random orbit orientation. Mass ratio , when neede d, is combinations of initial distributions result in synthetic randomly drawn from distribution , where is datasets incompatible with observational data at certain adopted to be 0.5, 0 or 0.5 . The lower limit for is significance level and, on the contrary, whether certain determined by mass limits∝ [0.08 100] . Certain initial distributions or combinations of initial pairing functions,− such as −RP, PCRP, PSCP and TPP, do ⊙ distributions provide synthetic dataset best compatible not allow independent random distributi⋯ on of mass with observational data, hopefully, at certain significance ratios, it is calculated from masses of components. level. Table 2 contains short summary on initial The model also accounts for star formation rate, distributions used in the modelling. Some cells are empty stellar evolution and takes into account observational because the pre-planned distributions are not selection effects. The model is compared to the dataset implemented as yet. The total number of possible compiled as described by Kovaleva et al [18] with combinations of initial distributions considered as yet is addition of the data on parallaxes from Gaia DR1 TGAS 144, equal to the number of possible combinations of , [9]. , , , in Table 2 and regarding that 0 and 5 Besides, our model allows to obtain estimates for the scenarios do not imply independent initial distribution fraction of binary stars that remains unseen for different over (see Table 1). Any combination of distributions reasons and is observed as single objects and to listed in Table 2 can be conveniently referred, for investigate how these fractions depend on the initial instance, as “s2m0q5a1e0”. distributions of parameters. Such estimates are To account for star formation rate we adopt SFR(t) = important, for instance, as an approach toward 15 e / , where the time t is expressed in Gyr (Yu & recovering actual multiplicity fraction, mass hidden in Jeffery−t 72010 [36]). Disc age is assumed to be equal to 14 binaries, as well as toward models of different stellar Gyr. populations. Currently, we consider the following stellar The model and observational data are described in evolutionary stages: MS-star, red giant, white dwarf, chapters 2 and 3, respectively. Some considerations on neutron star, black hole. The objects in the two latter the choice of theoretical models are described in chanter stages do not produce visual binaries (though they 4. Results and conclusions are presented in chapter5. In contribute to the statistics of pairs, observed as single chapter 6 we outline the plans of future studies. stars, see Section 5.2 below). We do not consider brown dwarfs and pre-MS stars here, as they are extremely 2 The model rarely observed among visual binaries and their Visual binaries are observed, mostly, in the immediate multiplicity rate is substantially lower than for more solar vicinity. Therefore, we consider them to be massive stars (Allers 2012) [1]. As we deal with wide distributed up to the distance of 500 pc in radial direction pairs only, we assume the components to evolve and according to a barometric function along z. The scale independently. To calculate evolution of stars and their height z for the stars of different spectral types and, observational properties we used analytical expressions respectively, masses was studied, e. g., in derived by Hurley et al [15] and assumed solar [3,10,12,20,31]. Synthesizing results of these studies, we metallicity for all generated stars. assume |z| = 340 pc for low-mass ( 1 ) stars, 50 To normalize the number of simulated objects, we use estimates of stellar density in the solar neighborhood, pc for high-mass ( 10 ) stars, and linear |z| ⊙ based on recent Gaia results [4]. The data for A0V-K4V log relation for intermediate masses.≤ ⊙ stars presented by Bovy (2017) [4] give 0.01033 stars For such a small≥ volume we can neglect the radial− per pc3. This means that in the 500 pc sphere we generate gradient (Huang et al. 2015) [14]. We also ignore about 43300 pairs of stars. interstellar extinction. For the generated objects, we determine To simulate stellar pairs we use different pairing observational parameters, in particular, the brightness of functions (scenarios), mostly taken from components, their evolutionary stage and projected Kouwenhowen's list [16]. separation. Then we apply a filter to select a sample of It includes random pairing and other scenarios, where stars, which can be compared with observational data two of the four parameters (primary mass, secondary (see the next section). mass, total mass of the system, mass ratio) are randomized, and other are calculated. Table 1 contains 99 Table 1 Summary of considered pairing functions (scenarios) Abbreviation Full name Scheme RP Random Pairing rand(M , M , [M M ]); sort(M , M ); 1 2 calc( ). ⋯ 1 2 PCRP Primary Constrained Random rand(M , [M M ]); Pairing rand(M , [M M ], M = until M < M ); 1 calc( ). ⋯ 2 ⋯ 1 2 1 PCP Primary Constrained Pairing rand(M , ); calc(M ). 1 SCP Split-Core Pairing rand(M2 , [2M 2M ]); rand( ); calc(M , M ). ⋯ PSCP Primary Split-Core Pairing rand(M1 ,2[2M 2M ]); rand(M , [0.5(M +M ) M ], until M < M ); calc(M ); ⋯ 1 1 2 1 calc(q). ⋯ 2 TPP Total Primary Pairing rand(M , [2M 2M ]); rand(M , [M M ], until M < M ); calc(M ); ⋯ 1 1 sort(M , M ); ⋯ 2 calc(q). 1 2 Note: M , M , M – total mass of the binary, primary mass and secondary mass, respectively; M , M – lower (0.08 ) and upper (100 ) limits set for masses; = / – mass ratio. The meaning of 1 2 abbreviations is the following: “rand” – randomizing, “calc” – calculation, “sort” – sorting. ⊙ ⊙ 2 1 Table 2 Summary of applied initial distributions sN Scenario mN IMF qN Mass ratio aN Semi-major axis eN Eccentricity ( ) ( ) ( ) ( ) ( ) 0 RP 0 Salpeter 0 flat, =1 0 power, ~ 0 thermal, = 2 −1.