Photometric Analysis of Eclipsing Binary Stars

Volume 2, Issue 5, May 2013 Page 45 ABSTRCT In this paper, photometric analysis of two eclipsing binaries systems CG Cyg and XY UMa is presented. New physical and geometric parameters were obtained by performing two computer modeling. The first model is software package PHOEBE based on the Wilson–Devinney method, and the second is Binary Maker 3 (BM3).Our results are in good agreement with those obtained using the same modeling


Introduction
The study of binary stars is vitally important in astronomy because it is only by carefully measuring the interactions between stars that we can accurately determine their absolute characteristics such as mass, luminosity, and radius. In this paper, we will be discussed two computer modeling PHOEBE (Physics of Eclipsing BinariEs) and Binary Maker 3(BM3) for analysis the light curves of RT And and BH Vir eclipsing binaries of the short period group RS CVn binaries. The active star RT And is a short-period eclipsing binary. It has been extensively observed since the beginning of the 20th century due to the variability of the light curve (LC). In 1981 Milano analyzed all available photoelectric LCs of RT and obtained up to 1978 and proposed that the photometric distortion waves were caused by the spots [1]. in 1989 Zeilik successfully explained the photometric distortion waves in the LCs by using dark circular star spots at middle-high latitudes on the primary with the temperature roughly 1100−1200 K below that of the photosphere [2]. The data were phased by the ephemeris of [3]: JHD(MinI)=2447803.5094+ 0.6289294* E In this paper, we used this observation for analysis the light curve. Fig.1 shows the Light curve of this binary [4]. BH Vir is a double-line eclipsing binary classified as a short period RS CVn system [5]. It is a close detached binary containing main-sequence stars with rapid rotation. The observations in different spectral ranges (from X-ray to radio) indicate chromospheric-coronal radiation from these stars [6]. The light curves and the photoelectric observations in B and V obtained in 1967 by Koch have been analyzed by using the Wilson-Devinney program [7]. The spectral data were phased according to the ephemeris [8]: In this work, we used this observation for analysis the light curve. Fig.2 shows the Light curve of this binary [9]. This paper is organized as follows. We analyzed photometric data in section 2. Section 2 .1 analyzed the light curves using PHOEBE and the physical parameters for the systems are calculated. Section2.2 analyzed the light curves using Binary maker 3.Section 3 is devoted to conclusions.

Data Analysis
In order to modeling the Light curves of eclipsing binaries RT And and BH Vir, we applied two different models: the first is PHOEBE (Prˇsa & Zwitter 2005) [10] which is released under the GNU public license., it is modeling software for eclipsing binaries which uses the Wilson-Devinney code. The second is BM3 (Binary maker 3).

Analysis with PHOEBE
In order to analysis the light curves of these eclipsing binaries using PHOEBE, we added the experimental data in arrange consists of two columns, the first column represents the independent variables, in this case is phase and the second column contains dependent in this case is flux. Then we plotted the synthetic and the experimental light curves of RT And and BH Vir as shown in Fig.3 and Fig.4, respectively.

Fig.4: Synthetic and plotted light curves of eclipsing binary BH Vir.
In this paper, we concentrate on the specific parameters identified in Table 1.

Parameters
Description q Mass ratio i Inclination of orbit g1, g2 Gravity darkening coefficients TAVH Temperature effect of primary star in K TAVC Temperature effect of secondary star in K PHSV Surface potential of primary star PCSV Surface potential of secondary star Log(g)1 Surface gravity of primary star Log(g)2 Surface gravity of secondary star In order to obtain the physical and geometric parameters of the binary components, we adjusted a numerical eclipsing binary model to the observations; the mass-ratio of RT And and BH Vir were fixed at the values of 0.74, 0.967, respectively. This model and for a given q has the following adjustable parameters: the orbital inclination (i), the non-dimensional potentials ( 2 1   and ), the effective temperature of the secondary component (T 2 ), and the relative luminosity of the primary L 1 . For a fixed value of the mass ratio q the potentials 2 1   and directly determine the relative radii of the components. The temperature of the primary component of RT And and BH Vir were adopted to be T 1 = 6100 k and 6000k, respectively. After some iteration we get the best match between the synthetic and the experimental light curve as shown in Figs. 5 for binary RT And and in Fig.6 for binary BH Vir. The light curves residuals windows plot the difference between experimental and synthetic light curves verses the phase; Fig.7 and Fig.8 show the residuals of both binaries and Fig.9 and Fig.10 show the shape of both binaries at different phases. Table 2 presents the physical parameters of RT And and BH Vir from using PHOEBE model.

Analysis with Binary maker 3
After providing experimental light curve data to the Binary Maker 3 we have to add input parameters to construct meaningful binary models. Binary Maker 3 was used to determine a preliminary solution to the light curves. Table 3 shows the light curve fit parameters for eclipsing binary RT And which are taken from [12] while Table 4 shows the light curve fit parameters for eclipsing binary BH Vir which are taken from [13].   Tables 5 and 6 show the output from Binary Maker3 for eclipsing binaries RT And and BH Vir, respectively.

Conclusions
The analysis of photometric data of the eclipsing binaries RT And and BH Vir using PHOEBE and BM3 models has allowed us to determine the physical and geometric parameters of the component stars such mass, radii, Luminosity, inclination angle, and temperatures. PHOEBE and BM3 create synthetic from light curves input data. By iterative adjustment parameters best fitted to experimental data are established. The data processing for PHOEBE is in essence easier than for BM3 despite the fact that is a far more sophisticated model. Both programs PHOEBE and BM3 plotted shape at different phases for system. According to the results obtained of fillout factor (f), both eclipsing binaries are detached system, and of the secondary star effective temperature in both systems after complete fitting with PHOEBE model have a higher value than its initial value.