International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Spectroscopic Analysis of Eclipsing Binary Stars Bushra Q. AL-Abudi1 and Rossul A. Abdulkareem 2 1,2University of Baghdad, College of Science, Astronomy and Space Department, Baghdad-Iraq ABSTRACT In this paper, spectroscopic analysis of two eclipsing binaries systems ER Vul and BX And is presented. New orbital parameters were obtained by performing three computer modeling. The first model is software package PHOEBE based on the Wilson– Devinney method, the second is Binary Maker 3 (BM3) and the third is Spectroscopic binary solver (SBS). Our results are in good agreement with those obtained using the same modeling. Key words: Eclipsing binaries, Spectroscopic, PHOEBE package, Binary Maker 3 and spectroscopic binary solver. 1. 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 three computer modeling PHOEBE, Binary Maker 3(BM3) and spectroscopic binary solver (SBS) for analysis the radial velocity of eclipsing binaries systems ER Vul and BX And of the short period group RS CVn binaries. ER Vulpeculae (HD 200391, BD+27° 3952, HIP 103833, V = 7. 36ᵐ, P = ) is a double-lined spectroscopic binary, its orbit was first determined by Northcott and Bakos (1956,1967)[1]. The spectroscopic orbit of the ER Vul was determined by McLean (1982) and several other radial velocity studies have been performed in recent years e.g. Hall et al. 1990; Gunn et al. 1996 [2]. Hall (1976) classified ER Vul as a member of the short-period group of RS CVn systems, with main sequence components in a detached configuration. The RV of both components of ER Vul has been the subject of intense studies over many decades by several researchers. The first radial velocity curves of both components of ER Vul, based on an average of a dozen lines, which are taken between1949–1951 at David Dunlap Observatory, were published by Northcott and Bakos (1956). They found a systemic velocity of -25.2 km⁄sec and derived RV curve semi- amplitudes of 138.5 and 149.3 for the primary and secondary component, respectively. Alexandru and Călin detected a periodicity in the O–C curve of ER Vul and proved its detectability. They investigated the standard mechanisms for orbital period modulation and they emphasized a statistically significant increase of the orbital period of ER Vul. They proposed a methodology for estimating the detectability of periodic signals [3]. The orbital phases have been calculated with the following ephemeris: HJD (MinI) = 2 449 564.31173+ × E In this paper, we used this observation for analysis the radial velocity. Figure 1 shows the radial velocity of this binary [2]. Figure 1: Radial velocity of ER Vul Ronald et.al observed the short-period eclipsing binary system BX And on five nights in 1976 at the Morgan Monroe station of the Goethe link Observatory of Indiana University. They found that BX And binary system consists of an F type primary component and a K secondary component [4]. The first radial velocity data and absolute dimensions of the system were obtained by Bell et. al. [5], where the data were phased according to the ephemeris: HJD (MinI) = 2446705.49310 0.00012 + E.0.61011258 In this paper, we used this observation for analysis the radial velocity. Figure 2 shows the radial velocity of this binary [5]. Volume 3, Issue 5, May 2014 Page 41 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Figure 2: Radial velocity of BX And This paper is organized as follows. We analyzed spectroscopic data in section 2. Section 2 .1 analyzed the radial velocities using PHOEBE and the physical parameters for the systems are calculated. Section 2 .2 analyzed the radial velocities using Binary maker 3 .Section 2 .3 analyzed the radial velocities using Spectroscopic Binary Solver (SBS). Section 3 is devoted to conclusions. 2. DATA ANALYSIS In order to modeling the radial velocities of eclipsing binaries ER Vul and BX And, we applied three different models: the first is PHOEBE (Prša and Zwitter 2005)[6] which is released under the GNU public license., it is modeling software for eclipsing binaries which uses the Wilson- Devinney code. The second is Binary maker 3 (BM3) and the third is Spectroscopic binary solver (SBS). 2.1 ANALYSIS with PHOEBE In order to analysis the radial velocities 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 cause is phase, Then we plotted the synthetic and the experimental radial velocities of ER Vul and BX And as shown in figure 3 and figure 4, respectively. Figure 3: Synthetic and plotted radial velocity curve of eclipsing binary ER Vul Figure 4: Synthetic and plotted radial velocity curves of eclipsing binary BX And Volume 3, Issue 5, May 2014 Page 42 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 In this paper, we concentrated on the specific parameters identified in table 1. Table 1: List of geometric and physical parameters in PHOEBE Parameters Description q Mass ratio i Inclination of orbit TAVH Temperature K effect of primary star in TAVC Temperature effect of secondary star in K SMA Semi - major axis VGA Center of mass velocity in km/s Ω Non-dimensional surface potential K1 Semi amplitude of the primary component K2 Semi amplitude of the secondary component Systematic velocity 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 ER Vul and BX And were fixed at the values of 0.96 and 0.49, respectively and we fixed the values of the effective temperature of the primary component (T1) ;these values are 6050 and 6600 for ER Vul and BX And binaries, respectively . This model and for a given q has the following adjustable parameters: the orbital inclination (i), the non-dimensional potentials ( 1 and 2 ), the effective temperature of the secondary component (T2). After some iteration we get the best match between the synthetic and the experimental radial velocity curve of the eclipsing binaries ER Vul and BX And as shown in the figure 5 and figure 6, respectively. The radial velocity curves residuals windows plot the difference between experimental and synthetic radial velocity curves verses the phase; Figure 7 and figure 8 show the residuals of both binaries. Table 2 presents the physical and orbital parameters of ER Vul and BX And from using PHOEBE model. Figure: 5 The best match between the synthetic and the experimental radial velocity curve of binary ER Vul Figure 6: The best match between the synthetic and the experimental radial velocity curve of binary BX And Volume 3, Issue 5, May 2014 Page 43 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Figure 7: Residuals obtained from fitting routine of eclipsing binary ER Vul Figure 8: Residuals obtained from fitting routine of eclipsing binary BX And Table 2: The physical and orbital parameters of ER Vul and BX And Using PHOEBE parameters ER Vul Cakırli et.al. [2] BX And Bell et.al.[5] Mass 1 1.11 1.09 1.63 1.52 0.05 Mass 2 1.06 1.06 0.81 0.75 0.03 TAVH 6050 6010 6600 6800 200 TAVC 6016 5883 5362 4500 200 R1 1.05 1.16 1.78 1.78 0.03 R2 0.88 1.18 1.40 1.30 0.03 Ω(L1) 3.68 - 2.87 - Ω(L2) 3.16 - 2.57 - Mbol 1 4.87 4.28 4.36 2.79 0.13 Mbol 2 4.47 4.31 3.98 5.26 0.20 Inclination 67.138 ° 66.32° 76.35° 75.50° PHSV 5.06 - 2.95 - PCSV 5.69 - 2.81 - SMA 4.29 4.27 4.21 4.32 VGA -24.95 −25.2 -45.36 -45.11 2.2 ANALYSIS with BINARY MAKER 3 After providing experimental radial velocity curve data to the Binary Maker 3 we added input parameters to construct meaningful binary models. Binary Maker 3 was used to determine a preliminary solution to the radial velocity curves. To create the synthetic radial velocity curves of eclipsing binaries ER Vul and BX And, we pressed the Render button at the bottom of the User Input dialog and the radial velocity curves are plotted in the radial velocity curve window as shown in figures 9 and 10, respectively. Tables 3 and 4 show the output from binary maker for ER Vul and BX And eclipsing binary stars respectively. Volume 3, Issue 5, May 2014 Page 44 International Journal of Application or Innovation in Engineering & Management (IJAIEM) Web Site: www.ijaiem.org Email: [email protected] Volume 3, Issue 5, May 2014 ISSN 2319 - 4847 Figure 9: : The synthetic and the experimental radial velocity curves of binary ER Vul Figure 10: The synthetic and the experimental radial velocity curves of binary BX And Table 3: The output from Binary Maker of eclipsing binary star ER Vul Ω1= 5.070 Ω 2 = 4.824 Mean radius 1 = 0.245 Mean radius 2 = 0.125 inclination = 68.300 Eccentricity = 0.000 mass ratio input = 0.961[7] Period = 0.698 temperature 1 = 6050 temperature 2 = 6016 K1 = 139.5 K2 = 145.8 V0= -24.6 Table 4: The output from Binary Maker of eclipsing binary star BX And Ω1= 2.864 Ω2= 2.864 Mean radius 1 = 0.442 Mean radius 2 = 0.320 inclination = 75.500 Eccentricity = 0.000 mass ratio input = 0.497[7] Period = 0.610 temperature 1 = 6600 temperature 2 = 4800 K1 = 105.5 K2 =212.3 V0= -45.1 2.3 Analysis with Spectroscopic Binary Solver (SBS) The radial velocity of star in a binary system is defined as follows [8]: V= Kcos( ) ecos………..(1) where is the systematic velocity, K is the semi-amplitude of the velocity curve and ,, e are the angular polar coordinate (true anomaly), the longitude of periastron and the eccentricity, respectively .