JPAR Journal of Physics and Astronomy Research Vol. 1(3), pp. 015-034, November, 2014. © www.premierpublishers.org, ISSN: XXXX-XXXX Research Article A Holistic study of the eclipsing binary EQ Tau M. M. Elkhateeb*,1,2 and M. I. Nouh1,2 E-mail: [email protected] 1Department of Astronomy, National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt 2Department of Physics, College of Science, Northern Border University, 1321 Arar, Saudi Arabia We present a new BVR light curves of the system EQ Tau carried out in the period from March to April 2006 using a 50-cm F/8.4 Ritchey–Chretien telescope (Ba50) of the Baja Astronomical Observatory (Hungary), and 512 × 512 Apogee AP-7 CCD camera. The observed light curves were analyzed using the 2004 version of the Wilson-Devinney code. The results show that the more massive component is hotter than the low massive one by 100 K. A long term orbital period study shows that the period increases by the rate 8.946 (±0.365) x10-11 days/cycle. Evolutionary state of the system has been investigated and showed that, the primary component of the system is located nearly on the ZAMS for both the M-L and M-R relations. The secondary component is close to the TAMS track for M-L and above the M-R relations. Key Words: Eclipsing binaries, contact, period variation, orbital solution, evolutionary status INTRODUCTION The variability of the system EQ Tau (G2, V=12.04, P=0.341349) was discovered by Tsesevich (1954). The system was included to the AAVSO list of eclipsing, while the first period was calculated by Whitney (1972), while the first CCD light curve was carried out in R band by Benbow and Mutel (1995). The system was monitored by Buckner, Nellermoe and Mutel (1998), and Nelson (2001). The first reliable spectroscopic elements of the system were estimated by Rucinski et al. (2001). Successive observations were carried out from 2000 to 2002 in BV band pass by Pribulla and Vanko (2002), and Vanko et al. (2004). They combined the calculated photometric elements resulting from their observations with published spectroscopic elements to yield the absolute parameters of the system. Light curves asymmetry was noted by Yang and Liu (2002) through their BV observations and they adopted the first spot model for the system EQ Tau. Many photometric studies were applied for the system light curve by Hrivnak et al. (2006), Yuan and Qian (2007) and Alton (2006, 2009). Recently, during the work in the present analysis, Li et al. (2014) presents a new light curve analysis for the system. In the present paper, we use the Wilson-Devinney (WD) code to estimate the physical parameters of the contact binary EQ Tau and to study its evolutionary status. A long term orbital period study was performed using O-C method and a possible connection between the light curve variation and the period change of the system was studied OBSERVATIONS Observations of EQ Tau were carried out on five nights from March to April 2006 in B, V and R band pass using a 50- cm F/8.4 Ritchey–Chretien telescope (Ba50) of the Baja Astronomical Observatory (Hungary), and 512 × 512 Apogee AP-7 CCD camera. Table (1) lists the coordinates of the variable, the comparison and the check stars. It’s clear that the comparison and check stars are close to the variable and they were in the same field, thus the extinction corrections can A Holistic study of the eclipsing binary EQ Tau Elkhateeb and Nouh 015 be ignored. The observed images were analyzed by the photometry software AIP4WIN (Berry and Buruell 2000) which is based on aperture photometry, including bias and dark subtraction and flat field correction. A complete light curves were obtained only in V and R filters. A total of 649 individual observations were obtained in VR band pass (252 in V and 397 in R), which covered a complete light curves in V and R bands, as displayed in Figure (1). The individual observations in both bands are listed in Table 2, with the magnitude difference (the variable minus the comparison). The phases were calculated using the ephemeris of Kreiner et al. (2000): Min I = 2440203.4343 + 0.d341347947 * E. (1) From the present observations, the times of three primary light minima were calculated using the Minima V2.3 Package (Nelson 2006) based on the Kwee and Van Worden (1956) fitting method. The calculated minima are shown in Table (3) and together with all published photoelectric and CCD minima in Table (4). Table 1. Coordinates of EQ Tau, comparison, and the check stars Star Name (2000.0) δ (2000.0) V B-V EQ Tau 03h48' 16.0'' +22o 17' 30.0'' 11.1 0.86 8 Comparison (TYC 1260-575-1) 03h48' 16.5'' +22o 17' 29.7'' 10.3 1.15 2 Check (GSC 01260-00800) 03h48' 17.4'' +22o 22' 43.0'' 8.19 1.05 0 Table 2. CCD Observations of EQ Tau in VR band. V-band observations of EQ R-band observations of EQ Tau Tau JD Phase ΔR Error JD Phase ΔV Error 2453796. 0.08 0.9 0.03 2453796.3 0.076 1.22 0.05 3086 21 62 93 077 5 9 02 2453796. 0.08 0.9 0.03 2453796.3 0.081 1.19 0.04 3104 72 44 85 095 7 9 90 2453796. 0.09 0.9 0.03 2453796.3 0.086 1.17 0.04 3122 25 23 77 113 8 7 81 2453796. 0.09 0.8 0.03 2453796.3 0.092 1.16 0.04 3139 76 97 67 130 0 6 76 2453796. 0.10 0.8 0.03 2453796.3 0.097 1.14 0.04 3157 28 89 64 148 2 7 68 2453796. 0.10 0.8 0.03 2453796.3 0.102 1.13 0.04 3175 80 73 56 166 4 1 62 2453796. 0.11 0.8 0.03 2453796.3 0.107 1.11 0.04 3192 32 67 54 183 6 6 56 2453796. 0.11 0.8 0.03 2453796.3 0.112 1.10 0.04 3210 84 44 45 201 8 3 50 2453796. 0.12 0.8 0.03 2453796.3 0.118 1.08 0.04 3228 35 32 40 219 0 9 45 2453796. 0.12 0.8 0.03 2453796.3 0.123 1.08 0.04 3245 87 18 34 237 1 0 41 2453796. 0.13 0.8 0.03 2453796.3 0.128 1.07 0.04 3263 39 08 30 254 3 4 39 2453796. 0.13 0.7 0.03 2453796.3 0.134 1.05 0.04 3284 99 95 25 275 3 8 32 2453796. 0.14 0.7 0.03 2453796.3 0.139 1.04 0.04 3301 51 88 22 292 5 1 25 2453796. 0.15 0.7 0.03 2453796.3 0.144 1.04 0.04 3319 03 76 17 310 7 2 25 A Holistic study of the eclipsing binary EQ Tau J. Physics Astron. Res. 016 Table 2. Cont. 2453796. 0.15 0.7 0.03 2453796.3 0.149 1.03 0.04 3337 55 65 12 328 9 2 21 2453796. 0.16 0.7 0.03 2453796.3 0.155 1.01 0.04 3354 07 57 09 346 1 9 16 2453796. 0.16 0.7 0.03 2453796.3 0.165 1 0.04 3372 58 51 07 381 4 000. 08 2453796. 0.17 0.7 0.03 2453796.3 0.170 0.99 0.04 3390 10 36 01 399 6 3 05 2453796. 0.17 0.7 0.03 2453796.3 0.175 0.98 0.04 3407 62 37 01 416 7 4 02 2453796. 0.18 0.7 0.02 2453796.3 0.180 0.98 0.04 3425 13 17 93 434 9 0 00 2453796. 0.18 0.7 0.02 2453796.3 0.201 0.95 0.03 3443 65 11 90 504 6 3 89 2453796. 0.19 0.6 0.02 2453796.3 0.206 0.95 0.03 3460 16 96 84 522 8 4 90 2453796. 0.19 0.6 0.02 2453796.3 0.217 0.95 0.03 3478 68 94 83 557 1 6 90 2453796. 0.20 0.6 0.02 2453796.3 0.227 0.95 0.03 3496 20 87 81 593 5 7 91 2453796. 0.20 0.7 0.02 2453796.3 0.232 0.96 0.03 3513 72 00 86 610 6 5 94 2453796. 0.21 0.6 0.02 2453796.3 0.237 0.96 0.03 3531 24 85 80 628 8 7 95 2453796. 0.22 0.6 0.02 2453796.3 0.243 0.96 0.03 3549 45 92 83 646 1 7 95 2453796. 0.22 0.6 0.02 2453796.3 0.248 0.96 0.03 3566 98 87 81 663 2 2 93 2453796. 0.23 0.6 0.02 2453796.3 0.253 0.96 0.03 3584 49 93 83 681 3 5 94 2453796. 0.24 0.6 0.02 2453796.3 0.258 0.96 0.03 3602 01 92 83 699 6 5 94 2453796. 0.24 0.6 0.02 2453796.3 0.268 0.97 0.03 3619 53 96 84 734 9 3 97 2453796. 0.25 0.6 0.02 2453796.3 0.274 0.97 0.03 3637 04 86 80 752 0 6 99 2453796.