The active W UMa type binary star V781 Tau revisited Li K.1,2, Gao, D.-Y.1, Hu, S.-M.1, Guo, D.-F.1, Jiang, Y.-G.1, Chen, X.1 ABSTRACT 6 1 0 2 In this paper, new determined BVR I light curves and radial velocities of c c n V781Tauarepresented. Byanalyzingthelightcurves andradialvelocities simul- a J taneously, we found that V781 Tau is a W-subtype medium contact binary star 4 with a mass ratio of q = 2.207±0.005 and a contact degree of f = 21.6(±1.0)%. ] The difference between the two light maxima was explained by a dark spot on the R less massive primary component. The orbitalperiodchange of V781Tauwas also S . investigated. Aseculardecreaseatarateof−6.01(±2.28)×10−8 d/yrandacyclic h p modulation with a period of 44.8±5.7 yr and an amplitude of 0.0064 ± 0.0011 - o day were discovered. The continuous period decrease may be caused by angular r t momentum loss due to magnetic stellar wind. Applegate mechanism failed to s a explain the cyclic modulation. It is highly possible that the cyclic oscillation is [ the result of the light travel time effect by a third companion. 1 v 2 Subject headings: stars: binaries: close — stars: binaries: eclipsing — stars: 1 4 individual (V781 Tau) 0 0 . 1 0 1. Introduction 6 1 : v The variability of V781 Tau was first discovered by Harris (1979) according to his two i X nights photoelectric observations. The light curve of V781 Tau shows typical W UMa type. r Two values of orbital period, 0.d33939 and 0.d34494, were determined by Harris (1979), but a he can not point out the more accurate one. Later, Berthold (1981, 1983) analyzed his pho- tographic observations and gave an ephemeris: Min. (HJD) = 2443874.954 + 0.d3449100× E. Diethelm (1981) also preferred the longer period by analyzing his photoelectric measure- ments. After that, several authors published many times of minimum light. Cereda et al. 1 ShandongProvincialKeyLaboratoryofOpticalAstronomyandSolar-TerrestrialEnvironment,Institute of Space Sciences, Shandong University,Weihai, 264209,China (e-mail: [email protected](Gao, D.- Y.), [email protected] (Hu, S.-M.)) 2 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences – 2 – (1988) carried out extensive photoelectric observations in B and V bands. With the Fourier analysistechnique proposedbyNiarchos(1983), Ceredaetal. (1988)obtainedtheinclination of the orbit to be 68◦±2◦. The first radial velocity observations of V781 Tau were started by Lu (1993), who reanalyzed the BV light curves of Cereda et al. (1988) combining his radial velocities, the absolute dimensions were determined. Yang & Liu (2000) investigated the or- bital period variation of V781 Tau and found that the period of V781 tau is secular decrease with a rate of dP/P = 5.0 × 10−11. New radial velocities of V781 Tau were obtained by Zwitter et al. (2003). They simultaneously analyzed the Hipparcos and Tycho photometry and radial velocity data. Recently, Yakut et al. (2005) and Kallrath et al. (2006) observed and analyzed V781 Tau. They all obtained the basic physical parameters and the orbital period change behavior. It has been nine years since the last investigation of V781 Tau, we started photometric and spectroscopic observations in order to determine the physical parameters and the orbital period variation. 2. Photometric and Spectroscopic Observations Photometric observations of V781 Tau were carried out using the 1.0-m telescope at Weihai Observatory of Shandong University (Hu et al. 2014) on November 4, 2013 and December 24, 2014. The observation made in 2013 was using a back-illuminated PIXIS 2048B CCD camera attached to the Cassegrain telescope, while an Andor DZ936 CCD × camera was used in 2014. Both of the two CCD cameras have 2048 2048 square pixels (13.5×13.5µm pixel−1), resulting an effective CCD field of about 11.8′ × 11.8′. The filter system is a standard Johnson-Cousin-Bessel UBVR I CCD photometric system. Each of c c the CCD images was differently exposed from 2 s to 5 s based on the used filters. During the observations, GSC 01870-00514 (α = 05h50m22s.39, δ = +26◦59′55.0′′, V = 2000.0 2000.0 9.68, B − V = 0.45 ) and 2MASS J05502287+2654060 (α = 05h50m22s.87, δ = 2000.0 2000.0 +26◦54′06.1′′, V = 10.96, B − V = 0.95 ) were chosen as the comparison and check stars, respectively. All the measured images were firstly corrected with bias and flat images and then processed using the aperture photometry (APPHOT) package in the Image Reduction and Analysis Facility (IRAF1). The observations on November 4, 2013 determined a time of minimum light only. Complete light curves were determined on December 24, 2014, the 1 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the As- sociation of Universities for Research in Astronomy under cooperative agreement with the National Science Foundation. – 3 – corresponding phased light curves are displayed in Figure 1 and the original photometric data are shown in Table 1. The phases are calculated using the following ephemeris: Min.I = HJD2457016.32177+0.d34490986E, (1) the period in this equation is taken from Kreiner (2004). Three times of minimum light are ± ± determined during the two observing nights, they are: 2456601.3948 0.0002,2457016.1504 ± 0.0002 and 2457016.3208 0.0003. B and V light curves of V781 Tau derived by Cereda et al. (1988), Yakut et al. (2005), Kallrath et al. (2006) and us are shown in Figure 2. In order to derive the change of the light curves, we shifted other light curves to our observations at the primary minimum. As seen in Figure 2, the light curve of V781 Tau is changed significantly and shows positive type of O’Connell effect (O’Connell 1951). The differences between the two light maximum of the four sets of light curves exhibit continuously variation. This may indicate that V781 Tau shows very strong magnetic activity. We used the Weihai Echelle Spectrograph (WES) to obtain spectra of V781 Tau for radialvelocity calculation. Weobtainedseven spectra ofV781Tauandaspectra ofHD50692 as Radial Velocity Standard Star with spectral type of G0V on February 4, 2015. The raw data were reduced using the echelle package. Radial velocities of V781 Tau were obtained using task fxcor in IRAF, with the spectrum of HD50692 as the template. The spectra from WES has 107 orders because of echelle spectrograph configuration. We calculated the arithmetic mean value of radial velocities from different spectral orders, and set the standard deviation divided by the square root of numbers as configuration error. The determined radial velocities of V781 Tau are listed in Table 2. 3. Photometric solutions We used the W-D program (Wilson & Devinney 1971; Wilson 1990, 1994) to analyze the four color light curves and radial velocities of V781 Tau simultaneously. The (B−V) ≈ 0 0m.55 was determined by Kallrath et al. (2006), which is corresponding to a spectral type of G0V. Therefore, the effective temperature of the primary component of V781 Tau was set to be T = 6000 K. Accordingly, the gravity-darkening coefficients and bolometric albedo 1 coefficients of the two components were fixed at g = 0.32 A = 0.5 based on Lucy (1967) 1,2 1,2 and Rucin´ski (1969), respectively. The limb darkening coefficients were adopted from the limb darkening table of Van Hamme (1993). Iterative studies have shown that V781 Tau is a contact binary. Mode 3 was used during the solutions. The orbital inclination i, the mass ratio q, the effective temperature of the second component T , the monochromatic 2 – 4 – Table 1: Original photometric data of V781 Tau observed on December 24, 2014, Hel. JD 2457000+ Hel. JD ∆m Hel. JD ∆m Hel. JD ∆m Hel. JD ∆m B V R I c c 15.9821 -0.442 15.9824 -0.560 15.9826 -0.633 -0.7140 -0.367 15.9830 -0.451 15.9833 -0.575 15.9834 -0.632 -0.7310 -0.359 15.9839 -0.449 15.9842 -0.564 15.9843 -0.654 -0.7230 -0.375 15.9848 -0.470 15.9850 -0.573 15.9852 -0.661 -0.7210 -0.363 15.9857 -0.467 15.9859 -0.586 15.9861 -0.656 -0.7420 -0.360 15.9865 -0.476 15.9868 -0.580 15.9869 -0.681 -0.7390 -0.371 15.9874 -0.476 15.9877 -0.588 15.9879 -0.677 -0.7490 -0.366 15.9883 -0.478 15.9886 -0.604 15.9887 -0.672 -0.7450 -0.362 (The full version of this table is available in electronic form in the online journal. A portion is shown here for guidance regarding its form and content.) -1.2 Ic -1.0 Rc V m B -0.8 -0.6 -0.4 0.0 H -0.5 Ic C-C --11..50 RVc -2.0 B 0.0 0.2 0.4 0.6 0.8 1.0 1.2 phase Fig. 1.— The observed four color light curves of V781 Tau. Different colors represent different filters. – 5 – -0.9 -0.8 m -0.7 -0.6 B Cereda et al. 1988 Yakut et al. 2005 -0.5 Kallrath et al. 2006 This paper -0.4 0.0 0.2 0.4 0.6 0.8 1.0 phase -1.0 -0.9 -0.8 m -0.7 V Cereda et al. 1988 Yakut et al. 2005 -0.6 Kallrath et al. 2006 This paper -0.5 0.0 0.2 0.4 0.6 0.8 1.0 phase Fig. 2.— Top panel shows the light curves comparison in B band, while the lower panel displays V band. – 6 – luminosity in each band of the primary component L and the dimensionless potentials of 1 the two components, Ω = Ω are adjustable parameters. 1 2 As shown in Figure 2, the light curve of V781 Tau is seasonally changed, the spot mode of the W-D programme was used. Extensive investigations reveal that a dark spot on the less massive primary component leads to the best fit. The solution results are listed in Table 3. The spectroscopic orbital elements are shown in Table 4. The radial velocities and the comparison between observed and synthetic light curves are displayed in Figures 3 and 1, respectively. The corresponding geometric structure at phase 0.75 is plotted in Figure 4. As seen in Figure 1, the theoretical light curves show a mismatch in the primary minimum. We tried to reanalyze the light curves with two or more spots. However, very similar results are obtained. Therefore, we investigated the B, V, R and I light curves individually. The c c derived photometric elements are listed in Table 3, the corresponding fitted light curves are shown in Figure 5, in which very well fit at the primary minimum can be seen. 4. Period investigation The latest analysis of the orbital period variation of V781 Tau was started by Kallrath et al. (2006). It has been more than nine years. Many times of minimum light has been determined during this period. So, we collected all available times of minimum light to analyze the orbital period changes. A total of 220 timings of minimum light, including ours, were compiled from literatures, and they are listed in Table 5. The (O − C) values were 1 calculated using the linear ephemeris determined by Kreiner (2004), Min.I = 2452500.0720+0.d34490986E. (2) The (O − C) values computed with Equation (2) are listed in the fourth column of 1 Table 5 and plotted in the top panel of Figure 6. We found that the (O−C) curve contains 1 a continuous period decrease and a cyclic change. We used the following equation given by Irwin (1952) β sin(ν +ω) (O−C) = T +∆T +(P +∆P )E + E2 +A[(1−e2) +esinω] 1 0 0 0 0 2 (1+ecosν) β = T +∆T +(P +∆P )E + E2 +A[p(1−e2)sinE∗cosω +cosE∗sinω], (3) 0 0 0 0 2 to fit the (O−C) values. In this equation, T and P are, respectively, the initial epoch and 1 0 0 the orbital period, ∆T and ∆P are their corrections, and β is the long-term period change. 0 0 Other parameters were taken from Irwin (1952), which can be determined by the Levenberg- Marquart method (Press et al. 1992). In the calculation, the weights for the visual and – 7 – Table 2: Heliocentric Radial Velocities of V781 Tau JD (Hel.) Phase∗ RV Errors RV Errors 1 2 2457000+ km s−1 km s−1 km s−1 km s−1 ± ± 57.98872 0.8053 258.2 17.8 -71.9 8.7 ± ± 58.02855 0.9208 147.6 16.1 -41.1 15.0 ± ± 58.05684 0.0028 26.3 6.9 26.3 6.9 ± ± 58.08512 0.0848 -123.2 18.1 93.5 9.8 ± ± 58.14682 0.2637 -215.6 16.6 141.8 7.2 ± ± 58.17511 0.3457 -170.9 8.9 118.6 9.0 ± ± 58.20350 0.4280 -84.5 21.8 85.4 25.3 ∗ Phases arecomputed withtheEquation(1). 300 200 s) 100 m/ k RV( 0 -100 -200 -300 0.0 0.2 0.4 0.6 0.8 1.0 phase Fig. 3.— The phased radial velocity curves for V781 Tau. The solid line shows a sine fit. – 8 – phase=0.75 Fig. 4.— Geometrical configuration at phase 0.75. -1.2 Ic -1.0 Rc V B m -0.8 -0.6 -0.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 phase Fig. 5.— Observed and synthetic light curves derived by analyzing the four color light curves individually. The synthetic light curves fit very well at the primary minimum. – 9 – Table 3: Photometric solutions for V781 Tau Parameters BVR I B V R I c c c c g = g 0.32a 1 2 A = A 0.5a 1 2 x , x 0.647, 0.649a 1bol 2bol y , y 0.221, 0.193a 1bol 2bol x , x 0.829, 0.847a 1B 2B y , y 0.185, 0.098a 1B 2B x , x 0.745, 0.778a 1V 2V y , y 0.256, 0.200a 1V 2V x , x 0.674, 0.708a 1Rc 2Rc y , y 0.269, 0.229a 1Rc 2Rc x , x 0.590, 0.623a 1Ic 2Ic y , y 0.260, 0.230a 1Ic 2Ic T (K) 6000a 1 q(M /M ) 2.207±0.005 2 1 Ω 5.5420a in Ω 4.9389a out T (K) 5575±5 5600±7 5525±10 5537±9 5494±10 2 i 65.9±0.2 66.4±0.2 66.6±0.2 66.7±0.2 66.4±0.2 L /L 0.4421±0.0008 0.4361±0.0010 1B B L /L 0.4128±0.0006 0.4240±0.0012 1V V L /L 0.3990±0.0005 0.4058±0.0009 1Rc Rc L /L 0.3889±0.0005 0.4001±0.0007 1Ic Ic Ω =Ω 5.3956±0.0039 5.3897±0.0062 5.4041±0.0041 5.4255±0.0039 1 2 r (pole) 0.3031±0.0006 0.3045±0.0003 0.3050±0.0005 0.3038±0.0004 0.3019±0.0003 1 r (side) 0.3179±0.0007 0.3196±0.0004 0.3202±0.0007 0.3187±0.0004 0.3164±0.0004 1 r (back) 0.3585±0.0013 0.3614±0.0007 0.3625±0.0011 0.3599±0.0007 0.3561±0.0007 1 r (pole) 0.4330±0.0005 0.4343±0.0003 0.4248±0.0005 0.4336±0.0003 0.4319±0.0003 2 r (side) 0.4634±0.0007 0.4765±0.0004 0.4658±0.0007 0.4642±0.0005 0.4619±0.0004 2 r (back) 0.4951±0.0009 0.4975±0.0010 0.4983±0.0009 0.4962±0.0006 0.4931±0.0006 2 f 21.6±1.0% 24.3±0.6% 25.3±1.0% 22.9±0.7% 19.3±0.6% θ(radian) 1.90±0.19 1.87±0.16 1.90±0.16 1.90±0.16 1.88±0.16 φ(radian) 1.40±0.15 1.48±0.11 1.42±0.11 1.57±0.11 1.56±0.11 r(radian) 0.44±0.06 0.44±0.04 0.44±0.04 0.44±0.04 0.41±0.04 T (T /T ) 0.75±0.07 0.69±0.07 0.71±0.08 0.74±0.08 0.75±0.07 f d 0 a Assumed parameters – 10 – photographic minima were 1 and that for the photoelectric and CCD minima were 8. The final solution parameters are listed in Table 6. A 44.8±5.7 yr cyclic variation superimposed on a long-term period decrease at a rate of −6.01(±2.28)×10−8 d/yr was discovered. When the long-term period decrease was removed, the (O−C) values are displayed in the middle 2 panel of Figure 6. After the full ephemeris were subtracted, the residuals are plotted in the lowest panel of Figure 6. 5. Discussion and conclusions New CCD light curves and radial velocities of V781 Tau were determined by the 1.0-m telescope at Weihai Observatory of Shandong University. Analyzing the light curves and radial velocities using the W-D code simultaneously, we derived that V781 Tau has a mass ratio of q = 2.207 ± 0.005 and a fill out factor of f = 21.6(±1.0)%. The system velocity was determined to be V = 26.3 ± 0.5 km/s. Combining the solution results and radial 0 velocities of the two components, we can determined the absolute parameters of V781 Tau, they are a = 2.72±0.18R , M = 0.71±0.07M , M = 1.57±0.11M , R = 0.89±0.05R , ⊙ 1 ⊙ 2 ⊙ 1 ⊙ R = 1.26±0.08R , L = 0.92±0.07L and L = 1.38±0.10L . 2 ⊙ 1 ⊙ 2 ⊙ Using all available times of minimum light, we investigated the orbital period changes of V781 Tau. It is found that the orbital period of V781 Tau is secular decrease at rate of −6.01(±2.28) × 10−8 d/yr, and has a cyclic modulation with a period of 44.8 ± 5.7 yr. Normally, the secular orbital period decrease is caused by mass transfer from the more massive component to the less massive one or by angular momentum loss via magnetic stellar wind. Assuming that the mass transfer is conservative, we can determined the mass transfer rate using the following equation, P˙ 1 1 = −3M˙ ( − ). (4) 1 P M M 1 2 Table 4: The spectroscopic orbital elements for V781 Tau Parameters Values Errors V (km/s) 26.3 ±0.5 0 K (km/s) 251.6 ±15.9 1 K (km/s) 114.0 ±13.8 2 asini(R ) 2.48 ±0.16 ⊙ M sin3i(M ) 0.54 ±0.05 1 ⊙ M sin3i(M ) 1.19 ±0.08 2 ⊙