Close Binary System GO Cyg
aa r X i v : . [ a s t r o - ph . S R ] S e p Close Binary System GO Cyg
B. Ula¸s a , B. Kalomeni a,b , V. Keskin a , O. K¨ose a , K. Yakut a,c, ∗ a Department of Astronomy and Space Sciences, University of Ege, 35100,Bornova– ˙Izmir, Turkey b Department of Physics, ˙Izmir Institute of Technology, Turkey c Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB30HA, UK
Abstract
In this study, we present long term photometric variations of the close binarysystem GO Cyg. Modelling of the system shows that the primary is fillingRoche lobe and the secondary of the system is almost filling its Roche lobe.The physical parameters of the system are M = 3 . ± . M ⊙ , M = 1 . ± . M ⊙ , R = 2 . ± . R ⊙ , R = 1 . ± . R ⊙ , L = 64 ± L ⊙ , L =4 . ± . L ⊙ , and a = 5 . ± . R ⊙ . Our results show that GO Cyg is themost massive system near contact binary (NCB). Analysis of times of theminima shows a sinusoidal variation with a period of 92 . ± . M ⊙ . Finally a period variation rateof − . × − d/yr has been determined using all available light curves. Keywords: stars: binaries: eclipsing — stars: binaries: close — stars:binaries: general — stars: fundamental parameters — stars: low-mass
1. Introduction
Studies of the evolution of late-type close binary systems reveal that theevolution of detached, semi-detached and contact systems are closely related(Yakut & Eggleton 2005, Eggleton 2010 and reference therein). The moremassive star in a detached binary system fills its Roche lobe first because ithas shorter evolutionary timescale before its companion. The system is semi-detached binary. In addition to nuclear evolution and mass loss, mass transferhas a crucial role in driving a binary towards a contact phase of evolution. ∗ Visiting astronomer during the summer of 2011
Preprint submitted to New Astronomy August 2, 2018 he observations of detached, contact and semi-detached binaries are crucialto our further understanding of the evolution of close binary systems.We therefore, include GO Cyg (HD 196628, GSC 02694-00550, V =8 m .47,A0V) into our close binary stars observation programme (see Ula¸s et al.2011, K¨ose et al. 2011). The system is a β -Lyr type (short period 0 d .71)binary system and observations of the binary cover eighty years. Followingits discovery by Schneller (1928) the system has been extensively studied bymany authors. (Payne-Gaposchkin, 1935; Pierce, 1939 and Popper, 1957).Ovenden (1954); Mannino (1963); Rovithis et al. (1990); Sezer et al. (1993);Jassur (1997); Rovithis-Livanou et al. (1997); Edalati & Atighi (1997); Oh etal (2000), and Zabihinpoor et al. (2006) studied the system photometrically.Using different methods in analysis most studies agree with the primaryfilling its Roche lobe. Asymmetry in the secondary minimum have beendiscussed in previous studies (e.g. Edalati & Atighi 1997, Zabihinpoor etal. 2006). Pearce (1933) found the mass function and mass ratio of 0 . difficult binary stars . In this group accurate radial velocities are not available.Pribulla et al. (2009) concluded that the temperature difference between thecomponents makes the system a difficult candidate in determination of theideal broadening function. A velocity value of v ≈
35 km/s for a third bodywas given in Pribulla et al. (2009).Period variation of GO Cyg has been studied by many investigators. Pe-riod increase was discussed in a number of studies (e.g. Sezer et al. 1985,Rovithis et al. 1997, Edalati & Atighi 1997, Zabihinpoor et al. 2006). Joneset al. (1994) reported a sinusoidal variation superimposed on a parabolictrend. Elkhateeb (2005) noted a period increase of dP/dt = 1 . × − which is close to that of Oh et al.’s (2000) value of 1 . × − . Hall & Louth(1990) discussed a magnetic cycle by studying the period decrease betweenthe year 1934 and 1984. Chochol et al. (2006) represented the O − C curve bya sinusoidal fit by using the Cracow database and their data. A third bodywith an orbital period of 90 years and a mass of 0.62 M ⊙ has been proposed.In the following sections, we present our new observations of GO Cyg.We preformed photometric analysis, period variations and compare our re-sults with its previously published works. All the available light curves werecollected from the literature and studied for various physical processes (e.g.magnetic activity, mass transfer, third light) and their variations. The O − C variation with recently obtained times of minima revealed the discrepancy2etween the results of the light curve solution and period study of earlierstudies. In this study, therefore, we investigate different possibilities thatcause period variation in order to reveal the most accurate structure and be-havior of the components. The physical parameters of the system are givenwith a discussion on the evolutionary status of the binary.
2. New Observations
The light variation and minima times of GO Cyg obtained in the Bessel B , V , and R bands in 16 nights between June – August 2007 and one night inApril 2011. The observations carried out at T ¨UB˙ITAK National Observatory(TUG) and Ege University Observatory with the 40cm telescope using anApogee CCD U47. Comparison and check stars are selected as GSC 02694-00280 and GSC 02694-00733, respectively. The total number of the pointsobtained during the observations are 3715 in B , 3726 in V , and 3698 in R band. IRAF (DIGIPHOT/APPHOT) packages are used in data reduction.Standard deviations of the data are estimated as 0 m .04, 0 m .017, and 0 m .015for B , V , and R bands, respectively.In Fig. 1 we show the B , V , and R light curves of GO Cyg. In this study,we do not find the apparent asymmetry in 0.6-0.7 orbital phase previouslyreported by Edalati & Atighi (1997) and Zabihinpoor et al. (2006). In dataour reduction and analysis, we used the linear ephemeris described by Sezeret al. (1993).
3. Eclipse Timings and Period Study
Cester et al. (1979) reported an orbital increase of Q = 0 . × − basedon seven nights observational data obtained between 1972-1975. Sezer et al.(1985) also reported an increase with a Q value of 1 . × − days. Hall& Louth (1990) consider the O − C curve and split it in three region. Thefirst and the third region of the curve showed sudden variation. Therefore theauthors analysed these regions under linear assumption while the second partwas presented by a quadratic fit with a period increase of Q = 1 . × − .The authors concluded that this behavior of the O − C curve can be attributedto a magnetic cycle. Jones et al. (1994) showed that the residuals of theparabolic fit show a sine-like variation with a period of 38.9 years. A periodincrease was also discussed by Rovithis-Livaniou et al. (1997). A periodwith Q = 1 . × − was noted by Edalati & Atighi (1997). Oh et al.32000) also represented the O − C curve by an upward parabola with Q =1 . × − . Elkhateeb (2005) found that the period is increasing witha value of Q = 1 . × − . The parabolic and third order polynomialfits were compared by Zabihinpoor et al. (2006). The authors give thequadratic term as 0 . × − . Zabihinpoor et al. (2006) also discussedthe inconsistency between geometric configuration and period variation rate.Recently, Chochol et al. (2006) suggested the light time effect for the periodvariation. The authors discussed that in a binary system where the primaryfills its Roche lobe and loses mass a decrease in orbital period can be expected.Recently we obtained two times of minima 24 54318.54864 ± . ± . O − C curve changes shape from early-assumed upward parabolato a sinusoidal variation that supports the previous discussion about a thirdbody in the system. The period variation is studied using a total of 194 datapoints obtained by photometric/CCD observations. The times of minima areobtained from the literature (Kreiner et al., 2001 and Erkan et al., 2010) andthose yielded by this study. The weighted least-squares method is used inorder to determine the orbital elements of the third body. Sinusoidal vari-ation in the O-C curve, where both the primary and the secondary minimafollow the same trend suggests a light-time effect because of the presence ofa third component that can be represented by following formula (Irwin 1959,Kalomeni et al. 2007): M inI = T o + P o E ++ a sin i ′ c (cid:20) − e ′ e ′ cos v ′ ( v ′ + ω ′ ) + e ′ sin ω ′ (cid:21) (1)where T o is the starting epoch for the primary minimum, E is the integereclipse cycle number, P o is the orbital period of the eclipsing binary a , i ′ , e ′ ,and ω ′ are the semi-major axis, inclination, eccentricity, and the longitudeof the periastron of eclipsing binary about the third body, and v ′ denotesthe true anomaly of the position of the center of mass. Time of periastronpassage T ′ and orbital period P ′ are the unknown parameters in Eq. (1).Our result from our analysis are shown in Fig. 2. Fig. 2a shows theconsistency between the observational and model prediction in the assump-tion of a third body. Fig. 2b shows the residuals from a Sinusoidal variation.The orbital elements of a third component are listed in Table 2. It can be4learly seen from the figure that any investigation of any detailed variationin (∆ T ) II points makes no sense. We have also investigated orbital periodvariation of the system with a different method from the O − C analysis. Wehave re–analysed the light curves from the available eighty years and we dis-cussed further in Section 5 below. We conclude that if the O − C variationshows a downward parabola its period that is too long to determine fromavailable times of minima.
4. Light Curve Solution
The light curve of the system has been analysed by numerous researchers.Ovenden (1954) obtained two-colour light curve and solved them by usingRussell’s method. The author assumed that the primary dominates observedlight. This results in a reflection effect that makes difficult to identify thesecondary in the spectrum. Asymmetry between maxima discussed as anintrinsic variation. Mannino (1963) solved the photoelectric B and V lightcurves of the system with the Russell–Merill method. Rovithis et al. (1990)analysed the light curves and estimated the geometric elements by using fre-quency domain techniques. The authors reported no difference between thelevel of maxima. The BV light curve combined with Holmgren’s radial veloc-ity curve was solved by Sezer et al. (1993) by using Wilson–Devinney (WD)method. The result indicated a semi–detached configuration where the pri-mary is filling its Roche lobe. A standard iterative optimization techniquewas used by Jassur (1997) to solve the U BV light curves. Rovithis-Livaniouet al. (1997) determined the absolute parameters and the geometrical ele-ments by applying the Wood’s model. Edalati & Atighi (1997) comparedsome parameters of their solution with previous works and confirmed thatthe system’s geometrical configuration is a reverse Algol. Oh et al. (2000)discussed that the system is at poor thermal contact phase of the thermalrelaxation oscillation. Recently, Zabihinpoor et al. (2006) analyzed the lightcurve and suggested new observations to uncover the discrepancy betweenthe suggested geometric shape and the orbital period variation.The shapes of the radial velocity curves of the system are controversialand no reliable spectroscopic mass ratio exist in the literature. In this study,therefore, we started to the solution by searching the appropriate photomet-ric mass ratio. q values between 0 .
25 and 0 .
65 are investigated on the V lightcurve by increasing the value by 0 .
05. We reached the minimum residualwhen q = 0 .
45 which is then taken as an initial value for our simultane-5us solution. The uncertainties of the spectral types also required to searchfor a suitable temperature for the primary component using the light curve. T h =10350 K turned out to be a suitable mean temperature of the hot com-ponent and has been used in other studies. Simultaneous solutions obtainedwith Phoebe (Pr˜sa & Zwitter 2005), which uses the WD code (Wilson &Devinney 1971), was applied to our observations (476 points in B and V , and474 in R ). The gravity darkening coefficients g and g are obtained fromvon Zeipel (1924) and Lucy (1967). The albedos A and A are adoptedfrom Rucinski (1969). The logarithmic limb-darkening law is used with co-efficients adopted from van Hamme (1993) for a solar composition (Table 2).The adjustable parameters are orbital inclination i , temperature of secondarycomponent T , surface potential of secondary component Ω , luminosity L ,and mass ratio q . The analysis results are summarized in Table 2. Thecomputed light curves are shown with solid lines in Fig. 1.All available light curves of the system between 1936–2007 are also col-lected from the literature and analysed separately (Table 3). These lightcurves are solved by using the initial values that are determined in this study.In addition, light contribution of the third body is set as a fixed parametersince no variation is expected in a period of eighty years. The results areshown in Fig. 3 and listed in Table 4. All available data are provided inTable 5.Some light curves (LC8, LC12, LC15) show slight asymmetry in the sec-ondary minimum while it is not detected in the others (LC3, LC7, LC14). Inthis study we also investigate any evidence of a magnetic activity as it wasdiscussed in earlier studies (Hall & Louth 1990). Either physical structure ofthe stars or the shape of the light curves did not let us to analyse the curveswith spotted model assumption. Some light curves (LC8, LC15), however,can be represented theoretically by a hot surface on the cooler companion.The presence of a hot region, that may be attributed to a mass transfer otherthan a magnetic activity, could not be proved with the long-term data.
5. Discussion and Conclusion
Long term photometric light and period variation of the close binarysystem GO Cyg are studied in detail. The physical parameters we havedetermined and listed in Table 6. Because of poor quality data in the previousstudies the O − C curve was inferred to be parabolic one. In this study withour data we show that the system has a third body with a 92.3 years orbital6eriod. Since the primary component filled its Roche lobe we searched fora clue for the mass transfer by a technique other than the O − C analysis.Separate solutions of six available light curves starting from 1950 to presentindicate a period decrease. The period change variation vs. years shows adownward parabola. This can be considered as a mass transfer from themore massive companion to the less massive one. This solution yields theamount of the period decrease as − . × − d/yr with a mass transfer rateof 1 . × − M ⊙ /yr. In addition, the period of this parabolic variation istoo long to detect in the O − C curve constructed with the available data.The system has been studied spectroscopically but no accurate radial ve-locity study of it is available in the literature. In systems like GO Cyg theluminous primary star makes it difficult to treat the system as a double-linedbinary. Determination of the physical parameters requires the knowledge ofaccurate mass ratio and the mass of the primary component. The best resultobtained by a q -search technique in the light curve analysis. In what followssolution to allowed the mass ratio to vary allowing with other parameterswhen the solve for an orbital the light curves. Our solutions all have similarresults for all nine light curves. Our results are given in Table 2-3. Spectralstudies of NCB systems (e.g. GO Cyg) are quite difficult because of theirnature. The mass of the primary, therefore, estimated according to theircolors, spectral types etc . In this study, we used recently published astro-physical data of well known stars (e.g., Torres et al., 2010, Yakut & Eggleton,2005, Drilling & Landolt 2000) to estimate the primary’s (the massive andlumonious one) mass. By studying stars with similar luminosities and spec-tral types, the mass of the primary is assumed to be 3.0 M ⊙ . This is alsoconsistent with the values given in the literature. The physical parametersof the system is given in Table 6, the results are consistent with the similarsystems on the M − R , M − L and the Hertzsprung–Russell diagrams givenby Yakut & Eggleton (2005). Our results shows that GO Cyg has the mostmassive components among the known NCB systems. We collected physicalparameters of the NCB systems whose primary components are relativelymassive (Table 7). Mass-luminosity diagram of binaries listed in Table 7 isshown in Fig 4. The locations of GO Cyg A and B in the M − L diagramare consistent with the other NCB systems.Observational results of semi-detached systems show that while in somecases the primary component fills its Roche lobe (GO Cyg) in other casesthe secondary fills its Roche lobe (V836 Cyg, Yakut et al., 2005). Thesedifferences are a sign for the evolutionary stage of the binary system (for7etails we refer Yakut & Eggleton 2005, Eggleton 2006, Eggleton 2010). Theorbital, geometrical, and physical parameters of GO Cyg presented in thisstudy indicate the Roche lobe filling star is the primary (the massive andthe hotter one). We show that the primary may even transfer mass with ata low rate. Contrary to the very low mass stars, mass loss rate due to themagnetic stellar winds can be expected since the convective layer is small inthe systems with intermediate/low mass components (e.g. GO Cyg). Theresults indicate the system GO Cyg evolves under the proximity effect, lowrate mass transfer between the components ( ˙ M = 1 . × − M ⊙ /yr) andthe third body can also remove angular momentum from the binary orbit. Acknowledgments
This study was supported by the Turkish Scientific and Research Coun-cil (T ¨UB˙ITAK 109T047 and 111T270) and Ege University Research Fund.KY+VK acknowledges support by the Turkish Academy of Sciences (T ¨UBA).We thank to an anonymous referee, J.J. Eldridge and E.R. Pek¨unl¨u for theirvaluable comments and suggestions.
References
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25 and 0 .
5, respectively, forthe sake of comparison.Table 1: Results of the period analysis and the orbital elements of the third body. Thestandard errors, 1 σ , are given in parentheses. Parameter Unit Value T o [HJD] 2433930.4283(7) P o [day] 0.717764585(15) P ′ [year] 92.3(5) T ′ [HJD] 2414756(300) e ′ ω ′ [ ◦ ] 20.3 (2.2) a sin i ′ [AU] 4.57 (4) f ( m ) [M ⊙ ] 0.0112(5) m i ′ =20 ◦ [M ⊙ ] 2.30 m i ′ =90 ◦ [M ⊙ ] 0.65 11 igure 2: (a) Residuals for the times of minimum light of GO Cyg. The solid line isobtained with the assumption of sine-like variation. (b) The difference between the obser-vations and the computed sinusoidal curve. igure 3: All available light curves (phase-intensity) of the system between 1936 and 2002.The theoretical curves (solid lines) are drawn using the results given in Table 6. At theright bottom of each panel observation years are given. igure 4: Plot of the M − L plane of the some NCB systems. The ZAMS line is takenfrom Pols et al. (1995). able 2: The photometric elements and their formal 1 σ errors of GO Cyg. See text fordetails. Parameter ValueGeometric parameters: i ( ◦ ) 75.67(3)Ω q T (K) 10350 T (K) 6490(90)Albedo A A g g x , x x B x B x V x V x R x R L L + L + l (%) B V R l L + L + l (%) B V R able 3: Available light curves of GO Cyg that are collected from the literature. JD ∗ refersto the time interval of data taken. In data availability column (Data), ”Yes” and ”No” isshortened by the letter Y and N, respectively. Photoelectric observations are abbreviatedby ”pe” while ”pg” and ”ccd” refers to the photographic and CCD observations. Lightcurves are LC1: Payne-Gaposchkin (1935), LC2: Liau (1935), LC3: Pierce (1939), LC4:Popper (1957), LC5: Ovenden (1954), LC6: Mannino (1963), LC7: Sezer et al. (1993),LC8: Rovithis et al. (1990), LC9: Oprescu et al. (1996), LC10: Jassur (1997), LC11:Rovithis-Livaniou et al. (1997), LC12: Edalati and Atighi (1997), LC13: Vukasovi´c 1997,LC14: Oh et al. (2000), LC15: Zabihinpoor et al. (2006), LC16: This study. ID Year JD ∗ (2400000+) Filters Type Comparison(s) Npoints DataLC1 1934 blue, red pg BD +36 4150 NBD +34 4098BD +35 4197LC2 1935 NLC3 1936 V vis BD +35 4188 122 YLC4 1950 33478.8-33498.0 B,V pe HD 196771 B:261, V:261 YLC5 1950-51 B,V pe BD +35 4197 B:64, V:68 YBD +34 4098LC6 1959-62 36782.4-37910.5 B, V pe BD +35 4197 B:333, V:353 YBD +34 4098LC7 1984-85 45866.4-46348.3 B,V pe HD 197 292 B:416, V:414 YHD 197 346LC8 1985 46264.3-46329.4 B,V pe BD +35 4180 B:631, V:633 YBD +34 4098LC9 1989-92 B,V pe BD +35 4197 NBD +34 4098LC10 1992 U,B,V pe BD +35 4180 NBD +34 4098LC11 1993-94 B,V pe BD +35 4197 NBD +34 4098LC12 1995 U,B,V pe BD +35 4180 NBD +34 4098LC13 1996 U,B,V pe SAO 70314 NLC14 1996 50366.0-50436.0 B,V pe BD +35 4197 B:398, V:397 YBD +34 4098LC15 2002 B,V pe HD 197292 B:545, V:521 YHD 197346LC16 2007 54361.5-54321.6 B, V, R ccd GSC 02694-00280 B:3711, V:3722, YGSC 02694-00733 R:3694 able 4: The photometric parameters and 1 σ errors obtained from the solution of allavailable light curves. See text for details. Parameter LC3 LC4 LC5 LC6 LC7 i ( ◦ ) 75.2(1.5) 77.1(3) 73.42(1.03) 75.57(8) 76.61(3) q T (K) 10350 10350 10350 10350 10350 T (K) 6111(240) 6667(64) 6516(144) 6721(30) 6743(18)Ω L L + L ) B - 0.934(47) 0.932(101) 0.927(18) 0.913(13) V R - - - - - r r LC16 i ( ◦ ) 77.02(2) 74.2(1) 74.5(1) 75.67(3) q T (K) 10350 10350 10350 10350 T (K) 6688(23) 6651(50) 6709(35) 6478(262)Ω L L + L ) B V R - - - 0.875(46) r r Table 5: Available light curves data. Phases are given for the light curves LC3, LC5, andLC15 since JDs are not provided. All data for 9 data sets can be found electronically atCDS.
Data Set Filter JD/Phase MagnitudeLC6 B 2436782.3973 0.156LC6 B 2436782.4034 0.158LC6 B 2436782.4117 0.173LC6 B 2436782.4184 0.184LC6 B 2436782.4198 0.187... ... ... ...17 able 6: Absolute parameters of GO Cyg. The standard errors 1 σ in the last digit aregiven in parentheses. Parameter Unit Pr. Sec.Mass (M) M ⊙ . . ⊙ . . eff ) K 10350 6490Luminosity (L) L ⊙ . b ) mag 0.23 3.03Period change rate ( ˙ P ) d/yr − . × − Mass transfer ratio ( ˙ M ) M ⊙ /yr 1 . × − Seperation between stars ( a ) R ⊙ Table 7: Physical parameters of some well known massive (
M > . ⊙ ) NCB systems.The data is taken from Yakut & Eggleton (2005) except RZ Dra (Erdem et al., 2011), RUUMi (Lee et al., 2008), GW Gem (Lee et al., 2009), EE Aqr (Wronka et al. 2010), KQGem (Zhang 2010). Name Sp.T P(d) M M log L log L2