Journal of The Korean Astronomical Society. 2015. Feb, 48(1): 1-7
Copyright © 2015, The Korean Astronomical Soiety
  • Received : June 02, 2014
  • Accepted : October 07, 2014
  • Published : February 28, 2015
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S. M. AMin

The orbital period changes of the W UMa eclipsing binary AU Ser are studied using the ( O−C ) method. We conclude that the period variation is due to mass transfer from the primary star to the secondary one at a very low and decreasing rate dP / dt = −8.872×10 −8 , superimposed on the sinusoidal variation due to a third body orbiting the binary with period 42.87±3.16 years, orbital eccentricity e = 0.52±0.12 and a longitude of periastron passage ω = 133°.7±15. On studying the magnetic activity, we have concluded that the Applegate mechanism failed to describe the cycling variation of the ( O−C ) diagram of AU Ser.
AU Ser ( α 2000 = 15 h 56 m 49 s , δ 2000 = +22°15′ 42′′ .3) was discovered by Hoffmeister (1935) and classified as a W-type binary system according to Binnendijk (1972) . It is a short period ( P = 0 d .386) W UMa system with magnitude Vmax . = 10 m .9 and spectral type G5V ( Kukarkin, 1970 ).
Visual observations were made by Soloviev (1936 , 1951) , while photographic observations by Huth (1964) . The radial velocity curve was obtained using the cross correlation technique by Hrivnak (1993) . He found a mass ratio q = m 2 / m 1 = 0.71. He also obtained a projected total mass of AU Ser of ( m 1 + m 2 ) sin 3 i = 1.51 M , a value similar to that obtained by Pribulla et al. (2009) from their spectroscopic observations.
The first photoelectric observations were made by Binnendijk (1972) and subsequently Rucinski (1974) , Kennedy (1985) , Li, et al. (1992 , 1998) , Djurasevic (1993) and Gürol (2005) . They obtained photoelectric light curves in different wavelengths. In addition, Gürol (2005) studied the period variation of the system suggesting its triplicity with a third body that orbiting the binary in about 94 years. However, many photoelectric and CCD minima times were observed and published during the last decade (39 minima) which motivated us to re-construct and analyze the O − C diagram in order to obtain more precise orbital parameters for the third body. The goal of the present study is to discuss the causes of variation in the orbital period; mainly to re-determine the third body orbital parameters of AU Ser.
To investigate the period changes of the W UMa system AU Ser, we have collected all the available times of minima since HJD 2428318.5 (≡ 30 May 1936) until 2456034.5 (≡ 17 April 2012) which cover about 75.9 years. The times of minima are listed in Table 2 (Appendix). The successive columns of the table are: HJD, the number of integer cycles, type of the minimum, the O-C residuals and the references.
The O − C residuals of Table 2 have been calculated using the ephemeris given by Kreiner et al. (2001) :
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where E is the number of integer cycles.
To predict timing of new minima, the last 147 minima times, which cover the interval from June 1976 till April 2012, have been linearly fitted ( Figure 1 ) and used to obtain the new light elements:
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The (O-C) diagram. The dashed line represents the linear fit to the last 143 minimum data.
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with residual mean squares = 0.0002.
We have constructed the ( O − C ) diagram of AU Ser ( Figure 2 ). It shows complicated period variations, which may be due to a combination of more than one of the following effects: mass transfer, light time effect, magnetic activity. Thus, we examine each reason affecting orbital period behavior.
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The (O − C) variation with quadratic and sinusoidal fit and their residuals of AU Ser. Filled circles represent primary minima while open circles are for secondary minima.
- 2.1. Mass Transfer
A quadratic least square fit concerning the first three terms of equation (5) has been performed. We obtained the coefficient of the quadratic term Q = −4.69×10 −11 and consequently we calculated the rate of change of the orbital period dP / dt = −8.872 × 10 −8 day/year. The quadratic fit is represented as the dashed line on Figure 2 .
In the simplest case of conservative mass transfer, if the more massive component loses mass, the orbital size will decrease and the period of the system must decrease too ( Pringle, 1985 ). So, the obtained orbital period decrease may be interpreted in terms of mass transfer from the more massive star to the less one ( Kwee and van Woerden, 1958 ). The rate of mass transfer in the conservative case could be estimated by using the formula derived by Kreiner and Ziolkowski (1978) :
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where the quadratic term coefficient Q , and the period P are in days. Adopting the values of the absolute parameters of AU Ser from Gürol (2005) : M 1 = 0.895 M and M 2 = 0.635 M , the rate of mass transfer:
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which is of the same order as the values given in the literature for contact binaries (see Liu & Yang 2003 ).
- 2.2. Light Time Effect
Observational detection of a periodic orbital period variation of a binary star system can be considered as a strong evidence of the existence of a third body around the binary system. This body causes the Light Time Effect (LITE) as displacement of the times of eclipse minimum light in a sinusoidal form with a period equal to the period of the third body, ( Woltjer 1922 ; Irwin 1959 ).
At first, it may be noticed that both the primary and the secondary minima have the same trend on the ( O − C ) diagram ( Figure 2 ). The time of mid eclipse can be computed as follows:
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where e 3 , ω 3 , ν , a 12 sin i and c are the eccentricity, longitude of the periastron, true anomaly of the binary orbit around the center of mass of the triple system, projected semi-major axis, and the speed of light, respectively.
Gürol was the first who considered the sine-like variation of the O − C curve of AU Ser. He calculated the light time effect (LITE) and obtained the orbital parameters of a third body of at least 0.53 solar mass orbiting the binary with an orbital period of 94.15 years. The recent photoelectric and CCD minima times (39 minima) together with the earlier minima could enable us to re-calculate the LITE and obtain a more real and precise solution.
Using the program prepared by Zasche, et al. (2009) , based on Irwin’s method (1959) , we have calculated the orbital parameters of the third body, and its LITE on the binary system. The program contains three modes 0, 1 and 2. These three modes correspond to computing the LITE due to the third body, the LITE together with the quadratic term and only the quadratic term, respectively.
Three different weights 1, 5 and 10 were applied to the data points for: visual (v), photographic (pg) and photoelectric (pe) or CCD minima times, respectively. Applying code 1, we obtain the orbital parameters of the third body as in Table 1 , and as represented by the solid sinusoidal (red) line in Figure 2 .
The light–time effect solution and the corresponding quadratic ephemeris of the binary system is also presented
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The light–time effect solution and the corresponding quadratic ephemeris of the binary system is also presented
On applying the well known mass function relation (cf., Albayrak et al., 1999 ):
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where M 12 and M 3 are the masses (in solar units) of the eclipsing pair and the third body, A is the amplitude in days, and P 3 is the period of the third body in years. The inclination i of the third body orbit was assumed to be equal to the inclination of the eclipsing binary orbit. The minimal mass M 3 min is then corresponding to i 3 = 90°.
From our new analysis and including all the recent minima times, we obtain a third body orbital period of about 43 years instead of the very large period (≃ 94 yr.) given by Gürol (2005) . Also, we obtain a significantly different value for the semi-amplitude. The comparison between the newly obtained set of parameters and those obtained earlier is given in Table 1 .
- 2.3. Magnetic Activity and Star Spots
Kalužny (1986) analyzed the light curves that were made by Binnendijk (1972) using the W-D code. He reported that the depth of the primary and the secondary minimum differs by about 0.2 mag and such difference is unusually large for a W UMa-type system. He also noticed the degree of asymmetry in maxima of the light curve and suggested that such pronounced asymmetry of the light curves may be due to a hot spot located at the neck between the stars.
Gürol (2005) has studied the published light curves (LCs) and reported that all the LCs can be modelled by hot or cool spots located on the secondary components. He also studied the O’Connell effect and attributed such complex nature of the light curve to variable starspot activity with 32 to 35 years as a probable period for the system. For a detailed discussion for the light curve analysis concerning the starspot activity one may review Gürol (2005) .
Changes in the magnetic field distribution result in changes of angular momentum distribution. Gravitational quadrupole coupling produces changes in the internal structure of the active star which results in a period variation. The Applegate (1992) model involves variations of the subsurface magnetic field. Such subsurface magnetic field may be compared to solar activity cycles. The model can give a plausible explanation of the cyclic period variations of late type active stars.
For AU Ser, the star-spots are expected to be presented on the cooler member i.e., the secondary less massive star (Sp. Type G5V) was considered as the active component when applying the Applegate (1992) mechanism. For more details about the mechanism see Applegate and Patterson (1987) , Applegate (1992) and references therein. We applied the Applegate mechanism using of all data.
The present ( O − C ) residual diagram for AU Ser contains a cycle of about 43 years. Assuming this long period P 3 to be the modulation period, Pmod , of the stellar magnetic activity of the convective secondary star, with semi amplitudes O − C = 0.0197 day, and accepting the parameters given by Gürol (2005) [ M 2 = 0.635 M , R 2 = 0.94 R , L 2 = 3.8 L and the orbital semi-major axis a = 1.19 R ] one can follow the Applegate procedure (see Applegate 1992).
The observed amplitude of the period modulation of the cycle, ∆ P / P = 2 π ( O − C )/ Pmod = 7.92 × 10 −6 gives the variation of the orbital period ∆ P = 0.264 second. The angular momentum transfer is ∆ J = 3.69 × 10 +46 g cm 2 s −1 . If the mass of the shell is Mshell = 0.1 M 2 , the moment of inertia of the shell is Ishell = 3.604 × 10 +53 g cm 2 , and the variable part of the differential rotation of the active star is ∆Ω/Ω = 0.00036. The energy budget needed to transfer the ∆ J is ∆ E = 7.564 × 10 +39 ergs. The luminosity change is ∆ LRMS = 1.757 × 10 +31 . This luminosity variation is ∆ LRMS / L = 0.0011 ≃ 0.0 of the luminosity of the active star. This value is inconsistent with the values suggested by Applegate (1992) model which should be around 10% to prove the presence of magnetic activity on similar chromospherically active stars.
In case of AU Ser especially for the observed light curves in 1992 and 1995, Kalimeris et al. (2002) studied the effects of star spots on the ( O − C ) diagrams of eclipsing binaries and showed that migrating star spots can only introduce high frequency, low amplitude disturbances. Because of this Gürol (2005) deduced that the main causes of the ( O − C ) variations of AU Ser may be only mass transfer between the two stars and/or light time effect due to the presence of a third body. This shows that our result is in agreement to that obtained by Gürol.
The present analysis of the O − C diagram of AU Ser, suggests a decrease in the orbital period due to mass transfer from the more massive primary component to the less massive secondary one by a rate of about dP / dt = −8.87 × 10 −8 day/year with a mass transfer rate of dM / dt = −1.67 × 10 −7 M /year. This period decrease is superimposed on a sinusoidal variation, as seen in Figure 2 , due to the presence of a third body orbiting the binary AU Ser in about 42.9 years with an orbital eccentricity e 3 = 0.52 and a longitude of periastron passage ω 3 = 133.7°.
Pribulla et al. (2009) observed the system spectroscopically to study its radial velocity. They did not see evidence for a third component when using the broadening functions technique described by Rusinski (2002) . However, this result does not dismiss the third body hypothesis proposed in the present work and by Gürol (2005) . Hence, more precise photoelectric and CCD observations are still needed to verify the obtained results.
I acknowledge the variable star observations from the BBSAG International Database, IBVS, and the NASA Astrophysics Data System Bibliographic Services. Thanks go also to Dr. Petr Zasche for his program for the determination of the LITE due to the presence of the third body.
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