Research Paper J. Astron. Space Sci. 28(3), 163-172 (2011) http://dx.doi.org/10.5140/JASS.2011.28.3.163

WZ Cephei: A Dynamically Active W UMa-Type Binary

Jang Hae Jeong1, 2 and Chun-Hwey Kim1, 2† 1Department of Astronomy and Space Science, Chungbuk National University, Cheongju 361-763, Korea 2Chungbuk National University Observatory, Chungbuk National University, Cheongju 361-763, Korea

An intensive analysis of 185 timings of WZ Cep, including our new three timings, was made to understand the dynami- cal picture of this active W UMa-type binary. It was found that the of the system has complexly varied in two cyclical components superposed on a secularly downward parabola over about 80y. The downward parabola, cor- responding to a secular period decrease of -9.d97 × 10-8 y-1, is most probably produced by the action of both angular mo- mentum loss (AML) due to magnetic braking and mass-transfer from the massive primary component to the secondary. The period decrease rate of -6.d72 × 10-8 y-1 due to AML contributes about 67% to the observed period decrease. The mass -8 -1 flow of about 5.16× 10 M⊙ y from the primary to the secondary results the remaining 33% period decrease. Two cycli- cal components have an 11.y8 period with amplitude of 0.d0054 and a 41.y3 period with amplitude of 0.d0178. It is very interesting that there seems to be exactly in a commensurable 7:2 relation between their mean motions. As the possible causes, two rival interpretations (i.e., light-time effects (LTE) by additional bodies and the Applegate model) were con- sidered. In the LTE interpretation, the minimum masses of 0.30 M⊙ for the shorter period and 0.49 M⊙ for the longer one were calculated. Their contributions to the total light were at most within 2%, if they were assumed to be main-sequence . If the LTE explanation is true for the WZ Cep system, the 7:2 relation found between their mean motions would be interpreted as a stable 7:2 resonance produced by a long-term gravitational interaction between two tertiary bodies. In the Applegate model interpretation, the deduced model parameters indicate that the mechanism could work only in the primary star for both of the two period modulations, but could not in the secondary. However, we couldn't find any meaningful relation between the light variation and the period variability from the historical light curve data. At present, we prefer the interpretation of the mechanical perturbation from the third and fourth stars as the possible cause of two cycling period changes.

Keywords: W UMa-type star, WZ Cep, period change, light-time effects, magnetic activities

1. INTRODUCTION analysis of his light curve using Russell's classical model. The first photoelectricBV light curves were secured by The W UMa-type , WZ Cep (AN 244.1928, Hoffmann (1984) who detected a strong O'Connell ef- 2MASS J23222421+7254566, 1RXS J232216.6+725505) fect in his light curves, as the brightness in the 0.25 phase was discovered by Schneller (1928), as an RR Lyr type (Max I) was significantly higher than that in the 0.75 phase with a period of 0.d260984. Nine later, (Max II). The spectral type was assigned as F5 in the Gen- a photographic light curve was obtained by Balázs (1937), eral Catalogue of Variable Stars (Kholopov et al. 1987). who correctly classified WZ Cep as a W UMa binary star Hoffmann's light curves were reanalyzed by Kałużny with an orbital period of 0.d41745. Detre (1940) also made (1986) with the Wilson Devinney binary model (WD; photographic observations of the system, confirmed Ba- Wilson & Devinney 1971). His solutions showed that WZ lázs' result, and gave basic system parameters from the Cep is a contact binary with the components of unequal

This is an Open Access article distributed under the terms of the Received Jun 27, 2011 Revised Jun 29, 2011 Accepted Jun 30, 2011 Creative Commons Attribution Non-Commercial License (http://cre- †Corresponding Author ativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, E-mail: [email protected] provided the original work is properly cited. Tel: +82-43-261-3139 Fax: +82-43-274-2312

Copyright © The Korean Space Science Society 163 http://janss.kr pISSN: 2093-5587 eISSN: 2093-1409 J. Astron. Space Sci. 28(3), 163-172 (2011)

surface temperatures (ΔT ≈ 1,000 K). The O'Connell ef- Camera exposure time ranged between 40 seconds and fect in the light curve was ascribed to a small hot spot on 60 seconds according to the quality of the night. the less massive component near the neck between stars. The instrumentation used and the reduction method These interpretations were questioned by Djurašević et for the raw CCD frames have been described in detail al. (1998), who obtained new BVR light curves that were by Kim et al. (2006). The resultant standard errors of our almost symmetrical. Their analysis of both their own observations in terms of comparison minus check star light curves and Hoffmann's using their own Roche com- were about ±0.m02. From our observations, three primary puter model (Djurašević 1992a, b) showed that the WZ times of minimum light were determined using the con- Cep system is a shallow contact binary (f = 9~14%) with ventional Kwee & van Woerden (1956) method, and are the components of slightly different temperatures (ΔT listed in Table 1. ≈ 140 K) and with two large dark spots on the surface of the massive, hotter primary star. Recently, WZ Cep was revisited by Lee et al. (2008) and Zhu & Qian (2009). Lee 3. PERIOD STUDY et al. (2008) presented symmetrical BVR light curves in the observing season in 2005, while Zhu & Qian (2009) To investigate the period variation of WZ Cep, a total of obtained an asymmetrical V light curve with a strong 185 (91 visual, 4 photographic, and 90 photoelectric and O'Connell effect. Both authors analyzed their light curves CCD) times of minimum light, including ours, have been using the WD method and confirmed the photometric re- collected from a modern database (Kreiner et al. 2001) sults of Djurašević et al. (1998). At the same time, Zhu & and from the recent literature. Table 1 lists only photo- Qian (2009) made the first intensive period study of WZ electric and CCD minima, which were not compiled by Cep with all timings available to them, and found that Zhu & Qian (2009) or published after their study. the period variation consists of both a periodic and secu- The (O-C ) residuals of all timings were calculated with larly decreasing terms. The periodic term has a period of the linear ephemeris of Kreiner et al. (2001), as follows: 34.y2 with amplitude of 0.d013, while the secular period -8 d decrease rate is about -8.8 × 10 day/. C1 = HJD 2449890.3582 + 0. 41744670 E. (1) Numerous timings just before and after the period study of Zhu & Qian (2009) have been published in the The (O-C1) diagram is shown in Fig. 1, where the times of literature. In this paper, all published and newly ob- minimum are marked by assorted symbols that differ in served timings have been reanalyzed. It is noticed that size and shape according to observational method and the ephemeris suggested by Zhu & Qian (2009) is not type of eclipse. The (O-C1) residuals were listed in the compatible with recent timing residuals. New ephemeris sixth column of Table 1. As can be seen in the figure, it is derived with a detection of a secondary cyclic modula- tion of the O-C residuals by a period of about 11.8 year. A discussion of the implications on the existing working hypotheses follows.

2. OBSERVATIONS

Charge-coupled device (CCD) photometric observa- tions of WZ Cep for the purpose of timing determination were made on the three nights of May 28 and October 9, 2005 and September 23, 2006 with the 35-cm reflector of the campus station of Chungbuk National University Observatory in Korea. The telescope was equipped with an SBIG ST-8 CCD imaging system, electrically cooled, with a 19' × 12' field of view. No filters were used in our The (O-C ) diagram of WZ Cep drawn together with the non- observations. GSC 4486-1402 and GSC 4486-1352 were Fig. 1. 1 linear terms (solid and dashed lines) of Eq. (2). The recent residuals from chosen as the comparison and check stars, respectively. Eq. (2) in the bottom are remarkably deviating from the non-linear terms Our comparison is the same one used by Lee et al. (2008). of Eq. (2).

http://dx.doi.org/10.5140/JASS.2011.28.3.163 164 Jang Hae Jeong & Chun-Hwey Kim WZ Cephei, A dynamically active binary star

is clear that the variation patterns of the residuals before although there is a large gap of about 25 years between and after 1995y are quite different from each other. The 1939y and 1964y. However, the period from 1995y to the orbital period before 1995y seemed to be nearly constant, present has dramatically decreased in a continuous way.

Table 1. Photoeletric and CCD times of minima of WZ Cep not listed in Zhu & Qian (2009) or published after their study. HJD Error MEa Ty b Cycle (O-C ) (O-C ) Reference (2400000+) 1 2 50,642.7978 0.0002 CC II 1,802.5 -0.0081 0.0003 Baldwin & Samolyk (2004) 51,088.6282 0.0002 CC II 2,870.5 -0.0108 0.0028 Baldwin & Samolyk (2004) 51,280.8540 CC I 3,331.0 -0.0192 -0.0029 In O-C gatewaya 51,452.6349 0.0003 CC II 3,742.5 -0.0176 0.0013 Baldwin & Samolyk (2004) 51,576.6148 0.0003 CC II 4,039.5 -0.0193 0.0014 Baldwin & Samolyk (2004) 52,146.8363 0.0003 CC II 5,405.5 -0.0300 -0.0003 Baldwin & Samolyk (2004) 52,223.6456 0.0002 CC II 5,589.5 -0.0309 0.0000 Baldwin & Samolyk (2004) 52,239.5049 0.0002 CC II 5,627.5 -0.0346 -0.0034 Baldwin & Samolyk (2004) 52,415.6677 0.0003 CC II 6,049.5 -0.0343 -0.0003 Baldwin & Samolyk (2004) 52,542.5700 0.0003 CC II 6,353.5 -0.0358 0.0004 Baldwin & Samolyk (2004) 52,603.5163 0.0001 CC II 6,499.5 -0.0367 0.0005 Baldwin & Samolyk (2004) 52,860.6585 0.0002 CC II 7,115.5 -0.0417 -0.0001 Baldwin & Samolyk (2004) 52,899.6884 0.0003 CC I 7,209.0 -0.0431 -0.0007 Baldwin & Samolyk (2004) 52,923.6920 0.0003 CC II 7,266.5 -0.0426 0.0001 Baldwin & Samolyk (2004) 53,097.7639 0.0003 CC II 7,683.5 -0.0460 -0.0003 Baldwin & Samolyk (2004) 53,223.6236 0.0003 CC I 7,985.0 -0.0465 0.0014 Baldwin & Samolyk (2007) 53,515.6212 0.0003 CC II 8,684.5 -0.0529 -0.0002 Baldwin & Samolyk (2007) 53,519.1720 0.0007 CC I 8,693.0 -0.0504 0.0024 This paper 53,558.8226 0.0003 CC I 8,788.0 -0.0572 -0.0038 Baldwin & Samolyk (2007) 53,615.5995 0.0002 CC I 8,924.0 -0.0531 0.0013 Baldwin & Samolyk (2007) 53,642.7343 0.0004 CC I 8,989.0 -0.0523 0.0025 Lee et al. (2008) 53,642.9406 0.0002 CC II 8,989.5 -0.0547 0.0000 Lee et al. (2008) 53,643.7754 0.0002 CC II 8,991.5 -0.0548 -0.0001 Lee et al. (2008) 53,643.9866 0.0003 CC I 8,992.0 -0.0523 0.0024 Lee et al. (2008) 53,644.8206 0.0003 CC I 8,994.0 -0.0532 0.0016 Lee et al. (2008) 53,653.1720 0.0003 CC I 9,014.0 -0.0508 0.0042 This paper 53,757.5264 0.0002 CC I 9,264.0 -0.0580 -0.0015 Baldwin & Samolyk (2007) 53,994.6318 0.0002 CC I 9,832.0 -0.0624 -0.0020 Baldwin & Samolyk (2007) 54,002.1471 0.0001 CC I 9,850.0 -0.0611 -0.0006 This paper 54,107.5509 0.0001 CC II 10,102.5 -0.0626 -0.0003 Baldwin & Samolyk (2007) 54,211.7021 0.0002 CC I 10,352.0 -0.0643 -0.0003 Baldwin & Samolyk (2007) 54,338.8138 0.0002 CC II 10,656.5 -0.0652 0.0012 Samolyk (2008a) 54,366.7809 0.0002 CC II 10,723.5 -0.0670 -0.0001 Samolyk (2008a) 54,433.3598 0.0008 CC I 10,883.0 -0.0708 -0.0027 Parimucha et al. (2009) 54,583.8498 0.0003 CC II 11,243.5 -0.0704 0.0008 Samolyk (2008b) 54,628.7261 0.0007 CC I 11,351.0 -0.0696 0.0025 Samolyk (2008b) 54,635.8208 0.0003 CC I 11,368.0 -0.0715 0.0007 Samolyk (2008b) 54,651.6853 0.0003 CC I 11,406.0 -0.0700 0.0026 Samolyk (2008b) 54,702.8179 0.0002 CC II 11,528.5 -0.0746 -0.0010 Samolyk (2008b) 54,768.5646 0.0002 CC I 11,686.0 -0.0757 -0.0007 Samolyk (2009) 54,797.5770 0.0002 CC II 11,755.5 -0.0759 -0.0003 Samolyk (2009) 54,832.6406 0.0003 CC II 11,839.5 -0.0778 -0.0014 Samolyk (2009) 54,986.6771 0.0003 CC II 12,208.5 -0.0791 0.0007 Samolyk (2010b) 55,029.4650 0.0002 PE I 12,311.0 -0.0795 0.0013 Parimucha et al. (2009) 55,051.3781 0.0001 PE II 12,363.5 -0.0824 -0.0010 Parimucha et al. (2011) 55,084.1487 CC I 12,442.0 -0.0813 0.0009 Nagai (2010) 55,114.6208 0.0003 CC I 12,515.0 -0.0829 -0.0000 Samolyk (2010a) 55,144.6758 0.0001 CC I 12,587.0 -0.0840 -0.0005 Diethelm (2010) 55,163.6693 0.0001 CC II 12,632.5 -0.0843 -0.0003 Samolyk (2010a) 55,238.5985 0.0002 CC I 12,812.0 -0.0868 -0.0010 Samolyk (2010a) 55,346.7168 CC I 13,071.0 -0.0872 0.0012 In O-C gatewayc 55,480.5036 0.0003 PE II 13,391.5 -0.0921 -0.0005 Parimucha et al. (2011) 55,503.6700 0.0002 CC I 13,447.0 -0.0940 -0.0018 Diethelm (2011) aMe: method, CCD and CC: charge coupled device, PE: photoelectric bTy: type, I: primary eclipse, II: secondary eclipse. cThe timing was listed at the web (http://var.astro.cz/ocgate/ocgate.php?star=wz+cep&submit=Submit&lang=en).

165 http://janss.kr J. Astron. Space Sci. 28(3), 163-172 (2011)

This fact was noticed by Zhu & Qian (2009), who adopted a quadratic plus sine ephemeris to explain the (O-C1) re- siduals constructed with the timings available to their time, as follows:

d6−−d112 OC−=−±1 0.0180( 0.0009) − 2. 76( ±× 0.16) 10E − 5. 04( ±× 0.39) 10 E +0.d 013( ± 0.001) sin{ 0. 012E −± 76.  5( 6. 7)} . (2)

In Eq. (2) the phase angle among the arguments in sine function should be read as +103.o5 rather than -76.o5, which must be a typo. The value of +103.o5 was calculated by us with the (O-C)1 and (O-C)2 values listed in the fifth and six columns of Table 2 in the paper of Zhu & Qian (2009). The dashed and solid lines in Fig. 1 denote the lin- The (O-C ) diagram of WZ Cep drawn together with the non-lin- ear plus quadratic and full terms in Eq. (2), respectively. Fig. 2. 1 ear terms (solid and dashed lines) of Eq. (3). The recent residuals from Eq. In the bottom of Fig. 1, the residuals from Eq. (2) where (3) in the bottom clearly show an oscillatory pattern with a short period of the recent timings since 1995y have been clearly deviat- about 10y and a small amplitude of about 0.d004. ing from the ephemeris are plotted, implying that Eq. (2) should be revised and/or the period change of WZ Cep may be more complicated. The standard deviation (σ) for Table 2. Final solution of Eq. (4) and related parameters. the photoelectric and CCD residuals was calculated to be Parameter Value Unit σ = ±0.d0029. Such a value cannot be neglected because of ΔT0 -0.0359 (3) HJD the accuracy of modern photoelectric and CCD timings ΔP 3.45 (4) × 10-6 day (Kim et al. 2005). T0 2,449,890.3371 (3) HJD P 0.41744325 (4) day As a first step in understanding the general behavior of A -5.70 (8) × 10-11 day/P period change of the WZ Cep system, we tried to fit all (O- B 0.0054 (3) day 0.932(52) AU C1) residuals to a quadratic plus sine ephemeris by using C 0.0350 (2) degree/P the Levenberg-Marquardt method (Press et al. 1992). The Psine 11.76 (16) year final solution was quickly converged as follows: D 66.9 (3.0) degree 8 a12 sin i12 5.14 (20) × 10 km

d6−−d112 3.43 (13) AU OC−=−1 0.0251( ± 0.0002) − 3. 47( ± 0.03) × 10E − 5. 76( ± 0.06) × 10 E ω12 143.8 (2.6) degree +0.d 0208 ± 0.0002 sin 0. 0089± 0.0001E −± 82. 4 0. 8 . ( ) { ( ) ( )} (3) e12 0.544 (25) -

P12 (=PLTE) 41.30 (64) year In this and subsequent calculations, we assigned dif- T12 2,452,780 (142) HJD ferent weights to each of the data according to the ob- servational method: 10 to photoelectric or CCD observa- tions, 3 to photographic, and 1 to visual data, which were the same weights as those used by Zhu & Qian (2009). To find the variation characteristics of the small oscil- The linear plus quadratic and full terms in Eq. (3) were lation in Fig. 2, several non-linear terms in addition to a drawn with the (O-C1) residuals as the dashed and solid linear plus quadratic ephemeris were considered, such lines in Fig. 2, respectively. The residuals from full terms as: 1) a light-time effect (LTE), 2) two sine curves, 3) a sine of Eq. (3) were plotted in the bottom of Fig. 2. As shown in curve plus an LTE, 4) two LTEs. Next, attempts were made Fig. 2, Eq. (3) gives a more satisfactory fit to the observed to fit all timings to each of the four ephemeris models. timings than Eq. (2). From the argument of 0.o0089 in the The result showed that the fits with the ephemeris mod- sine term of Eq. (3), the cyclic period is calculated as 46.y4 els of both 3) and 4) were superior to those with 1) and 2). (±0.y2), which is 12.y2 longer than that of Eq. (2) given by In addition, the solution with the ephemeris 4) gave zero Zhu & Qian (2009). It is interesting to note that the residu- eccentricity for the LTE orbit, with a shorter period and als from Eq. (3) show an oscillatory pattern, especially in smaller amplitude in two LTE . This means that the the photoelectric and CCD timings, with small amplitude ephemeris 3) is best for our purpose. The ephemeris 3) is of about 0.d005 and with a short period of about 10y. expressed as:

http://dx.doi.org/10.5140/JASS.2011.28.3.163 166 Jang Hae Jeong & Chun-Hwey Kim WZ Cephei, A dynamically active binary star

2 O− C13 =∆ T +∆ PE + AE + Bsin ( CE + D) +τ , (4) and solid lines represent the linear plus quadratic and full terms of Eq. (4), respectively. The residuals from all where τ3 is the light-time due to the assumed third body, terms of Eq. (4) were listed in the seventh column of Ta- and includes five parameters (a12 sin i12, e12, ω12, P12, T12) ble 1, and were plotted in the bottom of Fig. 3. The stan- which are the orbital parameters of the eclipsing pair dard deviation for the photoelectric and CCD residuals around the mass center of the triple system. The para- in the bottom of Fig. 3 is σ = ±0.d0002, which is excellently metric and differential forms of the orbital elements for compatible with that of the modern photoelectric and the light-time orbit were taken from Irwin (1952, 1959). CCD timing accuracy. Figs. 4 and 5 show two cyclic (O-C ) The Levenberg-Marquardt method was used again to diagrams phased with each of their periods, in which the solve Eq. (4) simultaneously. In this case, there are 11 pa- continuous lines were drawn with the solution param- rameters to be adjusted in Eq. (4). The calculations con- eters in Table 2. Summing up our analysis of all timings verged quickly to yield the solution listed in Table 2. The of WZ Cep, the period of the system has varied in two quality of the final solution represented by Eq. (4) is very cyclical components superposed on a global downward satisfactory, and may be judged from Fig. 3, in which the parabola over about 80y.

(O-C1) residuals were plotted with Eq. (1), and the dashed

Fig. 3. The (O-C1) diagram of WZ Cep drawn together with the non-linear terms (solid and dashed lines) in Table 2.

Fig. 4. The (O-C) diagram of WZ Cep phased with the shorter period of Fig. 5. The (O-C) diagram of WZ Cep phased with the longer period of 11.y8 in Table 2. 41.y3 in Table 2.

167 http://janss.kr J. Astron. Space Sci. 28(3), 163-172 (2011)

4. THE SECULAR PERIOD DECREASE ration constant typically ranging from 0.07 to 0.15 for solar-type stars, and P is the orbital period in days. Be- From the coefficient (A) of the quadratic term in Table fore solving Eqs. (5)-(7) above, we have to estimate the 2, the secularly decreasing rate of the period of WZ Cep absolute parameters of WZ Cep, because no reliably is calculated to be -9.d97 (±0.14) × 10-8 y-1. In principle, published absolute parameters currently exist. Thus, the there are two working mechanisms for the secular period absolute parameters of WZ Cep were estimated with the decrease observed in a close binary star such as the WZ photometric solution of Djurašević et al. (1998) and with Cep system: 1) secular mass transfer from the more mas- Harmanec's (1988) empirical relation between mass and sive (“primary” hereinafter) to the less massive (“second- temperature. Table 3 lists the resultant absolute param- ary” hereinafter) stars, 2) angular momentum loss (AML) eters. By using the parameters in Tables 2 and 3 and k2 = by magnetic braking via a magnetically controlled stel- 0.1 (Webbink 1976), Eq. (7) was solved to determine the lar wind from a magnetically active star in a binary. WZ rate of decrease of the period due to magnetic braking Cep has been known as a shallow contact system with a as -6.d72 × 10-8 y-1, which contributes about 67% to the fill-out factor of about 9-24% (Djurašević et al. 1998, Lee observed period decrease. Therefore, we note that mag- et al. 2008, Zhu & Qian 2009) and with the massive pri- netic braking may be a major mechanism contributing mary hotter than the secondary. Moreover, the primary to the observed secular period change. Inserting these star has a large and variable dark spot(s) (Djurašević et al. values into Eqs. (5) and (6), the mass transfer rate from 1998, Lee et al. 2008, Zhu & Qian 2009), indicating that it the primary to the secondary star was calculated as 1.69 -8 -1 is a magnetically active star. This would mean that both × 10 M⊙ y . If the observed decreasing rate of period is a secular transfer of a gaseous mass stream from the pri- assumed to occur purely by a continuous mass transfer, mary to the secondary star and the AML from the mag- the mass flow rate is calculated with Eq. (6) to yield about -8 -1 netically active primary star are occurring concurrently 5.16 × 10 M⊙ y , which is about three times larger than in the WZ Cep system. On this basis, the observed secular that obtained when the magnetic braking and the mass period decrease is expressed as follows: transfer are occurring simultaneously. From our discus- sions above, one may conclude that 1) the secular period dP dP  dP =  + , (5) decrease of WZ Cep has resulted from the combination of dtobs dt mt dt mb AML by magnetic braking and mass transfer from the pri- where the subscripts mt and mb denote mass transfer mary to the secondary components, and 2) AML is about and magnetic braking, respectively. The period change two times more effective than mass transfer in terms of by conservative mass transfer is expressed with the fol- its contribution to the observed secular period decrease. lowing well-known formula,

 1 dP  3MM11( − M 2)  = , (6) 5. TWO CYCLIC PERIOD CHANGES P dtmt M12 M where M1 and M2 denote the masses of the primary and In Section 3 we have decoupled two cyclic terms via secondary stars, respectively. The period change due to Eq. (4) from the observed (O-C1) residuals, shown in Fig. the AML by magnetic braking is approximately expressed 3 and listed in Table 2: One is a sine term with a semi- d y by the following formula (Bradstreet & Guinan 1994): amplitude of 0. 0054 and a period (Psine) of 11. 8, while the other an LTE term with a semi-amplitude of 0.d0178, a dP  2 −5/3 ≈−1.1 × 10−−8kq 2 1 1 + q M + M MR4 + MR4 P− 7/3, y  ( ) ( 1 2) ( 11 2 2) (7) period (PLTE) of 41. 3, and an eccentricity of 0.54. It is very dt mb interesting to note that there exists a commensurable 2:7 where R1 and R2 are the radii of the components in so- relation between Psine and PLTE; namely, 7 Psine = 2 PLTE. 2 lar units, q is the mass ratio (q = M2 / M1), k is the gy- There have been two rival theories to explain these cy- clic period changes: One explanation is the LTEs due to additional third- and fourth-bodies in the WZ Cep sys- Table 3. Absolute parameters of WZ Cep. tem, and the other is the Applegate (1992) mechanism. Parameter Primary Secondary Unit Firstly, if the LTEs are assumed to be the mechanism to produce two cyclic period changes, then mass functions, Mass 1.33 (8) 0.43 (3) M⊙

Radius 1.29 (1) 0.77 (1) R⊙ masses and bolometric of two tertiary bod- 2.56 (4) 0.85 (3) L⊙ ies were calculated for different inclinations by using the

http://dx.doi.org/10.5140/JASS.2011.28.3.163 168 Jang Hae Jeong & Chun-Hwey Kim WZ Cephei, A dynamically active binary star

absolute parameters in Table 3. The results were listed Using the modulation periods and amplitudes listed in in Table 4. In the calculation, the bolometric luminosi- Table 2 and adopting the absolute dimensions provided ties were obtained by using Harmanec's (1988) empirical in Table 3, the variations of parameters needed to change formula for main-sequence stars. As listed in Table 4, the the orbital period of WZ Cep by specified amounts can be o minimum masses (i' = 90 ) of 0.30 M⊙ for the third body obtained from the formulae given by Applegate (1992). and of 0.49 M⊙ for the fourth body would contribute very The calculations were made with the assumption that small fractions of about 0.1% and 2% lights, respectively, two cyclical changes of period are produced by both to the total luminosity (lt = l1 + l2 + l3 + l4). Therefore, l3 and components. The resultant parameters were listed in Ta- l4 would be hardly detectable in the light curve syntheses ble 5, and show that the Applegate mechanism could op- by the previous investigators (Djurašević et al. 1998, Lee erate only in the primary star for both two cyclic changes et al. 2008, Zhu & Qian 2009). of period, but cannot in the secondary because the cal-

Secondly, as an alternative explanation for the cyclical culated luminosity change (ΔLrms) is about 11 and 3 times components of the period variability of WZ Cep, Apple- larger for the shorter and longer periods, respectively, gate's (1992) model deserves attention. According to this than the values required by the model. Our determina- theory, the orbital period can be modulated from chang- tion that the primary may be the magnetically active star es in the distribution of angular momentum (and corre- could be supported by Mullan's (1975) conclusion that sponding changes in stellar oblateness) as the magneti- it is the more massive components of W UMa systems cally active star undergoes changes in magnetic activity. that should preferentially manifest star spots, and thus, magnetic activity (Eaton 1986). Previous investigators (Djurašević et al. 1998, Lee et al. 2008, Zhu & Qian 2009) also invoked a cool spot (s) on the surface of the more Table 4. Basic parameters for the hypothetical third- and fourth-bodies in the WZ Cep system. massive primary component to explain the light curve Parameter Shorter period Longer period Unit asymmetry of WZ Cep. y y (11. 8) (41. 3) Since the Applegate model predicts that the rms lumi- Mass function 0.0061 (11) 0.0238(29) M⊙ nosity of the active primary star would be variable with Mass the same period as that of the orbital period modula- o M⊙ i' = 30 0.66 (2) 1.18 (12) p p o tion, the relative lights (e.g., Max II [0. 75] - Max I [0. 25]) i' = 60 0.35 (1) 0.59 (1) M⊙ o i' = 90 0.295 (2) 0.494 (6) M⊙ from four V bandpass light curves published so far were Luminosity deduced, and their time variability was carefully inves- i' = 30o 0.24 (3) 2.25 (85) L⊙ tigated. But no meaningful relation between the light o L⊙ i' = 60 0.021 (6) 0.16 (1) variation and the period variability was found, although i' = 90o 0.012 (1) 0.082 (4) L⊙ the light asymmetry at a given is remarkable and Luminosity ratio (l / (l1 +l2 + l3 +l4 )) o variable with different epochs. Two major reasons for i' = 30 0.04 (1) 0.38 (9) L⊙ o i' = 60 0.006 (2) 0.045 (6) L⊙ this finding might be stressed: 1) The number of the light o i' = 90 0.003 (1) 0.023 (3) L⊙ curves is only four, which is too few to test the Applegate

Table 5. Applegate model parameters for the shorter and longer periods. Parameter Shorter period (11.y8) Longer period (41.y3) Unit

Primary star Secondary star Primary star Secondary star ΔP 0.2873 0.2873 0.2677 0.2677 s ΔP/P 7.97 × 10-6 7.97 × 10-6 7.42 × 10-6 7.42 × 10-6 - ΔJ 3.84 × 1047 1.90 × 1047 3.58 × 1047 1.77 × 1047 (gcm2s-1) 54 53 54 53 2 Is 1.42 × 10 1.68 × 10 1.42 × 10 1.68 × 10 (gcm ) ΔΩ 2.71 × 10-7 1.14 × 10-6 2.53 × 10-7 1.06 × 10-6 s ΔΩ/Ω 1.56 × 10-3 6.52 × 10-3 1.45 × 10-3 6.08 × 10-3 - ΔE 2.09 × 1041 4.33 × 1041 1.81 × 1041 3.76 × 1041 erg s 33 33 32 32 ΔLrms 1.77 × 10 3.66 × 10 4.37 × 10 9.06 × 10 erg s 0.46 0.96 0.11 0.24 L⊙

0.18 1.13 0.04 0.28 Lp, s ±0.15 ±0.36 ±0.04 ±0.04 mag 4 4 3 4 B 1.65 × 10 2.49 × 10 8.48 × 10 1.28 × 10 gauss

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model in detail, and 2) strong light variations produced a 33:10 relation between their amplitudes. As the possible by the localized spot activity (activities) may reside con- causes for the cyclical period changes, two rival interpre- currently with the rms luminosity variations, or may tations (LTE and Applegate model) were considered, and overwhelm the rms luminosity itself. This negative con- the parameters related with these were derived in Tables clusion somewhat strengthens the interpretation of the 4 and 5, respectively. In the LTE interpretation, the ob- mechanical perturbation from the third- and fourth stars tained minimum masses of 0.30 M⊙ and 0.49 M⊙ for the that was developed above. third and fourth bodies, respectively, would contribute very small fractions of about 0.1% and 2% lights, respec-

tively, to the total luminosity (lt = l1 + l2 + l3 + l4), if they are 6. DISCUSSION AND CONCLUSION assumed to be main-sequence stars. This explains why previous investigators (Djurašević et al. 1998, Lee et al.

We analyzed a total of 185 timings of WZ Cep, includ- 2008, Zhu & Qian 2009) could not detect the third light (l3) ing our new three timings, to understand the dynamical in their light curve syntheses. In the LTEs explanation, the picture of this very active W UMa binary system in detail. 7:2 relation found between their mean motions would be It was found that the orbital period of the system has var- interpreted as a stable 7:2 orbit resonance produced by a ied in two cyclical components superposed on a global long-term gravitational interaction between two tertiary downward parabola over about 80y. Three decoupled bodies (Peale 1976, Kley et al. 2004) components of the period variability were intensively In the interpretation with the Applegate model, the investigated. For further investigations of these com- model parameters in Table 5 indicate that the Applegate ponents, the absolute dimensions of WZ Cep were esti- mechanism could work only in the primary component mated with the photometric solutions of Djurašević et for both two cyclic changes of period, and cannot in the al. (1998) and with Harmanec's (1988) empirical relation secondary. This means that the primary may be the mag- between mass and temperature. netically active star, which is consistent with the studies The secular period decrease of -9.d97 (±0.14) × 10-8 y-1 of Mullan (1975) and previous investigators (Djurašević was calculated and interpreted as a combination of both et al. 1998, Lee et al. 2008, Zhu & Qian 2009). However, AML due to magnetic braking and mass-transfer from we couldn't find any meaningful relation between the the massive primary component to the secondary. The light variation and the period variability from the his- decreasing rate of period due to AML was obtained as torical light curve data observed at four different epochs, -6.d72 × 10-8 y-1, which contributes about 67% to the ob- although the light asymmetry at a given epoch is remark- served period decrease. The remaining 33% contribution able and variable with different epochs. We wait for fu- -8 -1 results from the mass flow of about 5.16× 10 M⊙ y from ture observations to resolve these unsolved and veiled the massive primary component to the secondary. In this matters. At the present, we somewhat prefer the inter- picture, the major driven contributor to the observed pe- pretation of mechanical perturbation from the third- and riod decrease is AML by magnetic braking, which is about fourth stars. two times larger than mass-transfer. At the moment, WZ Cep may be considered as on an evolutionary track from the present shallow contact state of about 15% to a more ACKNOWLEDGMENTS deep contact state during a thermal time scale, which is expected by the magnetic braking theories (van't Veer This research has made use of the Simbad database 1979, Rucinski 1982, Maceroni & van't Veer 1991, Brad- maintained at CDS, Strasbourg, France. This work was street & Guinan 1994, Stȩpień 1995, 2006, Demircan 1999) supported by a research grant from Chungbuk National and the thermal relaxation oscillation theories (Flannery University in 2009. 1976, Lucy 1976, Robertson & Eggleton 1977). In addition to the secular period decrease, WZ Cep has suffered from two cyclical period changes consisting of a REFERENCES sine curve with a shorter period of 11.y8 and a semi-am- plitude of 0.d0054, and an LTE orbit with a longer period Applegate JH, A mechanism for orbital period modulation of 41.y3, a semi-amplitude of 0.d0178, and an eccentricity in close binaries, ApJ, 385, 621-629 (1992). http://dx.doi. of 0.54. Very interestingly, there seem to exist in a com- org/10.1086/170967 mensurable 7:2 relation between their mean motion and Balázs J, WZ Cephei, Beob Zirk d A N, 19, 7 (1937).

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