CK Bootis: a W UMa system with a small mass ratio

Astron. Nachr. / AN 326, No. 5, 342–348 (2005) / DOI 10.1002/asna.200510361

CK Bootis: a W UMa system with a small mass ratio R. K ALCI and E. D ERMAN Department of Astronomy and Space Sciences, Faculty of Science, Ankara University, 06100 Tando˘gan, Ankara, Turkey

Received 28 February 2005; accepted 12 April 2005; published online 20 May 2005

Abstract. We present an analysis of BV R light curves of an eclipsing binary CK Bootis, a system with a very small mass ratio. The light curves appear to exhibit a typical O’Connell effect. The light curves are analyzed by means of the latest version of the WD program. The asymmetry of the light curves is explained by a cool star spot model. The simultaneous BV R synthetic light curve analysis gives a tiny mass ratio of 0.12, an extremely large fill-out factor of 0.65, and a very small difference between the component temperatures of 90 K. The absolute parameters of the system were also derived by combining the photometric solutions with the radial velocity data. The mass of the secondary is very low (0.15 M
) and it continues losing mass. Thirty seven new times of minimum are reported. It is found that the orbital period of the system has a quasi periodic variation, superimposed on a period increase. The long-term period increase rate is deduced to be dP/dt = 3.54x10−7 d yr−1 , which can be interpreted as being due to mass transfer from the less massive star to the more massive component. Key words: binaries: eclipsing – stars: individual (CK Boo) – stars: spots c
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1. Introduction The variability and W UMa-type nature of CK Boo (HD 128141) was discovered by Bond (1975) who gave the first light elements and estimated the spectral type as G. Aslan (1978), Aslan et al. (1981) and Aslan and Derman (1986) made extensive photoelectric observations of CK Boo. They conclude that a) Bond’s initial epoch corresponds to the secondary eclipse, b) there are night-to-night and seasonal variations in the light curve, c) the observed depths of the primary and secondary minima interchange, d) there is a small but definite change of color of the system from season to season, e) CK Boo also shows brightness variations consistent with a starspot cycle of approximately 7 years. After these compilations, three more complete light curves of CK Boo were observed by Pajdosz and Zola (1989), Jia et al. (1992) and Markworth (1993). Krzesinki et al. (1991) solved the light curve by Pajdosz and Zola (1989) with the assumption of dark spots and the binary being of W-type and found the photometric mass ratio to be 1.70. They estimated the spectral type of the system to be F6V. Markworth (1993) observed the CK Boo in May 1985 and combined the seasonal light curves of Aslan and Derman (1986) in order to study the evolution of spotting activity in the system. He tried both A- and W-type solution with a photometric mass ratio of 0.10 and 1.66. He Correspondence to: [email protected]

conclude that there are two types of solutions which are statistically indistinguishable. The first spectroscopic observations of CK Boo were made by Hrivnak (1993). His preliminary spectroscopic determination of the mass ratio, q = 0.16, was close to the A-type solution of Markworth (1993), but entirely different from the solution of Krzesinski et al. (1991). Rucinski and Lu (1999) also observed the system spectroscopically and their mass ratio, q = 0.111 ± 0.052, was even smaller than that of Hrivnak (1993). They concluded that the error of the spectroscopic determination is large for small values of q. Within the quoted errors, the mass ratio is similar to that given by Hrivnak (1993). They found that the spectral type of the system is F7/F8V and the systemic velocity γ = 37.04 ± 0.75 km s−1 .

2. New observations CK Boo has, since 1976, always been in the observing program of the Ankara University Observatory and we also observed the system in Ege University Observatory and ¨ ˙ITAK National Observatory (Turkey). In this paper we TUB will report only on last season’s observations (two nights on April 19th and 25th, 2004). The system was observed photoelectrically on the 40 cm Cassegrain telescope of the National Observatory, using a single-channel Optec SSP-5A photometer and standard BV R filters. The comparison star was HD c
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1.0 1.1 B

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Fig. 2. The fit parameter Σ as a function of the mass ratio q using two methods explained in the text. Fig. 1. Observed light and colour curves of CK Boo.

128186, and HD 128495 was used as an occasional check. All differential observations were reduced outside the atmosphere using the extinction coefficients calculated in the usual way, and heliocentric corrections were made for all the observations. The data were not reduced to the standard BV R system. The average standard error of one differential measure is ±0.m 012 in B, ±0.m 016 in V and is ±0.m 014 in R determined from observations of comparison and check stars. The differential B, V , and R light, and B − V and V − R colour curves are shown in Fig. 1. The photometric phases of the light and colour curves are calculated with the following ephemeris: Min I = HJD 2453121.5453 + 0.3551619 × E

(1)

The light curves show two evenly spaced minima of nearly equal depths, with the primary minimum being slightly deeper. The rounded maxima are of different heights, and there are some indications of variations between the two nights. Changes in the light curve have been noted previously by Aslan and Derman (1986).

3. Light curve solution We have determined light curve solutions of our data using the 2004 June updated version of 2003 (since the system has an extreme mass ratio) of the Wilson-Devinney code (Wilson and Devinney 1971; Wilson 1979). This version of WD has the capability of modeling the radiation of the stars using Kurucz (1993) atmospheres, and we used this feature in our solutions. All the observations were used to derive a model of the light curve of CK Boo. As the results of previous light curve analyses are available, we used Mode 3, which assumes that both of the components fill their Roche lobes. The following assumptions were made in the analysis: a mean surface temperature T1 = 6200 K according to the spectral type F8V given by Rucinski & Lu (1999); bolometric albedos A1 = A2 = 0.5 and gravity darkening coefficients g1 = g2 = 0.32 were assigned, which are values typical for

stars with convective envelopes; limb darkening coefficients x1 = x2 = 0.685 in B and x1 = x2 = 0.552 in V and x1 = x2 = 0.452 in R and bolometric linear limb darkening coefficients x1 = x2 = 0.487 were taken from van Hamme (1993). The adjustable parameters are the orbital inclination i; the mean temperature of Star 2 T2 ; the dimensionless potential of the components Ω1 (= Ω2 ); the monochromatic luminosity of Star 1 L1 , and the mass-ratio q = m2 /m1 . To avoid correlations between parameters, iterations were carried out using multiple subsets (Wilson and Biermann 1976). The variable parameters were divided into three subsets as follows: {i, T2 }, {L1 , q}, and {Ω1 }. B, V and R light curves were analysed simultaneously. The spectroscopic mass ratio of the system was determined by Hrivnak (1993) and Rucinski & Lu (1999). We were curious, however, about wrong setting of the photometric mass ratio by Krzesinski et al. (1991). A search for the solution was made with several fixed values for the massratio q in the range 0.1 − 0.9. Iterations were carried out until the suggested corrections were less than the estimated error for each parameter. The sum of the weighted squares of the residuals (Σ) is minimum in the case of q = 0.5 (Fig. 2a). It is possible to improve significantly the best fit by considering the effect of a starspot. We then put one cool spot on the massive component and the lowest value of Σ occurs around q = 0.15 (Fig. 2b). In order to find the final solution, we continued the analysis by applying the DC program for the value of q = 0.15 as a free parameter. The photometric mass ratio is found as q = 0.118, which is almost equal to the spectroscopic mass ratio (0.111) given by Rucinski & Lu (1999). We started the solution without spots by assuming that there are no spots on the components of the system. A preliminary set of input parameters for the DC program was obtained by the Binary Maker 2.0 program (Bradstreet 1993). For the radial velocity analysis we used all 28 data points given by Rucinski & Lu (1999). The results of the unspotted solution for the system is given in Table 1. The subscripts 1 and 2 refer to the components eclipsed at primary and secondary minimum, respectively. Since the secondary c
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1.00 0.95 B 0.90 0.85 0.80

1.00 0.95 0.90 V

ponent of the system has a cool spot of the same nature as solar spots. To obtain the initial spot parameters the Binary Maker program was used. The solution trials began by keeping the parameters of the spot (latitude, longitude, angular radius, temperature factor), and the subsets respectively as free adjustable parameters. Then each spot parameter is adjusted separately while keeping all the others fixed. Table I also includes the adopted spot solutions and the corresponding theoretical light curves shown as a solid line in Fig. 3.

0.85 1.00

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Fig. 3. The light curve solution of CK Boo with and without spotted. Table 1. The photometric solution of CK Boo Parametes i(◦ ) q(m2 /m1 ) T1 (K) T2 (K) Ω1 = Ω2 X1B = X2B X1V = X2V X1R = X2R A1 = A2 g1 = g2 (L1/(L1 + L2))B (L1/(L1 + L2))V (L1/(L1 + L2))R r1 (pole) r1 (side) r1 (back) r2 (pole) r2 (side) r2 (back) filling factor Σ Spot parameter latitude longitude radius temperature factor

Solution without spots 64.8 ±0.02 0.1087±0.0008 6200 6191±14 1.953 ±0.003 0.685 0.552 0.452 0.5 0.32 0.87±0.02 0.87±0.02 0.87±0.02 0.5385 ±0.0002 0.6031 ±0.0004 0.6242 ±0.0006 0.2060 ±0.0026 0.2157 ±0.0031 0.2622 ±0.0085 % 46 0.1402

Solution with spots 64.9 ±0.02 0.1088±0.0006 6200 6291±12 1.940 ±0.003 0.685 0.552 0.452 0.5 0.32 0.86 ±0.02 0.86 ±0.02 0.86 ±0.02 0.5422 ±0.0002 0.6093 ±0.0003 0.6316 ±0.0005 0.2217 ±0.0005 0.2786 ±0.0026 0.2353 ±0.0087 % 65 0.1147

(Tspot /Tphot )

75.0 ±4.9 83.1 ±5.9 20.2 ±0.7 0.939 ±0.004

minimum appears to be an occultation, the subscripts 1 and 2 refer respectively to the larger (more massive and hotter) and smaller (less massive and cooler) component. The errors in Table 1 are formal errors yielded by the Wilson-Devinney Code. In Fig. 3, the corresponding theoretical light curves are shown as dotted line. The computed light curve with this DC solution does not fit the observed light curve very well, especially near the secondary maximum (O’Connell effect). In order to take into consideration the decrease of brightness around Max II, a solution with spots was carried out by assuming the simplest spot model, i.e. that the larger comc
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The simultaneous solutions of the photometric and radial velocity curves yield absolute parameters of CK Boo, which are given in Table 2. Errors are given after each value. We used the absolute elements to estimate the evolutionary status of CK Boo by means of the mass-radius and mass-luminosity diagrams given by M¨uyessero˘glu (2004), Figs. 4 and 5. In these diagrams, the primary component of CK Boo lies on the zero-age main sequence, in a region where A- and Wtype primaries are found. The secondary is over-luminous for its mass in the mass-luminosity diagram, which is expected for A-type overcontact systems. Table 2. Absolute parameters of CK Boo Parameters M1 (M
) M2 (M
) R1 (R
) R2 (R
) L1 (L
) L2 (L
) Mbol1 (m ) Mbol2 (m )

Solution without spots 1.415 ±0.014 0.154 ±0.002 1.439 ±0.003 0.555 ±0.012 2.74 ±0.01 0.41 ±0.02 3.65 ±0.01 5.73 ±0.05

Solution with spots 1.415 ±0.014 0.154 ±0.002 1.453 ±0.003 0.577
±0.010 2.80 ±0.01 0.47 ±0.02 3.63 ±0.01 5.58 ±0.04

CK Boo is an A-type W Uma system considering the filling factor, period, and the mass ratio. It is well known that in general the primary star is hotter than the secondary in Atype systems. However, according to our analysis, the average surface temperature of the smaller component is found to be slightly hotter than the primary. This result may be explained by the fact that the minimum depths of CK Boo are interchanged and the system sometimes displays W-type characteristics as shown by Aslan (1981). Another explanation is that if one puts a cool spot on the primary star surface, then the temperature of the secondary increases in the WD analysis because the temperature of the primary is kept constant during the procedure.

5. Period variation The period changes of CK Boo have been studied by Qian and Liu (2000). They were not able to use the minimum time given by Bond (1975) because it was not the primary minimum time as explained by Aslan and Derman (1986). In our analysis, we used our data together with the ones kindly

R. Kalci and E. Derman: CK Bootis: a W UMa system with a small mass ratio

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(O-C) 2

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0.4 O

)

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Fig. 4. The mass-radius diagram for primary and secondary components of W UMa type binaries (M¨uyessero˘glu 2004) and the locii of CK Boo components. Main sequence and subgiants lines are from Straizys and Kuriliene (1981)

1971 0.12

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A-Type Primary W-Type Primary A-Type Secondary W-Type Secondary CK Boo Primary CK Boo Secondary Straizys and Kuriliene

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Fig. 6. (O − C)1 diagram of the period change for CK Boo. Residuals from a quadratic fit are also shown at the bottom of figure.

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) o

Fig. 5. The mass-luminosity diagram for primary and secondary components of W UMa type binaries (M¨uyessero˘glu 2004) and the locii of CK Boo components.

provided by Bond and Markworth. We determined minimum times by using the method of Kwee & Van Woerden (1956). The times of minima are tabulated in Table 3. The O − C values were calculated from the formula (Aslan 1978): Min I = HJD 2442897.3759 + 0.3551501 × E

(2)

These (O − C)1 values are listed in the third column of Table 3 and are presented graphically against epoch number in Figure 6. As displayed in this figure, the general trend of the (O − C)1 curve indicates clearly that the orbital period of CK Boo is increasing. Both primary and secondary times of minima follow the same trend in the (O − C) diagram. The least squares quadratic best fit to the (O − C)1 residuals (Fig. 6, solid line) reveals the following ephemeris with mean error for each term:

0

5000

10000

E

15000

20000

25000

30000

Fig. 7. Sixth-order polynomial fits the observed O-C values.

Min I = HJD 2442897.37734(170) + 0.3551491(3) × E (3) +1.72(8) × 10−10 × E 2 where the coefficient of the quadratic term represents the rate of change of the period. This ephemeris can be used for the estimation of future times of minima. A continuous period increase rate dP/dt = 3.54(±0.17) · 10−7 days/year is computed which is equivalent to a period increase of 3 s/century (compare this with Quian & Liu’s (2000) estimated value of 4.97x10−7 days/year using more limited data). The (O − C)2 residuals from the quadratic ephemeris are also displayed in Fig. 6. Recently, Kalimeris et al. (1994) have proposed a new method which enables the calculation of the orbital period and its rate of change as a continuous function of time. Following this method, the O − C data is described by a higher c
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Astron. Nachr. / AN 326, No. 5 (2005) / www.an-journal.org Table 3. Times of minima CK Boo

Fig. 8. The period of CK Boo as a function of time (solid line) and its rate of change, dP/dE (dashed line)

order least squares polynomial. Its derivative then gives information about the period changes. This method can give very good results for smooth continuous variations of period as is the case of CK Boo. We find that a single sixth-order polynomial fits the observed times of minimum light well (Fig. 7, solid curve). The residuals are shown in the same figure. Then using the equations given by Kalimeris et al. (1994), we calculated the real period P (E) and its rate of change dP/dE. The results are shown in Fig. 8, where we have plotted the difference between the real period P (E) and the ephemeris period P in unit of 10−5 days (solid line), and the relative rate of period change dP/dE in unit of 10−8 days/cycle (dashed line). It is clearly shown that the P (E) function may be composed of a small amplitude of oscillation superimposed on a long time increase term (shown by long dashed line in Fig.8) which is already found by the quadratic fit to the O − C variation. P *(E) is the difference between the original P (E) function and the linear increase term and it is also shown in Fig. 8 with the dotted line. If we consider the P *(E) function, it is clear that the orbital period could be modulated by some periodic mechanisms. There are four extreme points of P *(E) and the amplitudes of the variation at four turning points are respectively 0.33, 0.37, 0.65, and 0.86 seconds, indicating that the amplitude might be increasing with time. The time between two maxima and two minima are 15 and 16.4 years, respectively.

6. Discussion and conclusion In this paper, new photoelectric observations of CK Boo are reported. We have analysed the resulting light curves and the (O − C) diagram. The results from this analysis are as follows: 1. New light curves confirm that CK Boo is a partially eclipsing system which clearly shows asymmetry, the socalled O’Connell effect. Short term variations, added onto the observational scatter are apparent in the light curves. This c
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HJD 42537.6137 42537.4330 42897.3759 42898.4418 43225.5334 43229.4409 43230.5069 43341.3122 43573.5846 43667.3400 43670.3610 44753.3929 44756.4161 44790.3294 45054.5625 45057.5829 45132.3408 45140.3339 46183.4105 46207.7412 46209.6936 46210.7590 46212.7135 46229.4037 46231.3576 46232.4221 46233.4899 47241.5828 47288.4607 47290.4150 47291.4796 47292.3699 47298.4072 47356.2934 47359.3074 47587.4998 47596.5545 47643.4320 47659.4177 47973.5521 47982.4295 48356.4091 48362.0909

type I II I I I I I I I I II I II I I II I II II I II II I I II II II I I II II I I I II I II II II I I I I

O-C 0.00486 0.00173 0.00000 0.00045 -0.00119 -0.00034 0.00021 -0.00132 0.00291 -0.00132 0.00091 0.00258 0.00700 0.00347 0.00489 0.00652 0.00532 0.00754 0.00830 0.01118 0.01029 0.01028 0.01143 0.00952 0.01012 0.00916 0.01149 0.01084 0.00894 0.00989 0.00909 0.01151 0.01126 0.00803 0.00319 0.01166 0.01006 0.00774 0.01168 0.01578 0.01447 0.02101 0.02044

Ref. 14* 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 14* 14* 14* 14* 14 14 14 14 14 14 5 5 5 5 14 14 14 14 14 6 14 6 7 8

kind of variations is common among W-type W Uma binaries. 2. Using the absolute parameters and the bolometric correction, we find that the absolute magnitude of the system is 3.m 45. Adopting the V magnitude of a comparison star given by Rucinski and Duerbeck (1997), the maximum magnitude of the system is 8.m 92 in 2004. We find the distance of CK Boo from these values is 124 pc. This is marginally consistent with the Hipparcos result, which is 157 ±27 pc. 3. The analysis of the light curves reported here enabled us to give the first estimate of the parameters for CK Boo. The system is in contact configuration (f = 0.65) with a small temperature difference between components (dT = 90 K). This small temperature difference is very reliable because both minima have almost the same depth.

R. Kalci and E. Derman: CK Bootis: a W UMa system with a small mass ratio Table 3. (Continued) Times of minima CK Boo HJD 48385.1806 48386.0676 48386.2434 48387.1321 48388.1987 48409.3297 48714.5899 48716.5411 48735.3676 48735.5397 49069.5728 49071.5256 49135.4550 49500.3766 49502.3353 50248.3374 50260.4143 50597.4577 50598.3460 50926.5076 51657.4190 51772.3100 52032.4564 52053.4129 52074.3677 52347.4848 52399.5141 52399.6869 52403.4216 52410.3488 52462.3796 52725.5475 52739.3947 52760.5281 52760.3535 53121.3669 53121.5453

type I II I II II I II I I II I II II I II I I I II II II I II II II II I II I II I I I II I II I

O-C 0.02532 0.02445 0.02270 0.02350 0.02463 0.02428 0.03297 0.03077 0.03434 0.02888 0.04332 0.04275 0.04521 0.05004 0.05542 0.06473 0.06653 0.07248 0.07293 0.07581 0.08831 0.08825 0.08724 0.08987 0.09083 0.09750 0.09727 0.09250 0.09812 0.09991 0.10121 0.10285 0.09919 0.10118 0.10414 0.10749 0.10837

Ref. 8 8 8 8 8 14 14 14 14 14 14 14 14 9 9 9 9 10 14 10 11 11 14 14 14 14 12 12 14 14 13 14 14 14 14 14 14

1 Bond (1975); 2 Aslan (1978); 3 Aslan & Derman (1986); 4 Demircan (1987); 5 Pajdoz & Zola (1988); 6 Oglaza (1995); 7 Diethelm (1991); 8 Jia et al. (1992); 9 M¨uyessero˘glu et al. (1996); 10 Agerer & H¨ubscher (1999); 11 Zejda (2002); 12 Karska & Maciejewski (2003); 13 Bakis¸ et al. (2003); 14 this paper; 14* we found minimum times from the observing data provided by Bond and Markworth.

347

the broken-contact phase and may be in the expanding TRO stage. 5. As can be seen in Fig. 8, the orbital period of CK Boo exhibits a wavelike variation with a periodicity of approximately 15.75 years and an increasing amplitude. A periodic oscillation superimposed on a secular term is usually encountered for W UMa type binary stars. These periodic variations are usually explained either by: a) the light-time effect via the presence of a third body. We exclude the light-time effect because the (O−C)2 is not strictly periodic and there is no indication in the spectrum of CK Boo reported by any researcher. b) magnetic activity cycles in both components, because they are fast-rotating solar-type stars and observations show enhanced chromospheric and coronal activity in W UMa-type systems (Rucinski 1985; Cruddace & Dupree 1984; Stepie`n et al. 2001). Applegate (1992) and Lanza, Rodon`o & Rosner (1998) subsequently proposed that the orbital period changes in close binaries are a consequence of magnetic activity in one or both of the component stars. Lanza and Rodon`o (2004) also proposed that the ratio of orbital period cycle to starspot cycle is 2:1. In order to prove this situation, we need the starspot cycle, which is not yet available and we are still working on it. Concerning the magnetic activity effect on the light variation of eclipsing binaries, it should be noted that not only the light levels but also the minima times should be affected. If the light distribution in the hemispheres of the component stars is not homogeneous, or at least asymmetric, then the time of minima will not coincide with the time of conjunctions. As a result, some small erratic fluctuations of the period can be measured. This situation is calculated in detail by Kalimeris, Rovithis-Livaniou & Rovithis (2002) and Watson & Dhillon (2004) Acknowledgements. The authors would like to thank to the ¨ ˙ITAK National Observatory (TUG) for their kind support TUB (Project No: TUG-T40.04.009). We are grateful to A. AkalınPeletier for her generous support during this research. We thank Prof. Z.Aslan for helpful comments on the initial draft of this paper. Thanks are also due to Dr. R.Peletier for reading the manuscript. Special thanks are due to Dr. A.F.Lanza who acting as the referee, for several helpfull advice. This research has made use of the Simbad database, operated at CDS, Strasbourg, France, and of NASAs Astrophysics Data System Bibliographic Services.

References 4. The (O − C) analysis suggests that there is a long-term period increase. If the secular period increase is caused by a conservative mass transfer from the secondary to the primary component, then using the well-known equation, the mass transfer rate is estimated to be: dM/dt = 5.73 × 10−8 M /year. The secondary component has a mass of 0.15 M and if it continues to loose mass at the same rate, then it will vanish in 26000 years! The thermal-relaxation oscillation theory (TRO) of contact binaries (Lucy 1976; Flannery 1976), however, proposes such a kind of mass transfer if the system is oscillating around the marginal contact state, being temporarily in contact and non-contact phases. In this picture, the systems with increasing period are in a state before

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