Photometric analysis of the contact binary star V829 Hercules using light curves on three consecutive years

New Astronomy 12 (2006) 192–200 www.elsevier.com/locate/newast

Photometric analysis of the contact binary star V829 Hercules using light curves on three consecutive years ¨ zkardesß A. Erdem *, B. O C¸anakkale Onsekiz Mart University Observatory, Terziog˘lu Kampu¨su¨, 17040 C¸anakkale, Turkey Received 6 July 2006; received in revised form 18 August 2006; accepted 15 September 2006 Available online 4 October 2006 Communicated by W. Soon

Abstract New BVR light curves and photometric analysis of the contact binary star V829 Her are presented. The light curves were obtained at the C ¸ OMU Observatory in the consecutive years 2003, 2004 and 2005. Firstly, the variation of the orbital period of the system was studied. The sinusoidal and secular changes were found and examined in terms of two plausible mechanisms, namely (i) the conservative mass transfer between the components of the system and (ii) the light-time effect due to an unseen component in the system. The instrumental magnitudes of all observed stars in this study were converted into standard magnitudes. We also study nature of asymmetries and the intrinsic variability in the light curves of the system. Light variations are summarized: (a) changes of light levels of both maxima and (b) changes of the depths of both primary and secondary eclipses. These peculiar asymmetries were interpreted in terms of dark spot(s) on the surface of the large and more massive component star. The present BVR light curves and radial velocity curves obtained by Lu, W., Rucinski, S. M., 1999. AJ 118, 515 were analysed by means of the latest version of the Wilson–Devinney program, simultaneously. Thus, the absolute parameters of the system were also derived.  2006 Elsevier B.V. All rights reserved. PACS: 97.10.Nf; 97.10.Pg; 97.80.Fk; 97.80.Hn Keywords: Stars: binaries: close; Stars: binaries: eclipsing; Stars: individual: V829 Hercules

1. Introduction Contact binaries are generally taken to be stars that have both components surrounded by common convective envelope lying between the inner and outer Lagrangian zero-velocity equipotential surfaces (Mochnacki, 1981). Many observers have found it attractive to observe the contact binary stars, since they have the high space density (Rucinski, 1998) and it is relatively easy to obtain light and radial velocity curves of them in a short time due to short orbital periods. Absolute parameters for the contact binaries were provided by many researchers (Maceroni and van’t Veer, 1996). Also, much attention has been given to *

Corresponding author. Tel.: +90 286 2180019; fax: +90 286 2180533. E-mail address: [email protected] (A. Erdem).

1384-1076/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2006.09.002

the formation, structure and evolution of them. However, many of the theoretical problems on this field are still open. So, the new observations and their interpretations of contact binaries are very important test sources to help understand their formation, structure and evolution. We have chosen the recently discovered W UMa type binary star V829 Her (GSC 02597-00679 = TYC 2597679-1). This star was discovered serendipitously as an X-ray source during the Einstein Observatory Extended Medium Sensitivity Survey (Gioia et al., 1987). It was suspected of being a W UMa system by Fleming et al. (1989). They also, using the low-resolution spectra, estimated the spectral type of the system as G2V. Soon thereafter, Robb (1989) observed V829 Her in the Johnson VRI system photometrically and confirmed the W UMa type for the system. He found a period of 0.35813 days,

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

which was relatively approximate because of the short time span. He noted the system has a variable light curve with a large ‘O’Connell effect’. Later, Agerer and Hu¨bscher (1995, 1999, 2000), Dvorak (2005, 2006), Hu¨bscher et al. (2005) and Pribulla et al. (2005) obtained some times of minimum light. Lu and Rucinski (1999) observed this system spectroscopically and determined its spectroscopic orbit. They inferred that V829 Her is a W-subtype W UMa system. Moreover, they estimated the absolute parameters of the system, by combining their spectroscopic observations with light curves observed by Robb ¨ z(their private communication) in 1992. Erdem and O kardesß (2004) observed this star photoelectrically, obtained its full BVR light curves and made first analysis of the orbital period change of the system. They suggested the orbital period changes with a sinusoidal form, having very small amplitude. Zola et al. (2004) obtained complete BVRI light curves and said that there was an O’Connell effect in their light curves. They also presented the W-subtype model with one dark spot on the primary component to interpret this effect.

193

2.2. Seasonal light variations The star V829 Her was observed by Zola et al. (2004) in 2002 and by us in 2003, 2004 and 2005, photometrically. So, the comparison of light curves obtained in the consecutive 4 years could be done. For this, light levels of maxima and minima were determined, and then differences between maxima and minima were calculated. These values are presented in Table 3 and plotted in Fig. 1. However, only depths of minima and light level differences of maxima and minima were calculated from Zola et al.’s light curves, since Zola et al.’s photometric data were in differential instrumental magnitudes and ours were in standard magnitudes. Light variations of this system are summarized following items: (a) All light curves show clear evidence of O’Connell effect as lower light level at phase 0.75. However, this asymmetry of light levels between maxima is changing with time even day-to-day. For instance, the Max II (at phase 0.75) light levels observed in June 12 and September 10 of 2004 have larger asymmetries than those of other nights in the same year, while the light levels observing in three nights (July 12, 19 and August 17) in

2. Observations 2.1. Observational data

Table 1 The journal of photometric observations of the star V829 Her

The contact system V829 Her was observed at the C ¸ anakkale Onsekiz Mart University Observatory in the consecutive years 2003, 2004 and 2005. The journal of observations is shown in Table 1. The 40-cm Schmidt– Cassegrain reflector, equipped with a SSP5-A photometer and Hamamatsu R 6358 photomultiplier tube, was used in 2003 and 2004 observations, while the 30-cm Schmidt–Cassegrain reflector, equipped with the SBIG ST-10XME camera, was used in 2005 observations. All photoelectric (pe) and CCD observations were made with the BVR and BVRc filters, respectively. GSC 2601 117 and GSC 5082 1171 were used as comparison and check/standard stars for both pe and CCD observations, respectively. The data related to these stars are given in Table 2. All observations were corrected for atmospheric extinction and converted into standard magnitudes by using the extinction and transformation method of Hardie (1962). The standard V magnitude and colour indices B  V and V  R of the observed stars are given in Table 2. The BVR and BVRc light, and B  V, V  R, and V  Rc colour curves of the star V829 Her in the standard system are shown in Fig. 3.

Date

Method

Filters

dd/mm/yyyy 17/05/2003 06/06/2003 12/06/2003 27/06/2003 30/06/2003 24/07/2003 25/07/2003 02/09/2003 12/06/2004 09/07/2004 12/07/2004 19/07/2004 17/08/2004 19/08/2004 23/08/2004 26/08/2004 08/09/2004 10/09/2004 11/06/2005 27/06/2005 05/07/2005 15/07/2005 23/07/2005

pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe pe CCD CCD CCD CCD CCD

BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVR BVRc BVRc BVRc BVRc BVRc

Phase Start

Stop

0.869 0.784 0.555 0.549 0.894 0.851 0.424 0.317 0.681 0.988 0.155 0.675 0.627 0.107 0.322 0.785 0.891 0.594 0.707 0.402 0.740 0.786 0.420

0.448 0.291 0.050 0.965 0.164 0.302 0.318 0.710 0.909 0.301 0.769 0.260 0.866 0.330 0.680 0.055 0.275 0.842 0.282 0.975 0.325 0.232 0.958

Table 2 The fundamental information for V829 Her, the comparison and check starsa Star

GSC No.

a2000

d2000

V

BV

VR

V829 Her Comparison Check

2597 679 2601 117 5082 1171

16h55m48s 16h55m10s 17h45m43s

+3510 0 5800 +3539 0 2100 0021 0 3600

10.384(7) 10.045(6) 10.358

0.594(8) 0.471(7) 0.608

0.452(8) 0.553(7) 0.377

a

The probable errors in the last digits are given in parenthesis.

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

194

Table 3 Seasonal relative light levels and their differences in magnitudes for the star V829 Hera

Maximum light at 0.75

Maximum light at 0.25

Minimum light at 0.50

Minimum light at 0.00

DMax (m0.75  m0.25)

DMin (m0.50  m0.00)

Depth of Min I (m0.00  m0.75)

Depth of Min II (m0.50  m0.75)

a

2001 0

B

V

2003 2004 s1 2004 s2 2005

10.848(7) 10.880(9) 10.915(8) 10.870(6)

10.264(6) 10.293(12) 10.317(11) 10.283(8)

9.821(7) 9.847(10) 9.863(7) 9.829(7)

0.04

2003 2004 2005

10.831(9) 10.855(4) 10.845(15)

10.255(13) 10.279(17) 10.261(10)

9.815(10) 9.825(8) 9.808(14)

-0.1

2003 2004 2005

11.114(15) 11.097(15) 11.125(10)

10.516(15) 10.500(7) 10.516(10)

10.065(7) 10.047(10) 10.062(10)

2003 2004 2005

11.092(10) 11.159(8) 11.091(10)

10.500(10) 10.549(7) 10.499(12)

10.047(8) 10.079(5) 10.041(8)

R

0.020 0.017 0.025 0.060 0.025

0.012 0.009 0.014 0.038 0.022

0.020 0.006 0.022 0.038 0.021

0.046 0.022 0.062 0.034

0.034 0.016 0.049 0.017

0.043 0.018 0.032 0.021

2002 2003 2004 s1 2004 s2 2005

0.274 0.244 0.279 0.244 0.221

0.254 0.236 0.256 0.232 0.216

0.240 0.226 0.232 0.216 0.212

2002 2003 2004 s1 2004 s2 2005

0.228 0.266 0.217 0.182 0.255

0.220 0.252 0.207 0.183 0.233

0.197 0.244 0.200 0.184 0.233

2002 2003 2004 2005

2003

2004

2005

2006

2003

2004

2005

2006

MaxII-MaxI (B)

0.02

Year

2002 2003 2004 s1 2004 s2 2005

2002

The probable errors in the last digits are given in parenthesis.

0.06 0.08 MinII-MinI (B)

-0.06 -0.02 0.02 0.06 0.00

MaxII-MaxI (V)

0.01 0.03 0.04 -0.06

MinII-MinI (V)

-0.03 0 0.03

0

MaxII-MaxI (R)

0.02 0.04 -0.06

MinII-MinI (R)

-0.03

2004 exhibit more less asymmetries. For this reason, we considered two different light levels at phase 0.75 in the light curves observed in 2004 and code-named these less and large light level asymmetries ‘s1’ and ‘s2’, respectively. Moreover, the light curves in 2004, even which have two different light levels of Max II, show more larger asymmetries than those of other years (see Table 3 and Fig. 3). (b) Using the standard observations, we noticed that the light levels of both maxima in the light curves in 2004 are lower than those in 2003 and 2005 (see Table 3 and Fig. 3). So, there could be displacements of the brightness maxima in the light curves. (c) There are large changes of the depths of both primary and secondary eclipses in the light curves. In 2003 and 2005 observations, the depths of secondary minima are abnormally more deeper than those of primaries. In 2004 observations, as a opposite to this abnormal situation, the depths of primary minima are normally more deeper than those of secondaries. The similar effect was recorded in TZ Boo (Hoffmann, 1978). Moreover, the light levels of primary minima in the light curves in 2004 are

0 0.03 0.06 2001

2002

Fig. 1. The light level variations of V829 Her. Zola et al.’s (2004) 2002 data and our data are represented by crosses and circles, respectively; while only open circles denote our 2004 s2 data.

more about 0.05 magnitude lower than those of light curves in 2003 and 2005 (see Fig. 3). (d) There are also complex colour changes with the orbital phase (see Fig. 3). 3. Orbital period analysis During the observations of V829 Her, 11 primary and 8 secondary times of minimum light were obtained. These times of minima and their errors, which were determined by using the method of Kwee and van Woerden (1956), are given in Table 4. In order to investigate the period

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O Table 4 Photometric minima times of V829 Her obtained in this worka

1989

JD Hel. 2400000+

Method

Filter

Min type

53199.4552(8) 53206.4371(7) 53237.4198(13) 53241.3619(12) 53257.2965(12) 53533.4298(15) 53549.3707(16) 53557.4271(8) 53567.4539(10) 53578.3831(11)

pe pe pe pe pe CCD CCD CCD CCD CCD

BVR BVR BVR BVR BVR BVRc BVRc BVRc BVRc BVRc

II I II II I I II I I II

a

d 0.02

195

1993

1997

2001

2005

a

(O-C) 0.015 0.01 0.005 Min I Min II

Epoch Number

0

0.016

The probable errors in the last digits are given in parenthesis.

b -8000

-4000

0

4000

8000

0.012

variation of the system, we have used all CCD and photo¨ zelectric minima from the list compiled by Erdem and O kardesß (2004). We added a few photoelectric and CCD minima observed recently by Dvorak (2005, 2006), Hu¨bscher et al. (2005) and Pribulla et al. (2005). On the other hand, two times of minima were calculated from the data of Zola et al. (2004) and added to this analysis. As a first step, the O  C residuals were calculated using the following light elements: d

HJDðMin IÞ ¼ 2450585:4810 þ 0 :35815069  E:

0.008 0.004 0 -0.004 -0.008 0.016

ð1Þ

0

The O  C residuals versus E values are shown in Fig. 2a. The O  C diagram formed by all available times of eclipse minima seems either a pure parabola or a quasi-sinusoidal form superimposed on a parabola. We have tested which model fits the observations better by looking the difference in the values of sum of squared residuals of the fits to the O  C data with only a parabolic and a parabolic + cyclic approximations. However, v2 would be much more informative. But, since the standard errors of all published minima times are not available, we could not apply this v2 testing method. The sum of squared residuals turns out to be 0.00035 day2 and 0.00031 day2 for pure parabolic and parabolic + cyclic fits, respectively. On the other hand, if we use the standard deviation of the fits taking into account the number of degrees of freedom, which are three for the parabolic fit and nine for the parabolic + cyclic fit, we find the standard deviations to be 0.00312 day and 0.00289 day for pure parabolic and parabolic + cyclic fits, respectively. From these values, it seems that the parabolic + cyclic fit is more realistic than the pure parabolic fit to the observational data. The most possible cause of the sinusoidal variation of the O  C diagram is an unseen third star in the system. So, we applied this following the equation of the light-time effect, which is given by Irwin (1959), with a quadratic ephemeris to fit to the O  C variation in Fig. 2a:

-0.008

O  C ¼ Q  E2

  a12 sin i0 1  e02 0 0 0 0 þ sinðm þ x Þ þ e cos x ; c 1 þ e0 cos m0 ð2Þ

c

0.008

Epoch Number

-0.016 -10000

-6000

-2000

2000

6000

10000

Fig. 2. (a) The O  C diagram for all available minima times of V829 Her, (b) the tilted (eccentric) sinusoidal representation (solid line) superimposed on the parabolic form (dashed line) of the O  C variation and (c) the residuals from the best fit curve (solid line in (b)).

where c is the speed of light, a12, i 0 , e 0 and x 0 are the semimajor axis, inclination, eccentricity and the longitude of the periastron of the absolute orbit of the center of mass of the eclipsing pair around that of the triple system, respectively, and m 0 is true anomaly of the position of the eclipsing pair’s mass center on this orbit. The epoch of periastron passage T 0 and the period P12 of the orbit of the three-body system are hidden parameters in Eq. (2). An least-squares solution for T0, P, Q, a12, e 0 , i 0 , x 0 , T 0 and P12 is presented in Table 5. The observational curve and theoretical best fit curve,

Table 5 Parameters derived from the O  C analysis of V829 Her Parameter

Value

Standard deviation

T0 (HJD) Porb (days) Q (days) a12 sin i 0 (AU) e0 x 0 () T 0 (HJD) P12 (year) f (m3) (mx)

2450585.4879 0.35815016 4.1 · 1011 0.986 0.30 102 53428 12.61 0.0060

0.0003 0.00000001 5 · 1012 0.032 0.01 9 92 0.01 0.0006

196

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

and also the residuals, is plotted against epoch number in Fig. 2b and c. The coefficient of the quadratic term is positive and indicates an increase of orbital period of 0.007 ± 0.001 s/yr. If we consider the conservative mass transfer, we estimate that the current mass transfer rate from the less massive component to the more massive one to be about 7.8 · 108mx/yr. According to Table 5, the P12 period would be 12.61 ± 0.01 yr. The projected distance of the center of mass of the eclipsing pair to that of the triple system would be 0.99 ± 0.03 AU. These values lead to a small mass function of f(m3) = 0.0060 ± 0.0006mx for the hypothetical third body. The mass of such a third body would then range from 0.68mx for i 0 = 30 to 0.31mx for i 0 = 90. Here the sum of masses was taken as m1 + m2 = 1.87mx. If the orbit of the third body were co-planar with the eclipsing pair, the radius r3 of its orbit around the center of mass of the triple system would be about 5 AU, i.e. far beyond the outer Lagrangian points of V829 Her, and thus stable. The semi-amplitude of the radial velocity of the center of mass of the eclipsing pair, relative to that of the triple system, turns out to be 2.33 km/s. The distance of V829 Her was found to be 200 pc in this study (see Section 5). Thus, the maximum projected angular separation between the third star and the eclipsing pair would be 30 mas, which is too small for observational detection. On the other hand, the presence of the third component was suspected from large proper motion error by Pribulla and Rucinski (2006). But, both Lu and Rucinski (1999)’ light curve solutions and ours give no any evidence about third light. 4. Photometric analysis To analyze BVR light curves from this work and radial velocity curves from literature, simultaneously, we used the latest (2003) version of the Wilson–Devinney method (Wilson and Devinney, 1971). Light curves, which were obtained from observations on three consecutive years, were all put in four different sets according to observation time and light levels. So, we analysed each of the light curve sets separately. The brightness level of maxima in the light curves changes in time, and thus they are different in the light curves in given colour. For the normalization of the light curves before the analysis, we first choose the 2003 and 2005 light curves with almost equal maxima at phase 0.25. We then read the mean maxima levels at phase 0.25 and used them (which are 10.833 in B, 10.251 in V and 9.809 in R colours) in converting the measurements to intensities in respective light curves. However, due to variable O’Connell effect, the maximum intensity of light curves in given colour is not always unity (especially in 2004 light curves). In this method, some parameters should be fixed, and therefore, they should be estimated from a convenient theoretical model for analyzing binary star. As mentioned above, Fleming et al. (1989), studying the low-resolution

spectra of the system, assessed the spectral type as G2V. But, according to the colour index of B  V = 0.508 ± 0.046 given by the Hipparcos and Tycho Catalogues ESA (1997), it seems that the spectral type of the system should be F7. Also, Zola (2006), analyzing the new spectra of the system, assessed the spectral type as F7. So, the temperature of the primary component was taken from Zombeck (1990) as 6300 K, corresponding to the F7V spectral class. The logarithmic limb darkening coefficients were chosen from van Hamme (1993); the bolometric gravity-darkening coefficients gh,c were set to 0.32 for convective envelopes, following Lucy (1967); also, the bolometric albedos Ah,c were fixed to 0.5 for convective envelopes, following Rucinski (1969). Synchronous rotation for primary and secondary components of the system (Fh = Fc = 1) and circular orbit (e = 0) were accepted before the analysis. These parameters were kept constant during all the iterations. The adjustable parameters in solving light and radial velocity curves of the system are ephemeris parameters (reference epoch T0 and orbital period P) together with the length of the semimajor axis of the relative orbit A, the radial velocity of the binary system center of mass Vc, the binary orbital inclination to the plane of the sky i, the flux-weighted average surface temperature of the secondary component (T2), the non-dimensional normalize surface potential of the primary component (X1), and the fractional monochromatic luminosity of the primary component (L1/(L1 + L2)). Throughout this paper, the subscripts 1 and 2 refer to the primary (hotter) and secondary (cooler) component, respectively. The first time derivative of the orbital period dP was fixed at the value dt obtained from the O  C analysis (see Section 3). On the other hand, we fixed value of the mass ratio of the system as 2.3, which was taken from the photoelectric and spectroscopic study of Zola et al. (2004). Simultaneous convergent solutions of BVR light and radial velocity curves were obtained with the free parameters by iterating, as usual, until the corrections on the parameters became smaller than the corresponding probable errors. During the iterations, we also checked whether there is third light contribution in the light curve of the system or not, but we did not find any meaningful contribution. Our final solutions are given in Table 6. The comparison between observed and computed light curves are shown in Fig. 3. As is seen, the agreement appears satisfactory.

5. Results and discussions Collecting observed minima times of the system, we considered the possibility of the orbital period variation: The O  C diagram could be a quasi-sinusoidal form superimposed on a parabolic curve. The quasi-sinusoidal form with an amplitude of 0.006 days and a period of 12.6 years corresponds to a secular period change caused by the light-time effect due to an unseen third star in the system.

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

197

Table 6 Simultaneous solutions of the light and radial velocity curves of the contact binary system V829 Her in three distinct seasonsa Parameterb

2003

2004 s1

2004 s2

2005

T0 HJD P0 days dP/dt a (Rx) Vc (km/s) i () T1 (K) T2 (K) X1 = X2 q = m2/m1 f fill-out L1/(L1 + L2)  B L1/(L1 + L2)  V L1/(L1 + L2)  R r1(mean) r2(mean)

2452797.4250(1) 0.35815054(3) 2.27273 · 1010 2.60(1) 13.9(5) 57.7(3) 6300 6101(26) 5.557(8) 2.3 0.19 0.330(5) 0.322(4) 0.320(3) 0.3200(9) 0.4647(9)

2453257.2958(2) 0.35815106(3) 2.27273 · 1010 2.67(1) 13.9(5) 55.4(3) 6300 5576(24) 5.509(9) 2.3 0.27 0.440(6) 0.403(4) 0.385(3) 0.3258(11) 0.4700(11)

2453257.2962(2) 0.35815109(3) 2.27273 · 1010 2.68(1) 13.95(50) 55.0(3) 6300 5539(31) 5.531(10) 2.3 0.24 0.448(7) 0.411(5) 0.391(4) 0.3232(11) 0.4675(11)

2453557.4270(1) 0.35815117(2) 2.27273 · 1010 2.61(1) 13.95(35) 57.2(2) 6300 6194(17) 5.550(5) 2.3 0.20 0.311(3) 0.310(2) 0.309(2) 0.3208(6) 0.4654(5)

Spot parameters Spot 1 co-latitude () Spot 1 longitude () Spot 1 radius () Tspot1/Tstar Spot 2 co-latitude () Spot 2 longitude () Spot 2 radius () Tspot2/Tstar

43(2) 338(4) 11.5(9) 0.75 – – – –

45 270 11.5 0.75 135 90 10 0.75

45 270 16 0.75 135 90 10 0.75

65(2) 322(2) 13(1) 0.75 – – – –

Absolute parametersb m1 (mx) m2 (mx) R1 (Rx) R2 (Rx) log g1 (cgs) log g2 (cgs) Mbol,1 Mbol,2 MV,1 MV,2 L1 (Lx) L2 (Lx) MV d (pc) P W(O  C)2

0.56(3) 1.29(4) 0.83(1) 1.21(1) 4.34(2) 4.38(1) 4.78(15) 4.10(17) 4.83(15) 4.15(17) 0.98(14) 1.81(29) 3.69(14) 193(12) 0.02578

0.61(3) 1.39(4) 0.87(1) 1.25(1) 4.34(2) 4.38(1) 4.68(15) 4.41(19) 4.73(15) 4.52(19) 1.07(15) 1.36(24) 3.87(13) 177(11) 0.02508

0.61(3) 1.41(4) 0.87(1) 1.25(1) 4.35(2) 4.39(1) 4.69(15) 4.45(19) 4.74(15) 4.58(19) 1.06(15) 1.32(24) 3.90(13) 174(10) 0.01955

0.57(3) 1.30(3) 0.84(1) 1.22(1) 4.34(2) 4.38(1) 4.76(15) 4.03(16) 4.81(15) 4.08(16) 0.99(14) 1.95(29) 3.63(14) 198(13) 0.01899

a b

The probable errors in the last digits are given in parenthesis. 1 and 2 denote small and large components, respectively.

It was estimated that the unseen third star should be a low mass (lower than 0.7mx) and faint (5m fainter than the system V829 Her) star. If such a third body were a Main Sequence star, it should be a red dwarf of mid-K spectral type. We would recommend that this faint tertiary should be studied spectroscopically as in the D’Angelo et al.’s (2006) spectroscopic search. The parabolic curve corresponds to a secular period increase of about 0.007 ± 0.001 s/yr caused by a conservative mass transfer from the less massive secondary component to the more massive primary one. Our photometric results describe the V829 Her system as a W-subtype W UMa contact binary system, which has a fill-out factor of about 20 percent in a state of marginal contact. It also suggests that the large and more massive component has dark starspot(s). However, there are two

large differences between four separate photometric solution series of the system in Table 6: the surface temperature (therefore magnitude and luminosity) of the large component and the parameters of spots. All of the other parameters are almost same in the limits of standard errors. There are two reasons for the variation of the surface temperature of the large component: (i) dark spot(s) occur on its surface (for instance, the value of the surface temperature of the large component in the models of 2004 s1 and s2 light curve solutions, which have two dark spots, is about 500 K lower than those in the models of 2003 and 2005 light curve solutions, which have one dark spot) and (ii) the temperature assigned to the secondary from the light curve solutions is that of the common envelope around its core, rather than the value that it would have if it were separate star (e.g., Hilditch, 2001).

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

198 2003 pe

10.2

2004 pe

10.1

10.1 B - 0.7

10.2 B - 0.7

10.3

10.3

V

V

10.4

10.4

R + 0.55

R + 0.5 5

10.5

10.5

10.6

10.6

0.52

0.52

B-V

0.6

0.6

0.64

0.64

0.68

0.68

0.4

B-V

0.56

0.56

V-R

0.4

0.44

V-R

0.44

0.48

0.48

0.52 0.6 0.7 0.8 0.9

Phase

1

1.1 1.2 1.3 1.4 1.5 1.6

0.52 0.6 0.7 0.8 0.9

Phase

1

1.1 1.2 1.3 1.4 1.5 1.6

2005 CCD

10.1

10.2

2003 pe V, 2004 pe V & 2005 CCD V B - 0.7

10.25 10.3

V

10.3

10.4 R + 0.55

10.5

10.35

10.6

10.4

0.52

B-V

10.45

0.56 0.6 0.64

10.5

0.68 0.4

2003 2004 s1 2004 s2 2005

V-R

10.55

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Fig. 3. The observational pe and CCD light and colour curves of V829 Her in standard magnitudes. The lines represent the model fits given in Table 6. The figure at the bottom-right shows the comparison of observations and model fits in standard V magnitude.

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

As mentioned in Section 2, all light curves of the system show clear evidence of O’Connell effect as lower light level at phase 0.75 (see Fig. 3). This effect or difference between both maxima light levels was considered in terms of dark/ cold spots on the large and more massive component star. The reason for putting spots on this component, in binaries like this, is because the luminosity ratio, implies significant light curve asymmetries should be preferentially associated with this more massive component, in order to keep them in reasonable proportion to the known relative scale of effects. On the other hand, the X-ray emission of the system, which was observed by Gioia et al. (1987), can be taken as additional evidence supporting ‘dark/cold spots’ condition. For the spot parameters the starting values were taken as co-latitude = 45, longitude = 90 and 270 (according to the phase, in which the light level asymmetry occurs), angular radius = 15 and temperature factor of 0.75 (according to the solar analogue). Assuming spots are 1500 K cooler than the photosphere, a fixed temperature factor of 0.75 has been fed into the Wilson–Devinney code. Furthermore, the pe BVR light curves in 2004 have two peculiarities: (i) it has two different light level of Max. II at phase 0.75 and (ii) the standard observations show that the light levels of both maxima in the light curves in 2004 are lower than those in 2003 and 2005 (see Fig. 3). For the first peculiarity, we separated this 2004 observations to two different light curve sets according to the light levels of Max II. We code-named them s1 (for less light level asymmetry) and s2 (for large one) and solved them separately. For the second peculiarity, we putted two dark spots in opposite

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hemispheres of the large and more massive component. In Fig. 4, we present the three-dimensional model demonstrating the presence of the large dark starspots on the surface of the large component by using four separate photometric solution series. The simultaneous solution of the light and radial velocity curves allows to compute the absolute parameters of the system. The resulting parameters with their probable errors of V829 Her are given in Table 6. For solar values we have taken Teff = 5780 K, Mbol = 4m.75 and BC = 0m.14. The bolometric corrections for the components of the eclipsing pair were selected from the tabulation of Zombeck (1990). We obtained the colour index of (B  V)obs = 0.59 ± 0.01 from our standard observations of the system. On the other hand, assuming an intrinsic (i.e., unreddended) colour index of (B  V)int = 0.50 for the spectral type F7 of the system (Zola, 2006), we found a small reddening of E(B  V) = 0.09. Thus, we calculated the distance of the system with the corrections of the interstellar absorption by using the distance modulus, which were computed from the colour excess as AV = 3.1E(B  V). On the other hand, according to the period–colour–magnitude relation of Rucinski and Duerbeck (1997), it is found that the distance to V829 Her is about 200 pc, which agrees with the value of distance in the model of 2005 light curve solution. Bilir (2006) confirmed that the distance of 74 pc to the system given by Bilir et al. (2005) is a printing error. There are also some large differences between four separate photometric solution series of the system according to absolute parameters. These are especially luminosity and magnitude of large component (see Fig. 5) and the

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Fig. 4. The 3D model of the components of V829 Her and spot locations at phase 0.75, according to four separate photometric solution series (see Table 6). The 3D model of the system at the bottom denotes two spots on the surface of the large component.

¨ zkardesß / New Astronomy 12 (2006) 192–200 A. Erdem, B. O

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mass. Actually, this discrepancy is a famous puzzle for W UMa systems and discussed by many authors. According to Wang (1995), in W-subtypes, contraction of the secondary star releases some of gravitational energy thereby makes the secondary star be hotter.

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Acknowledgements

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We would like to thank Dr. E. Budding for his useful comments on this study. This work was supported partly by the C ¸ anakkale Onsekiz Mart University Research Foundation.

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References

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log T Fig. 5. The positions of the components of V829 Her in the HR diagram, according to four separate photometric solution series (see Table 6). The solid lines are the evolutionary tracks from Girardi et al. (2000). The attached numbers denote initial masses.

distance to the system. As mentioned above, these differences arise from the variation of the surface temperature of the large component for each light curve sets. On the other hand, masses and radii of the components, which are calculated from these different data sets, are almost same in the limits of standard errors. If our values of masses and radii of components are compared with those of Zola et al. (2004) (their values are m1 = 0.86(2)mx, m2 = 0.37(1)mx, R1 = 1.06(1)Rx, R2 = 0.71(1)Rx) and those of Lu and Rucinski (1999) (their values are m1 = 1.46(2)mx, m2 = 0.60(1)mx, R1 = 1.27(1)Rx, R2 = 0.85(1)Rx); it is seen that our results and those of Lu and Rucinski are almost the same, but Zola et al.’s are quite different from ours. It does not seem that Zola et al. arrived at unreliable parameters, it seems there is an error in their Table 3. In Fig. 5, the luminosities versus temperatures are plotted for the components of the system. In this HR diagram, the more massive primary star seems to act as a normal Main Sequence star. Whereas, the less massive secondary star is, unusually, found to be on the left of the Main Sequence, contrary to any expectations from standard stellar-evolution theory. Thus, the secondary component seems to be over luminous and over sized for its ZAMS

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