A CCD PHOTOMETRIC STUDY OF THE CONTACT BINARY STAR GSC 03526-01995

GSC 03526-01995(= ROTSE1 J182427.29+453902.0, V = 14.3 mag (VizieR database⁵) is a variable discovered by Akerlof et al. (2000) as a byproduct of the ROTSE1 CCD survey. Its orbital ephemeris and the first unfiltered light curve were derived by Blättler & Diethelm (2004). GSC 03526-01995 is a short-period close binary with a period of 0.292258 days (Blättler & Diethelm 2004). Several papers have given some times of light minimum, but so far no detailed photometric investigations of GSC 03526-01995 have been published. Therefore, GSC 03526-01995 has become one of the monitoring targets in our contact binary observation program.

In the present paper, the R-band and I-band light curves obtained by us were analyzed with the Wilson–Devinney (W-D) code. The first photometric solutions of the system were derived. Moreover, the variations in the orbital period of GSC 03526-01995 were analyzed based on all available photoelectric and CCD times of light minimum, and the photometric properties of the suspect third companion have been discussed.

R- and I-band observations of the GSC 03526-01995 were carried out on 2011 April 7 and 8 with the DW436 2048 × 2048 CCD photometric system attached to the 60 cm Cassegrain reflecting telescope at the Yunnan Observatory. The R and I filters, close to the standard Johnson UBVRI system, were used. The integration times of each image for R and I filters are 60 s and 40 s, respectively. The coordinates of the comparison star (GSC 03526-02086) used are 18^h24^m07105, +45°40'3234. The PHOT (measure magnitudes for a list of stars) of the aperture photometry package of IRAF was used to reduce the observed images. From the observation we obtained RI light curves. Afterward, considering a slightly large scatter of these two light curves, we tried to re-observe the star on 2012 May 24 and 26 with the PI 512 × 512 TE CCD photometric system attached to the 85 cm telescope at the Xinglong Station of National Astronomical Observatories of China. The effective field of view was 145 × 145. The filter system is a standard Johnson-Cousins-Bessel multicolor CCD photometric system built on the primary focus (Zhou et al. 2009). The bands, exposure times, and the comparison star are the same as those used in 2011. The original data are listed in Tables 1–4 with the Heliocentric Julian Date and the magnitude difference between GSC 03526-01995 and the comparison star.

The phase of the observations were calculated with the equation 2,455,875.99724 + 0.292258 days × E, where HJD₀ is one of the times of light minimum obtained with the 1 m telescope and a period of 0.292258 days (from Blättler & Diethelm 2004) was assumed. The light curves are displayed in Figure 1 for the R band and in Figure 2 for the I band, and both light variations in 2011 (LCs 1) and 2012 (LCs 2) are of EW type.

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Several timings of light minimum were obtained, which are listed in the last part of Table 5. Additionally, two times of light minimum in the R band were obtained on 2011 April 29 and November 10 by using the DW436 2048 × 2048 CCD photometric system attached to the 1 m reflecting telescope at the Yunnan Observatory. In our analysis, the value HJD2453150.462 obtained by Diethelm (2004) was not used because its (O − C) value shows large scatter when compared with the general trend formed by the other data points.

As shown in Figures 1 and 2, an obvious O'Connell effect (O'Connell 1951) could not be ignored, we added a spot on star 2, which proved in the following to be the cooler more massive component. We analyzed the light curves with spot models using the W-D program (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & van Hamme 2003). During the solution process, the effective temperature of star 1 was chosen as T₁ = 4830 K according to the J − H = 0.47 and H − K = 0.093 of GSC 03526-01995 from the VizieR database (Cox 2000). It must be pointed out here we had difficulty in estimating the effective temperature because these color indices often appear to be uncertain. Fortunately, in the W-D code the light curve depends much more strongly on the temperature ratio of T₂/T₁ than on the individual temperature (Yakut & Eggleton 2005). Thus the mass ratio, the inclination, and the degree of contact are probably not much affected by uncertainties in temperature. Hence, most of the time we need not worry about how large the uncertainty for the effective temperature might be (Liu et al. 2011). In our solution, T₁ was therefore fixed at the estimated value, 4830 K. The gravity-darkening coefficient, g₁ = g₂ = 0.32 (Lucy 1976), and the bolometric albedo, A₁ = A₂ = 0.5 (Ruciński 1969), were adopted, which correspond to the common convective envelope of both components. Bolometric and bandpass square-root limb-darkening coefficients were taken from Van Hamme (1993) and are listed in Table 6. We adjusted the mass ratio (q), the orbital inclination (i), the mean temperature of star 2 (T₂), the monochromatic luminosity of star 1 (L_1R, L_1I), and the dimensionless potential of star 1 (Ω₁ = Ω₂, mode 3 for contact configuration). To obtain initial input parameters, a q-search method was used, we assumed a series of trial values of q (0.3, 0.4, 0.5, and so on), as Figure 3 shows. It can be seen that the smallest value of squared residuals is achieved around q = 2.9. The final converged photometric solutions for LCs 1 and LCs 2 are listed in Table 6 and the corresponding theoretical light curves are shown in Figures 4 and 5 with solid lines, respectively. In Table 6, θ is the "latitude" of a star spot center, measured from 0 radians at the "north" (+z) pole to π radians at the "south" pole. ψ is the longitude of a star spot center, measured counter-clockwise (as viewed from above the +z axis) from the line of the star centers from 0° to 360°. Ω is the angular radius of a star spot, in degrees, T_s/T_* is the temperature factor of a spot, which specifies the ratio of the local spot temperature to the local temperature that would be obtained without the spot.

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The fit of computed light curves is good and more reliable for LCs 2, but worse for LCs 1 because of a slightly large scatter of LCs 1. Both solutions for LCs 1 and LCs 2 show that GSC 03526-01995 is a W UMa-type contact binary system. In the following estimations of the system parameters and dark spot parameters, only the values of Column 3 from Table 6 are used, due to their greater accuracy. The geometrical structure of GSC 03526-01995 with a dark spot on the more massive component at phase 0.75 in 2012 is plotted in Figure 6. As Maceroni & van't Veer (1993) pointed out that the spot determination by photometry alone is unreliable due to the uniqueness of the spotted solutions, the parameters with a spot shown in Table 6 are tentative.

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GSC 03526-01995 was neglected for period study. Though the time span of the investigation of this binary is not long (∼12.7 yr), the obtained data have already reflected some rules of its period variations. Having collected all useful times of light minima, the (O − C)₁ curve with respect to the linear ephemeris given by Diethelm (2007),

$$\begin{eqnarray} &&{\rm Min}\,I=2454014.3175 +0\mbox{$.\!\!^{\mathrm{d}}$}292258\times {E}, \end{eqnarray} \tag{ 1 }$$

is shown in the upper panel of Figure 7. It is no doubt that the general (O − C)₁ trend of GSC 03526-01995, shown in the upper panel of Figure 7, indicates a cyclic variation. Assuming that the period oscillation is cyclic, then, based on the least-squares method, a sinusoidal term was added to a linear ephemeris to give a better fit to the (O − C)₁ curve (solid line in the upper panel of Figure 7). The following equation is obtained:

$$\begin{eqnarray} {\rm Min}\,I & = & 2454014.31700(\pm 0.00099) \nonumber\\ && +0.29225601(\pm 0.00000009) \hbox{ days} \nonumber\\ && \times {E} +\,0.00896(\pm 0.00153)\,\sin [0\mbox{$.\!\!^\circ $}0390 \nonumber \\ && \times {E}+12\mbox{$.\!\!^\circ $}56(\pm 0\mbox{$.\!\!^\circ $}08)]. \end{eqnarray} \tag{ 2 }$$

The sinusoidal term in Equation (2) suggests a cyclic variation with a period of about 7.39 yr and a semiamplitude of about A₃ = 0.00896(± 0.00153) days, which is more easily seen from Figure 8, where the (O − C)₂ values with respect to the linear part of Equation (2) are displayed. The residuals computed from Equation (2) are given in the lower panel of Figure 7, which are in a horizontal line on average, except for some scatter.

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Based on our RI light curves, the photometric solutions for GSC 03526-01995 were derived. We found that GSC 03526-01995 is a W UMa-type contact binary system with a degree of contact factor f = 18.2%, and a mass ratio of q = M₂/M₁ = 2.84553, whose asymmetric light curves could be modeled by a dark spot on the more massive component. According to the classification of W UMa contact binaries given by Binnendijk (1970), GSC 03526-01995 is a W-subtype contact binary. Additionally, the discovery of a high-latitude dark spot in 2012 at phase 0.75 may make GSC 03526-01995 an interesting system to study.

By combining our 10 determinations of times of light minimum with those compiled from the literature, we found that the orbital period of GSC 03526-01995 shows a cyclic period variation with a period of 7.39 yr and a semiamplitude of 0.00896 days. The plot of the mass ratio versus secondary component's spectral type definitely rules out the magnetic activity cycles as a unique cause for a cyclical period variation among binaries with a late-type component (Liao & Qian 2010). Moreover, the statistical findings of ours also indicated that 64.2% of EW-type binaries show cyclical orbital period variation and the most plausible explanation of this is the light-travel time effect (Liao & Qian 2010), considering that the sinusoidal period change of GSC 03526-01995 is attributed to the light-time effect via the presence of an additional body. For GSC 03526-01995, it is a K spectral-type contact binary star according to the Allen's table (Cox 2000) for the values of J − H and H − K. Therefore, we estimated the mass of the more massive component of binary: M₂ = 0.8 M_☉ (Cox 2000). According to the photometric mass ratio of q = 2.84553 derived in our photometric analysis, the mass of the another component M₁ = 0.28 M_☉ can be estimated. Using the known equation,

$$\begin{equation} f(m) =\frac{(M_{3}\sin {i^{\prime }})^{3}}{(M_{1}+M_{2}+M_{3})^{2}}=\frac{4\pi ^{2}}{G{T}^{2}}\times (a^\prime _{12}\sin {i^{\prime }})^{3}, \end{equation} \tag{ 3 }$$

the parameters of the additional component star were estimated: the mass function for the additional component is determined to be f(m) = 0.069(± 0.035) M_☉, the lowest mass of the additional companion is 0.57(± 0.13) M_☉, and this body is orbiting the binary at a distance shorter than 2.93(± 0.82) AU. According to Allen's table (Cox 2000), this companion is estimated to be a K6–9 star, which is brighter than the star 1 in GSC 03526-01995 so that it should contribute light to the whole system. To verify the presence of a third body, during the photometric solution, we added a third light (i.e., we made l₃ an adjustable parameter), but l₃ is usually negative or too small for the contribution of such third body, which suggests that the third companion might itself be a binary composed of two nearly identical 0.285 stars. This situation appears in many eclipsing binaries, e.g., AD And (Liao & Qian 2009), V899 Her (Qian et al. 2006), VZ Lib (Qian et al. 2008), and ASAS J011328-3821.1 (Hełminiak et al. 2012). Therefore, the system may be a quadruple system containing four late-type stars. Of course, to check the existence of the third body, new photometric and spectroscopic observations and a detailed investigation of those data are urgently required in the future. Table 7 lists the physical parameters (i.e., the period P, the contact degree f, the orbital inclination i, mass ratio q, the spectral type) and the form of period changes for some available short-period (P_orb < 0.3 days) contact binary systems. From this table, we can see that the values of physical parameters and the form of period changes we derived for the short-period contact binary star GSC 03526-01995 are typical ones.

This work was partly supported by the Special Foundation of the President of the Chinese Academy of Sciences, Yunnan Natural Science Foundation (Y1XB041001), and the Chinese Natural Science Foundation (Nos. 11133007, 11203066, and 11103074).