1 INTRODUCTION
W UMa-type stars belong to the class of contact binaries and can be briefly characterised by (i) continuous light variations with amplitudes less than ~0.9 mag, (ii) orbital periods shorter than 24 h, (iii) almost equal depths of minima, and (iv) usual spectral types between F and K. The common envelope structure of W UMa stars was first introduced by Lucy (Reference Lucy1968). Physical structures and evolutionary stages of W UMa systems were discussed in detail by various authors (Binnendijk Reference Binnendijk1970, Reference Binnendijk1977; Eggleton Reference Eggleton, Milone and Mermilliod1996; Kähler Reference Kähler2004; Li et al. Reference Li, Zhang, Han, Jiang, Jiang, Deng and Chan2008).
Wide-angle sky surveys such as the Optical Gravitational Lensing Experiment (OGLE; Udalski et al. Reference Udalski, Szymanski, Kaluzny, Kubiak and Mateo1992, Reference Udalski, Szymanski, Kaluzny, Kubiak, Mateo and Krzeminski1994), the Robotic Optical Transient Search Experiment Telescope (ROTSE; Akerlof et al. Reference Akerlof2003) projects, as well as data from orbiting experiments, i.e. Kepler Mission (Borucki et al. Reference Borucki2010), the Optical Monitoring Camera (OMC) onboard the INTEGRAL satellite (Mas-Hesse et al. 2004) have extremely increased the photometric data to be evaluated to uncover the variability types and periodicities of the stellar objects. A total of 45 eclipsing binaries known as W UMa-type in the literature were selected from the database of the ROTSE-IIId telescope maintained by the TÜBİTAK National Observatory (TUG) in Turkey. The periodicity of unevenly sampled data for each system was determined by the Lomb–Scargle (L-S) algorithm (Lomb Reference Lomb1976; Scargle Reference Scargle1982) and used to construct folded light curves. Then, a classification technique, which was also successfully applied to Hipparcos light curves by Selam (Reference Selam2004), based on the Fourier decomposition of light curves in cosine series (Rucinski Reference Rucinski1993), was performed to obtain preliminary parameters of the systems. Approximate values of the degree of contact (f), mass ratio (q), and orbital inclination (i) of each system, together with periodicities and Fourier coefficients, are presented in this study.
We aim to extend this work to automatically recognise all W UMa-type systems in the full dataset of the ROTSE-IIId experiment. However, note that the distorting effects in the light curves, namely, the O’Connell effect, asymmetries because of spot activity, third light contamination or observational scattering, can strongly restrict the reliability of this classification method.
2 OBSERVATIONS AND DATA ANALYSIS
2.1 Observations
The observational data used in this study were provided by the Turkish part of the public records of the ROTSE-IIId telescope’s archival data. The ROTSE-III telescopes are located at four different regions around the world and they are dedicated to observe optical afterglows of gamma-ray bursts. One of these telescopes, ROTSE-IIId, is located at TUG in Antalya, Turkey. It has an aperture of 45 cm and a 2048×2048 CCD with the pixel scale of 3.3 arcsec pixel−1 for a total field of view of 1°.85×1°.85. It uses no filters but have a wide passband that peaks at 550 nm. The ROTSE-III telescopes were described in detail by Akerlof et al. (Reference Akerlof2003).
The Turkish side of the ROTSE-IIId archive consists of 422 different sky pointings with more than a quarter million of CCD frames taken from these pointings. Due to ROTSE-IIId’s observational limitations, each night, only 1–20 frames of individual pointings were observed with 60, 20, and mostly 5 s of exposure times. A total of 118 W UMa-type variables examined in this study were retrieved from a SIMBAD query which fell into only 48 different pointings in this archive.
2.2 Data Analysis
The ROTSE-IIId telescope is equipped with an automated data reduction pipeline. Dark frames that are accumulated each night are used in the data reduction pipeline, together with a proper sky-flat and fringe frame. For detection and in order to obtain instrumental magnitudes of the detected objects, aperture photometry is done with a 5-pixel (17 arcsec) diameter aperture by use of the SExtractor code (Bertin & Arnouts Reference Bertin and Arnouts1996). These magnitudes are calibrated by comparing all field stars against the USNO A2.0 R-band magnitudes (Monet Reference Monet1998).
According to the pointing, 162–2 238 frames were used in generating one light curve for each system. The outcome from the above analysis was a total of 118 light curves of well-known W UMa stars, of which 45 candidates had enough number of data points in their light curves for any period analysis in detail. Two of the systems, Cl* NGC 6791 KR V118 and V791 Cep were also excluded since they were 17.68 and 17.27 mag, respectively, which are ~1.0 mag fainter than the limiting magnitude of ROTSE-IIId (Güçsav et al. Reference Güçsav, Yeşilyaprak, Yerli, Aksaker, Kızıloğlu, Çoker, Dikicioğlu and Aydın2012). Times of all systems used in this study were corrected to the Solar System barycenter.
The L-S technique (Lomb Reference Lomb1976; Scargle Reference Scargle1982) was applied to discretely sampled data to obtain any meaningful periodicity. Periods were determined by a script, written based on the L-S algorithm, and the results were compared with the values given in the literature. Of the 43 stars we analyzed, 37 had periods consistent with those in the literature. However, our results point out different periods for the V455 Mon, XX Lyn, and V981 Cyg systems, which will be discussed in Section 3. Period determination has failed for the systems USNO-A2.00900−11608642, 2MASS J19033572+4336124, and 2MASS J20292467+6029444 when the L-S algorithm was applied. This was probably caused by fewer sampled data points or poor data quality of the light curves. Hence, these three systems were excluded in the Fourier series fitting step.
Rucinski (Reference Rucinski1973, Reference Rucinski1993) showed that light curves of W UMa-type systems strongly depend on geometrical parameters such as degree of contact f, orbital inclination i, and mass ratio q and that they can be represented well by a low-order cosine series,
$l(\theta ) = \sum _{i=0}^6 a_{i}\cos ( 2 \pi \text{i} \theta ),$
where l(θ), ai
, and θ are normalised light in light units, Fourier coefficients, and angular phase of the system in radians, respectively. To evaluate the values of f, i, and q, tables of Fourier coefficients listed in Rucinski’s personal Web siteFootnote
1
were used after modifying light curves as suggested by Rucinski (Reference Rucinski1993), by normalising to unity and shifting the primary, i.e. deeper, minimum to zero phase. Rucinski (Reference Rucinski1993) also computed the model light curves by adopting a representative solar case for the photometric band V. However, since the instrumental response curve of ROTSE-IIId has a central wavelength at 550 nm, any transformation to our data was not performed in our study. Fourier coefficients were first used to determine the degree of contact f for each system with steps of Δ f = 0.1. Then, using the Fourier coefficients of a
1, a
2, and a
4, corresponding geometrical parameters were tried to be determined for 40 W UMa systems.
3 RESULTS AND DISCUSSION
The main aim of this study is to recognise the W UMa-type binaries selected from the archival database of the ROTSE-IIId telescope and to obtain preliminary system parameters by fitting truncated Fourier series on the light curves. To achieve this aim, orbital periods were primarily calculated from discretely sampled data by an L-S-based algorithm and the results were compared with values in the literature. The periodicities on the basis of the L-S algorithm for 43 W UMa systems are presented in Table 1. Three of the systems, V455 Mon, XX Lyn, and V981 Cyg, produced periodicities different from those given in the literature. However, our results seem to be much more plausible since (i) false-alarm probability is very low, (ii) not only the L-S algorithm but ANOVA (Schwarzenberg-Czerny Reference Schwarzenberg-Czerny1996) and cleanest (Foster Reference Foster1995) algorithms also point out the same periods, and (iii) phase coverage and quality of the data are very satisfying for these three systems. The main reason for the rejection of three systems, USNO-A2.00900−11608642, 2MASS J19033572+4336124, and 2MASS J20292467+6029444, in the Fourier analysis is that the first two systems have fewer than 100 data points spread over a time span of 4 months and the third system has a brightness of 16.20 mag, which was pointed out earlier as the limiting magnitude of ROTSE-IIId. Hence, the light curves of these systems are extremely scattered or it is impossible to obtain any reasonable periodicities. Note also that the time span of the observations, i.e. 5 years, is too long when variation intervals in the light curves and periods of W UMa-type systems are considered (Karimie Reference Karimie1983; Derman, Demircan, & Selam Reference Derman, Demircan and Selam1991; Awadalla Reference Awadalla1988, Reference Awadalla1994). This common effect might have also caused extra scattering in the light curves of the systems we analyzed.
Table 1. Selected W UMa-Type Binaries from the ROTSE-IIId Database with Calculated Periods
Notes. Targets are in RA order. Periods given in bold are discusses in the text.
a References. (1) Gettel, Geske, & McKay (Reference Gettel, Geske and McKay2006); (2) Pigulski et al. (Reference Pigulski, Pojmański, Pilecki and Szczygieł2009); (3) Devor et al. (Reference Devor, Charbonneau, O’Donovan, Mandushev and Torres2008); (4) Akerlof et al. (Reference Akerlof2000); (5) Kafka et al. (Reference Kafka, Gibbs II, Henden and Honeycutt2004); (6) Samus et al. (Reference Samus2008); (7) Kreiner (Reference Kreiner2004); (8) Zhang et al. (Reference Zhang, Deng, Zhou and Xin2004); (9) Vanko & Pribulla (Reference Vanko and Pribulla2001); (10) Virnina (Reference Virnina2011); (11) Xin, Zhang, & Deng (Reference Xin, Zhang and Deng2002); (12) Hoffmann & Meinunger (Reference Hoffmann and Meinunger1983); (13) Kolesnikova et al. (Reference Kolesnikova, Sat, Sokolovsky, Antipin and Samus2008); (14) Rucinski et al. (Reference Rucinski2008); (15) Khruslov (Reference Khruslov2006); (16) Kuzmin (Reference Kuzmin2008); (17) Özkardeş & Erdem (Reference Özkardeş, Erdem, Demircan, Selam and Albayrak2007); (18) Kinman, Mahaffey & Wirtanen (Reference Kinman, Mahaffey and Wirtanen1982).
We extended our work to obtain Fourier coefficients by decomposing the light curves of 40 W UMa-type systems. Although the period determination was successful for the systems Cl* NGC 7789 XZD 10 and V473 And, the Fourier series fitting process has failed probably due to the large scatter in their light curves. Therefore, 38 systems were studied by this method. Figure 1 shows a representative Fourier fit for the system 2MASS J11403001+7111021.
Figure 1. A sample of the folded and unity normalised light curve of 2MASS J11403001+7111021, observed by the ROTSE-IIId telescope between 2004 and 2009, is presented. Period based on the L-S algorithm and theoretical curve (solid line) obtained by Fourier series fitting are also shown in the figure.
Rucinski (Reference Rucinski1997b) has shown that a boundary line between the a 2 and a 4 coefficients, which are always negative, as a 4 = a 2(0.125 − a 2) can be used to distinguish binary systems showing β Lyr (EB) or W UMa (EW) type light curves from detached (EA) binaries. They also took samples of pulsating stars to show that these systems can be easily distinguished from the eclipsing binaries by falling on the lower part (positive a 4 values) of the a 2–a 4 diagram (see Figure 4 of Rucinski Reference Rucinski1997b). Results of this study for the 38 systems are listed in Table 2 and shown graphically in Figure 2. Although five systems, NN Aqr, V472 And, Cl* NGC 7789 XZD 3, ROTSE1J190830.01+433601.5, and V441 Lac, are located inside the detached system area, they are very close to the boundary. This indicates that the candidates are contact or semi-detached systems.
Figure 2. Distribution of the 38 W UMa-type systems on the a 2–a 4 plane. There are no points below a 4 = 0 which would have been an indicator of a pulsating system (Rucinski Reference Rucinski1997b). All points that lie below the boundary line shown by the solid curve are either EW- or EB-type binary.
Figure 3. Distribution of the 38 W UMa-type systems on the a 1–a 2 plane. Fourier coefficient a 1 is related to the difference between the depths of the eclipses.
Table 2. Selected W UMa-Type Binaries from the ROTSE-IIId Database with Calculated Fourier Coefficients and Corresponding System Parameters
Notes. The numbers in the parentheses represent standard error of the last digit. Three system parameters, fl , il , and ql , if found in the literature are given between columns 7 and 10. Two systems that have failed in the Fourier series fitting process are discussed in the text.
a References. (1) Yakut et al. (Reference Yakut2009); (2) Yang et al. (Reference Yang, Qian, Zhu, He and Yuan2005); (3) Vanko & Pribulla (Reference Vanko and Pribulla2001); (4) Baran et al. (Reference Baran, Zola, Rucinski, Kreiner, Siwak and Drozdz2004); (5) Qian, Zhu, & Boonruksar (Reference Qian, Zhu and Boonruksar2005); (6) Zola et al. (Reference Zola, Gazeas, Kreiner, Ogloza, Siwak, Koziel-Wierzbowska and Winiarski2010); (7) Qian et al. (Reference Qian, He and Xiang2008); (8) Nelson et al. (Reference Nelson, Robb, Kaiser and Billings2002); (9) Deb & Singh (Reference Deb and Singh2011); (10) Erdem & Özkardeş (Reference Erdem and Özkardeş2006); (11) Branly et al. (Reference Branly, Athauda, Fillingim and van Hamme1996); (12) Svechnikov & Kuznetsova (Reference Svechnikov and Kuznetsova1990).
There is another correlation proposed by Rucinski (Reference Rucinski1997a) to separate EB systems from EW systems on the a 1 versus a 2 plane in which the a 1 = −0.02 line distinguishes EB systems from EW systems. This criterion is based on the fact that most of the EW-type systems show small differences in eclipse depths by the usage of Fourier coefficient a 1, which is related to the depths of the eclipses. Of the 38 EW-type binaries that have been analysed, only 2 systems, XX Lyn and V2203 Oph, seem to fall into the EB-type region. However, they are too close to the boundary for us to make any decisions when their error bars are also taken into account. This also indicates that all the 38 candidates are well represented to be genuine W UMa-type binaries on the basis of this second criterion (see Figure 3).
A few geometrical parameters, such as f, i, and q, can also be estimated using Fourier coefficients. The table of coefficients on distinct inclination angles and mass ratios for three set of fill-out parameters, f = 0, 0.5, and 1.0, was accessed from Rucinski’s personal Web site. As suggested by Rucinski (Reference Rucinski1993), the a 2 and a 4 coefficients were primarily used in estimating f values, and then only a 2, which is highly correlated with the depth of the eclipse, was used to obtain the i and q parameters. Calculated Fourier coefficients a 1, a 2, and a 4, and corresponding geometrical parameters f, i, and q with literature information, are given in Table 2 for 38 systems. Values of 27 systems are the first approximations.
4 CONCLUSION
Fourier series fitting in recognizing the types of variability was studied and tested using the light curves generated from the ROTSE-IIId archive data for a total of 45 W UMa-type sample systems. Among the dataset, some systems such as the three that failed in period determination, two with lower brightness than the ROTSE-IIId limiting magnitude, and two that have uncertain Fourier fitting, were excluded from further analysis. Therefore, Fourier series fitting and estimates on preliminary system parameters of the remaining 38 systems were performed. Results show that using combinations of the Fourier coefficient as a filtering technique is very successful in identifying the EW-type systems. However, in Table 2, there are some discrepancies in the system parameters f, i, and q, between exact solutions given in the literature and those predicted by this method. This unconformity may be attributed to scattered or distorted light curves by an instrumental effect, any third light contamination, O’Connell effect, or spot activity; i.e. see Yang et al. (Reference Yang, Qian, Zhu, He and Yuan2005) for a possible third light in CZ CMi, Zola et al. (Reference Zola, Gazeas, Kreiner, Ogloza, Siwak, Koziel-Wierzbowska and Winiarski2010) and Qian, He, & Xiang (Reference Qian, He and Xiang2008) for light-curve asymmetries in RT LMi, Özkardeş & Erdem (Reference Özkardeş, Erdem, Demircan, Selam and Albayrak2007) for the O’Connell effect and spot activity in V829 Her, and Nelson et al. (Reference Nelson, Robb, Kaiser and Billings2002) for spot activity in V2364 Cyg. In addition, this technique is not sensitive to recognising the systems with total eclipses as reported by Rucinski (Reference Rucinski1993). Such a system, AH Cnc, exhibits total eclipses in the light curves of Yakut et al. (Reference Yakut2009). However, our light curve of AH Cnc does not show any sign of totality. This may be the cause of the difference in the system parameters of AH Cnc between the light-curve solution and Fourier estimations in Table 2. If the light curves are contaminated by all these distorting effects, the reliability of the method decreases. Another difficulty encountered in defining the fill-out factor f emerges in the lower, i.e. near-zero, part of the a 2 versus a 4 plane where all values for each fill-out are mixed. However, the technique is still a very powerful tool for classifying huge amounts of photometric data gathered by automated sky surveys for a few decades. In the future, the plan is to apply this Fourier series fitting technique to identify all eclipsing W UMa-type systems in the full dataset of the ROTSE-IIId archive.
ACKNOWLEDGMENTS
This project utilises data obtained by the Robotic Optical Transient Search Experiment (ROTSE). ROTSE is a collaboration of the Lawrence Livermore National Laboratory, the Los Alamos National Laboratory, and the University of Michigan (http://www.rotse.net).
All observations were made with the ROTSE-IIId telescope and the archival data of ROTSE-IIId obtained at the TÜBİTAK (Turkish Scientific and Research Council) National Observatory (TUG); therefore, we thank the ROTSE-III Collaboration and TUG for the optical and archival facilities (TUG–ROTSE-IIId projects of Turkish observers).
We thank the anonymous referee for a positive review of the manuscript that has improved its content. We also thank Prof. Dr. Ü. Kızıloğlu for consultation, suggestions, and help.
This study was supported by TÜBİTAK with the project TBAG-108T475.
This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and the cdsclient tool located at CDS and NASA Astrophysics Data System Bibliographic Services.
