A&A 416, 1097-1105 (2004)
DOI: 10.1051/0004-6361:20034578

Key parameters of W UMa-type contact binaries discovered by HIPPARCOS[*]

S. O. Selam

Ankara University, Faculty of Science, Dept. of Astronomy & Space Sciences, 06100 Ankara, Turkey

Received 25 October 2003 / Accepted 10 December 2003

A sample of W UMa-type binaries which were discovered by the HIPPARCOS satellite was constructed with the aid of well defined selection criteria described in this work. The selection process showed up that several systems of which the variability types have been assigned as EB in HIPPARCOS catalogue are genuine contact binaries of W UMa-type. The light curves of the 64 selected systems based on HIPPARCOS photometry were analyzed with the aid of light curve synthesis method by Rucinski and their geometric elements (namely mass ratio q, degree of contact f, and orbital inclination i) were determined. The solutions were obtained for the first time for many of the systems in the sample and would be a good source for their future light curve analyses based on more precise follow-up observations.

Key words: stars: binaries: close - stars: binaries: eclipsing

1 Introduction

W UMa-type systems are eclipsing binaries with orbital periods between about 5 and 20 h showing continuous light variations. They consist of two solar-type component stars surrounded by a common envelope. There is a large scale energy transfer from larger, more massive component to the smaller, less massive one, roughly equalizing surface temperatures over the entire system. The equality of the effective temperatures of both components is one of the discriminating characteristics of the contact binaries of W UMa-type; it was initially one of the most difficult properties to explain and led to development of the successful "contact model" by Lucy (1968). The components of W UMa-type systems are rotating relatively fast (equatorial velocities of 100-200 km s-1) in spite of their old ages. This is the natural consequence of spin-orbit synchronization due to strong tidal interactions between the components. W UMa-type systems have the least amount of angular momentum that binary stars can have and therefore they attract special attention as laboratories to test the angular momentum evolution of binary stars. Several reviews have discussed properties of W UMa-type systems; the recent ones, concentrating respectively on theoretical and observational issues, have been published by Eggleton (1996) and by Rucinski (1993a). A very recent catalogue of field contact binaries which have been compiled by Pribulla et al. (2003) is a good source for their physical parameters.

This paper is concentrating on the determination of essential (key) parameters (namely mass ratio q, degree of contact f, and orbital inclination i) of W UMa-type systems discovered photometrically by HIPPARCOS satellite. The main aim of this work is to provide preliminary set of parameters of these system which can be used as input parameters in their analyses of future more precise light curves based on follow-up observations.

Initially 79 such systems were extracted from the HIPPARCOS Catalogue (ESA 1997, hereafter HIP) according to the selection criteria described in Sect. 2 and their numbers have been reduced to 64 genuine contact binaries of W UMa-type after excluding the detached and semi-detached systems according to the "Fourier filter'' described in Sect. 2. The light curves of these 64 systems based on HIPPARCOS photometry (data extracted from the Epoch Photometry Annex of HIP[*]) were analyzed with the aid of simplified light curve synthesis method by Rucinski (1993b). Section 3 of the paper describes the application of the Rucinski's method and analysis of the selected systems, and finally Sect. 4 is devoted to the summary and discussion.

2 Selection of the systems

W UMa-type systems discovered photometrically by HIPPARCOS satellite were extracted from the Variability Annex of HIP (hereafter HIPVA) according to the selection criteria itemized below:

The systems filtered with the above criteria are listed in Table 1. The columns are explained at the bottom of Table 1 which their entries for the first six were mostly extracted from HIPVA. The systems, CC Lyn, FH Cam and CU CVn which are fullfilling the above described criteria have been identified in HIP as EB type systems, but Rucinski and his collaborators have shown that they are pulsating variables (Rucinski 2002) and therefore they were excluded form the current sample list. On the contrary, 7 systems, incluled to the current sample list have been identified as pulsating variables in HIP and later have been proven by different authors that they are genuine contact binaries. These systems are FI Boo (Lu et al. 2001), HI Dra and V351 Peg (Gomez-Forrellad et al. 1999), ET Leo (Rucinski et al. 2002), V2357 Oph (Rucinski et al. 2003), HH UMa (Pribulla et al. 2003), and NN Vir (Rucinski & Lu 1999). Their light elements (namely T0 and P) and variability types were updated accordingly and marked with an explanatory $^{\rm {b}}$ footnote in Table 1. Two exceptions, DN Cam and IS CMa which are not being HIPPARCOS project discoveries were also included to the current sample, because they are neglected systems after their photometric discoveries (DN Cam by Strohmeier 1959 and IS CMa by Strohmeier & Knigge 1974). Several systems in the current sample were already observed and analysed spectroscopically or photometrically by different authors (see the references in last column in Table 1). These systems were also kept in the sample list for comparing their results with the parameters obtained in this study.

There is a number of low-amplitude short-period (P < 1 day) variables of which their variability types are unknown and denoted only by "P'' in HIPVA. These objects might be pulsating variables of low amplitude of types RRC, DSCT/DSCTC, or BCEP, as well as close binaries of types EW, EB, or EA seen at very low inclination angles (i.e., ELL-type). Duerbeck (1997) presented a method to discriminate the possible contact binaries among them based on the known period-colour relation for W UMa-type systems by Rucinski (1993a) and Rucinski & Duerbeck (1997). He showed that a polygon through the bluest confirmed contact binaries on $\log P-(B-V)$ plane could be used as the borderline between bluer pulsating variables and redder contact binaries for a given period. However, he noted that the sample of contact binary candidates separated in that way still may be contaminated by pulsating stars, since the RRC-type stars extend to relatively redder colours and longer periods. The working list of contact binary candidates of Duerbeck (1997) still waiting for spectroscopic or photometric verification (except FI Boo, ET Leo, V2357 Oph, and HH UMa as explained above) and therefore not considered in this study.

Table 1: Systems filtered from HIPPARCOS Catalog with the first selection criteria described in Sect. 2.

The literature on several systems in the current sample have shown that the HIP variability types are rather unreliable especially for the type EB. This was particularly so for the large number of small-amplitude systems called EB in HIP, most probably by some sort of an automated classifier. Of course, these could in fact be EW or EB binaries seen at small orbital inclination angles, but the tendency to call all variables EB seemed to increase for small amplitudes, exactly in the case where nothing can be said just from the shape of the light curve. On the other hand some EB-type system in HIP with deep unequal eclipses could be semi-detached or even detached systems. The most frequently occuring short-period EB objects appear to be binaries either just before establishing contact or in one of the broken-contact semi-detached stages, in any case, prior to the mass ratio reversal, with the more massive component close to or at its critical Roche surface. The distinction between EW and EB class in individual cases is frequently difficult and both types are evolutionary related to each other. This is the reason why EB systems in HIP were also included to the sample by the first selection criterion given above. So the filtered sample according to the above selection criteria should be clarified for variability type ambiguitiy.

Several among the systems in the sample have speckle interferometry, close visual or spectroscopic companions which are listed with their CCDM (Catalogue of Components of Double and Multiple Stars, Dommanget & Nys 2002) identifiers in Table 1. The observations of these systems maybe contaminated by the third light, due to the rather large instantaneous field of view of the detector of HIPPARCOS satellite (see Fig. 1.4.2 of HIP, Vol. 1, p. 78). This information can be easily retrieved by checking H48 field entry of HIP for an individual system. According to the entries in this field, the HIPPARCOS photometry of V410 Aur, ET Boo, V776 Cas, CT Cet, EE Cet, KR Com, V2150 Cyg, QW Gem, CN Hyi, V592 Per, BL Phe, VW Pic, V1055 Sco, V1123 Tau, HX UMa, II UMa, and LV Vir are contaminated by the light from their close companions. The H48 field in HIP for the systems HI Dra, IR Lib and V2388 Oph is empty and probably they can not be resolved or identified as multiple systems by the HIPPARCOS satellite. By looking at their astrometric data (separations between the visual components) in the CCDM catalog it was decided that their HIPPARCOS photometry are also contaminated by the third light, because, mostly the combined photometry of the components have been given in the HIP for the doubles with separations up to about 10 $\hbox{$^{\prime\prime}$ }$. PU Peg, V1128 Tau and QW Tel are far enough from their visual companions and therefore it was assumed that their HIPPARCOS photometry was not affected by the third light. The separate $H_{\rm p}$ magnitudes of the visual components were taken from the HIPPARCOS Double and Multiple System Annex and the third light parameter L3 in light units were calculated for the most of contaminated systems. Separate $H_{\rm p}$ magnitudes for HI Dra and IR Lib is absent in the HIPPARCOS Double and Multiple System Annex and their relevant data were taken from CCDM Catalog. For some systems the L3 parameter were prefered to be taken from the recent literature which are mostly based on more precise spectroscopic determinations. These systems are EE Cet, KR Com, V2388 Oph and II UMa (Rucinski et al. 2002), V899 Her (Özdemir et al. 2002), and VW Pic (Rucinski 2002). The calculated or collected L3 parameters for the contaminated systems were also listed in Table 1. The HIPPARCOS photometry of the contaminated systems have been corrected for the third light contribution by using these L3 parameters, before any attempt to analyse their light curves.

The photometric observations ($H_{\rm p}$ magnitudes) along with their standard errors ( $\sigma_{H_{\rm p}}$) for these system were taken from the Epoch Photometry Annex of HIP (hereafter HIPEPA) and the relevant light curves are constructed using the light elements (T0, P) given in Table 1. Only the $H_{\rm p}$ magnitudes having 0 (zero) and 1 (one) quality flag in the field HT4 of HIPEPA were used in this study. The final classification and selection (namely clarifiying the variability type ambiguity) of the objects listed in Table 1 have been done by performing the Fourier analysis of their HIPPARCOS light curves in the same way as described originally by Rucinski (1997a, 1997b, 2002). This "Fourier filter'' technique is depending on relations between some Fourier coefficients obtained by least-squares fits to the light curves which were normalized to unity at orbital quadratures (i.e., phases $\theta_{\rm maxI}=0.25$ or $\theta_{\rm maxII}=0.75$) and eliminated from the third light contribution if it is necessary. Normalization of the light curves were always made to the higher maxima in this study as suggested by Rucinski (1993b). The fit function;

\begin{displaymath}l(\theta)=\sum_{i=0}^{10} a_{i} ~ {\rm cos}(2\pi i \theta)
\end{displaymath} (1)

is a cosine series with 11 coefficients where ai, $\theta$ and $l(\theta)$ are denoting the Fourier coefficients, the orbital phase and normalized light in light units, respectively. This is the same fit function forming the basis of the Rucinski's simplified light curve synthesis method (Rucinski 1993b) which was used during the light curve analysis in this work. Figure 1 illustrates a typical Fourier fit for the system V2388 Oph. Only the resulting Fourier coefficients a1, a2 and a4 were listed in Table 1 which are necessary for "Fourier filter'' and light curve analyses. Their standard estimation errors were given in parentheses after each value which are in units of last decimal places. Sum of squared residuals $\Sigma\rm (O{-}C)^{2}$ for the fits were also listed in Table 1 as a goodness of fit parameter.
\end{figure} Figure 1: A typical Fourier fit illustrated for the system V2388 Oph as an example. The residuals from the fit are also displayed at top shifted by 1.1 light units.
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During the construction of an automated variability-type classifier for the very large OGLE sample of eclipsing binaries Rucinski (1997a, 1997b) explained in detail that detached binaries (EA) can be simply discriminated from the EW and EB-type binaries on the a2 - a4 plane by the boundary condition a4 < a2(0.125 - a2). On equality this expression corresponds to the theoretical position of systems at marginal (inner) contact. He also showed that EB-type binaries can be discriminated from the real EW-type binaries by the boundary condition a1 < -0.02. On equality this expression corresponds to the statistical upper-limit position of the systems having acceptable amount of difference between the eclipse depths (and thus temperature difference between the components) for being a contact binary. Although this boundary condition related only with a1 coefficient it was preferred to display the corresponding filtering results on a2- a1 plane just for visualization purposes. The results for our sample are shown in Fig. 2 on a2 - a4 plane and in Fig. 3 on a2 - a1 plane. The solid thick curve in Fig. 2 and the solid thick line in Fig. 3 illustrates the relevant boundary conditions described above. 12 systems; ET Boo, CK Cet, IQ CMa, HL Dra, FP Eri, QY Hya, V356 Hya, BS Ind, BL Phe, VW Pic, CP Psc and VY PsA were clearly separated as EA-type binaries by the "Fourier filter'' on a2 - a4 plane and 3 systems; BF Cap, BD Scl and V1055 Sco were separated as EB-type binaries by the "Fourier filter'' on a2 - a1 plane. In that way the number of genuine contact binaries in the sample has been reduced to 64 after removing these EA and EB-type systems and only the light curves of the 64 remaining systems were analysed in the next section. The removed EA and EB type systems are indicated by their new variability types at Col. 14 in Table 1. The variability types of all the remaining 64 systems should be assigned as EW.

\end{figure} Figure 2: Fourier coefficients a2 and a4 have been used to separate detached binaries from EW and EB binaries. The error bars are representing the standard estimation errors of the Fourier coefficients obtained during the least-square fits to the normalized light curves. The solid thick curve illustrates the "Fourier filter'' boundary a4=a2(0.125 - a2) which corresponds to the theoretical position of systems at marginal contact and separates the detached binaries (located above that curve) from real EW and EB binaries (located below that curve). The detached system which were filtered on a2-a4 plane are labeled by their variable-star names.
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\end{figure} Figure 3: Fourier coefficients a1 and a2 have been used to separate EB binaries from genuine EW binaries. The error bars are representing the standard estimation errors of the Fourier coefficients obtained during the least-square fits to the normalized light curves. The solid thick line illustrates the "Fourier filter" boundary a1=-0.02 which separates the EB binaries (located above that line) from EW binaries (located below that line) as suggested by Rucinski (1997a,b). The EB system which were filtered on a2-a1 plane are labeled by their variable-star names. The systems which passed the filter but very close to the boundary are also labeled by their variable-star names.
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3 Analyses of the light curves

The analyses of the HIPPARCOS light curves of the sample systems have been performed with the aid of the Rucinski's simplified light curve synthesis method (Rucinski 1993b). Basically the method can be described as a nomographic version of his well known WUMA code (see Rucinski 1973, 1974, 1976; Hill & Rucinski 1993) based on the original "contact model" by Lucy (1968). His basic idea during construction of the nomogram tables was that the brightness variations of contact binaries of the W UMa-type are totally dominated by geometrical causes and he showed that the light curves of EW-type systems depend practically only on three key parameters, the mass ratio q=m2/m1, orbital inclination i and degree of contact f (see Rucinski 1993b and references therein). The parameter f is defined through the Jacobi equipotentials C as

f=(C1-C)/(C2-C) (2)

where C1 and C2 are, respectively, for the inner (f=0) and outer (f=1) critical equipotentials. Using his WUMA code, he generated a series of theoretical light curves by systematically sampling the parameter space (f, q, i) for three values of f; 0.0, 0.5 and 1.0 with steps $\Delta q=0.05$ and $\Delta i=2\hbox{$.\!\!^\circ$ }5$ between $0.05\leq q\leq 1$ and $30\hbox{$^\circ$ }\leq i \leq 90\hbox{$^\circ$ }$. During the calculations he adopted a representative solar case for the radiative parameters in photometric V-band by taking $T_{\rm eff}=5770$ $^\circ$K, with the gravity brightening exponent $\beta=0.32$ and the bolometric albedo A=0.5. He also confirmed that this specific selection of radiative parameters is not too restrictive as the orbital variations are strongly dominated by the geometrical effects and valid through the bracketing atmospheres [ $T_{\rm eff}, u$] between [5900, 0.57] and [5660, 0.61], where u is the linear limb darkening coefficient. Then he has constructed the nomograms consisting of the Fourier coefficients ai ( i=0,1,...,10) obtained by the Fourier decomposition of these theoretical light curves as described in the previous section. He also generated nomograms for theoretical eclipse depths $d_{{\rm minI}-t}=1-l(0\hbox{$^\circ$ })$ and $d_{{\rm minII}-t}=1-l(180\hbox{$^\circ$ })$ in light units for the same parameter space which are very useful to decide the validity of the solution for a particular system.

The nomograms (for Fourier coefficients and eclipse depths) were retrieved electronically from Rucinski's anonymous FTP site[*] and interpolated in f with steps $\Delta f=0.1$to obtain a finer grid in degree of contact parameter. The application of the solution method using these nomograms is very easy. As described in Rucinski (1993b) just comparing the theoretical and observational values of the Fourier coefficients a2 and a4 on the a2-a4 plane and constraining the theoretical points near to observational one with their corresponding eclipse depths values would be enough to obtain an approximate solution for a particular system. More distinctly, one should find a theoretical point on a2-a4 plane close to the observationally determined point with its corresponding values of minima depths are also similar to the observational ones. The uniqueness of the solution obtained in that way is an important issue as any other method of solving light curves of contact systems and discussed in the final section of this paper.

The effective wavelengths of Johnson V-band and HIPPARCOS $H_{\rm p}$-band are more or less the same. These bands only differ by a colour-dependent offset (see HIP, Vol. 13, p. 275), but basically identical when one considers the variability. Thus the V-band theoretical predictions in nomograms were directly used for $H_{\rm p}$ variability without applying any transformation to the observational data.

Observational values of the eclipse depths in light units for 64 genuine EW-type system in the final sample were calculated using the Fourier descriptions of their HIPPARCOS light curves. Using these observational eclipse depths along with the Fourier coefficients obtained in the previous section, approximate solutions were obtained for each of the 64 systems and listed in Table 2. Corresponding literature data for those systems subjected to spectroscopic or photometric analysis were also listed in this table for comparison. The columns were explained at bottom of the table.

Table 2: The results of the light curve solutions for the 64 genuine EW-type systems.

4 Summary and discussion

A sample of W UMa-type contact binaries which were discovered by the HIPPARCOS satellite was constructed by well defined selection criteria and "Fourier filter'' described in Sect. 2 of this work. Through these selection processes all the HIPPARCOS discoveries of genuine W UMa-type contact binaries having orbital periods shorter than 1 day with spectral type later than A5 were covered by the sample. The HIPPARCOS light curves of 64 system in the current sample were analised with the aid of Rucinski's simplified light curve synthesis method (Rucinski 1993b) and their essential geometric parameters, namely the degree of contact f, mass ratio q=m1/m2 and orbital inclination i were obtained. As already discussed by Rucinski (1997a) the solution method used in this study is rather convinient if one takes in account the large databases of variables observed with moderate accuracy as in the case of the HIPPARCOS mission photometry. Therefore there wasn't any attempt to use more sophisticated light curve solution methods in this study.

As one compare the results in Table 2 reasonably consistent solutions were reached for those systems that are already subjected to photometric or spectroscopic analysis. This situation proven that the simplified light curve synthesis method by Rucinski (1993b) is a very powerful tool to find first approximations to the parameters of the W UMa-type systems. The observed inconsistency between the parameters obtained here and in the literature for some of these systems are mainly due to the bad phase coverage, large scatter, erroneous observations or relatively large asymmetries between the maxima (so called O'Connell effect) in their HIPPARCOS light curves. As can be seen from Eq. (1) the light curve synthesis method by Rucinski (1993b) uses only the cosine terms during the Fourier decomposition of the light curves. Cosine terms are insensitive to the asymmetrical features in the light curves and therefore the solutions for the systems showing O'Connell effect in their light curves became more uncertain according to the amount of the O'Connell effect. Due to that reason WY Hor is the only system in the sample, that no acceptable solution were found.

Another limitation of the solution method used in this study comes from the low amplitude systems. The a2 and a4 coefficients of the low amplitude W UMa-type systems are very close to zero and this would bring an uncertainity during the determination of the degree of contact f parameter as one can see from Fig. 6 of Rucinski's (1993b) paper. Therefore the obtained solutions for such systems (i.e., $\vert a_{2} \vert < 0.03$) like V335 Peg, XY Pic and V851 Ara are rather uncertain. The classification of several systems based on "Fourier filter'' technique is also complicated due to the combined effect of the low amplitude and bad phase coverage with largely scattered or erroneous observations in their light curves. Visual inspection of their HIPPARCOS light curves does not support the classification obtained solely by the "Fourier filter''. Such are the systems very close to the boundries on a2 - a4 and a2 - a1 planes; FP Eri, QY Hya, VW Pic, V1055 Sco, MS Vir, and V870 Ara.

The analysis method used in this study faces the same difficulty as any other method of solving light curves of contact systems. If we do not know q exactly (namely, spectroscopically determined mass ratio  $q_{\rm sp}$), then we do not know which component (more or less massive) is eclipsed at each eclipse. However, even in this case the nomogram tables provide a means of determining the valid pairs of (q,i) parameters for an assumed f. If we see total eclipses, than we can hope for a full solution. The method by Mochnacki & Doughty (1972) permits to find another (q,i) dependence from the angles of the internal eclipse contacts. Intersection of the two relations will give correct q and i separately. Unfortunately the moderate accuracy of the HIPPARCOS mission photometry does not allow us to discriminate the systems showing total eclipses and prevent us to apply Mochnacki & Doughty's (1972) method in this study. It is believed that rather large deviations of the solution results obtained in this study from more precisely determined literature values in Table 2 are due to the above described uniqueness problem. Such are the systems EE Cet (q=0.65 while $q_{\rm sp}=0.315$), EX Leo (q=0.35 while $q_{\rm sp}=0.199$) and V2377 Oph (q=0.10 while $q_{\rm sp}=0.395$).

A certain amount of uncertainty in the solution results can also be expected for the systems of spectral types (i.e., surface temperatures) that are outside the defined limits of bracketing atmospheres (see Sect. 3). According to the effective temperature calibration of dwarf stars by Gray & Corbally (1994) the upper and lower limits of the bracketing atmospheres correspond to the spectral types F9 and G3, respectively. As one can see from Table 1, most of the systems have mainly mid to late F spectral types and lying outside but very close to the defined upper limit. Since the geometry is the dominant cause of the brightness variations of W UMa-type binaries, it is believed that the uncertainty due to the above described reason should be very small.

Preliminary photometric solutions were obtained for 53 systems in this study for the first time. It is believed that their approximate parameters determined from these solutions would be a good source for their future light curve analyses based on more precise follow-up observations. Especially 19 of them have spectroscopically determined mass ratios (see Table 2) in the literature and are urgently waiting for good photometric light curves for full solution.

The author would like to thank Dr. Slavek M. Rucinski for his useful comments on application the light curve analysis method and to the anonymous referee for his/her constructive comments. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France and NASA's Astrophysics Data System.


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