Light-curve analysis and orbital period change of the extreme mass-ratio overcontact binary AW CrB

Abstract

1 INTRODUCTION

The evolution of W UMa-type binary stars is still not well understood. The traditional view for the origin of these contact binaries is that they are formed from detached cool binaries with initial orbital periods of a few days. By a combination of evolutionary expansion of both components and angular momentum loss arising from the magnetic stellar wind, a contact binary is formed. Model calculations suggest that these binary systems ultimately coalesce into single stars and may be progenitors of the poorly understood blue straggler and FK Com–-type stars (e.g. Rasio 1995; Stepień 2006, 2011). It was recently demonstrated that the eruption of V1309 Sco was the result of a merger of the components of a cool contact binary (Tylenda et al. 2011). Extreme mass-ratio contact binaries with a high degree of overcontact may be in the late evolutionary stages of the contact phase. Detailed photometric analyses and orbital period studies of those systems can provide invaluable information for the evolution and coalescence scenario of these binary systems.

The variability of AW CrB was discovered in the course of the ROTSE-I experiment, and classified as a δ Scuti-type star with a period of 0.180465 d (Akerlof et al. 2000). The variable identification, period determination and type classification were conducted by automatic algorithms. Jin et al. (2003) found, from visual inspections of the light curves of the ROTSE-I δ Scuti stars, that several of these stars were misclassified. In order to re-classify some of these stars, they started a multiband photometric CCD observing programme for 20 of the 91 stars classified as δ Scuti star in the initial ROTSE-I variable star catalogue. From their single night observations they found AW CrB to be a W UMa-type star with an amplitude of about 0.3 mag. By combining the ROTSE-I data with their observations, they derived a period of 0.360 920 d. Their light curve of AW CrB displays total eclipses, making this star very suitable for a photometric study. The mass-ratio of W UMa-type stars exhibiting total eclipses can be accurately determined from photometric observations (Terrell & Wilson 2005). The long total eclipses of AW CrB, lasting about 10 per cent of the orbital period, in combination with the small amplitude suggest a low mass-ratio making this star particularly interesting.

The position of AW CrB furthermore coincides with the ROSAT X-ray source 1RXS J161520.0+354218 (Geske, Gettel & McKay 2006) indicating chromospheric activity. Since no light-curve model has been published yet, new photometric VR_cI_c CCD observations were obtained. In this paper the photometric analysis of these observations, using the Wilson–Devinney (WD) code (Wilson & Devinney 1971, 1972; Wilson 1979, 1994), is presented together with a period study. For the orbital period study also the observations published by Jin et al. (2003) and photometric data obtained by the ROTSE and Wide Angle Search for Planets (WASP) robotic telescopes are used.

2 OBSERVATIONS

AW CrB was observed on eight nights in 2011 from a private observatory located near the town of Mol, Belgium, at an altitude of about 40 m above sea-level. The images were acquired using a 20-cm Celestron Schmidt–Cassegrain telescope, equipped with a SBIG ST-7XMEI CCD camera, and VR_cI_c filters which are close to the standard Johnson–Cousins system. The use of a focal reducer yields a field of view of 16.8 arcmin by 11.2 arcmin and a plate scale of 1.32 arcsec pixel⁻¹. The operating temperature of the CCD was kept constant at a temperature about 30°C below the ambient temperature. For most of the nights the operating temperature was kept constant at −20°C. On the second night the CCD was cooled to −25°C and on the last two nights to −15°C. The observations were made under good to excellent sky conditions, i.e. no sudden drops in the instrumental magnitudes, e.g. due to cirrus clouds, have been observed. However, on JD 245 5672 the observations had to be stopped early due to deteriorating weather conditions.

The integration time for each image was 60 s. By using the CCD camera's additional autoguider chip, the stars were kept on approximately the same pixels during an observing session. The full width at half-maximum of the stellar images was typically around 4 pixels, occasionally increasing to more than five pixels partly due to a focus drift caused by the decreasing ambient temperature.

The images were processed with dark removal and flat-field correction using the imred packages in iraf.¹ Twilight flat-field images were obtained on all but two nights on which the flat-fields were obtained from a diffuse reflector indirectly illuminated by an incandescent lamp. Vignetting is evident in the flat-field images with about 5 to 10 per cent loss of intensity at the very corners of the image. The variable, comparison and check star are well located around the central area of the image which is not affected by the vignetting.

Differential aperture photometry was performed using the digiphot/apphot package in iraf. GSC 2586−1883 and GSC 2586−1807 were chosen as the comparison and the check star, respectively. The coordinates, V magnitude and colours of AW CrB, the comparison, and the check star are listed in Table 1. The magnitude and colours for the comparison and check star are taken from the AAVSO Photometric All Sky Survey (APASS), which is conducted in five filters: Johnson B and V, plus Sloan g^′, r^′ and i^′ (Henden et al., in preparation). Using the equations from Jester et al. (2005), the APASS Sloan magnitudes of the comparison and check star have been transformed to V − R_c and R_c − I_c colours in order to transform the differential observations of AW CrB to the standard Johnson–Cousins system. The comparison star was close enough to the variable that extinction differences were negligible. The observations were made at airmasses smaller than 1.90.

Depending on the airmass and the sky conditions, the integration time of 60 s results in a signal-to-noise ratio for the V filter between 251 and 521 for the variable, between 215 and 451 for the comparison star, and between 332 and 531 for the check star. For the R_c and I_c filters the signal-to-noise ratio is somewhat higher. An estimate of the uncertainty of the CCD photometry was obtained from the standard deviation of the differential light curve between comparison and check star, viz. 0.01 mag in all filters. Since the photometric error is dominated by the fainter star, in this case the comparison star, the above figure is a good estimate for the uncertainty of the variable minus comparison star light curve (e.g. Howell, Warnock & Mitchell 1988). About 46 h of CCD photometry was secured in each passband covering all orbital phases of AW CrB several times. The complete observation log is given in Table 2 and phased light curves are shown in Fig. 1. All observations are available from the AAVSO International Database,² maintained by the American Association of Variable Star Observers (AAVSO), or upon request from the author.

Figure 1.

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VR_cI_c light curves (a) and colour curves (b and c) of AW CrB; the solid line is the synthetical light curve of the model with a cool starspot on the primary. The dots in the colour curves represent mean values calculated in a phase bins of ϕ = 0.015. The lower panels display the residuals of the unspotted and spotted model fits for the V (d and e), R_c (f and g) and I_c passband (h and i), respectively.

3 ECLIPSE TIMINGS AND ORBITAL PERIOD STUDY

Up to now no times of minimum light had been published yet. From the observations reported in the present paper two timings of primary minimum and five timings of secondary minimum were determined using the Kwee & van Woerden (1956) method. This method was also applied on the primary and secondary minimum observed by Jin et al. (2003) and to the publicly available photometry from the WASP project (Butters et al. 2010). To calculate the time of minimum light from the data of the Northern Sky Variability Survey (NSVS) (Wozniak et al. 2004), the observations were first phased before applying the Kwee & van Woerden method. All timings of minimum light, spanning almost 12 years or about 12 000 orbital revolutions, are listed in Table 3. The timings from our observations and from Jin et al. (2003) are weighted means from the timings of minimum light in the, respectively, 3 and 2 observation bandpasses.

Figure 2.

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O − C diagram of AW CrB. Dashed lines refer to a sudden period increase and solid line to a continuous period increase.

Figure 3.

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Phase diagram of AW CrB constructed using the ephemeris in equation (3). The solid line represents averaged WASP observations. The circles, triangles and filled squares are, respectively, the R_c observations presented in this paper, the NSVS observations and the I-band data from Jin et al. (2003). The observations were shifted in magnitude to fit the observations presented in this paper.

The period analysis has been repeated using the timings of primary and secondary minimum separately. The results are not significantly different from those obtained with both the primary and secondary minima included in the analysis.

4 LIGHT-CURVE ANALYSIS

The WD method, as implemented in the software package phoebe version 0.31a (Prša & Zwitter 2005), was used to analyse our V, R_c and I_c light curves simultaneously. All individual data points were used in the analysis. Based on the colour indices B − V = 0.505 ± 0.024, V − R_c = 0.309 ± 0.017, R_c − I_c = 0.286 ± 0.005, and interstellar reddening of E(B − V) = 0.019 published by Terrell, Gross & Cooney (2012) and the 2MASS colours J − H = 0.210, H − K_s = 0.055, the temperature of star 1 (the star eclipsed at primary minimum, i.e. phase ϕ = 0) was fixed at |${T_{\rm eff}} = 6700\,{\rm K}$| (Drilling & Landolt 2000). Based on the temperature, convective atmospheres are assumed. The bolometric albedos A₁ = A₂ = 0.5 (Rucinski 1969) and the gravity-darkening coefficients g₁ = g₂ = 0.32 (Lucy 1967), appropriate for convective envelopes, were assigned. The logarithmic limb-darkening law is used with coefficients adopted from van Hamme (1993) for a solar composition star. The analysis is performed in mode 3, which is appropriate for overcontact systems that are not in thermal contact. A q-search method was applied to determine the initial mass-ratio. For a range of discrete values of q, the adjustable parameters were: the orbital inclination i; the mean temperature of star 2, T₂; the monochromatic luminosities of star 1, L₁; and the dimensionless potential of star 1 (Ω₁ = Ω₂, for overcontact binaries). From Fig. 4, it can be seen that the resulting chi-square value of the convergent solutions reached its minimum for q = 0.10. At this point the mass-ratio q, with initial value 0.10, was included in the set of the adjustable parameters. The mass-ratio converged to a value of q = 0.0992 ± 0.0004 in the final solution, with a total χ² = 0.129. The solution reveals a high degree of overcontact f = (Ω_in − Ω)/(Ω_in − Ω_out) = 75 per cent ± 3. The photometric parameters are listed in Table 5 and the residuals of the fit are plotted in Fig. 1 (panels d, f and h) for the V, R_c and I_c passband, respectively. The errors given in this paper are the formal errors from the WD code and are known to be unrealistically small.

Figure 4.

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Total χ² for an unspotted model versus a number of fixed mass-ratios q.

While the overall fit of the computed light curves is quite satisfactory, Fig. 1 shows the maximum at phase ϕ = 0.25 (Max I) slightly fainter than at phase ϕ = 0.75 (Max II) by about 0.02, 0.01 and 0.01 mag in the V, R_c and I_c bandpasses, respectively. Table 4 lists the average magnitudes calculated in a phase interval of ±0.02 around the maxima and minima, with the standard deviation in units of the last digit given between parentheses. The unequal light level between primary maximum and secondary maximum, the so-called O’Connell effect, is known in many eclipsing binaries. It is often explained as surface inhomogeneities on either or both components and modelled by placing circular dark or hot starspots on the components.

We assumed that either a hot starspot or a cool starspot was on star 1 or star 2. For these four combinations and with the parameters from the spotless solution fixed, the parameter space of colatitudes ϕ, longitudes θ, spot radius r_s, and temperature factor T_s/T_⋆, with T_⋆ being the local effective temperature of the surrounding photosphere was explored using the phoebe-scripter. The best solution was found for a cool starspot on the primary, with T_s/T_⋆ = 0.96, spot radius r_s = 21°, colatitude ϕ = 114° and longitude θ = 290°. Since a solution did not converge with subsets of spot parameters made adjustable, these spot values were fixed while the higher mentioned set of star parameters was made adjustable again. This resulted in a solution with a total χ² = 0.104. All parameters are listed in Table 5 and the fit of the computed light and colour curves is plotted in Fig. 1 (panels a, b and c). The corresponding geometric structures at phases ϕ = 0.00 and ϕ = 0.25 are displayed in Fig. 5. As shown by Maceroni & van’t Veer (1993), spot determination by photometry alone is unreliable because of the non-uniqueness of photometric solutions for spotted W UMa-type binaries. The spot parameters listed in Table 5 are therefore only provisional. Since Pribulla & Rucinski (2008a) argue that perhaps all cool contact binaries are members of multiple systems, and a cyclic period variation cannot be ruled out, a third light contribution to the light curves has been investigated. The analysis, however, did not reveal a third light contamination. Mochnacki & Doughty (1972) have shown that the internal contact angle for a given mass-ratio q, and inclination i, is almost independent of the degree of overcontact f. The contact angle diagram plotted in their fig. 3 can be used as a consistency check on the solution found by the WD method. By estimating the internal contact angle from the light curve, and by using the inclination found by the WD method, a mass-ratio q ∼ 0.11 is estimated from this diagram. This is in good agreement with the solution found by the WD model. A significant difference would indicate third light or another complication.

Figure 5.

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Geometrical representation of AW CrB at phases ϕ = 0.0 and ϕ = 0.25.

5 RESULTS AND CONCLUSION

The light curves obtained by CCD photometric observations in the V, R_c and I_c passbands were analysed simultaneously with the WD method, as implemented in phoebe. Since AW CrB shows total eclipses the photometric parameters can be determined reliably. The photometric solutions suggest that AW CrB is an extreme low mass-ratio overcontact binary with q = 0.10 and a high degree of overcontact f = 75 per cent ± 3. This places AW CrB among the few contact binaries with the lowest mass-ratios known up to now. The mass-ratio of the components, which is related to the angular momentum loss and mass transfer, is one of the crucial parameters in the evolution of close binary systems. Table 6 lists the currently known contact binaries with mass-ratios q ≲ 0.12.

The light curves displayed in Fig. 1 suggest that AW CrB is an A-type overcontact binary system according to the classification of Binnendijk (1970). However, we derived a secondary temperature of |${T_{\rm eff}} = 6808 \pm 10\,{\rm K}$|⁠, which is higher than that of the primary component. A weak O’Connell effect is observed with Max I slightly fainter than Max II. The position of AW CrB coincides furthermore with the ROSAT X-ray source 1RXS J161520.0+354218 (Geske et al. 2006) indicating enhanced chromospheric and coronal activity. The O’Connell effect may be explained by a model with a cool starspot on the primary component. The best model is obtained with a cool spot on star 1, with T_s/T_⋆ = 0.96, spot radius r_s = 21°, colatitude  ϕ = 114° and longitude θ = 290°.

Figure 6.

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Corrected colour–mean density diagram for W-type (open circles) and A-type (crosses) primaries. The low mass-ratio W-type and A-type primaries are plotted with filled circles and filled triangles, respectively. AW CrB is indicated with a filled square. The ZAMS and terminal-age sequence lines are taken from fig. 3 of Mochnacki (1981) .

The orbital period analysis based on observations collected from public available data of the NSVS and WASP project, the Jin et al. (2003) paper and the present paper reveals an increasing period for AW CrB. The form of this period change is unclear. Additional timings of minimum light over a longer time-span are required to be conclusive. A sudden period increase of |$\Delta P = 2.3\times 10^{-6}\, {\rm d}$| or 0.2 s may have occurred around 2005–2007. However, continuous period variations are commonly encountered in contact binaries and are more acceptable. Table 7 lists the period change rates for a number of extreme mass-ratio contact binaries. In case of a continuously increasing period, the period change rate for AW CrB is estimated to be |${{\mathrm{d}}P/{\mathrm{d}}t} = 3.58\times 10^{-7} {\rm d\ yr}^{-1}$| or |$0.03\ {\rm s\ yr}^{-1}$|⁠. Such a period change is usually attributed to mass transfer. If a mass of 1.4  M_⊙ is assumed for the primary component based on the colour indices, then a conservative mass transfer rate from the less massive to the more massive component is estimated to be |$5.1\times 10^{-8} {\,{\rm M}_{\odot }}\ {\rm yr}^{-1}$|⁠. With mass transferring, the orbital angular momentum decreases while the spin angular momentum increases. When the spin angular momentum of the system is more than a third of its orbital angular momentum, this kind of low mass-ratio binaries with a high degree of overcontact may evolve into a rapidly rotating single star (Hut 1980).

Due to the short time-span of the observations, about 12 year or only 12 000 orbital revolutions, a cyclic period variation cannot be ruled out. Periodic variations, sometimes superimposed on a secular period change, have been reported for several W UMa-type stars. These periodic variations are usually explained by a light-time effect via the presence of a third body, e.g. GR Vir (Qian & Yang 2004) and XY Leo (Yakut et al. 2003) among other stars. Pribulla & Rucinski (2008a) argue that perhaps all cool contact binaries are members of multiple systems, supporting the theory that Kozai cycles accompanied by the tidal friction may play an important role in close binary formation (Stepień 2011, and references therein). In case period variations are not strictly periodic, they are usually explained by magnetic activity cycles in both components, e.g. FG Hya (Qian & Yang 2005) and CK Boo (Kalci & Derman 2005). The W UMa stars are fast-rotating solar-type stars and are known to show enhanced chromospheric and coronal activity. Applegate (1992) and Lanza, Rodonó & Rosner (1998) proposed that the orbital period changes in close binaries are a consequence of magnetic activity in one or both of the component stars.

Since the period variation of AW CrB is very important to understand its evolutionary state, it needs further long-term photometric monitoring for accurate epochs of light minimum. In order to obtain the absolute parameters of AW CrB, and to check the derived photometric mass-ratio, spectroscopic observations are required.

I gratefully acknowledge the AAVSO and the Curry Foundation for providing the CCD camera on loan. I thank Patrick Wils for proofreading the draft of this paper and the referee, Professor S. W. Mochnacki, for suggesting several improvements to the paper. This study used data from the NSVS created jointly by the Los Alamos National Laboratory and the University of Michigan, and funded by the US Department of Energy, the National Aeronautics and Space Administration (NASA) and the National Science Foundation (NSF). This research also used data from the WASP public archive. The WASP consortium comprises the University of Cambridge, Keele University, University of Leicester, The Open University, The Queen's University Belfast, St. Andrews University and the Isaac Newton Group. Funding for WASP comes from the consortium universities and from the UK's Science and Technology Facilities Council. Additionally this study made use of NASA's Astrophysics Data System, and the SIMBAD and VizieR data bases operated at the CDS, Strasbourg, France.

REFERENCES