Photometric Solutions of Three Eclipsing Binary Stars Observed from Dome A, Antarctica

High-quality photometric and spectroscopic observations for eclipsing binary stars could provide good opportunities for one to derive the stellar parameters, such as masses, radii, and effective temperatures of the component stars and to investigate the star formation and chemical evolution histories (Torres et al. 2010; Feiden 2015).

Based on the Roche lobe configurations, eclipsing binaries can be classified as three types (Alcock et al. 1997): detached, semi-detached, and contact. Some authors indicated that a detached binary can evolve to be a semi-detached binary followed by a contact binary (Iben 1991; Tutukov et al. 2004; Yakut & Eggleton 2005; Stȩpień & Gazeas 2012). For binary systems, although the evolution toward contact binaries has been confirmed, the evolution during and beyond the contact phase is not well identified due to the lack of observation data (Stȩpień & Gazeas 2012). The evolutionary paths transform cool contact binaries (i.e., W UMa type binaries) to two subtypes: A-type and W-type. The evolutionary paths of the two subtypes are similar, whereas the different mass/energy transfer rates modify their physical parameters, influence their evolutions and lead to different results (Gazeas & Stȩpień 2008). Using the light curves and the radial-velocity curves of W UMa type binaries, an alternative evolutionary scenario was presented by Binnendijk (1970). In an A-type binary, the more massive component is hotter; whereas in a W-type binary, the secondary less massive component is hotter. The spectral types of A- and W-type systems range from A to G and F to K, respectively, but a significant overlap is present (Hilditch et al. 1988). The A- and W-type binaries differ substantially in mass ratio, and the temperature difference is usually a few hundred kelvin (Smith 1984), whereas, for some binaries, the temperature difference may be close to zero or even sometimes alternating between A- and W-type. At present, it is unconfirmed whether the division of A- and W-type is superficial or fundamental (Gazeas & Stȩpień 2008). In this case, more observations of eclipsing binaries at some special phases are expected.

Long, continuous, and multi-color time-series photometric observations may lead to significant insights into the astrophysical properties and evolutionary states for each component of eclipsing binary stars. Due to the unparalleled advantages of observational conditions (e.g., the high altitude, low temperature, low absolute humidity, low wind, and extremely stable atmosphere), Dome A of the Antarctic plateau is deemed as one of the best astronomical observing sites on the Earth for long-term near-continuous time-series observations (Saunders et al. 2009; Wang et al. 2011, 2017). The Chinese Small Telescope ARray (CSTAR) was deployed at Dome A (77°21' east, 80°22' south, 4093 m elevation) and made observations during the winters of 2008–2011. CSTAR consists of four 14.5 cm optical Schmidt-Cassegrain telescopes, each of which has a field of view of 45 × 45 with different (g, r, i and open) Sloan filters (Frei et al. 1996; Zhou et al. 2010). Fifty-three eclipsing binaries among more than 260 variable stars have been detected from the three-year observations (Yang et al. 2015). Three stars, CSTAR 036162, CSTAR 055495, and CSTAR 057775, are found to have relatively high precision and long duration coverage data in three filters, and they receive top priority to be analyzed among these eclipsing binary stars.

The three eclipsing binary stars CSTAR 036162, CSTAR 055495, and CSTAR 057775 were observed by CSTAR during the winters of 2008, 2009, and 2010 (Zou et al. 2010; Wang et al. 2011, 2013, 2014; Oelkers et al. 2015; Zong et al. 2015). Following Wang et al. (2011),⁹ we adopted the IDs of the three eclipsing binary stars, which are identified as variable stars by the General Catalog of Variable Stars (GCVS; Samus et al. 1997), All-sky Automated Survey (ASAS; Pojmanski 2002), and Two Micron All-sky Survey (2MASS; Skrutskie et al. 2006) as well.

Photometric light curves of the three binaries in the i band were collected by CSTAR in 2008 and extracted by Wang et al. (2011). With the light curves, Yang et al. (2015) provided the orbital parameters, including the temperature ratio (T₂/T₁), eccentricity (e), and sine of inclination (sin i) of the systems by using the Eclipsing Binaries via Articial Intelligence method (EBAI; automated modeling, Devinney et al. 2005, 2006). The results indicate that CSTAR 036162 and CSTAR 055495 are semi-detached systems while CSTAR 057775 is a contact system. The fundamental parameters of the three binaries are listed in Table 1. The bi-color photometric observations of the three binaries were performed by CSTAR in the winter of 2009. The light curves had been extracted by Zong et al. (2015) and Oelkers et al. (2015). Based on the long-term light curves in the i, g, and r bands in 2008 and 2009 and the spectroscopic observations carried out in 2016 and 2017, we aim to find more precise solutions of the geometrical configurations and evolutionary stages of the three binaries. This paper consists of six sections. The observations and data reduction are presented in Section 2. The new linear ephemeris is presented in Section 3. Synthetic light curves and geometric parameters of the three binaries are provided in Section 4. Comparison of parameters derived from this work and previous work, together with the discussion, are presented in Section 5. Section 6 presents the conclusions.

Table 1.  Parameters of the Three Eclipsing Binary Systems

Objects	CSTAR 036162	CSTAR 055495	CSTAR 057775
R.A.	09h03m59287a	07h43m5449b	06h40m47150c
Decl.	−88°33'07 61''a	−89°07'37 3''b	−88°15'21 34''c
2MASS ID	09035917–8833075	07435276–8907369	06404718–8815211
ASAS ID	090354–8833.1	074400–8815.4	064047–8815.4
GSC 2.3 ID	S3YB000243	S3Y8000078	S3YA000492
Tycho-2 ID	TYC 9518–443-1	⋯	TYC 9505–187-1
i (mag)	11.327	12.456	11.580
r, g (mag)	11.66, 11.80	12.68, 13.08	11.93, 12.08
J, H, K (mag)	10.540, 10.309, 10.230	11.443, 11.500, 11.418	10.717, 10.451, 11.82
V (mag)	11.53	12.594	11.82
B (mag)	12.19	⋯	12.63
Period (days)	0.873857	0.798017	0.438659
Amplitude V (mag)	0.29	0.65	0.45
μα, μδ (mas yr−1)	1.5, −3.4	0.8, 5.0	5.8, −1.0

Notes.

^aData source: Skrutskie et al. (2006). ^bData source: Wang et al. (2011). ^cData source: Pojmanski (2003).

The row descriptions are as follows: Header: CSTAR identifier (Wang et al. 2011). Rows 1 and 2: α₂₀₀₀ and δ₂₀₀₀ from SIMBAD. Row 3: 2Mass identifier (Skrutskie et al. 2006). Row 4: ASAS identifier (Pojmanski 2003). Row 5: GSC identifier (Samus et al. 1997). Row 6: Tycho-2 identifier (Høg et al. 2000) Row 7: Median apparent magnitude in the i band (Wang et al. 2011). Row 8: magnitude in the r and g bands (Oelkers et al. 2015). Rows 9: JHK near-infrared magnitude from the 2MASS catalog (Skrutskie et al. 2006). Row 10: Johnson V magnitude from the ASAS catalog (Pojmanski 2003). Row 11: Johnson B magnitude from the GCVS (Høg et al. 2000). Row 12: Period of the eclipsing binaries (Wang et al. 2011). Row 13: Amplitude in V band (Pojmanski 2003). Row 14: Proper motions in right ascension and declination from the PPMXL catalog (Roeser et al. 2010).

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Time-series photometric observations in the i, g, and r bands of CSTAR 036162, CSTAR 055495, and CSTAR 057775 were made with CSTAR during the winters of 2008 and 2009. In the winter of 2008, the telescopes equipped with the g, r and "open" filters had technical problems and obtained no useful data (Wang et al. 2011). Fortunately, the telescope equipped with the i filter ran with no issues. In the winter of 2009, observations in the g and r bands were made continuously. Figure 1 shows a sample image in the r band of the three objects observed by CSTAR on 2009 June 23 with the exposure time of 20 s. The preliminary reduction of the raw images includes bias subtraction, flat-fielding and fringe correction (Zhou et al. 2010; Wang et al. 2011; Zong et al. 2015). The DAOFIND program of the IRAF¹⁰ (Tody 1986, 1993) package was used to identify stars on each image; While DAOPHOT and ALLSTAR were used to perform synthetic aperture photometry for the stars (Stetson 1987). The magnitude calibration was made based on the Tycho catalog (Ofek 2008). The log of the observation data of the three binaries is listed in Table 2. Using the color index g − r in 2009 and Equation (23) of Fukugita et al. (1996), magnitude transformation from the SLOAN system to the Johnson–Morgan–Cousins system (B − V) is performed. The temperature of the primary star is estimated by using the empirical formula: T_eff = 8540/[(B − V) + 0.865] (4000 < T < 10,000). The effective temperatures of CSTAR 036162, CSTAR 055495, and CSTAR 057775 are derived as 6060 ± 330 K, 5564 ± 900 K and 5960 ± 520 K, respectively.

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Spectroscopic observations of CSTAR 036162 and CSTAR 055495 were carried out in 2016 with the 2.3 m telescope at the Siding Spring Observatory (SSO), Research School of Astronomy and Astrophysics (RSAA) of the Australian National University (ANU). The telescope was equipped with the Wide-field Spectrograph (WiFeS; Dopita et al. 2007, 2010) and 4096 × 4096 Fairchild Imaging CCDs. The wavelength range extended from 350 to 570 nm in blue arm and from 540 to 700 nm in red arm, respectively. The spectral resolution was 3000 (Dopita et al. 2010). A detailed reduction procedure is performed with PyWiFeS¹¹ which is a newly-developed Python-based data reduction pipeline for the WiFeS (Childress et al. 2014). The reduction procedure includes: image pre-processing (e.g., overscan subtraction, bias subtraction, slitlets separation, cosmic ray rejection, flat correction, scattered light accounting), "data cube" generating from the raw WiFeS CCD frames, flux, and wavelength calibration, and blue and red band spectrum stitching.

The spectroscopic observation of CSTAR 036162 was made on 2016 October 15 with the exposure time of 120 s. After data reduction, the obtained spectrum is shown in the top panel of Figure 2. After comparing with the spectrum flow library presented by Pickles (1998), the spectral type of CSTAR 036162 is preliminarily identified as G0. The low-resolution optical spectrum of CSTAR 055495 was obtained on 2016 August 29 with the exposure time of 180 s. The reduced spectrum is shown in the bottom panel of Figure 2. After comparing with the spectrum flow library, the spectral type of the primary star of CSTAR 055495 is preliminarily identified as G0. Based on the spectra, the effective temperatures of the primary stars are derived as 5848 K and 5848 K for CSTAR 036162 and CSTAR 055495, respectively. Both values are in agreement with temperatures derived from the color indices within the uncertainties.

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The spectroscopic observations of CSTAR 057775 were made by using the Magellan Echellette Spectrograph (MagE; Marshall et al. 2008), a moderate-resolution optical echellette of the 6.5 m Magellan I telescope at Las Campanas Observatory (LCO) in Chile, during the night of 2017 September 07 with the exposure time of 350 s. The slit was 10 arcsec long with a plate scale of 0.3 arcsec/pixel on the detector and the spectral coverage spans roughly from 320 to 1000 nm.

The data were reduced using a combination of the "mtools" package¹² and usual IRAF echelle routines, following standard procedures for bias correction, flat-fielding, wavelength calibration, and order stitching. We use the ULySS package¹³ (Koleva et al. 2009) to determine the stellar atmospheric parameters as T_eff = 6397 ± 5 K, logg = 3.788 ± 13 and [Fe/H] = −0.0175± 0.008 and derive the spectral type of the primary star as F6 V. The temperature value from the spectrum is in agreement with that determined from the color indices within the uncertainties. The spectrum of CSTAR 057775 is shown in Figure 3.

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A total of 121 occurrences (34 in the i band, 33 in the g band, and 54 in the r band) of minimum light of CSTAR 036162 are derived via parabolic fitting. The errors are estimated with the Monte Carlo method. Based on these data, the linear ephemeris is calculated as,

$$\begin{eqnarray}\mathrm{CSTAR}\,036162\,:\mathrm{Min}.I & = & {HJD}\ 2454571.34300(8)\\ & & +0\buildrel{\rm{d}}\over{.} 873777(1)\times E,\end{eqnarray} \tag{ 1 }$$

where the errors are shown in the parentheses. T₀ = HJD2454571.34300 is the time of a primary eclipse. Min I means the primary eclipse time. HJD refers to the heliocentric Julian date. E is the cycle number.

For CSTAR 055495, 38 times of primary eclipse in the i band, 68 in the r band, and 24 in the g band are determined. The linear ephemeris is derived as,

$$\begin{eqnarray}\mathrm{CSTAR}\,055495\,:\mathrm{Min}.I & = & {HJD}\ 2454584.43917(9)\\ & & +0\buildrel{\rm{d}}\over{.} 798004(6)\,\times \,E.\end{eqnarray} \tag{ 2 }$$

For CSTAR 057775, 77 times of primary eclipse in the i band, 157 in the r band, and 93 in the g band are obtained. A linear fit leads to,

$$\begin{eqnarray}\mathrm{CSTAR}\,057775\,:\mathrm{Min}.I & = & {HJD}\ 2454580.16095(8)\\ & & +0\buildrel{\rm{d}}\over{.} 4386203(1)\,\times \,E.\end{eqnarray} \tag{ 3 }$$

The Observed − Calculated (hereafter, O − C) diagrams of the three binary systems are shown in Figure 4. The data can be clearly divided into two groups in time due to a gap of observation. The linear solid lines show the straight line fits.

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For the three binaries, the photometric observations in the i band in 2008, along with those in the g and r bands in 2009, are used to deduce the photometric solutions with the Wilson–Devinney (W–D) code¹⁴ (Wilson 1971, 1979, 1990, 2012) and the Kurucz atmosphere model (Kallrath et al. 1998). The effective temperatures of the primary star of CSTAR 036162, CSTAR 055495, and CSTAR 057775 are derived from the spectra. The light curves of the binaries are averaged to 2000 points in each band. g₁ and g₂ as the input parameters of the W–D mode refer to the exponents in the bolometric gravity darkening law for the two components, respectively. For the convective envelopes of late-type stars, g₁ and g₂ are generally taken as 4 × β = 0.32 (β = 0.08; Lucy 1967; Rovithis & Rovithis-Livaniou 2007). The input parameters A₁ and A₂ refer to the bolometric albedos for reflection heating and re-radiation on the two components, respectively. The bolometric albedo is the local ratio of the re-radiated bolometric energy to receive bolometric energy. For convective envelopes, it is taken as 0.5 (Ruciński 1969). The parameters X₁, X₂, Y₁, and Y₂ refer to the coefficients in the bolometric limb-darkening law (van Hamme 1993). They are used in the computation of reflection in detail. Alencar & Vaz (1999) indicated that better results could be obtained by using a logarithmic law for cooler stars, so in this paper, we use the logarithmic law. The parameters x_1band, y_1band, x_2band and y_2band refer to the wavelength-specific limb-darkening coefficients. We also use the logarithmic law to calculate these four parameters (Claret 2004). The limb-darkening effect is analyzed by using the method of Qian et al. (2015). First, we set the values of the corresponding coefficients of the two components (X₁ = X₂, Y₁ = Y₂, x_1i = x_2i, and y_1i = y_2i) according to the effective temperatures of the primary components. Then, we derive the actual effective temperatures of the secondary stars. The values of the bolometric and limb-darkening coefficients of the secondary stars are redetermined based on the actual temperatures. At last, the values of the convergence parameters are obtained by using the W–D program.

As no radial-velocity curves are obtained for the three binaries, the photometric solutions are tested by adopting the assumed mass ratios of q = 0.1–3.0 with the interval step of 0.1 to look for the most probable mass-ratio values. With the assumed q values, we run the Differential Corrections main program (hereafter, DC) of the W–D code from mode 2 (detached configuration). After several iterations, the converged solutions are reached. Figure 5 shows the residuals between the synthetic and observed light curves versus the q values, where the most probable q values are obtained at the minimum residual values. We run the DC program again with the most probable q values and adjust the parameters freely, which include the q values, the temperatures of the secondary star (T₂), the orbital inclinations (i), the surface potentials of both components (Ω₁ and Ω₂), and the monochromatic luminosities of the primary star (L₁). The best-fitting solutions are obtained and listed in Table 3. Based on the solutions in this table, the syntheses of the observed light curves of the three binaries are shown in Figures 6–8, respectively. The results show that: (1) CSTAR 036162 has a detached configuration; (2) CSTAR 055495 has a semi-detached configuration with the secondary companion filling its Roche lobe, and (3) CSTAR 057775 has a contact configuration (Ω₁ = Ω₂).

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Table 3.  Photometric Solutions of the Three Sample Binaries

Parameter	CSTAR 036162	CSTAR 055495	CSTAR 057775
T1 (K)	5848	5848	6397
T2 (K)	3820 ± 6	4494 ± 5	6327 ± 8
q = m2/m1	0.354 ± 0.0009	0.946 ± 0.0006	0.301 ± 0.0008
i(°)	82.54 ± 0.04	68.38 ± 0.05	72.80 ± 0.03
Ω1	3.151 ± 0.002	4.029 ± 0.01	2.418 ± 0.002
Ω2	3.958 ± 0.006	⋯	⋯
${L}_{1}/{({L}_{1}+{L}_{2})}_{g}$	0.99 ± 0.02	0.68 ± 0.08	0.77 ± 0.07
${L}_{1}/{({L}_{1}+{L}_{2})}_{r}$	0.99 ± 0.02	0.76 ± 0.06	0.78 ± 0.04
${L}_{1}/{({L}_{1}+{L}_{2})}_{i}$	0.98 ± 0.02	0.72 ± 0.06	0.78 ± 0.04
${r}_{{1}_{,\mathrm{pole}}}$	0.3548 ± 0.0003	0.2622 ± 0.0006	0.4662 ± 0.0002
${r}_{{1}_{,\mathrm{point}}}$	0.3824 ± 0.0004	0.2956 ± 0.0009	⋯
${r}_{{1}_{,\mathrm{side}}}$	0.3665 ± 0.0003	0.2695 ± 0.0007	0.5041 ± 0.0002
${r}_{{1}_{,\mathrm{back}}}$	0.3750 ± 0.0004	0.2849 ± 0.0008	0.5330 ± 0.0002
${r}_{{2}_{,\mathrm{pole}}}$	0.1338 ± 0.0008	0.4114 ± 0.0013	0.2730 ± 0.0009
${r}_{{2}_{,\mathrm{point}}}$	0.1360 ± 0.0005	0.5673 ± 0.0014	⋯
${r}_{{2}_{,\mathrm{side}}}$	0.1344 ± 0.0005	0.4366 ± 0.0013	0.2860 ± 0.001
${r}_{{2}_{,\mathrm{back}}}$	0.1357 ± 0.0005	0.4648 ± 0.0014	0.3286 ± 0.002

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5.1. CSTAR 036162

5.2. CSTAR 055495

5.3. CSTAR 057775

We report a study of three eclipsing binaries: CSTAR 036162, CSTAR 055495, and CSTAR 057775, based on spectroscopic observations in 2016 and 2017 and multi-color time-series photometric observations from Dome A in 2008 and 2009. The geometrical configurations and the physical parameters of the three systems are derived.

• 1.  
  CSTAR 036162 has a short-period detached configuration with the mass ratio q = 0.354 ± 0.0009. Both components could be cool main-sequence stars. With the nuclear evolution of the components, the more massive one expands and probably experiences orbital shrinking owing to angular momentum loss. When the more massive star fills its Roche lobe, its matter flows through the L₁ into the Roche lobe of the less massive companion. At this time, the system becomes a semi-detached binary. The semi-detached configuration is hence probably the next stage of CSTAR 036162.
• 2.  
  CSTAR 055495 is a semi-detached binary system with the unusual q = 0.946 ± 0.0006, which indicates that CSTAR 055495 may be a rare binary system with the mass ratio close to one and the secondary component filling its Roche lobe. This means that a mass-ratio reversal just occurred, and CSTAR 055495 might be at a key evolutionary stage just after the mass-ratio reversal stage.
• 3.  
  CSTAR 057775 is an A-type contact binary with q = 0.301 ± 0.0008 and fill-out factor of f = 0.742(8). The geometrical configuration of CSTAR 057775 suggests that it is a short-period binary in which both components are in contact with each other and share a common convective envelope.

Our results suggest that continuous photometric observations in multiple bands from Dome A of Antarctica, together with follow-up spectroscopic observations, can help to obtain detailed photometric solutions of different types of eclipsing binaries, and hence shed light on our understandings of binary systems.

The authors are grateful to the anonymous referee for the valuable comments. This work is supported by the National Natural Science Foundation of China (NSFC) through grants 10673003 and 11373037, and the National Basic Research Program of China (973 Program 2014CB845700 and 2013CB834900). W.Z. hosts the LAMOST Fellowship, which is supported by Special Funding for Advanced Users, budgeted and administrated by Center for Astronomical Mega-Science, Chinese Academy of Science (CAMS). J.R.M. acknowledges support from an Australian Research Council DP14 grant.

Facilities: DOME A: CSTAR - , ATT (WiFeS) - , Magellan: Baade (Magellan Echellette Spectrograph) - .

Software: IRAF (Tody 1986, 1993), DAOPHOT: IRAF (Stetson 1987), PyWiFeS (Dopita et al. 2010, 2007), mtools: IRAF, UlySS (Koleva et al. 2009), W–D code 2013 version (Wilson 1971, 1979, 1990, 2012).