ECLIPSING BINARIES FROM THE CSTAR PROJECT AT DOME A, ANTARCTICA

In the first step, periodic signals are extracted from each light curve. A bin size of five minutes has been adopted to filter out extremely high-frequency noises because CSTAR has a very short cadence. Periodic signals are recognized using three methods: Lomb–Scargle (Lomb 1976; Scargle 1982), Phase Dispersion Minimization (PDM; Stellingwerf 1978; Schwarzenberg-Czerny 1989), and Box Least Squares (BLS; Kovács et al. 2002). We set the range of period scan from 0.1 to 30 days for the PDM and BLS methods. Meanwhile, for the Lomb–Scargle method the lower limit is increased to 1.05 days. For each light curve, we calculate its Lomb–Scargle signal-to-noise ratio (S/N) R, PDM statistic Θ (see Stellingwerf 1978, Equation (3)), and Signal Detection Efficiency (SDE; see Kovács et al. 2002, Equation (6)). A false alarm probability (FAP) of 10⁻⁴ is assigned to the Lomb–Scargle method to obtain the power threshold ${{\sigma }_{{\rm LS}}}$. We set

$$\begin{eqnarray*}&&R={{S}_{{\rm LS}}}/{{\sigma }_{{\rm LS}}},\end{eqnarray*}$$

where ${{S}_{{\rm LS}}}$ is the power of the highest peak in the Lomb–Scargle periodogram. A higher R value indicates more significant periodic signal. Θ is between 0 and 1. A lower Θ value indicates a more significant periodic signal. SDE can reflect the effective S/N of eclipses. This has been discussed in detail by Kovács et al. (2002). We choose the criteria

$$\begin{eqnarray*}&&{{R}_{c}}=10,\;{{{\Theta}}_{c}}=0.85,\;{\rm SD}{{{\rm E}}_{c}}=6,\end{eqnarray*}$$

where the subscript "c" represents "criteria." The Lomb–Scargle, PDM, and BLS methods contribute 225, 107, and 244 variable candidates, respectively. Ninety-three of them are detected using two methods and 27 are detected by all the three methods. Therefore, there are 429 variable candidates in total when any one of the condition is met.

False positives come from four sources. The first source is diurnal variation. Though very weak after detrending, it still should be taken into consideration. Second, stars at the edges of the FOV have regular gaps because stars move in and out of the FOV repeatedly every day. This may cause additional periodic variations. Third, an exposure time of 20 or 30 s is too long for a bright variable star, which can pollute its neighborhood. A typical phenomenon is that they appear to have the same variations. Therefore, when two or more targets show nearly the same period, it is necessary to check if they are very close and if their light curves vary simultaneously. Additionally, a large plate scale of $15^{\prime\prime} \;{\rm pi}{{{\rm x}}^{-1}}$ may also produce false eclipses induced by a nearby non-variable star. Other sources of contamination include solar brightness or moonlight at some epochs and the occasional aurora, all of which can brighten the sky background. Images with high background have been discarded in the data reduction process. Therefore, such contaminations have little effect.

All variable stars are checked in three ways. Their positions, periods, and variable trends are compared. False positives are confirmed if any one of the following conditions is met.

• 1.  
  Distance less than 10 pixels to a saturated star.
• 2.  
  Period equals one Sidereal Day or diurnal harmonics.
• 3.  
  Variable trend resembles that of its neighborhood.

All remaining light curves after culling false positives are manually inspected to exclude variables with similar shapes as eclipsing binaries, e.g., γ Doradus, δ Scuti, RR Lyrae, etc. To check if there exist eclipsing binaries in other types of variable stars, we subtract the strongest period of each variable star and analyze the residuals using the same method described above. A detached RS Canum Venaticorum variable is found as shown in Figure 1.

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The visual inspection of variables is carried out by two groups of authors (M. Yang et al. and S. Wang et al.) independently. Eclipsing binaries are selected out and classified into four types according to their morphologies (Paczyński et al. 2006; Prša et al. 2011):

• 1.  
  Eclipsing Detached binary (ED)—neither component fills its Roche Lobe;
• 2.  
  Eclipsing Semi-detached binary (ESD)—only one component fills its Roche Lobe;
• 3.  
  Eclipsing Contact binary (EC)—both components fill their Roche lobes;
• 4.  
  Ellipsoidal variable (ELL)—low-inclination binaries with close ellipsoidal components.

ED light curves are nearly flat-topped with separate eclipses. ESD light curves are continuously variable with a large difference in depth between the primary and the secondary eclipses. Therefore, detached and semi-detached systems are easy to be recognized due to their distinct eclipses. However, for a contact system with indistinct ingress and egress points of the eclipses, visual inspection is not reliable. Challenges mainly come from δ Scuti variables and ELLs because both δ Scuti and ELL light curves exhibit sinusoidal variations. If a contact system appears with approximately equal primary and secondary eclipses, it is difficult to distinguish the EC light curve from the δ Scuti and ELL light curves. We adopt the methods of frequency spectrum analysis and the Locally Linear Embedding (LLE; Roweis & Saul 2000) technique to solve the problem.

The frequency spectra of ECs and δ Scutis are different. δ Scuti light curves exhibit variations due to both radial and non-radial pulsations of the star's surface. Therefore, the frequency spectrum of a δ Scuti usually contains more peaks caused by multi-mode pulsations. On the other hand, the frequency spectrum of an EC light curve contains only one strong signal and harmonics of the signal. For CSTAR data with a short cadence of ∼30 s, the harmonics are usually very weak. We calculate the frequency spectra of all sinusoidal variables using the Lomb–Scargle method from 0.025 day to 0.95 day for further reference.

ELL light curves exhibit sinusoidal variations due to the changing emitting area toward the observer. We adopt the LLE method proposed by Matijevič et al. (2012) to distinguish ECs and ELLs. LLE is a nonlinear dimensionality reduction technique. This method has been applied to KEPLER data to classify eclipsing binary light curves and has turned out to be successful. LLE can remember the local geometry of a higher-dimensional data set and reconstruct a lower-dimensional projection with the same local geometry. Therefore, light curves with similar features will stay adjacent to each other in the lower dimensional projection. We generate 1000 EC light curves and 1000 ELL light curves using the PHOEBE package, respectively. The amplitudes of these light curves are scaled to the [0, 1] interval. The light curves are sampled at 100 equidistant phases; in other words, each light curve can be treated as a point in a D = 100 dimensional space. To preserve the local geometry, every light curve is characterized by a linear combination of its k = 20 neighbors. We reduce the D = 100 dimensional space to a d = 2 dimensional space. The final two-dimensional LLE projection is shown in Figure 2. Each point represents a light curve sampled at 100 equidistant phases. Sampled EC light curves (red circles) are clustered in the red region, and sampled ELL light curves (blue circles) in blue region. Three light curves fall into the ELL region. They are listed in Table 1. The periods and ephemerides of the ELLs are derived in Section 4.

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Combining visual inspection, frequency spectrum analysis, and the LLE technique, eclipsing binaries are selected out and voted on by all members. Finally, 53 systems are classified into 24 EDs (45%), 8 ESDs (15%), 18 ECs (34%), and 3 ELLs (6%). Compared with other projects, the fractions of different types of eclipsing binaries from the University of New South Wales (UNSW) Extrasolar Planet Search are $43.1\%$ for EDs and ESDs, and $56.9\%$ for ECs (Christiansen et al. 2008); Kepler fractions are $58.2\%$ for EDs, 7% for ESDs, $21.7\%$ for ECs, $6.3\%$ for ELLs, and $6.8\%$ for uncertain types (Slawson et al. 2011). The longer observation time and unprecedented precision of Kepler make it sensitive to long-period EDs. Our result lies between the two projects.

For EDs and ESDs, we choose five principal parameters: the temperature ratio ${{T}_{2}}\;/\;{{T}_{1}}$, which determines the eclipse depth ratio; the sum of fractional radii ${{\rho }_{1}}+{{\rho }_{2}}$, which determines eclipse width; the eccentricity e and the argument of periastron ω in orthogonal forms $e\cdot {\rm sin} \omega$ and $e\cdot {\rm cos} \omega$, which determine the separation between primary and secondary eclipse; and the sine of inclination ${\rm sin} i$, which determines the eclipse shape. We generate 30,000 simulated light curves by randomly sampling the five parameters as a training set for EBAI. After 200,000 training iterations, a correlation matrix which can recognize parameters from eclipsing binary light curves is generated. We test the correlation matrix with 30,000 unknown light curves. The recognition results and the parameter error distributions are shown in Figure 3. All the parameters have been linearly scaled to the [0.1, 0.9] interval by EBAI. The ranges of the parameters are shown in Table 2 apjs510733t2.

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We fold the observed light curves to one period, normalize the flux and time, and fit the profiles with a bin size which is the same with the modeled light curves. Parameters are obtained rapidly by applying the trained EBAI matrix to the folded light curves, as shown in Tables 3 and 4. The light curve of CSTAR J183057.87-884317.5 only shows primary eclipses. However, it has been found as an ED system with a high radial velocity amplitude of 12 km s⁻¹ by Wang et al. (2014b). We list it in the ED catalog but do not calculate its parameters. Figure 4 illustrates some ED and ESD light curves. The left-hand panels show the star brightness in magnitudes during the whole observation season. The right-hand panels show the phased and binned light curves in relative flux. Periods and CSTAR IDs are given at the top of every left-hand panel.

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Table 3.  Parameters of Eclipsing Detached Binaries

CSTAR ID	mag	HJD	Period	Crowding	${{T}_{2}}/{{T}_{1}}$	${{\rho }_{1}}+{{\rho }_{2}}$	$e{\rm sin} \omega$	$e{\rm cos} \omega$	${\rm sin} i$
		(JD-2454500)	(days)
CSTAR J000116.84-874402.9	11.911 (±0.015)	51.595627 (±0.000812)	9.480642 (±0.000146)	0.045	0.994	0.076	0.051	0.126	1.000
CSTAR J022528.30-875808.9	13.580 (±0.033)	55.026981 (±0.002729)	16.129131 (±0.001444)	0.016	0.091	0.085	−0.382	0.295	0.999
CSTAR J031401.11-883253.1	14.491 (±0.070)	50.940662 (±0.001158)	1.208837 (±0.000021)	0.087	0.565	0.260	0.027	−0.003	1.000
CSTAR J033130.30-880424.4	13.997 (±0.050)	47.732536 (±0.002857)	1.444413 (±0.000062)	0.006	0.752	0.234	−0.117	0.000	0.993
CSTAR J061801.34-873953.9	13.371 (±0.031)	55.336460 (±0.017812)	6.048977 (±0.001605)	0.009	0.940	0.114	−0.040	0.003	0.998
CSTAR J062842.76-880241.7	12.336 (±0.017)	55.236904 (±0.000568)	7.249134 (±0.000062)	0.095	0.596	0.117	0.056	0.011	1.000
CSTAR J080846.28-880002.0	13.623 (±0.034)	50.397514 (±0.001443)	0.822784 (±0.000016)	0.006	0.574	0.423	0.005	0.004	0.945
CSTAR J083940.85-873902.3	12.174 (±0.016)	57.158970 (±0.001962)	7.164405 (±0.000241)	0.011	0.357	0.079	−0.256	0.063	0.999
CSTAR J090220.82-873741.0	12.355 (±0.017)	44.738434 (±0.004217)	1.627418 (±0.000089)	0.022	0.542	0.555	0.199	−0.023	0.943
CSTAR J095836.02-882359.9	12.785 (±0.020)	50.778557 (±0.001152)	2.065943 (±0.000035)	0.025	0.461	0.289	0.006	0.003	0.976
CSTAR J103232.73-882502.6	13.660 (±0.023)	53.738533 (±0.008547)	7.069140 (±0.000943)	0.015	1.045	0.109	0.138	−0.001	0.998
CSTAR J104016.05-872929.8	11.102 (±0.013)	49.466064 (±0.000481)	0.868841 (±0.000006)	0.032	0.821	0.425	−0.029	−0.001	0.948
CSTAR J130158.40-873956.3	8.984 (±0.004)	55.650978 (±0.000596)	5.800400 (±0.000059)	0.003	0.825	0.208	0.057	−0.002	0.998
CSTAR J150537.60-873551.6	12.345 (±0.016)	52.568558 (±0.001329)	7.450763 (±0.000322)	0.088	0.647	0.125	0.112	0.001	0.997
CSTAR J155705.55-873005.2	11.915 (±0.014)	51.797089 (±0.005051)	3.111666 (±0.000207)	0.004	0.500	0.230	−0.332	−0.011	0.993
CSTAR J155917.54-880042.5	14.146 (±0.056)	48.417747 (±0.015527)	6.852954 (±0.001552)	0.013	0.629	0.106	0.086	0.002	0.999
CSTAR J163136.82-874007.7	12.078 (±0.015)	58.014969 (±0.002532)	10.771624 (±0.000552)	0.006	0.988	0.061	0.054	−0.001	1.000
CSTAR J183057.87-884317.5	9.839 (±0.007)	53.714790 (±0.002772)	9.922610 (±0.000403)	⋯	⋯	⋯	⋯	⋯	⋯
CSTAR J193827.80-885055.9	12.884 (±0.021)	49.421947 (±0.001194)	6.752321 (±0.000111)	0.024	0.163	0.118	−0.139	−0.198	0.997
CSTAR J200218.84-880250.0	11.977 (±0.015)	62.606724 (±0.003508)	19.141005 (±0.001177)	0.038	0.739	0.059	0.577	−0.357	1.000
CSTAR J202830.07-874616.5	11.805 (±0.009)	51.365967 (±0.000346)	2.192940 (±0.000012)	0.000	0.417	0.340	0.196	−0.001	0.984
CSTAR J205410.67-890348.2	10.030 (±0.008)	51.062473 (±0.001411)	1.857557 (±0.000038)	0.059	0.400	0.419	0.066	0.004	0.939
CSTAR J224601.56-880459.2	13.823 (±0.040)	49.954193 (±0.003384)	7.760361 (±0.000409)	0.004	0.559	0.107	−0.013	0.005	0.999
CSTAR J235727.17-882454.5	12.396 (±0.017)	50.875061 (±0.002693)	6.199004 (±0.000262)	0.008	0.291	0.131	0.007	−0.002	0.997

Note. Columns 1–10 represent CSTAR ID, magnitude, the reference time of primary minimum, period, crowding, temperature ratio, the sum of fractional radii, the radial component of eccentricity, the tangential component of eccentricity, and the sine of inclination. J represents J2000.0. The errors of the physical parameters follow the distributions as shown in Figure 3.

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Table 4.  Parameters of Eclipsing Semi-detached Binaries

CSTAR ID	mag	HJD	Period	Crowding	${{T}_{2}}/{{T}_{1}}$	${{\rho }_{1}}+{{\rho }_{2}}$	$e{\rm sin} \omega$	$e{\rm cos} \omega$	${\rm sin} i$
		(JD-2454500)	(days)
CSTAR J074354.49-890737.3	12.538 (±0.018)	49.325817 (±0.000537)	0.797987 (±0.000006)	0.007	0.481	0.669	0.003	0.006	0.948
CSTAR J084028.89-884700.4	13.807 (±0.039)	52.206177 (±0.029051)	13.027298 (±0.004186)	0.001	0.828	0.723	0.001	−0.003	0.913
CSTAR J090359.29-883307.6	11.361 (±0.013)	49.491791 (±0.000177)	0.873754 (±0.000002)	0.000	0.596	0.677	0.000	0.000	0.871
CSTAR J093334.26-865501.1	12.676 (±0.022)	52.293953 (±0.057799)	4.427421 (±0.003756)	0.022	0.748	0.609	0.000	0.000	0.987
CSTAR J110803.52-870114.0	12.233 (±0.017)	49.716991 (±0.000752)	0.511559 (±0.000005)	0.018	0.506	0.615	0.066	0.021	0.915
CSTAR J122135.82-880014.5	12.172 (±0.016)	50.905312 (±0.000439)	1.892200 (±0.000011)	0.002	0.582	0.613	0.000	0.000	0.913
CSTAR J132349.26-881604.3	12.260 (±0.016)	51.587410 (±0.001441)	2.509739 (±0.000051)	0.003	0.835	0.689	0.000	0.000	0.907
CSTAR J220502.55-895206.7	13.070 (±0.023)	79.778481 (±0.003821)	1.988110 (±0.000091)	0.000	0.473	0.575	0.039	0.000	0.919

Note. Columns 1–10 represent CSTAR ID, magnitude, the reference time of primary minimum, period, crowding, temperature ratio, the sum of fractional radii, the radial component of eccentricity, the tangential component of eccentricity, and the sine of inclination. J represents J2000.0. The errors of the physical parameters follow the distributions as shown in Figure 3.

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For ECs, there is no handle on eccentricity and argument of periastron. Instead, the lobe-filling configuration of a contact system links the Roche model with the radii of the components. As a result, the photometric mass ratio q can be estimated. In order to describe the contact degree, the fillout factor F is given by Prša et al. (2011):

$$\begin{eqnarray}&&F=\frac{{\Omega}-{{{\Omega}}_{{{L}_{2}}}}}{{{{\Omega}}_{{{L}_{1}}}}-{{{\Omega}}_{{{L}_{2}}}}},\end{eqnarray} \tag{ 1 }$$

where Ω (see Wilson & Devinney 1971, Equation (1)) is the surface potential of the common envelope, ${{{\Omega}}_{{{L}_{1}}}}$ is the potential at the inner Lagrangian surface, and ${{{\Omega}}_{{{L}_{2}}}}$ is the potential at the outer Lagrangian surface. A star in a contact system will transfer mass to its companion through the the inner Lagrangian point ${{L}_{1}}$, or lose mass through the the outer Lagrangian point ${{L}_{2}}$.

From the above consideration, four principal parameters are chosen for EC: ${{T}_{2}}\;/\;{{T}_{1}}$, q, F, and ${\rm sin} i$. The network is trained on 20,000 simulated light curves for 1,000,000 iterations. We test the correlation matrix with 10,000 unknown EC light curves. The recognition results and the parameter error distributions are shown in Figure 5. We apply the correlation matrix to EC light curves of CSTAR. The parameters are given in Table 5. Figure 6 shows some EC light curves.

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Table 5.  Parameters of Eclipsing Contact Binaries

CSTAR ID	mag	HJD	Period	Crowding	${{T}_{2}}/{{T}_{1}}$	${{M}_{2}}/{{M}_{1}}$	Fillout	${\rm sin} i$
		(JD-2454500)	(days)
CSTAR J005240.76-891732.4	13.997 (±0.044)	51.531921 (±0.000272)	0.292963 (±0.000002)	0.006	0.941	0.287	0.898	0.959
CSTAR J031348.84-891511.7	13.047 (±0.023)	49.405579 (±0.000492)	0.344662 (±0.000002)	0.011	0.922	0.646	0.016	0.598
CSTAR J042011.85-882503.5	12.647 (±0.019)	55.389160 (±0.000478)	0.395481 (±0.000003)	0.001	1.008	1.012	0.842	0.714
CSTAR J051329.62-871942.6	11.939 (±0.016)	75.154015 (±0.000354)	0.384112 (±0.000003)	0.003	0.987	0.483	0.570	0.893
CSTAR J051503.40-893226.6	14.431 (±0.079)	49.452221 (±0.001148)	0.358253 (±0.000006)	0.002	0.954	0.272	0.953	0.910
CSTAR J061954.94-872047.5	12.399 (±0.019)	49.499104 (±0.001138)	0.491358 (±0.000008)	0.000	0.759	0.892	0.364	0.631
CSTAR J064047.15-881521.3	11.721 (±0.014)	49.455452 (±0.000166)	0.438606 (±0.000001)	0.003	0.988	0.849	0.856	0.936
CSTAR J071652.61-872856.4	13.472 (±0.035)	50.483288 (±0.000911)	0.383167 (±0.000005)	0.007	0.936	0.508	0.943	0.909
CSTAR J073412.18-874037.3	13.218 (±0.021)	50.181190 (±0.000760)	0.331216 (±0.000003)	0.000	0.858	0.531	0.984	0.828
CSTAR J084612.64-883342.9	11.997 (±0.015)	49.312592 (±0.000119)	0.267121 (±0.000000)	0.003	0.921	1.077	0.872	0.960
CSTAR J123242.99-872622.8	11.100 (±0.013)	49.395302 (±0.000284)	0.338527 (±0.000001)	0.003	0.975	1.256	0.973	0.983
CSTAR J124916.22-881117.6	13.834 (±0.040)	55.331085 (±0.000464)	0.352423 (±0.000002)	0.002	0.998	0.889	0.788	0.883
CSTAR J135318.49-885414.6	12.783 (±0.020)	49.365437 (±0.000142)	0.266899 (±0.000001)	0.004	0.978	1.087	0.922	0.959
CSTAR J142052.04-881433.4	12.599 (±0.018)	49.326588 (±0.000607)	0.400883 (±0.000003)	0.000	0.970	0.979	0.254	0.498
CSTAR J142901.63-873816.2	13.542 (±0.032)	55.409655 (±0.000463)	0.348147 (±0.000003)	0.004	0.699	1.293	0.532	0.830
CSTAR J181735.42-870602.2	10.819 (±0.012)	49.649178 (±0.002350)	0.352821 (±0.000012)	0.001	0.703	1.398	1.082	0.796
CSTAR J195026.13-874450.7	12.832 (±0.021)	49.474827 (±0.000413)	0.416432 (±0.000002)	0.002	1.022	0.792	1.017	0.879
CSTAR J223707.30-872849.9	11.624 (±0.014)	50.040791 (±0.001524)	0.848425 (±0.000017)	0.005	0.910	1.058	1.014	0.959

Note. Columns 1–9 represent CSTAR ID, magnitude, the reference time of primary minimum, period, crowding, temperature ratio, mass ratio, fillout factor, and the sine of inclination. J represents J2000.0. The errors of the physical parameters follow the distributions as shown in Figure 5.

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To estimate the primary eclipse mid-times, a simple linear increment is applied with known eclipse epoch and period. Then, the whole light curve is divided into many small segments. Each segment centers around a primary eclipse mid-time. We exclude segments with fewer points because such segments can reduce the fit precision. To obtain the eclipse template, we fold all of the remaining segments. The template is fit using the following function (see Rappaport et al. 2013, Equation (2)):

$$\begin{eqnarray}&&f=\alpha {{\left( t-{{t}_{0}} \right)}^{2}}+\beta {{\left( t-{{t}_{0}} \right)}^{4}}+{{f}_{0}},\end{eqnarray} \tag{ 2 }$$

where f is the eclipse flux, f₀ is the minimum flux, t is the eclipse time, and t₀ is the eclipse mid-time. Observed mid-times are obtained by comparing each segment with the theoretical template. All the other parameters except the eclipse mid-time are fixed to be the same as the template when comparing. A linear fit is applied to all of the fitted mid-times. The differences between the fitted mid-times and their linear trend are ETVs. The same processes are applied to secondary eclipses to derive secondary ETVs.

The relationship between the primary and the secondary ETVs for a binary system may be correlated or anti-correlated. The correlation can be explained with a tertiary companion (Conroy et al. 2014) and the anti-correlation may be attribute to sunspots (Tran et al. 2013). However, when observed ETVs are less than one cycle, it is necessary to consider the probability of mass transfer. Conroy et al. (2014) adopt a Bayesian Information Criterion to distinguish between the two cases.

To check the relationship between the primary and the secondary ETVs, we choose a similar method as for searching planets (Steffen et al. 2012). ETVs are fitted using the following function (see Ming et al. 2013, Equation(2)):

$$\begin{eqnarray}&&f=A{\rm sin} \left( \frac{2\pi t}{P} \right)+B{\rm cos} \left( \frac{2\pi t}{P} \right)+Ct+D,\end{eqnarray} \tag{ 3 }$$

where A, B, C, and D are model parameters and P is the test period. P is increased from 20 to 100 days with a step of 0.1 day. The degree of correlation is estimated by

$$\begin{eqnarray}&&{\Xi}\left( P \right)=\frac{{{A}_{p}}{{A}_{s}}}{{{\sigma }_{{{A}_{p}}}}{{\sigma }_{{{A}_{s}}}}}+\frac{{{B}_{p}}{{B}_{s}}}{{{\sigma }_{{{B}_{p}}}}{{\sigma }_{{{B}_{s}}}}},\end{eqnarray} \tag{ 4 }$$

where the subscript "p" represents "primary" and "s" represents "secondary"; ${{\sigma }_{A}}$, ${{\sigma }_{B}}$, ${{\sigma }_{C}}$, and ${{\sigma }_{D}}$ are the uncertainties of A, B, C, and D. The maximum $|{\Xi}|$ is adopted, which represents the degree of correlation. Positive Ξ represents correlation and negative Ξ represents anti-correlation. To confirm correlated ETVs, we calculate the FAPs by a bootstrap randomization process: the ETVs are randomly scrambled 10⁴ times to obtain the corresponding ${\Xi}_{{\rm max} }^{{\prime} }$. The proportion of ${\Xi}_{{\rm max} }^{{\prime} }$ larger than ${{{\Xi}}_{{\rm max} }}$ represents the FAP. Induced periods are calculated to exclude the effect of sampling cadence. Finally, two systems pass the FAP criteria of 10⁻³. CSTAR J084612.64-883342.9 has a FAP lower then 10⁻⁴ and CSTAR J220502.55-895206.7 has a FAP of about ${{10}^{-3.4}}$. Qian et al. (2014) also claimed that a third body may exist around CSTAR J084612.64-883342.9.

Figure 7 shows correlated ETVs of CSTAR J220502.55-895206.7 and Figure 8 shows anti-correlated ETVs. For a correlated system, we sum its primary and secondary ETVs and divide the sum by two as the synthetic ETV of the binary system. If there is only a primary eclipse or only a secondary eclipse in one orbital period, then the ETV of the available eclipse is approximated as the synthetic ETV directly. To derive the parameters of the third companion, the synthetic ETV is fitted using a triple-star model (Rappaport et al. 2013; Conroy et al. 2014):

$$\begin{eqnarray}\begin{array}{rcl} {\rm ETV} & = & A\left[ {{\left( 1-e_{3}^{2} \right)}^{1/2}}{\rm sin} {{u}_{3}}\left( t \right){\rm cos} {{\omega }_{3}} \right. \\ {} & {} & +\left. \left( {\rm cos} {{u}_{3}}\left( t \right)-{{e}_{3}} \right){\rm sin} {{\omega }_{3}} \right], \\ \end{array}\end{eqnarray} \tag{ 5 }$$

where

$$\begin{eqnarray}&&{{u}_{3}}\left( t \right)={{M}_{3}}\left( t \right)+{{e}_{3}}{\rm sin} {{u}_{3}}\left( t \right),\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{{M}_{3}}\left( t \right)=\left( t-{{t}_{0}} \right)\frac{2\pi }{{{P}_{3}}},\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{{A}_{{\rm LTTE}}}=\frac{{{G}^{1/3}}}{c{{\left( 2\pi \right)}^{2/3}}}\left[ \frac{{{m}_{3}}}{m_{123}^{2/3}}{\rm sin} {{i}_{3}} \right]P_{3}^{2/3},\end{eqnarray} \tag{ 8 }$$

where subscript "3" represents the third companion, A is the amplitude, e₃ is eccentricity, P₃ is orbital period, ${{u}_{3}}\left( t \right)$ is eccentric anomaly, ${{M}_{3}}\left( t \right)$ is mean anomaly, i₃ is inclination, ${{\omega }_{3}}$ is argument of periastron, and m₁₂₃ is the mass of the whole system. The parameters we choose to give are A, e₃, P₃, and ${{\omega }_{3}}$. We fix the period corresponding to the maximum Ξ. Other parameters are changeable. For a more reliable fit, we choose the Markov Chain Monte Carlo method instead of the Levenberg–Marquardt algorithm. The results are shown in Table 6.

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Eclipsing binary parameters are given in Tables 3–5. The distributions of the physical parameters (see Table 2) are shown in Figure 9. Because samples in this paper are limited, we use a large bin size to test some typical characteristics.

For detached and semi-detached systems, the eclipse depth ratio reflects the temperature ratio. In equal depth eclipses, its value is one. The temperature ratios of the EDs and ESDs in this paper center around a value lower than one. Prša et al. (2011) explain that it is because the orbital eccentricity and star radii can affect the eclipse depth, thus increasing the scatter when the temperature ratio approaches one. The inclinations are close to 90° for detached and semi-detached systems. This is because eclipses can only be seen in the edge-on geometrical configuration when the two components are not very close. The sum of the fractional radii distribute around 0.1 for EDs and 0.6 for ESDs.

What is interesting for EDs and ESDs is their eccentricity distribution. Most of the eccentricities are close to zero. However, the highest eccentricity can reach 0.679 (CSTAR J200218.84-880250.0). Hut (1981) analyzes the tidal evolution of binaries and concludes that the timescale of circularization can be a relatively slow process. Mazeh (2008) plots the eccentricities as a function of the orbital periods using all 2751 binaries from the official IAU catalog of spectroscopic binaries (SB9). He derives an "upper envelope" to constrain the binary eccentricity (see Mazeh 2008, Equation (4.4)):

$$\begin{eqnarray}&&f\left( P \right)=E-A{\rm exp} \left( -{{\left( pB \right)}^{C}} \right),\end{eqnarray} \tag{ 9 }$$

where $E=0.98,A=3.25,B=6.3$, and C = 0.23. The EDs and ESDs in this paper are all below the upper envelope as shown in Figure 11. Two detached systems (CSTAR J200218.84-880250.0 and J022528.30-875808.9) at the upper right of Figure 11 have longer periods and larger eccentricities. Such systems have experienced less of the circularization process. Therefore, they are important to investigate how the circularization process can affect the binary components by comparing high-eccentricity binaries with circular binaries (Shivvers et al. 2014).

For contact systems, the two lobe-filling components can transfer mass to each other through the inner Lagrangian point. They can easily reach a thermal contact because of the common envelope. Therefore their temperature ratios center around one as shown in Figure 9(a). The relatively larger size of the Roche lobe also relax the limitation of edge-on geometrical requirement. ECs with lower inclinations can be detected as shown in Figure 9(b). The photometric mass ratios of ECs peak at 1. The fillout factors for the ECs are not roughly uniform because overcontact systems and close-to-contact systems contribute to the peak at 1.

Many CSTAR phased light curves of ECs and ESDs appear different maxima in brightness as shown in Figure 12. These light curves have been phased and binned to 5000 equally spaced points. Such a phenomenon is called the O'Connell effect (O'Connell 1951; Davidge & Milone 1984). The O'Connell Effect can be quantitatively expressed by measuring the difference between the two out-of-eclipse maxima

$$\begin{eqnarray}&&{\Delta}m={{m}_{{\rm II}}}-{{m}_{{\rm I}}},\end{eqnarray} \tag{ 10 }$$

where ${{m}_{{\rm I}}}$ and ${{m}_{{\rm II}}}$ are the peak magnitude after primary minimum and secondary minimum, respectively. To derive ${{m}_{{\rm I}}}$ and ${{m}_{{\rm II}}}$, we fold each light curve with its orbital period and fit the parts centered around each maximum using Equation (2).

Table 7 presents the contact and semi-detached systems with $|{\Delta}m|$ greater than 0.01. Nearly half of the contact systems are listed in this table. Therefore, the O'Connell Effect is common among eclipsing binary systems. The reasons for O'Connell effect are still debatable. Mullan (1975) proposed that large toroidal magnetic fields may be generated because of enforced rapid rotation in deep convection zones of contact binaries. The toroidal magnetic fields can cause active low-temperature zones, namely, spots. The spots can be used to explain the reason for the O'Connell effect. However, not all the ESDs have deep convection zones like the ECs. Instead, they may have hot spots because of mass transfer. In addition, the O'Connell effect can also be found in some EDs. Davidge & Milone (1984) have discovered that the O'Connell effect of detached systems is significantly correlated with the color index. Therefore, the O'Connell effect may be caused by more than one mechanism. More eclipsing binaries with a different color index are needed to study it.

Table 7.  Contact and Semi-detached Systems with the O'Connell Effect

CSTAR ID	${\Delta}m$	Type	CSTAR ID	${\Delta}m$	Type
	(mag)			(mag)
CSTAR J031348.84-891511.7	0.015	EC	CSTAR J061954.94-872047.5	0.036	EC
CSTAR J071652.61-872856.4	−0.016	EC	CSTAR J073412.18-874037.3	0.015	EC
CSTAR J084612.64-883342.9	−0.022	EC	CSTAR J124916.22-881117.6	0.015	EC
CSTAR J135318.49-885414.6	0.023	EC	CSTAR J142901.63-873816.2	0.024	EC
CSTAR J181735.42-870602.2	−0.019	EC	CSTAR J223707.30-872849.9	0.017	EC
CSTAR J110803.52-870114.0	0.030	ESD	CSTAR J132349.26-881604.3	0.037	ESD
CSTAR J220502.55-895206.7	0.022	ESD	⋯	⋯	⋯

Note. ${\Delta}m={{m}_{{\rm II}}}-{{m}_{{\rm I}}}$, where ${{m}_{{\rm I}}}$ is the peak magnitude after primary minimum and ${{m}_{{\rm II}}}$ is the peak magnitude after secondary minimum.

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ETVs are useful for studying the apsidal motion, mass transfer and loss, solar-like activities in late-type stars, light-time effect of a third companion, etc. They are helpful in understanding the formation and evolution of binary systems. The light curves of short-period binaries from Antarctica are available for tens of days thanks to the polar nights. Therefore, their ETVs are more continuous.

We only calculate ETVs for semi-detached and contact binaries. The spin–orbit transfer of angular momentum (Applegate 1992) does not create observable signals because their orbital periods are very short and the best precision of our ETVs is one minute, as shown in Figure 7. Apsidal motion is ignored because the eccentricities of semi-detached and contact binaries are close to zero.

Systems with potential large spots are shown in Figure 8. For each system, we can see obvious anti-correlation between the primary and the secondary eclipses. We find two eclipsing binary systems with a potential third body: CSTAR J084612.64-883342.9 and CSTAR J220502.55-895206.7. Recently, Qian et al. (2014) also claimed that CSTAR J084612.64-883342.9 is a triple system and derived the parameters of the third body with more observations (see Qian et al. 2014, Table 5). In this paper, we analyze the other system CSTAR J220502.55-895206.7. The ETVs of CSTAR J220502.55-895206.7 are given in Figure 7. The parameters of the close-in third body are given in Table 6. The orbital period of the third body is 25.36 days, indicating a close distance from the binary. Because the mass of the third companion and the orbital inclination are coupled in the amplitude, we cannot discern the nature of the third companion.