Orbital period correction and light curve modeling of the W-subtype shallow contact binary OW Leo

Contact binaries, both inside and outside our Galaxy, have been proved to be powerful tools for studying a wide spectrum of astrophysical problems. They usually consist of F, G and K type stars and the component stars are embedded in a common envelope. Due to the strong interactions between the component stars, the formation and evolution scenario for contact binaries are entirely and totally different from those of single stars, and still remain to be an open issue. A few years ago, many contact binaries were observed by the photometric method. However, only very few targets have spectral information due to the low efficiency of spectroscopic observations. Owe to the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) (Cui et al. 2012; Zhao et al. 2012), hundreds of thousands of contact binaries are provided with stellar atmospheric parameters, which makes it a better time to investigate contact binaries (Qian et al. 2017, 2018).

OW Leo, also named GSC 01443-00087 or NSVS 10352593, is a newly reported EW-type binary (Diethelm 2010). Its period was given as P = 0.325545 days in the International Variable Star Index (VSX) (Watson et al. 2006). The binary system was observed by the LAMOST project for two times, which were on 2013 March 24 and 2018 February 6. The low resolution spectra gave out two sets of stellar atmospheric parameters, which were listed in Table 1. There is no radial velocity curve published for the target and its light curves have not been analysed yet. In the present work, we will state our photometric observation on OW Leo in Section 2. Then, all available mid-eclipse times are gathered to investigate the orbital period changes of OW Leo in Section 3, and our observational light curves and the light curve from All- Sky Automated Survey for SuperNovae (ASAS-SN) are modeled to obtain its physical parameters in Section 4. Finally, the formation and evolution theories of OW Leo are discussed in Section 5.

The multi-color light curves of OW Leo were obtained on 2019 January 5 and 8 with the Xinglong 85cm optical telescope of National Astronomical Observatories, Chinese Academy of Sciences. The telescope was equipped with a 2K × 2K CCD Camera, and its field of view (FOV) was 32.8 square arc-minutes (Zhou et al. 2009; Zhang et al. 2018b). Four filters (B, V, R_C and I_C ) from Johnson-Cousins' filters systems were chosen for the observations and the observational images were processed with the Image Reduction and Analysis Facility (IRAF) (Tody 1986). UCAC4 546-051376 and UCAC4 546-051360 in the same field of view were chosen as the Comparison (C) star and Check (Ch) star since we used the differential photometry method to obtain the light variations of OW Leo. Their coordinates in J2000.0 epoch andmagnitudes in V band are listed in Table 2. Finally, we obtained the light variations of OW Leo and the observational light curves were plotted in Figure 1.

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As shown in Figure 1, we got the primary minimum (left of Fig. 1) and secondary minimum (right of Fig. 1) of the eclipsing binary system. Then, parabola fit was applied on the observed light minima curves and the mid-eclipse times were determined, which were listed in Table 3.

Orbital period variations are quite common among close binary systems due to the possible angular momentumloss (ALM) from binary systems or mass transfer between the primary or secondary stars (Zhang et al. 2018a; Liu et al. 2018). Thus, the O − C method was widely used in correcting orbital period or calculating orbital period variations of close binaries (Pi et al. 2017; He & Wang 2019). For analysis the orbital period of OW Leo, all available mid-eclipse times are gathered and listed Table 4. The O − C values listed in Column (4) of Table 4 are calculated with the linear equation:

$$\begin{eqnarray}&&{\rm{Min}}.I({\rm{HJD}})=2453175.509+{0}^{d}.325545\times E.\end{eqnarray} \tag{ 1 }$$

As displayed in Figure 2, linear fit is performed on the observed O − C curve, which means the orbital period of OW Leo should be corrected from 0.325545 days to 0.32554052 days. The new ephemeris is determined to be:

$$\begin{eqnarray}\begin{array}{lll}{\rm{Min}}.I & = & 2453175.5153(\pm 0.0002)\\ & & +{0}^{d}.32554052(\pm 0.00000002)\times E\end{array}\end{eqnarray} \tag{ 2 }$$

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The modeling of OW Leo's light curves have been left out since the eclipsing binary system was discovered.We will model its light curves with the Wilson-Devinney program (Wilson & Devinney 1971). The target have been observed by the LAMOST sky survey project for two times and the low resolution spectra show that OW Leo is a solartype binary system. The averaged temperature of 5665 K was assumed to the component star. The gravity-darkening coefficients are correspondingly assumed to be g₁ = g₂ = 0.32 (Lucy 1967), and the bolometric albedo coefficients are assumed to be A₁ = A₂ = 0.5 (Ruciński 1969), and the limb darkening coefficients are chosen accordingly (van Hamme 1993). The phased light curves are calculated from the linear ephemeris equation:

$$\begin{eqnarray}&&{\rm{Min}}.I({\rm{HJD}})=2458488.3337+{0}^{d}.32554052\times E.\end{eqnarray} \tag{ 3 }$$

4.1. Light Curves From Xinglong 85cm Telescope

As displayed in Figure 3, the observed light curves are EW-type. Thus, Mode 3 for contact binary, Mode 4 and Mode 5 for semi-contact binary are chosen to modeling the observational light curves. Since there is no radial velocity curve published, the q-search method is used to get the initial mass ratio (Zhou et al. 2018). Firstly, the temperature of 5665 K was assumed to the primary star (T₂), and the adjustable parameters are orbital inclination (i), modified dimensionless surface potential of the two component stars (Ω₁, Ω₂), mean surface temperature of the secondary star (T₂), bandpass luminosity of the two component stars (L₁, L₂). We then find that the light curves of OW Leo converged in Mode 3 and its mass ratio (M₂/M₁) should be larger than 1, which mean that OW Leo is a W-subtype contact binary system. Therefore, the temperature of 5665K is assumed to the secondary star (T₂). The corresponding q-search diagram are shown in Figure 4. Then, the initial mass ratio is given to be q = 3.05 and set as a free parameter to run the Wilson-Devinney program again. Finally, the physical parameter of the binary system are determined, which are listed in Table 5. The synthetic light curves are also plotted in Figure 3. It should be pointed out that we also try to set third light (l₃) as a free parameter, but the light contribution from a tertiary component is not detected.

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Table 5. Photometric Results of OW Leo

Parameter	Value
T2(K)	5665(assumed)
q (M2/M1)	3.05(± 0.05)
i(°)	68.2(± 0.1)
T1(K)	5885(± 5)
ΔT(K)	220(± 5)
L1/(L1 + L2) (B)	0.3169(± 0.0008)
L1/(L1 + L2) (V)	0.3041(± 0.0006)
L1/(L1 + L2) (Rc )	0.2981(± 0.0005)
L1/(L1 + L2) (Ic )	0.2937(± 0.0005)
r1(pole)	0.2731(± 0.0002)
r1(side)	0.2852(± 0.0003)
r1(back)	0.3220(± 0.0005)
r2(pole)	0.4540(± 0.0002)
r2(side)	0.4883(± 0.0003)
r2(back)	0.5157(± 0.0004)
Ω1 = Ω2	6.603(± 0.003)
f	12.8 %(±0.5 %)
Σω(O − C)2	0.0018

4.2. Light Curves From ASAS-SN

OW Leo was also observed by the ASAS-SN (Shappee et al. 2014; Jayasinghe et al. 2018) from 2013 January 25 to 2018 November 28. The data from the ASAS-SN was plotted in Figure 5(a). To modeling the data, we converted it to phased light curve. The light curve in Figure 5(b) was calculated based on the original orbital period P = 0.325545 days and the light curve in Figure 5(c) was calculated with the corrected orbital period P = 0.32554052 days. It is obviously that the orbital period correction is necessary. Then, the phased light curve in Figure 5(c) was also modeled with the Wilson-Devinney program, and the synthetic light curve was plotted with red line in Figure 5(c).

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The orbital period and light curves of OW Leo are investigated for the first time, which reveal that its orbital period should be corrected from P = 0.325545 days to P = 0.32554052 days. According to the photometric results listed in Table 5, we can conclude that OW Leo is a W-subtype shallow contact binary system with its mass ratio to be q = 3.05(5) and fill-out factor to be f = 12.8(5)%. The mass of the secondary star is estimated to be M₂ = 0.95(3) M_⊙ basing on its effective temperature of T₂ = 5665 K (Cox 2000). Then, the other absolute parameters of the two component stars are calculated and listed in Table 6. The orbital semi-major axis is calculated to be a = 2.15(± 0.02)R_⊙ according to the Kepler's third law.

Although research on contact binaries has a very long history, the formation and evolution theories of contact binaries are still incomplete. Webbink (1976) proposed that contact binaries are evolved from initially detached binary systems. The more massive component in a binary system expanded first and filled its critical Roche lobe, and then transfer masses to the less massive companion star through the inner Lagrangian point of the binary system. In recent years, more and more contact binaries have been reported to have additional components orbiting around the central binaries (Yang et al. 2019; Zhou & Soonthornthum 2019; Zhang et al. 2020). The additional components may be ejected from the center of initially multiple star system and pump out angular momentum from the multiple star system, and left out a tight binary system, which will evolve to a contact binary system finally, especially for the formation of M-type contact binaries (Goodwin et al. 2004; Qian et al. 2015). Based on the statistical research of stellar atmospheric parameters of EW-type binaries from the LAMOST, Qian et al. (2019) pointed out that the metal abundance of over 80% EW-type binaries are lower than the Sun, which means that they are old population stars. They may evolve from initially detached binary systems through nuclear evolution and angular momentum loss via magnetic braking.

According to the stellar atmospheric parameters in Table 1, we can see that OW Leo is a shallow contact binary with very low metal abundance. Thus, it may have not been contaminated by material from an additional component. It should be evolved from an initially detached binary system through a very long time of main sequence evolution. The absolute parameters of several more Wsubtype shallow contact binaries are collected and listed in Table 7. Their evolutionary status is shown in Figure 6. We can see that the less massive stars have already evolved away from the terminal-agemain sequence (TAMS), while most of more massive stars are still stay in the main sequence belt. For W-subtype shallow contact binaries, the more massive stars expand and fill the critical Roche lobe on its way evolving to the red giant branch (RGB), and transfer masses to the less evolved component stars. The transferred masses also filled the critical Roche lobe of the less massive star and formed the thin common envelope with the two component star embedded inside. Therefore, the less massive stars seem more evolved than the more massive components.

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This research was supported by the National Natural Science Foundation of China (Grant Nos. 11703080, 11703082 and 11873017), the Joint Research Fund in Astronomy (Grant No. U1931101) under cooperative agreement between the National Natural Science Foundation of China and Chinese Academy of Sciences, and the Yunnan Fundamental Research Projects (Grant No. 2018FB006). We acknowledge the support of the staff of the Xinglong 85cm telescope. This work was partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. Guo Shou Jing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.