First photometric study of a short-period detached eclipsing binary NSVS 10441882

New Astronomy 70 (2019) 1–6

Contents lists available at ScienceDirect

New Astronomy journal homepage: www.elsevier.com/locate/newast

First photometric study of a short-period detached eclipsing binary NSVS 10441882

T

Zhang Bin ,a,b, Qian Sheng-Banga,b,c,d,e,f, Liu Nian-Pingc,d,e, Zhi Qi-Juna,b, Zhu Li-Yingc,d,e, Dong Ai-Juna,b, Jiang Lin-Qiaog ⁎

a

School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550001 China Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University, Guiyang 550001, China c Yunnan Observatories, Chinese Academy of Sciences (CAS), Kunming, P. O. Box 110, 650216 China d Key Laboratory of the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, P. O. Box 110, 650216 China e University of Chinese Academy of Sciences, Yuquan Road 19#, Sijingshang Block, Beijing, 100049 China f Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, 100012, China g School of Physics and Electronic Engineering, Sichuan University of Science and Engineering, Zigong 643000, China b

ARTICLE INFO

ABSTRACT

Keywords: Binary Eclipsing binary Light curve Orbital period

NSVS 10441882 is a newly discovered eclipsing binary system with strong magnetic activity and an orbital period of ∼ 0.5166 days. In order to study this eclipsing binary system, we analyzed its first four-color (BVRcIc) light curves. The observed light curves were asymmetric, so we used the 2013 version of the Wilson–Devinney (W–D) program with cool star-spots to analyze these data. We discovered that NSVS 10441882 is a detached total eclipsing binary system with an orbit inclination of 85°.34 ± 0.07 and a mass ratio of q = 0.94 ± 0.03. Based on the CCD times of the light minima according to our observations and those reported previously, the orbital period changes of NSVS 10441882 were studied using the traditional O–C method for the first time. The O–C diagram of the target exhibited a cyclic oscillation with a period of 16.7 ± 0.20 years and an amplitude of 0.00349 ± 0.00029 days, probably due to the presence of an unseen third body. If we assume that the total mass of NSVS 10441882 is 1.3M⊙ (according to our calculated results for the average color index and mass ratio), then the mass of the third body is no less than 0.12 ± 0.01 M⊙. Moreover, the orbital evolution of the central system will be accelerated due to the presence of this additional component.

1. Introduction Detached eclipsing binaries (DEBs) with similar components are important samples for measuring the fundamental parameters (such as the radius, mass, and luminosity) of stars (Becker et al., 2008), and these parameters provide key information to help understand the formation, evolution and activity of stars. For example, for the low-mass DEBs (less than 1 M⊙), the stellar structure models have difficulty accurately predicting the radii and masses of these stars due to the inadequate understanding of their interior structures and inflation mechanisms (Ribas, 2006; Morales et al., 2010; Davenport et al., 2013). In addition, the EW-type binaries (EWs) are formed from the DEBs, so we may be able to understand the formation and evolution of these shortperiod EWs by studying their progenitors. Unfortunately, few DEBs have been studied well compared with the number of eclipsing binaries that exist in our universe (Rucinski, 2002), where some of familiar

⁎

members include CM Dra (Metcalfe et al., 1996; Morales et al., 2009), CU Cnc (Ribas, 2003; Qian et al., 2012; Wilson et al., 2017), YY Gem (Torres and Ribas, 2002; Butler et al., 2015), GU Boo (López-Morales and Ribas, 2005; Windmiller et al., 2010), BW3 V38 (Maceroni and Rucinski, 1997; Maceroni and Montalbán, 2004), and GJ 3236 (Irwin ̆ et al., 2009; Smelcer et al., 2017). Due to the development of technology and Sky Surveys throughout the world, such as the WFCAM Transit Survey (Nefs et al., 2013), NSVS (Woźniak et al., 2004), LAMOST (Wu et al., 2011; Luo et al., 2015), and Kepler Mission (Shan et al., 2015), more DEBs have now been discovered. More importantly, many eclipsing binaries that formed with close-in tertiary components have also been discovered (Qian et al., 2013a; 2013b). Using data released by LAMOST, recent statistical studies suggest that some EWs with high metallicity may be formed via the action of the third body, which could explain the existence of EWs below the period limit (Qian and Zhang, 2015a; Qian et al., 2017a;

Corresponding author. E-mail address: [email protected] (Z. Bin).

https://doi.org/10.1016/j.newast.2018.12.005 Received 20 November 2018; Received in revised form 11 December 2018; Accepted 21 December 2018 Available online 27 December 2018 1384-1076/ © 2018 Elsevier B.V. All rights reserved.

New Astronomy 70 (2019) 1–6

Z. Bin et al.

2018). As discussed by Liu et al. (2015), the existence of additional components may be a common phenomenon in close binaries, and these multi-body candidates have been discovered using the O–C method, such as V1104 Her (Liu et al., 2015), V776 Cas (Zhou et al., 2016), and V502 Her (Zhao et al., 2018). Recently, this method has also been used to detect possible exoplanets and brown dwarf stars around close binaries (Qian et al., 2010; Bruch, 2014; Han et al., 2017a). NSVS 10441882 (1SWASP J133024.89+134932.0, V0642 Vir) was first reported in 2008 by Hoffman et al. (2008) as a questionable candidate because it was difficult to determine the binary type to which it belongs based on the light curve (LC) shape alone. Observations of the CCD photometric LCs, spectrum observations, and radial velocity curves have not been reported previously. According to the color index results calculated based on 2MASS (Cutri et al., 2003), the average spectral type of NSVS 10441882 was calculated as K5. In the present study, we analyzed the period changes in NSVS 10441882 for the first time. We discovered a short-period oscillation in the O–C diagram for NSVS 10441882. In addition, the first photometric solutions for the target were obtained by using the Wilson–Devinney (W–D) code. Finally, the orbital parameters of the third body and the evolutionary states of this target were investigated.

Fig. 1. LCs obtained for NSVS 10441882 in the BVRcIc-bands during 2011 at Xinglong Station. Different symbols refer to the data observed on different nights.

2. Observations and data reductions

Table 2) were observed using the 85 cm telescope at the Xinglong Station of the National Astronomical Observatories of the Chinese Academy of Sciences, and the other two (2458142.3753 and 2458207.2155) were observed using the 60 cm and 1.0 m telescopes at the Yunnan Observatories, respectively. Second, we calculated the O–C values for these data by using the following linear ephemeris:

New LCs were obtained for NSVS 10441882 in four bands (BVRcIc) on March 28, and April 4, 2011, by using the 1024 × 1024 PI1024 BFT CCD camera attached to the 85 cm telescope at the Xinglong Station of the National Astronomical Observatories of the Chinese Academy of Sciences (Liu et al., 2011). The field of view for this camera measures 16. 5 × 16. 5 and its filter system is a standard Johnson–Cousin–Bessel multi-color photometric system (Zhou et al., 2009). The coordinates of the stars are listed in Table 1. The integration times were 50 s for the Bband, 40 s for the V-band, 30 s for the Rc-band, and 30 s for the Ic-band. More than 920 CCD images were obtained over two nights and they were all reduced by using the aperture photometric package PHOT of IRAF (Zhang et al., 2018a). The phases of the LCs were calculated using the following equation:

Min. I (HJD) = 2454538.782 + 0d . 51664433 × E .

All of the original data and their O–C values are listed in Table 2. We then fitted these data using a least-squares method. Two methods were used in our analysis: quadratic ephemeris and sine function. The best fitting curve is plotted in the upper panel in Fig. 2and the corresponding residuals are plotted in the bottom panel. Fig. 2 shows that the results obtained by parabola fitting were not adequate. In fact, the fitting residual after parabola fitting was 3.50 × 10 5, whereas the sine function for this value was 2.30 × 10 5 . Thus, the fitting result obtained by the sine function was treated as our final solution. In our analysis, weights of 1/σ2 were assigned to the data, where σ is the error for the eclipse times (Liu et al., 2018). The final ephemeris was obtained as:

(1)

Min. I (HJD) = 2, 455, 656.27877 + 0d . 51664433 × E

(see Fig. 1). It should be noted that the differences in magnitude shown in Fig. 1 were calculated by using the values measured by IRAF between the variable star and the comparison star. The LCs between the comparison star and check star are also shown in Fig. 1, where these flat curves suggest the authenticity of the changes in the LCs for NSVS 10441882.

Min. I (HJD ) = 2454538.78027(± 0.00022) + 0d . 516644401(± 0.000000669) × E + 0.00349( ±0.00029)sin[0. 0305( ±0.0001) × E + 167. 96( ± 6. 44)]

3. Analysis of the orbital period changes

According to the new ephemeris, the sinusoidal term indicated a cyclic variation with a period of 16.7 years and an amplitude of 0.00349 days. This period was calculated using the formula: P3 = (360°/ω × Porb), where ω = 0.0305 is the frequency and Porb = 0.51664433 days is the orbital period of the binary system.

Due to the deep and symmetric eclipses of DEBs, we can obtain the individual minimum light times of their mid-eclipses with an error of only a few seconds (Wolf et al., 2016). The variations in the orbital periods of eclipsing binaries are usually studied based on high-precision eclipse times obtained during long-term observations, where this traditional approach is also called the O–C method. First, we collected all of the eclipse times for NSVS 10441882, including four light minima times determined from our observations. Two of the four light minima times (2455649.3049 and 2455656.2788l see

4. Photometric solutions obtained with the W–D program In order to obtain the orbital parameters for NSVS 10441882, we used the 2013 version of the W–D program to analyze its LCs (Van Hamme, 1993; Wilson, 2012; Wilson and Devinney, 1971). According to the results calculated for the average color index, the temperature of the primary component of the system was set as T1 = 4240 K (Cox, 2000). In addition, the bolometric albedo and gravity-darkening coefficients for both components were fixed and assigned the same value, i.e., A1 = A2 = 0.5 for late-type stars with a convective envelope (Rucinski, 1969; Zhang et al., 2014) and g1 = g2 = 0.32 according to the stellar temperatures given by Lucy (1967). The adjustable parameters M comprised the mass ratio q ≡ M2 , orbital inclination i, mean

Table 1 Coordinates of NSVS 10441882,comparison, and check stars. Stars

αj2000 h

δj2000 m

s

NSVS 10441882

13 30 24 .89

Comparison

13h30m15s.14

Check

13h29m56s.42

(2)

+ 13 49 32 . 0 + 13 55 11 . 3 + 13 56 12 . 5

1

2

New Astronomy 70 (2019) 1–6

Z. Bin et al.

Table 2 (O C ) values of the light minima for NSVS 10441882. HJD(2450000+) 2639.34 4524.5729 4538.782 4882.8642 4891.9068 5629.9301 5649.3049 5656.2788 5688.8263 6000.8827 6073.7288 6444.6774 6444.6774 6444.6808 6832.4199 6846.3698 8142.3753 8207.2155

Error 0.00003 0.0007 0.0012 0.0002 0.00014 0.00011 0.0002 0.0002 0.0005 0.0002 0.0003 0.0003 0.00023 0.00012 0.00014 0.00011

Epoch

Min.

Method

−3676.5 −27.5 0 666 683.5 2112 2149.5 2163 2226 2830 2971 3689 3689 3689 4439.5 4466.5 6975 7100.5

II II I I II I II I I I I I I I II II I II

CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD

Filter R V V V BVRcIc BVRcIc V V V B V R R R RI VRI

(O–C)

Reference

0.0009 −0.0014 0.0000 −0.0029 −0.0016 −0.0047 −0.0040 −0.0049 −0.0060 −0.0028 −0.0035 −0.0055 −0.0055 −0.0021 −0.0046 −0.0041 −0.0009 0.0004

(1) (2) (3) (3) (3) (4) Present Present (4) (5) (5) (6) (6) (6) (1) (1) Present Present

paper paper

paper paper

(1) http://var2.astro.cz/ocgate/ ; (2) Zasche et al., 2011 (3) Diethelm, 2009; (4) Diethelm, 2011; (5) Diethelm, 2012; (6) Diethelm, 2013.

temperature of the secondary component T2, monochromatic luminosity of the primary L1B, L1V, L1R c , and L1Ic , and the dimensionless potentials of the two components Ω1 and Ω2 (Zhang et al., 2015). There was no mass ratio according to the spectroscopic observations, so a q-search method was used, where the aim of this method is to search for the best fitting value of the mass ratio, before treating it as an adjustable parameter to obtain the final photometric solution for the binary system (Zhang et al., 2017b). We tested different fitting models in the W–D program and the final solutions converged to a detached model. We searched for primal mass ratios ranging from 0.3 to 2.0, and a series of photometric solutions was considered. The final q-search results are plotted in Fig. 3 where the lowest value was at q = 0.90 . After inputting the mass ratio value obtained by the q-search method and setting it as an adjustable parameter, we found that the fitting curves were still not adequate. Thus, for this particular case where the observed LCs were asymmetric, the cool star-spot model was employed

to get better results. The cool star-spot model can be described by four parameters. In general, the spot radius and spot temperature are strongly correlated and the temperature is a constant for a given spot, so it is not necessary to consider all of these parameters. A series of converged results was obtained by adjusting these parameters. We found that one spot on the primary component and another on the second component could obtain a better fit (with the minimum residuals). In order to check the existence of the third light in the system, we tested the effect of adding the third light in our calculations. However, the contribution of the third light to the overall luminosity was very small and it could be ignored, which implies that the tertiary companion may be a faint and cool object in a similar manner to V0474 Cam (Guo et al., 2018). The best photometric elements with and without cool star-spots are listed in Table 3. In addition, the theoretical LCs computed with cool star-spots are shown in Fig. 4. The geometrical structure of the system is shown in Fig. 5.

Fig. 2. The upper panel shows the fitting results obtained using different methods and the bottom panel shows the residuals with Eq. (3). 3

New Astronomy 70 (2019) 1–6

Z. Bin et al.

Fig. 3. q-search curve obtained for NSVS 10441882. The ordinate (∑) represents the fitting residuals under each fixed mass ratio.

Fig. 4. Observed (open circles with different colors) and theoretical (black solid lines) LCs with cool star-spots for NSVS 10441884. The fitting residuals in different bands are displayed in the bottom panel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 3 Photometric solutions obtained for NSVS 10441882. Parameters

Without spot Photometric elements

Errors

g1 = g2 A1 = A2 T1(K) q T2(K) i(°) L1/(L1 + L2)(B ) L1/(L1 + L2)(V ) L1/(L1 + L2)(R c ) L1/(L1 + L2)(Ic ) Ω1 Ω2 r1(pole) r1(point) r1(side) r1(back) r2(pole) r2(point) r2(side) r2(back) θs(°)

0.32 0.50 4240 0.930 4280 87.83 0.5288 0.5265 0.5249 0.5210 4.3883 5.1164 0.2863 0.3086 0.2930 0.3025 0.2263 0.2350 0.2291 0.2333

Assumed Assumed Assumed ± 0.035 ±5 ± 0.28 ± 0.0041 ± 0.0036 ± 0.0033 ± 0.0031 ± 0.0431 ± 0.1452 ± 0.0011 ± 0.0012 ± 0.0011 ± 0.0011 ± 0.0100 ± 0.0120 ± 0.0106 ± 0.0115

With spot Photometric elements 0.32 0.50 4240 0.937 4209 85.34 0.5456 0.5425 0.5403 0.5380 4.6662 4.7275 0.2663 0.2825 0.2714 0.2785 0.2511 0.2647 0.2553 0.2615 44.71, 124.97

ψs(°)

164.52, 238.47

rs(°)

20.06, 17.20

Ts

(O

C )i2

0.00234

0.85, 0.85 0.000915

Errors Assumed Assumed Assumed ± 0.025 ±5 ± 0.07 ± 0.0045 ± 0.0046 ± 0.0046 ± 0.0048 ± 0.0335 ± 0.0884 ± 0.0015 ± 0.0019 ± 0.0016 ± 0.0018 ± 0.0074 ± 0.0096 ± 0.0080 ± 0.0089 ± 1.72, ± 1.72 ± 1.72, ± 2.87 ± 0.03, ± 0.05 Fixed

Fig. 5. Geometric structure of the detached eclipsing binary NSVS 10441882 at 0.75 phase.

quality radial velocity curves are urgently needed for the target in the future. In addition, our results indicated the star-spot activity of NSVS 10441882. In general, late-type stars with a deeper convective envelope and faster rotation (Zhang et al., 2017a) will produce a strong magnetic field. The magnetic activity of these stars will be detected during observations, such as cool star-spots, flares, and the Hα emission line from their chromosphere. Remarkably, the presence of cool star-spots made the observed LCs appear asymmetrical (Li et al., 2015; Zhang et al., 2018a). Similar observations were also reported for stars such as NSVS 10653195 (Zhang et al., 2015), 1SWASP J200503.05–343726.5 (Zhang et al., 2017a), 1SWASP J074658.62+224448.5 (Jiang et al., 2015), GN Boo (Wang et al., 2015), and 1SWASP J015100.23–100524.2 (Qian and Zhang, 2015a). More importantly, if the spots are located at the L1 (the inner Lagrangian point) region of the secondary component in a cataclysmic variable, the outburst may be produced with a sudden mass accretion of the white dwarf, such as 1SWASP J162117.36+441254.2 (Qian et al., 2017b). The O–C diagram obtained for the system indicated cyclic variation. Similar late-type DEBs include YY Gem (Qian et al., 2002), NSVS 02502726 (Lee et al., 2013), and NSVS 10653195 (Zhang et al., 2015). This cyclic change in DEBs is probably caused by the magnetic activity cycle for one or two active late-type stars (Applegate, 1992), or the presence of an unseen third body around the close binaries (Liao and Qian, 2010). We estimated the mass of the primary component as M1 = 0.67M (the average spectral type was determined as K5; Cox, 2000) and M2 = M1 × q = 0.63M . If magnetic activity cycles occur in the components, we can calculate the quadruple moment required using the following formula (Lanza and Rodonó, 2002; Qian et al., 2002):

5. Discussion and conclusions In this study, we obtained the first photometric solutions for the short-period DEB system NSVS 10441882 using the 2013 version of the W–D code with cool star-spots. The best fitting results that we obtained suggest that this target is a detached total eclipsing binary system, with a mass ratio of q = 0.94 and orbital inclination of about 85°.34. The temperature of the two components is very similar with a small difference of ∼ 30 K. It should be noted that the standard errors obtained using the W–D program are only approximately correct and the actual parameter uncertainties may be two to four times higher as a consequence (Liu et al., 2015; Popper, 1984). The mass ratio determined in this study may be changed after adding radial velocity data. Thus, high4

New Astronomy 70 (2019) 1–6

Z. Bin et al.

of the cyclic change. Thus, further observations are urgently required to check the results of our analysis.

Table 4 Orbital parameters of the third body in NSVS 10441882. Parameters

Values

Units

P3 A3

16.70( ± 0.21) 0.00349( ± 0.00029) 0.60 ± 0.13

Years Days A.U.

7.92( ± 0.02) × 10 0.12( ± 0.01) 6.50 ( ± 0.08)

M⊙ A.U.

a12 sin(i3) f(m)

M3sin(i3) a3(i3=90°)

P = Porb

9

4

Q , Ma2

Acknowledgments We thank the anonymous referee for useful comments and suggestions that improved the quality of the manuscript. This study was partly supported by the Chinese Natural Science Foundation (Nos. 11573063, 11611530685, U1731238, U1831120, 11565010, and 11503077), Science Foundation of Yunnan Province (No. 2012HC011), Key Science Foundation of Yunnan Province (No. 2017FA001), Joint Research Fund in Astronomy (grant number U1631108) under a cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS), and the research fund of Sichuan University of Science and Engineering (grant number 2015RC42). We acknowledge the support of staff at the Xinglong 85 cm telescope, and this work was partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. New light minima times for NSVS 10441882 were observed using the 60 cm and 1.0 m telescopes at the Yunnan Observatories.

M⊙

(3)

where ΔP = 0.15 s, a = 2.72 R⊙, and M is the mass of the active star. The values calculated for each component were ΔQ1 = 0.93 × 1049 g cm2 and ΔQ2 = 0.78 × 1049 g cm2, respectively. However, for close binaries, the representative value of ΔQ usually ranges from 1051 to 1052 g cm2 (Lanza and Rodonó, 1999). Thus, magnetic activity cycles might not work occur in the system, or they might not have a major effect. Therefore, the most probable interpretation for the O–C oscillation in this system is the light-travel time effect. We assumed a circular orbit in our analysis, i.e., the eccentricity e = 0. According to the best fitting parameters that we obtained, the projected radius of the orbit around which the eclipsing binary rotates at the barycenter of the triple system was calculated with the following equation (Qian et al., 2013b):

a12 sin i3 = A3 × c,

References Applegate, J.H., 1992. ApJ 385, 621. Becker, A.C., Agol, E., Silvestri, N.M., et al., 2008. MNRAS 386, 416. Bruch, A., 2014. A&A 566, 101. Butler, C.J., Erkan, N., Budding, E., et al., 2015. MNRAS 446, 4205B. Coughlin, J.L., Shaw, J.S., 2007. JSARA 1, 7. Cox, A.N., 2000. Allen’s Astrophysical Quantities, 4th ed. Springer, New York. Cutri, R.M., Skrutskie, M.F., et al., 2003. VizieR Online Data Catalog 2246, 0. Davenport, J.R.A., Becker, A.C., West, A.A., et al., 2013. ApJ 764, 62. Diethelm, R., 2009. IBVS 5894, 1. Diethelm, R., 2011. IBVS 5992, 1. Diethelm, R., 2012. IBVS 6029, 1. Diethelm, R., 2013. IBVS, 6063, 1. Guo, D.F., Li, K., et al., 2018. PASP 130, 4201. Han, Z.T., Qian, S.B., Irina, V., Zhu, L.Y., 2017a. AP&SS 362, 109. Han, Z.T., Qian, S.B., Irina, V., Zhu, L.Y., 2017b. AJ 153, 238. Hoffman, D.I., Harrison, T.E., Coughlin, J.L., et al., 2008. AJ 136, 1067. Irwin, J., Charbonneau, D., Berta, Z.K., et al., 2009. ApJ 701, 1436. Jiang, L.Q., Qian, S.B., Zhang, J., Zhou, X., 2015. AJ 149, 169. Koo, J.R., Lee, J.W., Hong, K., 2017. AJ 154, 235. Lanza, A.F., Rodonó, M., 1999. A&A 349, 887. Lanza, A.F., Rodonó, M., 2002. AN 323, 424. Lee, J.W., Youn, J.H., Kim, S.L., Lee, C.U., 2013. AJ 145, 16. Li, K., Hu, S.M., Guo, D.F., et al., 2015. ApJ 149, 120. Liao, W.P., Qian, S.B., 2010. MNRAS 405, 1930. Liu, L., Qian, S.B., Fernandez, L., et al., 2018. Ap&SS 363, 15. Liu, L., Qian, S.B., Zhu, L.Y., et al., 2011. AJ 141, 147. Liu, N.P., Qian, S.B., Soonthornthum, B., et al., 2015. AJ 149, 148. Lohr, M.E., Norton, A.J., Payne, S.G., et al., 2015. A&A 578, 136. López-Morales, M., Ribas, I., 2005. ApJ 631, 1120. Lucy, L.B., 1967. ZA 65, 89. Luo, A.L., Zhao, Y.H., Zhao, G., et al., 2015. RAA 15, 1095. Maceroni, C., Montalbán, J., 2004. A&A 426, 577. Maceroni, C., Rucinski, S.M., 1997. PASP 109, 782. Metcalfe, T.S., Mathieu, R.D., Latham, D.W., Torres, G., 1996. ApJ 456, 356. Morales, J.C., Gallardo, J., Ribas, I., et al., 2010. ApJ 718, 502. Morales, J.C., Ribas, I., Jordi, C., et al., 2009. ApJ 691, 1400M. Nefs, S.V., Birkby, J.L., Snellen, I.A.G., et al., 2013. MNRAS 431, 3240. Popper, D.M., 1984. AJ 89, 132. Qian, S.B., Han, Z.T., Zhang, B., et al., 2017b. ApJ 848, 131. Qian, S.B., He, J.J., Zhang, J., et al., 2017a. RAA 17, 87. Qian, S.B., Jiang, L.Q., Fernández Lajús, E., et al., 2015b. ApJ 798L, 42. Qian, S.B., Liao, W.P., Zhu, L.Y., et al., 2010. MNRAS 401, 34. Qian, S.B., Liu, D.L., Tan, W.L., Boonrucksar, S., 2002. AJ 124, 1060. Qian, S.B., Liu, N.P., Li, K., et al., 2013b. ApJS 209, 13. Qian, S.B., Zhang, B., et al., 2015a. AJ 150, 117. Qian, S.B., Zhang, J., He, J.J., et al., 2018. ApJS 235, 5. Qian, S.B., Zhang, J., Wang, J.J., et al., 2013a. ApJS 207, 22. Qian, S.B., Zhang, J., Zhu, L.Y., et al., 2012. MNRAS 423, 3646. Rappaport, S., Deck, K., Levine, A., et al., 2013. ApJ 768, 33. Ribas, I., 2003. A&A 400, 297R. Ribas, I., 2006. Ap&SS 304, 89. Rucinski, S.M., 1969. AcA 19, 245. Rucinski, S.M., 2002. PASP 114, 1124. Shan, Y.T., Johnson, J.A., Morton, T.D., 2015. ApJ 813, 75S.

(4)

where c is the speed of light, A3 is the amplitude of the O–C oscillation, and i3 is the orbital inclination of the third body, i.e., a12 sin(i3)= 0.60 AU. The mass function of the tertiary companion was then computed with:

f (m ) =

4 2 (M3 sin i3)3 × (a12 sin i3)3 = , (M1 + M2 + M3)2 GP32

(5)

where G is the gravitational constant, P3 is the period of the O–C oscillation, and M3 is the mass of the third body. The mass function of the third body was calculated as f(M3) = 0.00079 M⊙, its mass as M3sin(i3) = 0.12 M⊙, and the orbital separation between the central binary and the third body as ∼ 6.5 AU (see Table 4). It is known that many close binaries are formed with a close-in companion and the survey of Kepler eclipsing binaries showed that at least 20% of all close binaries have tertiary companions (Rappaport et al., 2013). A wider scale survey by Lohr et al. (2015) found that tertiary systems comprised 24% of nearly 14,000 SuperWASP eclipsing binaries. Many triple system candidates have been discovered using the O–C method, such as DV Uma (Han et al., 2017b), WW Dra (Liao and Qian, 2010), SDSS J001641-000925 (Qian et al., 2015b), NSVS 02502726 (Lee et al., 2013), KIC 10581918, KIC 10686876 (Zasche et al., 2015), and NSVS 01286630 (Zhang et al., 2018b). However, the origins of these multi-body systems remain unclear. Qian et al. (2013a,b) considered that these additional components in close eclipsing binaries may speed up the orbital evolution of the central system by removing angular momentum. Studies also suggest that the same angular momentum events usually occur in the early dynamical interactions or late evolutionary phase for close eclipsing binaries. For some triple EAs, we note that the mass ratios of these systems are usually high, such as NSVS 01286630 (Coughlin & Shaw, 2007; Wolf et al., 2016; Zhang et al., 2018b) and V2281 Cyg (Koo et al., 2017). For the EWs with an additional companion, the progenitors may also be triple systems. Under the effect of the third body, these EWs may be formed with higher metallicities than their progenitors and with a short time scale for pre-contact evolution (Qian et al., 2018). However, the data coverage for NSVS 10441882 is currently less than two cycles 5

New Astronomy 70 (2019) 1–6

Z. Bin et al. Torres, G., Ribas, I., 2002. ApJ 567, 1140. ̆ Smelcer, L., Wolf, M., Kućáková, H., et al., 2017. MNRAS 466, 2542. Van Hamme, W., 1993. AJ 106, 2096. Wang, J.J., Qian, S.B., Zhang, Y.P., et al., 2015. AJ 149, 164. Wilson, R.E., 2012. AJ 144, 73. Wilson, R.E., Devinney, E.J., 1971. ApJ 166, 605. Wilson, R.E., Pilachowski, C.A., Terrell, D., 2017. ApJ 835, 251. Windmiller, G., Orosz, J.A., Etzel, P.B., 2010. ApJ 712, 1003. Wolf, M., Zasche, P., Kućáková, H., et al., 2016. A&A 587, 82. Woźniak, P.R., Vestrand, W.T., Akerlof, C.W., et al., 2004. AJ 127, 2436. Wu, Y., Luo, A.L., Li, H.N., et al., 2011. RAA 11, 924.

Zasche, P., Uhlar, R., Kućáková, H., Svoboda, P., 2011. IBVS 6007, 1. Zasche, P., Wolf, M., Kućáková, H., et al., 2015. AJ 149, 197. Zhang, B., Qian, S.B., Liao, W.P., et al., 2015. NewA 41, 37. Zhang, B., Qian, S.B., Michel, R., et al., 2018a. RAA 18, 30. Zhang, B., Qian, S.B., Zejda, M., et al., 2017a. NewA 54, 52. Zhang, B., Qian, S.B., Zhu, L.Y., et al., 2018b. RAA 18, 116. Zhang, J., Qian, S.B., Han, Z.T., Wu, Y., 2017b. MNRAS 466, 1118. Zhang, L.Y., Pi, Q.F., Yang, Y.G., 2014. MNRAS 442, 2620. Zhao, E.G., Qian, S.B., liao, W.P., et al., 2018. PASP 130, 4201. Zhou, A.Y., Jiang, X.J., Zhang, Y.P., Wei, J.Y., 2009. RAA 9, 349. Zhou, X., Qian, S.B., Zhang, J., et al., 2016. ApJ 817, 133.

6