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The first orbital parameters and period variation of the short-period eclipsing binary AQ Boo
New Astronomy 48 (2016) 42–48
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The first orbital parameters and period variation of the short-period eclipsing binary AQ Boo Shuai Wang a,b, Liyun Zhang a,b,∗, Qingfeng Pi a,b, Xianming L. Han c, Xiliang Zhang d, Hongpeng Lu a,b, Daimei Wang a,b, TongAn Li a,b a
College of Science/Department of Physics & NAOC-GZU-Sponsored Center for Astronomy Research, Guizhou University, Guiyang 550025, P.R. China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650011, P.R. China Dept. of Physics and Astronomy, Butler University, Indianapolis, IN 46208, USA d National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming, 65 0011, P.R. China b c
h i g h l i g h t s • • •
The first VRI light curves of an eclipsing contact binary AQ Boo were obtained. By using WD program, the photometric orbital parameters of AQ Boo were obtained. The orbital period of AQ Boo shows a decreasing tendency.
a r t i c l e
i n f o
Article history: Received 2 February 2016 Revised 20 April 2016 Accepted 20 April 2016 Available online 26 April 2016 Keywords: Stars Binaries Eclipsing – stars Period variation – stars Individual AQ Boo
a b s t r a c t We obtained the first VRI CCD light curves of the short-period contact eclipsing binary AQ Boo, which was observed on March 22 and April 19 in 2014 at Xinglong station of National Astronomical Observatories, and on January 20, 21 and February 28 in 2015 at Kunming station of Yunnan Observatories of Chinese Academy of Sciences, China. Using our six newly obtained minima and the minima that other authors obtained previously, we revised the ephemeris of AQ Boo. By fitting the O-C (observed minus calculated) values of the minima, the orbital period of AQ Boo shows a decreasing tendency P˙ = −1.47(0.17 ) × 10−7 days/year. We interpret the phenomenon by mass transfer from the secondary (more massive) component to the primary (less massive) one. By using the updated Wilson & Devinney program, we also derived the photometric orbital parameters of AQ Boo for the first time. We conclude that AQ Boo is a near contact binary with a low contact factor of 14.43%, and will become an over-contact system as the mass transfer continues. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The orbital period of W UMa stars is in the range of about 5– 20 h (Selam, 2004). It is important to study the orbital parameters, period variation, and stellar evolution (Lucy, 1967; Qian, 2002; Zhu et al., 2010; Qian et al., 2013a; Yang and Qian, 2015, etc). The orbital parameters of an eclipsing binary can be obtained by analyzing the photometric light curves (LCs) and spectra. In 1964, Hoffmeister (1964) discovered that AQ Boo is a variable star. Later, it was classified as one of the W UMa type eclipsing binaries by Blättler (20 0 0), who also obtained the preliminary ephemeris of Min.I = HJD2451602.3922(6 ) + 0d .33314114(8 ) (Blättler, 20 0 0). New minima times of AQ Boo were published (Diethelm, 2005; 2009; etc) and are available at O-C gate (Paschke and Brát, 2006) ∗
Corresponding author. Fax: +86 851 362 7662. E-mail address: [email protected] (L. Zhang).
http://dx.doi.org/10.1016/j.newast.2016.04.005 1384-1076/© 2016 Elsevier B.V. All rights reserved.
in recent years. However, an orbital solution had not been obtained and the period variation of AQ Boo has also not been investigated until now. In this paper, the primary aim is to study the first Multi-band CCD light curves of AQ Boo in order to obtain its orbital period variation and photometric orbital parameters. Multi-color CCD observations and data are described in Section 2. The period variation is analyzed in Section 3 and orbital parameters are derived in Section 4. Finally, the results are briefly discussed in Section 5. 2. Photometric observations On March 22 and April 19 in 2014, we observed AQ Boo with the 60 cm telescope at Xinglong Station of the National Astronomical Observatories of China (NAOC). The CCD camera on this telescope has a resolution of 1024 × 1024 pixels and its corresponding field of view is 17’ × 17’ (Yang, 2013). The other three days of data
S. Wang et al. / New Astronomy 48 (2016) 42–48
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Table 1 The relevant parameters of AQ Boo, check and comparison stars, such as coordinates and magnitudes. Targets
Name
Variable Comparison Check Check Check
AQ Boo GSC 01460-0 0 0 03 GSC 01460-00206 2mass J13470701+1719518 2mass J13470309+1714495
Coordinates
Mag− J
Mag− H
Mag− K
Reference
13:47:26.90;+17:18:24.0 13:47:03.82;+17:22:05.4 13:47:28.62;+17:19:09.7 13:47:07.01;+17:19:51.8 13:47:03.09;+17:14:49.5
11.270 11.353 11.714 12.919 11.661
10.943 10.962 11.224 12.345 11.130
10.880 10.905 11.127 12.224 10.968
Cutri Cutri Cutri Cutri Cutri
et et et et et
al. al. al. al. al.
(2003); (2003); (2003); (2003); (2003);
Samus et Morrison Morrison Morrison Morrison
al. (2003) et al. (2001) et al. (2001) et al. (2001) et al. (2001)
Fig. 1. The VRI light curves observed using 60 cm and 1 M telescope with squares () representing Mar. 22, 2014 data, circles (◦) representing Apr. 19, 2014 data, triangles () representing Jan. 20, 2015 data, stars () representing Jan. 21, 2015 data, and diamonds () representing Feb. 28, 2015 data.
Table 2 Our photometric data of AQ Boo in V R and I bands observed using 60 cm and 1 m telescope. V band
R band
I band
Telescope
HJD
mag
HJD
mag
HJD
mag
2456739.0797 2456739.0832 2456739.0866 2456739.0900 2456739.0935 2456739.0969 ... 2456767.0442 2456767.0410 2456767.0474 2456767.0506 2456767.0538 2456767.0608 ... 2457043.3468 2457043.3499 2457043.3537 2457043.3573 ... 2457044.3733 2457044.3769 2457044.3805 2457044.3841 ... 2457082.1552 2457082.1594 2457082.1637 2457082.1680 2457082.1723 2457082.1765
−0.076 −0.127 −0.158 −0.195 −0.224 −0.255 ... 0.102 0.119 0.083 0.053 0.045 −0.061 ... −0.236 −0.207 −0.195 −0.147 ... −0.041 −0.027 0.001 −0.004 ... −0.183 −0.084 −0.087 −0.101 0.024 0.024
2456739.0811 2456739.0846 2456739.0880 2456739.0914 2456739.0949 2456739.0983 ... 2456767.0422 2456767.0454 2456767.0486 2456767.0518 2456767.0588 2456767.0620 ... 2457043.3477 2457043.3513 2457043.3551 2457043.3587 ... 2457044.3747 2457044.3783 2457044.3819 2457044.3855 ... 2457082.1567 2457082.1610 2457082.1610 2457082.1653 2457082.1696 2457082.1739
−0.062 −0.078 −0.131 −0.155 −0.168 −0.188 ... 0.168 0.153 0.129 0.096 0.019 −0.025 ... −0.144 −0.109 −0.109 −0.030 ... 0.054 0.087 0.046 0.027 ... −0.165 −0.140 −0.140 −0.117 0.069 0.026
2456739.0819 2456739.0854 2456739.0888 2456739.0923 2456739.0957 2456739.0991 ... 2456767.0432 2456767.0464 2456767.0496 2456767.0528 2456767.0598 2456767.0630 ... 2457043.3483 2457043.3522 2457043.3560 2457043.3596 ... 2457044.3756 2457044.3792 2457044.3828 2457044.3864 ... 2457082.1577 2457082.1621 2457082.1664 2457082.1707 2457082.1750 2457082.1793
−0.023 −0.032 −0.080 −0.091 −0.131 −0.150 ... 0.226 0.215 0.187 0.144 0.077 0.036 ... −0.071 −0.054 0.011 0.036 ... 0.106 0.121 0.078 0.121 ... −0.106 −0.096 −0.040 0.070 0.029 0.156
60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m
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S. Wang et al. / New Astronomy 48 (2016) 42–48 Table 3 The minimum times and their relevant parameters of AQ Boo, such as the uncertainties of the minima, the type of the minima, the method of the observation, the epochs of those light curve minima and their residuals. JD(Hel.(24,0 0 0 0 0+)) 50518.5170 50941.4413 51262.5888 51262.5925 51273.9120 51278.4144 51278.5804 51301.4008 51301.5657 51334.5469 51358.3650 51602.3928 51602.5585 52031.4740 52039.4706 52296.4871 52296.6547 52371.4443 52652.7810 52716.4051 52717.4065 52723.4063 52730.4004 53515.4450 53815.7686 54202.3780 54202.5430 54948.7748 54948.9395 55294.4080 55294.5743 55310.3964 55310.5638 55629.8760 55631.8750 55658.3588 55694.8381 56009.4855 56356.6148 53898.3872 55624.5458 55668.3533 55699.5011 55961.6813 56011.4845 56404.4211 56739.2256 56767.2086 57043.3785 57044.3799 57082.3574 57082.1903 a
Error
0.0012
0.0 0 04 0.0 0 04 0.0 0 02 0.0 0 05
0.0 0 04
0.0018 0.0013 0.0 0 07 0.0 0 09 0.0059 0.0017 0.0 0 01
0.0 0 06 0.0 0 07 0.0032 0.0022 0.0044 0.0012 0.0 0 04 0.0 0 03 0.0 0 05 0.0 0 01 0.0023 0.0029 0.0 0 02 0.0 0 05 0.0 0 01 0.0 0 01 0.0 0 02 0.0 0 023 0.0 0 02 0.0 0 02 0.0 0 09 0.0086 0.0012 0.0016
Type
Method
Cycle
(O-C)I
(O-C)II
Reference
sec pri pri pri pri sec pri sec pri pri sec pri sec pri pri sec pri sec pri pri pri pri pri sec pri sec pri pri sec sec pri sec pri sec sec pri sec pri pri pri sec pri sec sec pri sec sec sec sec sec sec pri
ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd
−3253.5 −1984 −1020 −1020 −986 −972.5 −972 −903.5 −903 −804 −732.5 0 0.5 1288 1312 2083.5 2084 2308.5 3153 3344 3347 3365 3386 5742.5 6644 7804.5 7805 10045 10045.5 11082.5 11083 11130.5 11131 12089.5 12095.5 12175 12284.5 13229 14271 6892 12073.5 12205 12298.5 13085.5 13235 14414.5 15419.5 15503.5 16332.5 16335.5 16449.5 16449
−.0070 −.0026 −.0011 .0026 −.0046 .0 0 04 −.0 0 01 .0 0 03 −.0014 −.0010 −.0023 .0012 .0 0 04 −.0 0 05 .0 0 07 .0 0 05 .0016 .0015 .0024 −.0031 −.0011 .0022 .0 0 04 .0031 .0019 .0036 .0020 .0026 .0 0 07 .0041 .0039 .0019 .0027 .0012 .0014 .0 0 06 .0012 −.0011 −.0026 .0021 .0012 .0010 .0 0 03 .0 0 01 −.0 0 09 −.0017 −.0019 −.0025 −.0048 −.0028 −.0032 −.0037
−.0028 .0 0 0 0 .0 0 05 .0042 −.0031 .0019 .0014 .0017 .0 0 0 0 .0 0 03 −.0011 .0018 .0 0 09 −.0011 .0 0 02 −.0 0 05 .0 0 05 .0 0 03 .0 0 06 −.0049 −.0029 .0 0 04 −.0014 .0 0 05 −.0 0 07 .0010 −.0 0 06 .0 0 06 −.0012 .0027 .0024 .0 0 04 .0013 .0 0 04 .0 0 06 −.0 0 01 .0 0 06 −.0010 −.0015 −.0 0 06 .0 0 04 .0 0 02 −.0 0 04 .0 0 01 −.0 0 09 −.0 0 05 .0 0 04 −.0 0 01 −.0015 .0 0 06 .0 0 03 −.0 0 02
Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Diethelm (2003) Zejda (2004) Diethelm (2005) Nelson (2007) Paschke and Brát (2006) Paschke and Brát (2006) Diethelm (2009) Diethelm (2009) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Paschke and Brát (2006) Diethelm (2011) Hübscher (2012) Diethelm (2011) Hübscher (2013a) Hübscher (2013b) Brát et al. (2007) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2014) a a a a a a
This study.
were obtained using the 1-m telescope at Yunnan Observatory of Chinese Academy of Sciences, on January 20, 21 and February 28 in 2015. The CCD camera on this telescope has a resolution of 2048 × 2048 pixels and its corresponding field of view is 7’.3 × 7’.3. Bessel VRI filters were used. The exposure times are 100-170 s, 50-100 s and 50-80 s in the V, R, I bands, respectively. We listed the parameters of the comparison star and the check stars in Table 1, which are near our target star. Using the IRAF package in standard fashion, which includes trimming, bias-substraction, flat-field correction, cosmic-rays removal and aperture photometry, all magnitudes were measured. The light curves in V,R,and I band of AQ Boo are shown in Fig. 1, where squares () represent the Mar. 22, 2014 data, circles (◦) represent the Apr. 19, 2014 data, triangles () represent the Jan. 20, 2015 data, stars () represent the Jan. 21, 2015 data, and dia-
monds () represent the Feb. 28, 2015 data. The magnitude differences between the target star and its comparison star are listed in Table 2, where the HJD of the object star are also shown. 3. Period investigation Based on our new observed light curve of AQ Boo, we obtained six new minima (one primary and five secondary minima) and their uncertainties in VRI bands were obtained by using the polynomial fitting method of Kwee and van Woerden (1956).While investigating the period variation, we used every available minimum time from the literature (Agerer and Hübscher, 2003; Diethelm, 20 03; Zejda, 20 04; Diethelm, 20 05; Nelson, 20 07; Diethelm, 20 09, etc) and the Eclipsing Binaries Minima Database (http://var2.astro. cz/EN/; Paschke and Brát, 2006). We show the results in Table 3, which contains the HJD of the minima and their uncertainties, the
S. Wang et al. / New Astronomy 48 (2016) 42–48
45
Fig. 2. The O-C values for all available minimum times of AQ Boo with the solid line representing the polynomial fitting. The open circles represent the O-C of CCD observations by other authors and the solid points are our data.
type (the primary or secondary) of the minima, the technique of the observation, and the epochs of those light curve minima, which have beencalculated using the linear ephemeris of the Eclipsing Binaries Minima Database (Paschke and Brát, 2006). The data have been analyzed by the no-error weighted least squares method, since there is no uncertainties for most of the data. Finally, the linear ephemeride for AQ Boo was obtained:
Min.I = HJD2451602.3916(±0.0 0 05 ) +0d .33313893(±0.0 0 0 0 0 0 05 )E
(1)
where E is the number of epoch. By linear fitting, we obtained the values of (O - C)1 of the residuals, which were listed in the sixth column of Table 3. They are plotted as a function of the epoch in Fig. 2, indicating a downward parabolic curve. The following quadratic ephemeris was obtained:
Min.I = HJD2451602.3910(±0.0 0 02 ) +0d .3331399(±0.0 0 0 0 0 01 )E − 6.69(±0.76 ) × 10−11 E 2 . (2) We also calculated the residuals by fitting polynomes that are listed in the seventh column of Table 3. The quadratic term of 6.69(0.76) × 10−11 shows that the orbital period has a decreasing tendency. The rate of the period decrease is −1.47(0.17 ) × 10−7 days/year. 4. Orbital parameters A photometric solution has been obtained by using the 2003 version of the Wilson-Devinney program (Wilson and Devinney, 1971; Wilson, 1979; 1990; 1994; Wilson and Van Hamme, 2004, etc). AQ Boo is a W Uma binary (Blättler, 20 0 0), therefore mode 3 was used in the program (appropriate for contact binaries) for obtaining the solution. In view of the color index (J-H = 0.33 ± 0.03), the effective temperature of the primary has been estimated through the following equation derived by Collier Cameron et al. (2007)
Te f f = −4369.5(J − H ) + 7188.2, 40 0 0K < Te f f < 70 0 0K
(3)
where the J and H magnitudes were collected from the 2MASS All-Sky Catalog of Point Sources (Cutri et al., 2003). Eq. (2) gives the effective temperature of the primary component of AQ Boo of 5759 ± 127 K,which we will use in subsequent orbital parameter analysis. We calculated the uncertainty in the effective
Table 4 The theoretical orbital parameters of AQ Boo calculated using the 2003 version of the Wilson-Devinney program. Parameters
Mode 3
T1 T2
5759 K 5315 ± 14K 5.532 4.929 5.445 ± 0.007 2.200 ± 0.003 71.9 ± 0.1 0.421 ± 0.002 0.403 ± 0.002 0.389 ± 0.001 0.2996 ± 0.0 0 06 0.3136 ± 0.0 0 07 0.3512 ± 0.0011 0.4292 ± 0.0 0 06 0.4583 ± 0.0 0 07 0.4886 ± 0.0010 0.6918
in out 1 = 2 q(m2 /m1 ) i(°) L1 /(L1 +L2 )(V) L1 /(L1 +L2 )(R) L1 /(L1 +L2 )(I) r1 (pole) r1 (side) r1 (back) r2 (pole) r2 (side) r2 (back)
temperature through the uncertainties in the J and H magnitudes. We chose the gravity-darkening coefficients as g1 = g2 = 0.32 for convective envelopes (Lucy, 1967) and the bolometric albedo A1 = A2 = 0.5 (Rucinski, 1973). The bolometric limb-darkening coefficients xbolo, the limb-darkening coefficients for different bands V, R, and I are x1bolo=0.51, x2bolo=0.52; x1V =0.61, x2V =0.64; x1R =0.50, x2R =0.53, and x1I =0.41, x2I =0.44, respectively. The modulatory parameters are the orbital inclination i, the mean temperature of secondary component T2 , the monochromatic luminosity of primary (L1V , L1R , and L1I ), and the mass ratio q (the ratio of the secondary mass to primary mass). The dimensionless potentials of the primary and secondary components 1 = 2 can be set as the same because AQ Boo is a contact binary. In order to obtain the orbital solution, we adjusted the parameters and ran the program in a similar way as the previous works of our group (Zhang and Gu, 2007; Zhang, 2010; Zhang et al., 2014). A reliable photometric mass ratio q can be obtained by using the sigma - q relation for converged solution and the different mass ratios. In Fig. 3 the -q relation was plotted. The most reliable mass ratio is found to be 2.2. The corresponding orbital parameters are listed in Table 4. We plotted the theoretical light
46
S. Wang et al. / New Astronomy 48 (2016) 42–48
Fig. 3. The relations of -q of AQ Boo in mode 3 with the solid points representing the residual data.
Fig. 4. Our observational and theoretical light curves of AQ Boo with the circles (◦) representing the observational data, and the solid line representing the theoretical light curve.
curves in Figure 4 as the solid line. The corresponding configuration is in Figure 5. 5. Results and discussions New V, R, and I CCD light curves for AQ Boo are presented and its period variation is discussed. The ephemeris for AQ Boo has been updated and for the first time we found that its period is decreasing. The rate of the orbital period decrease is P˙ = −1.47(0.17 ) × 10−7 days/year. The reason of the period decreasing might be mass transfer from the more massive one (secondary) to the less massive one (primary) (Hoffman et al., 2006) or magnetic braking (Applegate, 1992; Lanza et al., 1998; etc). The following equation (Singh and Chaubey, 1986) allows us to obtain the mass transfer rate:
P˙ /P = 3(1 − M2 /M1 )m˙ /M2
on the mass ratio of our orbital solution. The mass transfer rate of AQ Boo is determined to be dm/dt = 1.52 × 10−7 M /year. The photometric solution for AQ Boo was obtained as follows. The orbital inclination is about 71 °.9 and the mass ratio is 2.20 (0.003). The ratios of the luminosity of the primary component of AQ Boo to the total luminosity are 0.42 in V, 0.40 in R and 0.39 in I band. The dimensionless potential of the primary and secondary components is 5.45. We obtained a degree of contact factor f = 14.43 (± 0.03)% through the equation: f = (in -)/(in -out ). Our photometric results indicate that AQ Boo is a contact binary system with relatively low contact factor. The temperature difference is approximately 440K between the primary and secondary components. We collected some other short period contact eclipsing binaries with rate of orbital period decrease and mass ratio greater than 1, which are listed in Table 5. The orbital period change rate of AQ Boo is similar to them.
(4)
Usually the total mass of such a WUMa system is practically never larger than 2 solar masses. The mass of the primary component was calculated to be M1 = 0.56M . The mass of the secondary component has also been obtained (M2 = 1.24M ) based
Acknowledgements We thank the Chinese Academy of Sciences (CAS) Grant Nos 11263001, and the Joint Fund of Astronomy of the National Natural
S. Wang et al. / New Astronomy 48 (2016) 42–48
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Fig. 5. The geometric structure of AQ Boo at phases 0.25 and 0.75, with the darker color part representing the primary component, and the lighter color part representing the secondary component. Table 5 Contact eclipsing binaries with rate of orbital period decrease and mass ratio greater than 1, similar to AQ Boo. Objects MR Com BI Vul BE Cep TY Boo V524 Mon EH Cnc VW Boo V396 Mon BS Cas CW Cas AQ Boo a
Type contact contact contact contact contact contact contact contact contact contact contact
Mass Ratio 3.90 1.037 2.34 2.15 2.099 2.51 2.336 2.554 2.718 2.234 2.20
Period(days) 0.412 0.252 0.424 0.317 0.283 0.418 0.342 0.396 0.440 0.318 0.333
Orbital Period Rate(dy−1 ) −7
−5.3 ×10 −9.5 ×10−8 −4.84×10−8 −3.65 ×10−8 −1.52 ×10−10 −1.01×10−7 −1.454 ×10−7 −8.57 ×10−8 −2.45×10−7 −3.44×10−8 −1.47×10−7
Reference Qian et al. (2013a) Qian et al. (2013b) Dai et al. (2012) Christopoulou et al. (2012) He et al. (2012) Yang et al. (2011) Liu et al. (2011a) Liu et al. (2011b) He et al. (2010) Jiang et al. (2010) a
This study.
Science Foundation of China (NSFC) and the Chinese Academy of Sciences (CAS) grant Nos. 10978010 and U1431114. This work was also supported by the Joint Fund of Department of Science and Technology of Guizhou Province and Guizou University Grant No. [2014]7642.
Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.newast.2016.04.005
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The first orbital parameters and period variation of the short-period eclipsing binary AQ Boo Shuai Wang a,b, Liyun Zhang a,b,∗, Qingfeng Pi a,b, Xianming L. Han c, Xiliang Zhang d, Hongpeng Lu a,b, Daimei Wang a,b, TongAn Li a,b a
College of Science/Department of Physics & NAOC-GZU-Sponsored Center for Astronomy Research, Guizhou University, Guiyang 550025, P.R. China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650011, P.R. China Dept. of Physics and Astronomy, Butler University, Indianapolis, IN 46208, USA d National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming, 65 0011, P.R. China b c
h i g h l i g h t s • • •
The first VRI light curves of an eclipsing contact binary AQ Boo were obtained. By using WD program, the photometric orbital parameters of AQ Boo were obtained. The orbital period of AQ Boo shows a decreasing tendency.
a r t i c l e
i n f o
Article history: Received 2 February 2016 Revised 20 April 2016 Accepted 20 April 2016 Available online 26 April 2016 Keywords: Stars Binaries Eclipsing – stars Period variation – stars Individual AQ Boo
a b s t r a c t We obtained the first VRI CCD light curves of the short-period contact eclipsing binary AQ Boo, which was observed on March 22 and April 19 in 2014 at Xinglong station of National Astronomical Observatories, and on January 20, 21 and February 28 in 2015 at Kunming station of Yunnan Observatories of Chinese Academy of Sciences, China. Using our six newly obtained minima and the minima that other authors obtained previously, we revised the ephemeris of AQ Boo. By fitting the O-C (observed minus calculated) values of the minima, the orbital period of AQ Boo shows a decreasing tendency P˙ = −1.47(0.17 ) × 10−7 days/year. We interpret the phenomenon by mass transfer from the secondary (more massive) component to the primary (less massive) one. By using the updated Wilson & Devinney program, we also derived the photometric orbital parameters of AQ Boo for the first time. We conclude that AQ Boo is a near contact binary with a low contact factor of 14.43%, and will become an over-contact system as the mass transfer continues. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The orbital period of W UMa stars is in the range of about 5– 20 h (Selam, 2004). It is important to study the orbital parameters, period variation, and stellar evolution (Lucy, 1967; Qian, 2002; Zhu et al., 2010; Qian et al., 2013a; Yang and Qian, 2015, etc). The orbital parameters of an eclipsing binary can be obtained by analyzing the photometric light curves (LCs) and spectra. In 1964, Hoffmeister (1964) discovered that AQ Boo is a variable star. Later, it was classified as one of the W UMa type eclipsing binaries by Blättler (20 0 0), who also obtained the preliminary ephemeris of Min.I = HJD2451602.3922(6 ) + 0d .33314114(8 ) (Blättler, 20 0 0). New minima times of AQ Boo were published (Diethelm, 2005; 2009; etc) and are available at O-C gate (Paschke and Brát, 2006) ∗
Corresponding author. Fax: +86 851 362 7662. E-mail address: [email protected] (L. Zhang).
http://dx.doi.org/10.1016/j.newast.2016.04.005 1384-1076/© 2016 Elsevier B.V. All rights reserved.
in recent years. However, an orbital solution had not been obtained and the period variation of AQ Boo has also not been investigated until now. In this paper, the primary aim is to study the first Multi-band CCD light curves of AQ Boo in order to obtain its orbital period variation and photometric orbital parameters. Multi-color CCD observations and data are described in Section 2. The period variation is analyzed in Section 3 and orbital parameters are derived in Section 4. Finally, the results are briefly discussed in Section 5. 2. Photometric observations On March 22 and April 19 in 2014, we observed AQ Boo with the 60 cm telescope at Xinglong Station of the National Astronomical Observatories of China (NAOC). The CCD camera on this telescope has a resolution of 1024 × 1024 pixels and its corresponding field of view is 17’ × 17’ (Yang, 2013). The other three days of data
S. Wang et al. / New Astronomy 48 (2016) 42–48
43
Table 1 The relevant parameters of AQ Boo, check and comparison stars, such as coordinates and magnitudes. Targets
Name
Variable Comparison Check Check Check
AQ Boo GSC 01460-0 0 0 03 GSC 01460-00206 2mass J13470701+1719518 2mass J13470309+1714495
Coordinates
Mag− J
Mag− H
Mag− K
Reference
13:47:26.90;+17:18:24.0 13:47:03.82;+17:22:05.4 13:47:28.62;+17:19:09.7 13:47:07.01;+17:19:51.8 13:47:03.09;+17:14:49.5
11.270 11.353 11.714 12.919 11.661
10.943 10.962 11.224 12.345 11.130
10.880 10.905 11.127 12.224 10.968
Cutri Cutri Cutri Cutri Cutri
et et et et et
al. al. al. al. al.
(2003); (2003); (2003); (2003); (2003);
Samus et Morrison Morrison Morrison Morrison
al. (2003) et al. (2001) et al. (2001) et al. (2001) et al. (2001)
Fig. 1. The VRI light curves observed using 60 cm and 1 M telescope with squares () representing Mar. 22, 2014 data, circles (◦) representing Apr. 19, 2014 data, triangles () representing Jan. 20, 2015 data, stars () representing Jan. 21, 2015 data, and diamonds () representing Feb. 28, 2015 data.
Table 2 Our photometric data of AQ Boo in V R and I bands observed using 60 cm and 1 m telescope. V band
R band
I band
Telescope
HJD
mag
HJD
mag
HJD
mag
2456739.0797 2456739.0832 2456739.0866 2456739.0900 2456739.0935 2456739.0969 ... 2456767.0442 2456767.0410 2456767.0474 2456767.0506 2456767.0538 2456767.0608 ... 2457043.3468 2457043.3499 2457043.3537 2457043.3573 ... 2457044.3733 2457044.3769 2457044.3805 2457044.3841 ... 2457082.1552 2457082.1594 2457082.1637 2457082.1680 2457082.1723 2457082.1765
−0.076 −0.127 −0.158 −0.195 −0.224 −0.255 ... 0.102 0.119 0.083 0.053 0.045 −0.061 ... −0.236 −0.207 −0.195 −0.147 ... −0.041 −0.027 0.001 −0.004 ... −0.183 −0.084 −0.087 −0.101 0.024 0.024
2456739.0811 2456739.0846 2456739.0880 2456739.0914 2456739.0949 2456739.0983 ... 2456767.0422 2456767.0454 2456767.0486 2456767.0518 2456767.0588 2456767.0620 ... 2457043.3477 2457043.3513 2457043.3551 2457043.3587 ... 2457044.3747 2457044.3783 2457044.3819 2457044.3855 ... 2457082.1567 2457082.1610 2457082.1610 2457082.1653 2457082.1696 2457082.1739
−0.062 −0.078 −0.131 −0.155 −0.168 −0.188 ... 0.168 0.153 0.129 0.096 0.019 −0.025 ... −0.144 −0.109 −0.109 −0.030 ... 0.054 0.087 0.046 0.027 ... −0.165 −0.140 −0.140 −0.117 0.069 0.026
2456739.0819 2456739.0854 2456739.0888 2456739.0923 2456739.0957 2456739.0991 ... 2456767.0432 2456767.0464 2456767.0496 2456767.0528 2456767.0598 2456767.0630 ... 2457043.3483 2457043.3522 2457043.3560 2457043.3596 ... 2457044.3756 2457044.3792 2457044.3828 2457044.3864 ... 2457082.1577 2457082.1621 2457082.1664 2457082.1707 2457082.1750 2457082.1793
−0.023 −0.032 −0.080 −0.091 −0.131 −0.150 ... 0.226 0.215 0.187 0.144 0.077 0.036 ... −0.071 −0.054 0.011 0.036 ... 0.106 0.121 0.078 0.121 ... −0.106 −0.096 −0.040 0.070 0.029 0.156
60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 60cm 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m 1m
44
S. Wang et al. / New Astronomy 48 (2016) 42–48 Table 3 The minimum times and their relevant parameters of AQ Boo, such as the uncertainties of the minima, the type of the minima, the method of the observation, the epochs of those light curve minima and their residuals. JD(Hel.(24,0 0 0 0 0+)) 50518.5170 50941.4413 51262.5888 51262.5925 51273.9120 51278.4144 51278.5804 51301.4008 51301.5657 51334.5469 51358.3650 51602.3928 51602.5585 52031.4740 52039.4706 52296.4871 52296.6547 52371.4443 52652.7810 52716.4051 52717.4065 52723.4063 52730.4004 53515.4450 53815.7686 54202.3780 54202.5430 54948.7748 54948.9395 55294.4080 55294.5743 55310.3964 55310.5638 55629.8760 55631.8750 55658.3588 55694.8381 56009.4855 56356.6148 53898.3872 55624.5458 55668.3533 55699.5011 55961.6813 56011.4845 56404.4211 56739.2256 56767.2086 57043.3785 57044.3799 57082.3574 57082.1903 a
Error
0.0012
0.0 0 04 0.0 0 04 0.0 0 02 0.0 0 05
0.0 0 04
0.0018 0.0013 0.0 0 07 0.0 0 09 0.0059 0.0017 0.0 0 01
0.0 0 06 0.0 0 07 0.0032 0.0022 0.0044 0.0012 0.0 0 04 0.0 0 03 0.0 0 05 0.0 0 01 0.0023 0.0029 0.0 0 02 0.0 0 05 0.0 0 01 0.0 0 01 0.0 0 02 0.0 0 023 0.0 0 02 0.0 0 02 0.0 0 09 0.0086 0.0012 0.0016
Type
Method
Cycle
(O-C)I
(O-C)II
Reference
sec pri pri pri pri sec pri sec pri pri sec pri sec pri pri sec pri sec pri pri pri pri pri sec pri sec pri pri sec sec pri sec pri sec sec pri sec pri pri pri sec pri sec sec pri sec sec sec sec sec sec pri
ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd ccd
−3253.5 −1984 −1020 −1020 −986 −972.5 −972 −903.5 −903 −804 −732.5 0 0.5 1288 1312 2083.5 2084 2308.5 3153 3344 3347 3365 3386 5742.5 6644 7804.5 7805 10045 10045.5 11082.5 11083 11130.5 11131 12089.5 12095.5 12175 12284.5 13229 14271 6892 12073.5 12205 12298.5 13085.5 13235 14414.5 15419.5 15503.5 16332.5 16335.5 16449.5 16449
−.0070 −.0026 −.0011 .0026 −.0046 .0 0 04 −.0 0 01 .0 0 03 −.0014 −.0010 −.0023 .0012 .0 0 04 −.0 0 05 .0 0 07 .0 0 05 .0016 .0015 .0024 −.0031 −.0011 .0022 .0 0 04 .0031 .0019 .0036 .0020 .0026 .0 0 07 .0041 .0039 .0019 .0027 .0012 .0014 .0 0 06 .0012 −.0011 −.0026 .0021 .0012 .0010 .0 0 03 .0 0 01 −.0 0 09 −.0017 −.0019 −.0025 −.0048 −.0028 −.0032 −.0037
−.0028 .0 0 0 0 .0 0 05 .0042 −.0031 .0019 .0014 .0017 .0 0 0 0 .0 0 03 −.0011 .0018 .0 0 09 −.0011 .0 0 02 −.0 0 05 .0 0 05 .0 0 03 .0 0 06 −.0049 −.0029 .0 0 04 −.0014 .0 0 05 −.0 0 07 .0010 −.0 0 06 .0 0 06 −.0012 .0027 .0024 .0 0 04 .0013 .0 0 04 .0 0 06 −.0 0 01 .0 0 06 −.0010 −.0015 −.0 0 06 .0 0 04 .0 0 02 −.0 0 04 .0 0 01 −.0 0 09 −.0 0 05 .0 0 04 −.0 0 01 −.0015 .0 0 06 .0 0 03 −.0 0 02
Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Paschke and Brát (2006) Paschke and Brát (2006) Agerer and Hübscher (2003) Paschke and Brát (2006) Agerer and Hübscher (2003) Agerer and Hübscher (2003) Diethelm (2003) Zejda (2004) Diethelm (2005) Nelson (2007) Paschke and Brát (2006) Paschke and Brát (2006) Diethelm (2009) Diethelm (2009) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Hübscher and Monninger (2011) Paschke and Brát (2006) Diethelm (2011) Hübscher (2012) Diethelm (2011) Hübscher (2013a) Hübscher (2013b) Brát et al. (2007) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2013) ˇ Honková et al. (2014) a a a a a a
This study.
were obtained using the 1-m telescope at Yunnan Observatory of Chinese Academy of Sciences, on January 20, 21 and February 28 in 2015. The CCD camera on this telescope has a resolution of 2048 × 2048 pixels and its corresponding field of view is 7’.3 × 7’.3. Bessel VRI filters were used. The exposure times are 100-170 s, 50-100 s and 50-80 s in the V, R, I bands, respectively. We listed the parameters of the comparison star and the check stars in Table 1, which are near our target star. Using the IRAF package in standard fashion, which includes trimming, bias-substraction, flat-field correction, cosmic-rays removal and aperture photometry, all magnitudes were measured. The light curves in V,R,and I band of AQ Boo are shown in Fig. 1, where squares () represent the Mar. 22, 2014 data, circles (◦) represent the Apr. 19, 2014 data, triangles () represent the Jan. 20, 2015 data, stars () represent the Jan. 21, 2015 data, and dia-
monds () represent the Feb. 28, 2015 data. The magnitude differences between the target star and its comparison star are listed in Table 2, where the HJD of the object star are also shown. 3. Period investigation Based on our new observed light curve of AQ Boo, we obtained six new minima (one primary and five secondary minima) and their uncertainties in VRI bands were obtained by using the polynomial fitting method of Kwee and van Woerden (1956).While investigating the period variation, we used every available minimum time from the literature (Agerer and Hübscher, 2003; Diethelm, 20 03; Zejda, 20 04; Diethelm, 20 05; Nelson, 20 07; Diethelm, 20 09, etc) and the Eclipsing Binaries Minima Database (http://var2.astro. cz/EN/; Paschke and Brát, 2006). We show the results in Table 3, which contains the HJD of the minima and their uncertainties, the
S. Wang et al. / New Astronomy 48 (2016) 42–48
45
Fig. 2. The O-C values for all available minimum times of AQ Boo with the solid line representing the polynomial fitting. The open circles represent the O-C of CCD observations by other authors and the solid points are our data.
type (the primary or secondary) of the minima, the technique of the observation, and the epochs of those light curve minima, which have beencalculated using the linear ephemeris of the Eclipsing Binaries Minima Database (Paschke and Brát, 2006). The data have been analyzed by the no-error weighted least squares method, since there is no uncertainties for most of the data. Finally, the linear ephemeride for AQ Boo was obtained:
Min.I = HJD2451602.3916(±0.0 0 05 ) +0d .33313893(±0.0 0 0 0 0 0 05 )E
(1)
where E is the number of epoch. By linear fitting, we obtained the values of (O - C)1 of the residuals, which were listed in the sixth column of Table 3. They are plotted as a function of the epoch in Fig. 2, indicating a downward parabolic curve. The following quadratic ephemeris was obtained:
Min.I = HJD2451602.3910(±0.0 0 02 ) +0d .3331399(±0.0 0 0 0 0 01 )E − 6.69(±0.76 ) × 10−11 E 2 . (2) We also calculated the residuals by fitting polynomes that are listed in the seventh column of Table 3. The quadratic term of 6.69(0.76) × 10−11 shows that the orbital period has a decreasing tendency. The rate of the period decrease is −1.47(0.17 ) × 10−7 days/year. 4. Orbital parameters A photometric solution has been obtained by using the 2003 version of the Wilson-Devinney program (Wilson and Devinney, 1971; Wilson, 1979; 1990; 1994; Wilson and Van Hamme, 2004, etc). AQ Boo is a W Uma binary (Blättler, 20 0 0), therefore mode 3 was used in the program (appropriate for contact binaries) for obtaining the solution. In view of the color index (J-H = 0.33 ± 0.03), the effective temperature of the primary has been estimated through the following equation derived by Collier Cameron et al. (2007)
Te f f = −4369.5(J − H ) + 7188.2, 40 0 0K < Te f f < 70 0 0K
(3)
where the J and H magnitudes were collected from the 2MASS All-Sky Catalog of Point Sources (Cutri et al., 2003). Eq. (2) gives the effective temperature of the primary component of AQ Boo of 5759 ± 127 K,which we will use in subsequent orbital parameter analysis. We calculated the uncertainty in the effective
Table 4 The theoretical orbital parameters of AQ Boo calculated using the 2003 version of the Wilson-Devinney program. Parameters
Mode 3
T1 T2
5759 K 5315 ± 14K 5.532 4.929 5.445 ± 0.007 2.200 ± 0.003 71.9 ± 0.1 0.421 ± 0.002 0.403 ± 0.002 0.389 ± 0.001 0.2996 ± 0.0 0 06 0.3136 ± 0.0 0 07 0.3512 ± 0.0011 0.4292 ± 0.0 0 06 0.4583 ± 0.0 0 07 0.4886 ± 0.0010 0.6918
in out 1 = 2 q(m2 /m1 ) i(°) L1 /(L1 +L2 )(V) L1 /(L1 +L2 )(R) L1 /(L1 +L2 )(I) r1 (pole) r1 (side) r1 (back) r2 (pole) r2 (side) r2 (back)
temperature through the uncertainties in the J and H magnitudes. We chose the gravity-darkening coefficients as g1 = g2 = 0.32 for convective envelopes (Lucy, 1967) and the bolometric albedo A1 = A2 = 0.5 (Rucinski, 1973). The bolometric limb-darkening coefficients xbolo, the limb-darkening coefficients for different bands V, R, and I are x1bolo=0.51, x2bolo=0.52; x1V =0.61, x2V =0.64; x1R =0.50, x2R =0.53, and x1I =0.41, x2I =0.44, respectively. The modulatory parameters are the orbital inclination i, the mean temperature of secondary component T2 , the monochromatic luminosity of primary (L1V , L1R , and L1I ), and the mass ratio q (the ratio of the secondary mass to primary mass). The dimensionless potentials of the primary and secondary components 1 = 2 can be set as the same because AQ Boo is a contact binary. In order to obtain the orbital solution, we adjusted the parameters and ran the program in a similar way as the previous works of our group (Zhang and Gu, 2007; Zhang, 2010; Zhang et al., 2014). A reliable photometric mass ratio q can be obtained by using the sigma - q relation for converged solution and the different mass ratios. In Fig. 3 the -q relation was plotted. The most reliable mass ratio is found to be 2.2. The corresponding orbital parameters are listed in Table 4. We plotted the theoretical light
46
S. Wang et al. / New Astronomy 48 (2016) 42–48
Fig. 3. The relations of -q of AQ Boo in mode 3 with the solid points representing the residual data.
Fig. 4. Our observational and theoretical light curves of AQ Boo with the circles (◦) representing the observational data, and the solid line representing the theoretical light curve.
curves in Figure 4 as the solid line. The corresponding configuration is in Figure 5. 5. Results and discussions New V, R, and I CCD light curves for AQ Boo are presented and its period variation is discussed. The ephemeris for AQ Boo has been updated and for the first time we found that its period is decreasing. The rate of the orbital period decrease is P˙ = −1.47(0.17 ) × 10−7 days/year. The reason of the period decreasing might be mass transfer from the more massive one (secondary) to the less massive one (primary) (Hoffman et al., 2006) or magnetic braking (Applegate, 1992; Lanza et al., 1998; etc). The following equation (Singh and Chaubey, 1986) allows us to obtain the mass transfer rate:
P˙ /P = 3(1 − M2 /M1 )m˙ /M2
on the mass ratio of our orbital solution. The mass transfer rate of AQ Boo is determined to be dm/dt = 1.52 × 10−7 M /year. The photometric solution for AQ Boo was obtained as follows. The orbital inclination is about 71 °.9 and the mass ratio is 2.20 (0.003). The ratios of the luminosity of the primary component of AQ Boo to the total luminosity are 0.42 in V, 0.40 in R and 0.39 in I band. The dimensionless potential of the primary and secondary components is 5.45. We obtained a degree of contact factor f = 14.43 (± 0.03)% through the equation: f = (in -)/(in -out ). Our photometric results indicate that AQ Boo is a contact binary system with relatively low contact factor. The temperature difference is approximately 440K between the primary and secondary components. We collected some other short period contact eclipsing binaries with rate of orbital period decrease and mass ratio greater than 1, which are listed in Table 5. The orbital period change rate of AQ Boo is similar to them.
(4)
Usually the total mass of such a WUMa system is practically never larger than 2 solar masses. The mass of the primary component was calculated to be M1 = 0.56M . The mass of the secondary component has also been obtained (M2 = 1.24M ) based
Acknowledgements We thank the Chinese Academy of Sciences (CAS) Grant Nos 11263001, and the Joint Fund of Astronomy of the National Natural
S. Wang et al. / New Astronomy 48 (2016) 42–48
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Fig. 5. The geometric structure of AQ Boo at phases 0.25 and 0.75, with the darker color part representing the primary component, and the lighter color part representing the secondary component. Table 5 Contact eclipsing binaries with rate of orbital period decrease and mass ratio greater than 1, similar to AQ Boo. Objects MR Com BI Vul BE Cep TY Boo V524 Mon EH Cnc VW Boo V396 Mon BS Cas CW Cas AQ Boo a
Type contact contact contact contact contact contact contact contact contact contact contact
Mass Ratio 3.90 1.037 2.34 2.15 2.099 2.51 2.336 2.554 2.718 2.234 2.20
Period(days) 0.412 0.252 0.424 0.317 0.283 0.418 0.342 0.396 0.440 0.318 0.333
Orbital Period Rate(dy−1 ) −7
−5.3 ×10 −9.5 ×10−8 −4.84×10−8 −3.65 ×10−8 −1.52 ×10−10 −1.01×10−7 −1.454 ×10−7 −8.57 ×10−8 −2.45×10−7 −3.44×10−8 −1.47×10−7
Reference Qian et al. (2013a) Qian et al. (2013b) Dai et al. (2012) Christopoulou et al. (2012) He et al. (2012) Yang et al. (2011) Liu et al. (2011a) Liu et al. (2011b) He et al. (2010) Jiang et al. (2010) a
This study.
Science Foundation of China (NSFC) and the Chinese Academy of Sciences (CAS) grant Nos. 10978010 and U1431114. This work was also supported by the Joint Fund of Department of Science and Technology of Guizhou Province and Guizou University Grant No. [2014]7642.
Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.newast.2016.04.005
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