Starspot activity and period change in RT CrB

12-1 Publ. Astron. Soc. Japan (2015) 67 (1), 12 (1–6) doi: 10.1093/pasj/psu143 Starspot activity and period change in RT CrB Fu-Yuan XIANG,∗ Ting-Yu XIAO, and Yun-Xia YU Department of Physics Xiangtan University, 411105 Xiangtan, Hunan, China *E-mail: Received 2014 October 27; Accepted 2014 November 5 Abstract The light curves of RT CrB in the B and V bands observed by İbanoğlu et al. (1985, Ap&SS, 112, 133), and in the V band and the radial velocity curves observed by Sabby and Lacy (2003, AJ, 125, 1448), are analyzed using the Wilson–Devinney code. The results show that the distortions in the light curve observed by Sabby and Lacy (2003) can be fitted by two spots, a hot spot on the primary component and a cool spot on the secondary star. The temperature ratios of the spotted region to the photosphere, Ts /Tph , are 1.181(±0.053) and 0.803(±0.057) respectively. Combining the radial velocity curves with the light curves, our analysis gives reliable, accurate estimates of the physical parameters of the system, M1 = 1.35(±0.01)M and R1 = 2.88(±0.05)R for the primary (hotter) component, M2 = 1.36(±0.01)M and R2 = 2.92(±0.04)R for the secondary (cooler) component. In addition, the orbital period variations of RT CrB are investigated based on all available times of light minima collected from literature and databases. We find that the orbital period exhibits a possible long-term period decrease with a rate of dP/dt = −3.11 × 10−7 d yr−1 , suggesting that RT CrB is undergoing an angular momentum loss via magnetic braking. Key words: binaries: eclipsing — stars: individual (RT CrB) — stars: mass-loss — starspots 1 Introduction RT CrB is an RS CVn-type system with two nearly equal mass components (q = m2 /m1 = 1.011). Its light variation was discovered by Ceraski (1911). Beyer (1935) first published the light elements. After Beyer (1935), spectroscopic studies and photometric observations were published by several authors (Popper 1970, 1990; Popper & Dumont 1977; Zhai et al. 1982; İbanoğlu et al. 1985; Frasca & Catalano 1994; Montes et al. 1996; Liu et al. 1996; Sabby & Lacy 2003). Popper (1970) reported that RT CrB shows Ca II H&K emission in at least one component. Popper and Dumont (1977) and İbanoğlu et al. (1985) published photometric light curves showing smoothness and symmetry. Zhai et al. (1982) found a wave-like distortion in the outside of eclipsing with an amplitude of 0.06 mag in 1978. Popper (1990) first determined the absolute parameters of the system to be M1 = 1.40(±0.05) M and R1 = 2.6(±0.2) R for the primary component, M2 = 1.42(±0.02) M and R2 = 3.0(±0.2) R for the secondary star, based on his own spectroscopic data and the photometric observations of Popper and Dumont (1977), Zhai et al. (1982), and İbanoğlu et al. (1985). He stated that the spectral type of the system is G2+G5-8IV. Frasca and Catalano (1994) found that the hotter component of RT CrB shows a double Hα absorption. Montes et al. (1996) reported that both components of the system exhibit Ca II H&K emission. Liu et al. (1996) performed an Hα emission survey for 30 chromospherically active binaries, including RT CrB. They also found that the system shows a normal absorption line. Sabby and Lacy (2003) published radial velocity curves and photometric observations in the V band light curve which also shows wave-like distortion. They obtained a preliminary  C The Author 2015. Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved. For Permissions, please email: Publications of the Astronomical Society of Japan (2015), Vol. 67, No. 1 absolute elements which lack of considering the effect of spot, M1 = 1.343(±0.010) M , R1 = 2.615(±0.04) R , M2 = 1.359(±0.009) M , and R2 = 2.946(±0.05) R . The orbital period change of RT CrB was noticed by Hall and Kreiner (1980), and was then investigated by Qian et al. (2003). Based on reports of all available times of light minima published before 2002, Qian et al. (2003) found that the orbital period of RT CrB shows a cyclic oscillation with a period of 53.9 yr. They attribute it to the magnetic activity cycle of both components. In this paper, we re-analyze the light curves of RT CrB in the B and V bands observed by İbanoğlu et al. (1985), and in the V band observed by Sabby and Lacy (2003), with the Wilson–Devinney code. The current status of spot activity and the physical parameters of the system are carefully determined. In addition, we investigate the period changes in RT CrB based on all available times of the minimum collected from literature and databases. 2 Photometric and spectroscopic solution İbanoğlu et al. (1985) made complete B and V-band light curves observed from 1979 to 1981. They used the WINK program and the Nelson–Davis–Etzel (NDE) model (Etzel 1981; Popper & Etzel 1981) to solve the preliminary photometric elements. Here, we re-analyzed these data using the 2003 version of the Wilson–Devinney code (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & Van Hamme 2003). The observations in each band combined into 110 normal points. The number of observations in each normal point was taken as the corresponding weight. Because the spectral type, G2+G58IV (Popper 1990), or the temperature of the primary component of 5781 ± 100 K estimated by Sabby and Lacy (2003), we adopt a temperature for star 1 (the primary, hotter component) of 5770 K, according to the calibration of Johnson (1966). The other adopted parameters in the solution are as follows: the bolometric albedo of the two components, A1,2 = 0.5 (Rucinski 1969); the gravity-darkening exponents, g1,2 = 0.32 (Lucy 1967); and the linear limb-darkening coefficients, x1V = 0.67, x2V = 0.72, x1B = 0.81, x2B = 0.86 (Claret & Gimenez 1990). The adjustable parameters are the orbital inclination, i, the dimensionless potentials of star 1 and star 2 (the secondary, cooler component), 1 and 2 , the mean temperature of star 2, T2 , the monochromatic luminosity of star 1, L1 , and the mass ratio, q. The relative brightness of the secondary star is calculated from the stellar atmosphere model. The reflection effect is computed with the detailed model of Wilson (1990). The spectroscopic ratio, q = 1.011, given by Sabby and Lacy (2003), is taken to be the initial value in the solution. 12-2 Table 1. Photometric solutions for RT CrB. Parameter 1985 2001 i g1 = g2 A1 = A2 x1V x2V x1B x2B 1 2 T1 T2 q = m2 /m1 L1 /(L1 + L2 )(V) L1 /(L1 + L2 )(B) r1 (pole) r1 (point) r1 (side) r1 (back) r2 (pole) r2 (point) r2 (side) r2 (back)  [w i (O − C)i ]2 85 ◦. 085 ± 0 ◦. 404 0.32 (assumed) 0.50 (assumed) 0.67 (assumed) 0.72 (assumed) 0.81 (assumed) 0.86 (assumed) 7.3243 ± 0.3221 7.1351 ± 0.2120 5770 K (assumed) 5092 ± 28 K 1.012 ± 0.024 0.6336 ± 0.0133 0.6810 ± 0.0410 0.1581 ± 0.0091 0.1599 ± 0.0095 0.1587 ± 0.0092 0.1596 ± 0.0094 0.1644 ± 0.0057 0.1664 ± 0.0060 0.1652 ± 0.0058 0.1662 ± 0.0060 0.00139 84 ◦. 284 ± 0 ◦. 230 (...truncated)