V957 Cep is a Zero-Age Eclipsing System

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Abstract

New high-precision photometric measurements of the V957 Cep system (P = 1.99d, V = 11.17m, e = 0.127, B6 V+B8 V), as well as an integrated approach to orbital parameters determining based both on photometric solutions of the light curves and on the study of the course of residual deviations of the minima timings from the linear formula O – C made it possible for the first time to accurately measure the apsidal motion rate: ω˙obs = 2.91°/year, which coincided with the theoretical value under the condition of the orbital and axial rotations synchronism: ω˙theor = 2.92°/year. The physical parameters of the component stars were obtained: T1 = 14550 ± 300 K, M1 = 4.0 ± 0.2 M•, R1 = 2.55 ± 0.05 R•, T2 = 12400 ± 250 K, M2 = 3.0 ± 0.15 M•, R2 = 1.88 ± 0.05 R•. This set of parameters corresponds to stars of zero age, recently descended to ZAMS. The secondary component is a pulsating variable star of the β Cephei type.

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About the authors

I. M. Volkov

Lomonosov Moscow State University

Author for correspondence.
Email: hwp@yandex.ru
Russian Federation, Moscow

S. A. Naroenkov

Institute of Astronomy of the Russian Academy of Sciences

Email: snaroenkov@inasan.ru
Russian Federation, Moscow

A. S. Kravtsova

Lomonosov Moscow State University

Email: kravts@yandex.ru
Russian Federation, Moscow

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Supplementary files

Supplementary Files
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2. Fig. 1. Two-colour diagram of (U - B), (B -V). The cross shows the position of V957 Cep. Black circles - colour indices of all components, including the third light. Empty circles are individual colour indices corrected for interstellar reddening. The solid line corresponds to the normal colour indices of stars of the fifth luminosity class according to [9]. Grey background - catalogue data [10]. Oblique crosses - comparison stars

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3. Fig. 2. Observations in the V band in the main minimum obtained in this work (upper panel). The O - C deviations of the observed points from the model curves for all photometric bands are presented below. Ic is the solution for TESS observations in the absence of the third light; immediately below are the same observations but solved by the Wilson-Devinea method (Ic W - D; Ic L3 are TESS observations in which the third light is present. The vertical scale is the same for all observation bands, which gives a clear indication of both the accuracy of the observations and their fit to the found model

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4. Fig. 3. Observations in the secondary minimum, notations are the same as in Fig. 2

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5. Fig. 4. TESS observations convolved with orbital period. The top panel shows the raw data, the scale on the ordinate axis is enlarged, and the sinusoidal oscillations on the plateau are visible. The middle panel shows the same observations, but corrected for the secondary component pulsations. Proximity effects are noticeable. The lower panel shows the residual deviations of the observations from the theoretical model constructed by the Wilson-Devinea method, σ = 0.0034m

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6. Fig. 5. Evolutionary tracks showing the dependence of the free-fall acceleration on the stellar temperature plotted from data [38] for selected stellar masses. The solid bold line shows the position of the Initial Main Sequence, ZAMS. The main component is indicated by a filled square, the secondary component by a circle. The errors in the parameter determination are shown. For scale estimation, solid curved lines show the isochrones for the two ages indicated in the figure, in Ma. All theoretical data are given for solar chemical composition

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7. Fig. 6. Dependence of stellar luminosity in solar units on temperature for selected masses [38]. The notations are the same as in Fig. 5

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8. Fig. 7. Course of the residual O - C biases of the moments of minima in the best model of apsidal rotation at different values of the initial epoch, for which the value of the periastral longitude ω = 90° is taken. The minimum of the divergences corresponds to the date JD 2 423 857

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9. Fig. 8. Residual deviations of the moments of minima from the linear formula at P1 = P2 = Ps - sideric period. Upper panel - secondary minima, indicated by empty circles. Middle panel - main minima (filled circles). The solid lines show the theoretical course of the O - C residuals plotted with the parameters from Table 9. The errors in the determination of the moments are smaller than the size of the circles. The bottom panel shows, on a larger scale, the deviations of the observed points from the theoretical calculations. Four points from the literature that we considered to be gross errors are bracketed. In the lower panel, one pair of these points has gone beyond the upper edge of the figure

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