A photometric study of the Algol-type binary AB Cas

Abstract

We present new photoelectric observations of the eclipsing binary system AB Cas, together with an analysis of the light curves. Using the available times of light minimum reported in the literature together with our own minima, period changes are monitored, and the possible thirdbody parameters are obtained. The absolute properties of the system and the delta-Scuti behavior of the primary are also discussed.

δ Scuti light variations as a test for choosing the mechanism of cyclic orbital period changes in Algols

“…The above authors concluded that the period of this system undergoes both secular changes due to mass transfer (d P /d t = 0.03 s yr −1 ) and cyclic period modulations due to the presence of a third body with a period of P 3 = 40.3 yr and a mass of M 3 ≥ 0.31 M ⊙ . Later, a similar study was carried out by Abedi & Riazi (2007). They also interpreted the O−C curve as a secular period change superimposed on cyclic variations in P , and found the rate of period change to be d P /d t = 0.05 s yr −1 and the parameters of the third body to be P 3 = 25.6 yr and M 3 ≥ 0.21 M ⊙ .…”

“…The derivative of JD with respect to E yields the period at any arbitrary time‐instant: We now differentiate this formula with respect to time to obtain because , . We then substitute formula (6) for into to obtain (with the approximation P ≈ P 0 ) The parameters of the star AB Cas are equal to: M 1 = 1.875 M ⊙ , M 2 = 0.375 M ⊙ (Abedi & Riazi 2007), q = 0.20, 2 A = 1.374 × 10 −9 d, P = 1.366 88 d. We substitute these quantities into to obtain M ⊙ yr −1 .…”

“…It is natural to first try to explain the form of (O−C) 2 by invoking the hypothesis of a third body. Apsidal rotation can be ruled out, because the orbit of AB Cas is circular (Abedi & Riazi 2007). If interpreted as due to the presence of a third body in the system, the (O−C) 2 differences can be written in terms of the parameters of the long‐period orbit via the so‐called light‐time equation: where υ and E are the true and eccentric anomalies, respectively, a 3 is the semi‐major axis, i 3 is the inclination, e 3 is the eccentricity, ω 3 is the longitude of periastron of the orbit of the eclipsing binary about the barycentre of the triple system, and c is the speed of light.…”

“…The continuous line passing through the (O−C) 2 data points in Figs 1 and 2 shows the theoretical light‐time curve computed with the parameters listed in Table 2. Our inferred parameters of the light‐time equation can be used to compute the mass function We adopt M 1 + M 2 = 2.25 M ⊙ , in accordance with Abedi & Riazi (2007), and assume that i 3 = 90° to infer a lower boundary for the mass of the third body: It is evident from Figs 1 and 2 that cyclic period changes of the eclipsing binary AB Cas can be mathematically well described by the light‐time equation; however, such an interpretation of the (O−C) 2 plot is inconsistent with other observational data, which we discuss in the next section.…”

“…The variability of AB Cas (BD + 70° 139, HIP 12235, V = 10.32 mag, P = 1.3669 d) was discovered by Hoffmeister (1928). The star is an Algol‐type semi‐detached eclipsing binary consisting of an A4V‐type primary and a K‐type subgiant secondary, which fills its Roche lobe (Abedi & Riazi 2007). Tempesti (1971) found the primary to be a δ Scuti type star with 0.05‐mag‐amplitude light variations and a pulsation period of P sct = 0.058 d. Kreiner (1971) and Ahnert (1973) were the first to report orbital period changes in AB Cas.…”