HH UMa and V1175 Her are two W UMa contact binary systems whose periods were reported as undergoing secular increase. In this paper, we improved their period analyses with a more extensive database of eclipse timings, finding that both periods show cyclic variation. The cyclic variation could be attributed to a Light Travel Time Effect (LTTE) induced by a third body. Both circular orbit and eccentric orbit cases were considered. For HH UMa, A cyclic variation with a period of around 20 yr has been detected, which may be caused by a third body with the mass larger than 0.23 M⊙. However, no parabolic variation was detected in its O-C curve, implying the balance of the mass transfer between the two components and the angular momentum loss from the binary system. As to V1175 Her, a long-term period increase superposed on a periodic oscillation was detected. The period increase at a rate of about dP/dt = 2×10−7d · yr−1 indicates the mass transfer from the less massive component to its companion. And the cyclic variation of about 7.5 yr could be caused by a hierarchical third body with a minimal mass exceeding 0.46M⊙ orbiting around the central binary. This mass is larger than that of the less massive component of the binary, which means that the secondary component was not replaced by the third body during early stellar interactions, implying it keeps original dynamical information. By removing angular momentum from the central binary system, the tertiary component has played a significant role in the formation of contact binaries.
We present new multi-color light curves of V1309 Her and AS CrB, which were observed by the 60 cm telescope located at the Maidanak Astronomical Observatory. Combined with the Large-Sky-Area Multi-Object Fiber Spectroscopic Telescope atmospheric parameters, we analyzed our BVRCIC light curves for both systems by employing the Wilson–Devinney program. Our results show that both systems are low-mass-ratio overcontact binaries (V1309 Her: q = 0.213, AS CrB: q = 0.16). AS CrB has a high fill-out factor, while that of V1309 Her is moderate. By adding our new times of minimum light, we found the periodic oscillations in their O − C curves, which could be explained by the light travel-time effect of the third bodies. The third lights detected during the light curve analysis support the existence of the third bodies in V1309 Her and AS CrB. Third bodies usually play an important role for the origin and evolution of the central pair by removing their angular momentum. With the angular momentum loss, a moderate-fill-out overcontact binary like V1309 Her will evolve to a deep one like AS CrB. AS CrB lies at the late evolutionary stage of contact binaries. A long-term period increase at a rate of dP/dt = 5.22(± 0.28) × 10−7 d yr−1 was detected in our O − C diagram analysis. When its orbital angular momentum is less than three times the total spin angular momentum, a system may finally evolve into a rapid-rotating single star.
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