SDSS J143547.87+373338.5 is a detached eclipsing binary that contains a white dwarf with a mass of 0.5 M⊙ and a fully convective star with a mass of 0.21 M⊙. The eclipsing binary was monitored photometrically from 2009 March 24 to 2015 April 10, by using two 2.4-m telescopes in China and in Thailand. The changes in the orbital period are analyzed based on eight newly determined eclipse times together with those compiled from the literature. It is found that the observed–calculated (O–C) diagram shows a downward parabolic change that reveals a continuous period decrease at a rate of s s?1. According to the standard theory of cataclysmic variables, angular momentum loss (AML) via magnetic braking (MB) is stopped for fully convective stars. However, this period decrease is too large to be caused by AML via gravitational radiation (GR), indicating that there could be some extra source of AML beyond GR, but the predicted mass-loss rates from MB seem unrealistically large. The other possibility is that the O–C diagram may show a cyclic oscillation with a period of 7.72 years and a small amplitude of 0000525. The cyclic change can be explained as the light-travel-time effect via the presence of a third body because the required energy for the magnetic activity cycle is much larger than that radiated from the secondary in a whole cycle. The mass of the potential third body is determined to be M⊙ when a total mass of 0.71 M⊙ for SDSS J143547.87+373338.5 is adopted. For orbital inclinations , it would be below the stable hydrogen-burning limit of M3?~?0.072 M⊙, and thus the third body would be a brown dwarf.
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