Eclipsing time variations in close binary systems: Planetary hypothesis vs. Applegate mechanism

The observed eclipsing time variations in post-common-envelope binaries (PCEBs) can be interpreted as potential evidence for massive Jupiter-like planets, or as a result of magnetic activity, leading to quasi-periodic changes in the quadrupole moment of the secondary star. The latter is commonly referred to as the Applegate mechanism. We employ an improved version of Applegate's model including the angular momentum exchange between a finite shell and the core of the star. The framework is employed to derive the general conditions under which the Applegate mechanism can work, and is subsequently applied to a sample of 16 close binary systems with potential planets, including eleven PCEBs. Further, we present a detailed derivation and study of analytical models that allow for an straightforward extension to other systems. Using our full numerical framework, we show that the Applegate mechanism can clearly explain the observed eclipsing time variations in four of the systems, while the required energy to produce the quadrupole moment variations is too high in at least eight systems. In the remaining four systems, the required energy is comparable to the available energy produced by the stars, which we consider borderline cases. Therefore, the Applegate mechanism cannot uniquely explain the observed period time variations for this entire population. Even in systems where the required energy is too high, the Applegate mechanism may provide an additional scatter, which needs to be considered in the derivation and analysis of planetary models.