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.

In this paper, we study the general impact of stellar mass-ejection events in planetary orbits in post-common envelope binaries with circumbinary planets like those around NN Serpentis. We discuss a set of simple equations that determine upper and lower limits for orbital expansion and investigate the effect of initial eccentricity. We deduce the range of possible semi-major axes and initial eccentricity values of the planets prior to the common-envelope event. In addition to spherically-symmetric mass-ejection events, we consider planetary dynamics under the influence of an expanding disk. In order to have survived, we suggest that the present planets in NN Ser must have had semi-major axes > ∼ 10 AU and high eccentricity values which is in conflict with current observations. Consequently, we argue that these planets were not formed together with their hosting stellar system, but rather originated from the fraction of matter of the envelope that remained bound to the binary. According to the cooling age of the white dwarf primary of 10 6 yr, the planets around NN Ser might be the youngest known so far and open up a wide range of further study of second generation planet formation.

Since its proposal in 1992, the Applegate mechanism has been discussed as a potential intrinsical mechanism to explain transit timing variations in various kinds of close binary systems. Most analytical arguments presented so far focused on the energetic feasibility of the mechanism, while applying rather crude one-or two-zone prescriptions to describe the exchange of angular momentum within the star. In this paper, we present the most detailed approach to date to describe the physics giving rise to the modulation period from kinetic and magnetic fluctuations. Assuming moderate levels of stellar parameter fluctuations, we find that the resulting binary period variations are one or two orders of magnitude lower than the observed values in RS-CVn like systems, supporting the conclusion of existing theoretical work that the Applegate mechanism may not suffice to produce the observed variations in these systems. The most promising Applegate candidates are low-mass post-common-envelope binaries (PCEBs) with binary separations 1 R ⊙ and secondary masses in the range of 0.30 M ⊙ and 0.36 M ⊙ .

Context. Eclipsing time variations are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the Observed minus Calculated (O-C) diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. Aims. In this work we explore the feasibility of driving eclipsing time variations via the Applegate mechanism for a sample of PCEB systems, including a range of different rotation rates. Methods. We used the MESA code to evolve 12 stars with different masses and rotation rates. We applied simple dynamo models to their radial profiles to investigate the scale at which the predicted activity cycle matches the observed modulation period, and quantifiy the uncertainty. We further calculated the required energies to drive the Applegate mechanism. Results. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems. In RX J2130.6+4710, it may be feasible as well considering the uncertainties. We note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star.Conclusions. The results suggest that the ratio of physical to critical rotation rate in the main sequence star is an important indicator for the feasibility of Applegate's mechanism, but exploring larger samples will be necessary to probe this hypothesis.