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We present 36 new mid-eclipse times obtained between 2017 and 2023 using theT100 telescope in Turkey, extending the time span of the $O-C$ diagram to 25years. Once again, these new observations show significant deviations fromprevious published models that were able to explain the observed variations ofthe binary period. We investigate two plausible explanations for thisvariability: the LTT effect due to the presence of one or two invisiblelow-mass (planetary) companion(s) in distant circumbinary orbits; othermechanisms, like e.g. the Applegate mechanism, associated with the magneticcycles of the M-dwarf component of the WD+dM binary. Through MCMC analyzes, wedemonstrate that the observed $O-C$ variability can be explained by thepresence of a planet with a minimum mass of $\sim9.5 M_J$. This circumbinaryplanet orbits around the binary system with a period of about 19.5 years,maintaining a stable orbit for a timeline of 10 Myr. By adding a weak LTTsignal from a secondary hypothetical planet we achieve statistically betterresults. However, the orbits of the bodies in a two-planet system remain stableonly for a small range of the parameter space. The energy required to power theApplegate and other Applegate-like mechanisms is too high to explain the periodvariations observed. Thus, on the one hand there is substantial evidencesupporting the existence of a planet in the NN Ser system, but on the otherhand there are also compelling indications that cast doubt on the existence ofa second hypothetical planet.

monthly notices of the royal astronomical society

Investigation on the Orbital Period Variations of NN Ser: Implications  for the Hypothetical Planets, the Applegate Mechanism and the Orbital  Stability