2024A&A...691A.115Z

Context. Recent period investigations of the post-common envelop binary (PCEB) NSVS 14256825 suggest that two circumbinary companions are necessary to explain the observed eclipse timing variations (ETVs).
Aims. Our objective in this work was to search for the best-fitting curve of two LTTE terms of the ETV diagram by implementing a grid search optimization scheme of Keplerian (kinematic) and Newtonian (N-body) fits alongside a dynamical stability analysis of N-body simulations.
Methods. We compiled two datasets of archival photometric data covering different timelines and updated them with new observations and with three new times of minima calculated from the Transiting Exoplanet Survey Satellite (TESS). A grid search optimization process was implemented, and the resulting solutions that fell within the 90% confidence interval of the best-fitting curve of the ETV diagram were tested for orbital stability using N-body simulations and the MEGNO chaos indicator.
Results. The Keplerian and Netwonian fits are in close agreement, and hundreds of stable configurations were identified for both datasets reaching a lifetime of 1 Myr. Our results suggest that the ETV data can be explained by the presence of a circumbinary planet with mass m_b = 11 M_Jup in a nearly circular inner orbit of period P_b = 7 yr. The outer orbit is unconstrained with a period range P_c = 20 - 50 yr (from 3:1 to 7:1 MMR) for a circumbinary body of substellar mass (m_c = 11 - 70 M_Jup). The stable solutions of the minimum- and maximum-reduced chi-square value were integrated for 100 Myr and confirmed a non-chaotic behavior. Their residuals in the ETV data could be explained by a spin-orbit coupling model (Applegate-Lanza). However, continuous monitoring of the system is required in order to refine and constrain the proposed solutions.