Detection of periodic transit timing variations in the warm sub-Saturn planet HD 332231 b

Transit timing variations (TTVs) provide a powerful means to detect and characterise additional bodies in known planetary systems, even when they do not transit their host stars. We aim to investigate the dynamical architecture of the HD 332231 system by analysing the TTVs of its close-in gas giant, HD 332231 b. Our goal is to assess whether the observed deviations from a linear ephemeris can be explained by the presence of an additional planetary companion. We refined the transit ephemeris of HD 332231 b using high-precision photometry from the Transiting Exoplanet Survey Satellite and complementary ground-based observations. We extracted individual transit mid-times, constructed an observed minus calculated (O--C) diagram for transit timing data, and modelled the observed TTV signal through an extensive suite of N-body integrations covering a broad range of possible companion masses and orbital configurations. We detected a coherent TTV pattern with a period of approximately 6.7 years and an amplitude of about 45 minutes. Although numerous orbital configurations reproduce the observed TTVs, the combination of current radial velocity and photometric constraints yields a modest improvement in likelihood for solutions with an external planet on an orbit longer than 60 days, likely near a high-order mean-motion resonance and with moderate to high eccentricity. Our results suggest that HD 332231 b is part of a dynamically interacting multi-planet system. Continued transit monitoring and radial-velocity follow-up will be essential to confirm the perturber's nature and refine the system's dynamical architecture.