Constraining the Presence of Companion Planets in Hot Jupiter Planetary System Using TTV Observation from TESS

The presence of another planetary companion in a transiting exoplanet system can impact its transit light curve, leading to sinusoidal transit timing variations (TTV). By utilizing both $\chi^2$ and RMS analysis, we have combined the TESS observation data with an N-body simulation to investigate the existence of an additional planet in the system and put a limit on its mass. We have developed CMAT, an efficient and user-friendly tool for fitting transit light curves and calculating TTV with a theoretical period, based on which we can give a limit on its hidden companion's mass. We use 260 hot Jupiter systems from the complete TESS data set to demonstrate the use of CMAT. Our findings indicate that, for most systems, the upper mass limit of a companion planet can be restricted to several Jupiter masses. This constraint becomes stronger near resonance orbits, such as the 1:2, 2:1, 3:1, and 4:1 mean motion resonance, where the limit is reduced to several Earth masses. These findings align with previous studies suggesting that a lack of companion planets with resonance in hot Jupiter systems could potentially support the high eccentricity migration theory. Additionally, we observed that the choice between $\chi^2$ or {root mean square (RMS)} method does not significantly affect the upper limit on companion mass; however, $\chi^2$ analysis may result in weaker restrictions but is statistically more robust compared to RMS analysis in most cases.