Dynamics and habitability of the TESS circumbinary systems TOI-1338 and TIC-172900988

Two circumbinary planets have been recently discovered by TESS. The main aim of this work is to explore whether it is possible, besides the discovered circumbinary planet, to have an Earth-like planet within the habitable zone of the system. We carry out numerical simulations over the whole range of the two habitable zones in order to see whether an Earth mass planet can exist there. We find that both systems seem to be able to host an additional planet in their habitable zone. We construct dynamically informed habitable zones and we find that a large percentage of the habitable zone can be suitable for a planet to retain liquid water on its surface no matter what its orbital evolution will be. Moreover, we investigate the possibility to detect an Earth-like planet in the habitable zone of the two systems. We find that for both systems, if such a planet existed, the radial velocity and astrometry signals would be rather small to be detected by our current instruments. Some discussion is also made for the dynamical evolution of the existing planet.