TrES-1 b: A Case Study in Detecting Secular Evolution of Exoplanet Orbits

We present a comprehensive analysis of transit, eclipse, and radial velocity data of the hot Jupiter TrES-1 b and confirm evidence of orbital variations on secular timescales. Apparent variations due to systemic motion and light travel time effects have been ruled out, indicating that the observed changes are dynamical in origin. Joint modeling of the TrES-1 b data favors an apsidal precession model, but the rapid precession rate of $4^\circ$ yr$^{-1}$ cannot be explained without invoking an undetected close-in planetary companion, which remains unseen in the data. While radial velocity measurements reveal a previously undetected companion candidate on a wide, eccentric orbit, it is unlikely to drive the observed evolution of TrES-1 b. However, an orbital decay model provides a plausible alternative if the loss of orbital energy is driven by planetary obliquity tides. We find that the best-fit orbital decay rate of $-7.1^{ +1.5}_{-1.6}$ ms yr$^{-1}$ is aligned with theoretical predictions for modified tidal quality factors of hot Jupiters if TrES-1 b has a planetary obliquity $\varepsilon_p > 30^\circ$. We encourage follow-up observations of this system, particularly of eclipse timing and radial velocities, to further constrain the nature of the observed evolution. This paper provides a practical framework for studying secular variations and aims to accelerate future research on similar systems.