Orbital Characteristics of Planets Orbiting Highly Evolved Giants Using the SENS Sample

The stellar evolutionary stage is considered vital to the planetary orbital architecture. We investigate this relationship by comparing 18 planets orbiting highly evolved red giants from the Search for Exoplanet around Northern circumpolar Stars (SENS) survey to 228 cold Jupiters orbiting main sequence (MS), subgiant (SG), and red giant (RG) hosts from the NASA Exoplanet Archive (NEA). By using scaled distance $a/R_{\ast}$ to incorporate the stellar evolutionary state, we examine whether tidal geometry can influence eccentricity distributions across evolutionary stages. While the NEA population exhibits weakly positive eccentricity--period and eccentricity--scaled distance trends, the SENS population shows a negative eccentricity--period slope and a shift in trend near $a/R_{\ast} \approx 15$. We find that eccentricities are tightly clustered at low dispersion in the inner regime ($a/R_{\ast} \lesssim 15$), characteristic of strong tidal suppression, and increasingly scattered in the outer regime, where the SENS population rejoins the eccentricity trend of the NEA red giant subsample. The $a/R_{\ast}$--$P$ relation preserves near-Keplerian slopes ($\approx 2/3$) across all stages, but systematic intercept shifts imply inward migration in scaled distance as stellar radii expand throughout stellar evolution. Quantifying tidal torque, dissipation rates, and orbital decay timescales demonstrates increases in tidal efficiency across this boundary and decreases in decay timescales at a greater rate for the highly evolved giants compared to their less evolved counterparts. We interpret $a/R_{\ast} \approx 15$ as an empirical trend boundary between strong and weak tidal regimes, marking where stellar expansion begins to dominate orbital stability. This may explain the scarcity of short-period gas giants around highly evolved stars and establish a physically motivated framework for interpreting orbital survival and migration across stellar evolutionary stages.