A non-extensive diagnostic of spin-orbit coupling in close-in giant exoplanets

Abstract The spin-orbit coupling of star--planet systems results from the competition between magnetic braking and tidal interactions, especially in systems hosting close--in gas giants. In this work, we apply the non–extensive tidal index $q$, which we introduced in a previous study based on the Tsallis statistical formalism, to a \textbf{restricted working sample of cool main–sequence exoplanet hosts with measured stellar rotation periods and the stellar, planetary and orbital parameters required to evaluate tidal coupling.} The index $q$ is computed directly from observable stellar and planetary parameters, providing a physically grounded proxy for the strength of tidal coupling. Our dataset spans planetary masses from 0.0017 to $10.1\,M_{\mathrm{J}}$ and orbital periods from $0.28$ to $282.5$ days \textbf{and F-, G-, K-, and M-type host stars. We find that most close--in giants in our sample exhibit $q>3$ and orbit inside the stellar corotation radius, a configuration consistent with enhanced tidal coupling. We also identify systematic trends between $q$ and planetary mean density, stellar rotation, and corotation radius, with high-$q$ systems preferentially associated with inflated, low-density gas giants around rapidly rotating stars. These results suggest that $q$ can be a useful diagnostic of the observed tidal state of close-in giant exoplanets, tracing long-term spin-orbit coupling and proximity to corotation within the restricted parameter space explored here.}