Terminal Tidal Evolution of TOI-2431 b in the Primary-Centric Framework

Abstract

Bijay K. Sharma

Ultra–short-period exoplanets represent terminal configurations of tidal evolution in close star–planet systems. In the Primary- Centric Framework (PCF), orbital evolution is governed by the angular-momentum ratio Λ(a) = ωâ??/Ω(a) which defines a characteristic topological structure with two Clarke radii and a global maximum separating inner and outer evolutionary branches. We apply this framework to the Earth-sized exoplanet TOI-2431b, which orbits its host star with a period of 5.37h. Using solar-approximation parameters, we compute the present orbital radius and the corresponding Clarke radii and show that anow < aG1, placing the planet deep on the inner branch where Λ(a) < 1. In this regime, inspiral is topologically irreversible: no continuous tidal evolution can restore a torque-balanced configuration without external angular-momentum injection. Dissipation controls the timescale, but the directional inevitability of orbital decay is fixed by the inequality Λ(a) < 1. TOI-2431b therefore provides a concrete realization of terminal tidal evolution in which angular-momentum topology predetermines inward migration and ultimate disruption. The analysis illustrates how PCF supplies a global classification scheme for planetary fates beyond detailed tidal microphysics.Independent tidal-decay modeling suggests a remaining lifetime of ∼ 3 × 107 yr , consistent with the PCF classification of TOI-2431b as a terminal inner-branch system.

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