Image Details
Caption: Figure 4.
Thermally coupled tidal migration tracks for eccentric Neptune-like planets with final circular periods Pf = 3, 4, and 5 days. The integrations begin at e = 0.9 and Tc = 2000 K. Panels show the evolution of (a) eccentricity, (b) effective tidal quality factor, (c) tidal heating and cooling, (d) orbital period and instantaneous equilibrium spin period, (e) ωeffτM, and (f) effective core temperature. The tidal response uses kf = 0.9, while ke, kf − ke, and τm are recomputed from the instantaneous shear modulus and gravitational rigidity of the core. Open circles mark where the integrations are terminated at e = 0.1. At lower eccentricity, tidal heating approaches zero, and the core cools toward the elastic regime; continued integrations fully circularize. Dashed curves in panel (d) show Pspin = 2π/Ωs, while solid curves show Porb. The horizontal dashed line in panel (f) marks the adopted solidus temperature. The tracks rapidly approach a quasi-steady state in which tidal heating balances cooling, and then circularize after a few Gyr with only very weak dependence on Pf.
© 2026. The Author(s). Published by the American Astronomical Society.