Evolution of the semimajor axis and eccentricity of a Jupiter-mass planet due to type II migration for different disk lifetimes τ_disk and different assumptions on the stellar tide. The dashed lines correspond to the case where only the equilibrium tide in the star is accounted for; the solid lines correspond to cases where both the equilibrium tide and dynamical tide are taken into account (initial fast stellar rotation period of 1 day). We note that the rotation of the star is evolving, here mainly due to the contraction of the radius, and its evolution is encoded in the corotation radius curve (i.e., where the orbital frequency is equal to the stellar spin). For clarity, we only plot two cases in the bottom panel (τ_disk = 2 × 10⁴ yr and 5 × 10⁴ yr). The equilibrium tide is still represented with dashed lines, but also with transparency to ease identification.