Torques exerted on a Jupiter-mass planet embedded in a proto-planetary disk around a young, solar-type star. a: nominal parameterization of the star–planet–disk model, with R_⋆ = 2 R_⊙, P_rot = 1 d, , Σ_p,0 = 1000 g cm⁻², α = 10⁻³, μ = 1.85, κ = 10⁻⁷ m² kg⁻¹, and r_mc = 0.05 AU. The blue dashed curve refers to the tidal torque (Γ_t), the red dotted line to the type-II migration torque of the disk (Γ_II), and the thick solid line to the total torque. The location of zero total torque at 0.031 AU is indicated with a black circle. The factors Γ_t, and therefore also Γ_t + Γ_II, swap signs at the stellar corotation radius, interior to which any planet would be rapidly pulled into the star. (b) similar to (a) but with P_rot = 8 d.