Time dependence of torque on b for different physical mechanisms. The dashed lines represent the minimum dynamical torque on (blue) or mass loss rate for (green) planet b required to induce a high enough migration of planet c, which ensures sustained orbital expansion of the (b, c, e) system. These torques decay with time according to the models by Wang & Lin (2023) (mass loss) and Ahuir et al. (2021) (dynamical torques). For reference, the green solid line represents the torque on b due to a 2% mass loss (Wang & Lin 2023) and the blue solid line fits the dynamical tide model of Ahuir et al. (2021). The black line represents the torque due to equilibrium tides assuming Q_⋆′ = 10⁶.