Comparison of orbital elements damping efficiencies 1/τ_mig (upper panel), 1/τ_e (middle panel), and 1/τ_a (lower panel) obtained from the output of our hydrodynamical simulations and from analytical formulas in the literature (CN2008 for Cresswell & Nelson 2008, P2011 for Paardekooper et al. 2010, and JM2017 for Jiménez & Masset 2017). The figures here are for the case of a m_pl = 1 × 10⁻⁵M_* planet with α = 3 × 10⁻⁴ and h = 0.05. τ_mig is obtained from the torque felt by the planet from the disc and typically shows good agreement between hydro and analytical predictions within the latter’s margin of uncertainty (20%). The analytical expression for τ_e comes from Cresswell & Nelson (2008) or from our fit presented in Sect. 4.3. τ_a is obtained from τ_mig and τ_e using Eq. (19).