Migration speed and timescale of a growing planet in different viscous discs. Top panel: migration speed in absolute value of a planet growing from zero to Saturn’s mass, M_S, in 800 initial orbital periods. The dashed black line shows the type I migration speed from Tanaka et al. (2002, at r = r₀ constant). Bottom panel: migration timescale τ = a/|ȧ| normalised by the angular velocity of the planet. The black dashed and dotted lines represent the critical migration timescale, calculated with Eq. (3), beyond which the planet would cross the 2:1 or 3:2 resonance, respectively. These simulations were run for viscosities corresponding to α = 10⁻⁴ and 10⁻³. The migration timescales plotted in this figure were smoothed by means of a sliding window average with a size of then and 50 points (which represents a time interval of about 100 and 600 yr) for the case α = 10⁻³ and α = 10⁻⁴, respectively.