Relative migration timescale in a simulation where Saturn migrates in the cold disc perturbed by Jupiter, without feeling Jupiter’s gravity. The normalised timescale is plotted as a function of a_S/ a_J, and the vertical black dashed line marks the location of the 2:1 MMR, while the grey dotted vertical line marks the position of the 5:2 MMR. The horizontal dashed line marks the critical migration timescale, calculated from Eq. (3) (for M_p = M_s), above which the planets should not cross the 2:1 resonance. The migration timescale was smoothed by means of a sliding window average with a size of 100 points (which represents a time interval of about 12 000 yr), in order to suitably reduce the noise.