Top: spatial evolution of the second core radius as a function of time for all the collapse scenarios with different initial cloud core masses ranging from 0.5 M_⊙ to 100 M_⊙ as indicated in the colour bar. The evolution is traced from the onset of the second core formation until the central density reaches ≈0.5−0.8 g cm⁻³. The inset in the upper left zooms in on the back and forth behaviour for one of the curves. This results from the jump between the two local minima in the velocity profile of the accretion shock, which is used to define the second core radius. Bottom: comparison of the Kelvin–Helmholtz and accretion timescales. A large (small) ratio is associated with an expansion (contraction) phase of the second hydrostatic core (see top panel).