Same as Figure 1, but for various softening lengths, ε, and two different softening kernels (Appendix G). The level of transparency corresponds to different softening lengths (Equation G.1) with the bottom (resp. top) line corresponding to 20% (resp. 80%) contours over 100 independent realisations with N​ = ​25​ × ​10⁶ particles. The case Kuzmin ε​ = ​0.16 corresponds to Figure 1. For the Plummer kernel, the larger the softening length, the slower the relaxation, and the more delayed the transition to instability. This kernel introduces a strong gravitational bias when compared with non-softened theoretical predictions (Figure G.1). On the contrary, simulations using the Kuzmin kernel behave similarly across softening lengths. Interestingly, we note that, in every case, the dispersion among realisations increases near phase transition.