Temporal evolution of the softening length h in (a) and (b), the smallest cell radius within the softened spheres min(R_cell)|_h in (c) and (d) as well as the system time step Δt_sys in (e) and (f). The simulations conducted with κ = 1 (see Sect. 2.3) are shown in light blue, while the simulations with κ = 0 (Moreno et al. 2022) are shown in black. The plots on the left feature the system involving a BH companion and the plots on the right the CE models involving the NS companion, respectively.