Time evolution of SIDM halos according to Yang et al. (2024). The timescale is parameterized in terms of the core-collapse timescale, t_cc – Eqs. (3) and (7). The halos start off as NFW profiles of characteristic density and radius ρ_s0 and r_s0, respectively. (a) Radial density at different timesteps going from almost the initial conditions (t_age/t_cc = 0) to core-collapse (t_age/t_cc = 1), including the formation of a maximum core (t_age/t_cc = t_c/t_cc ≃ 0.12). Profiles before the maximum core formation (t_age ≤ t_c) are represented as dashed lines whereas profiles after this core-formation are shown as solid lines. (b) Same profiles as (a) but normalized to the central density and to the core radius defined in Eq. (6). The black bullet symbol indicates the location of the core radius. (c) Time variation of the true core (the blue solid line; r_c in Eq. (17)) and of the model core (the orange dashed line; r′_c in Eq. (15)). (d) Time variation of the central density (the blue solid line; ρ_SIDM(0)) and of the characteristic density (the orange dashed line; ρ_s′ in Eq. (15)). The green arrow in (c) and (d) marks the timescale for maximum core formation.