The temporal evolution of the central density ρ₀ (left panel) and velocity dispersion ν₀ (right panel) of an SIDM core with M₂₀₀ = 1 × 10¹¹ M_⊙. Considering the degeneracy between the formation time t_age and the scattering cross section σ_m, we choose their product as the horizontal axis, with time measured in units of the cosmic time of J0946+1006 (11.06 Gyr). The blue, orange, and magenta scatter points represent the evolution for the low-density solution, high-density solution, and mirrored high-density solution, respectively. The moments corresponding to t_merge and t_coll are marked by a green dashed line and a purple dashed–dotted line, respectively. The black dots represent the moments we chose to examine the evolution of the SIDM profile, while the red star represents the moment closest to the result of Q. Minor et al. (2021) in the 2D observational space.