Redshift function z (top panel) and redshift function “excess” (middle panel for the RAR model and lower panel for the central massive BH model) with respect to the Keplerian (Newtonian) contribution, i.e., Δz = z − z_K (see Appendix B), for the S2 motion at about its pericenter passage. The theoretical models are calculated by solving the equations of motion of a test particle in the gravitational field of (1) a Schwarzschild BH of 4.075 × 10⁶ M_⊙ (dashed blue curves), and (2) the DM distribution obtained from the extended RAR model for 56 keV fermions (red curves). The mass of the quantum core in the RAR model is 3.5 × 10⁶ M_⊙. Table 1 shows the parameters of each model.