Counterpart evolution of the Bondi radius r_B(z) of Figure 1, assuming the average-halo density of Equation (12). The y-axis is in parsecs (logarithmic), while the x-axis is linear in redshift from z = 30 (left) to z = 7. This demonstrates how the Bondi radius expands across cosmic epochs, eventually approaching or crossing the Milky Way–like inner-halo scale (﹩{r}_{{\rm{core}}}\approx 0.05{R}_{{\rm{vir}}}﹩, represented by the gray dashed line and shaded band). This enables efficient SIDM feeding in the late growth phase to form SMBHs with masses ≥10⁹M_⊙ if the crossing occurs at z  >  7.