Feedback driven interactions between dark and luminous matter to explain tight galaxy scaling relations

The tight empirical correlation linking the stellar disk scale length $R_d$ to the dark matter scale radius $r_0$ has been proposed as possible evidence for a fundamental coupling between baryons and dark matter beyond gravity. We re-examine the physical origin of this relation using a sample of 31 galaxies from the NIHAO cosmological hydrodynamical simulations, which include no dark matter-baryon interactions beyond gravity and baryonic feedback processes. NIHAO naturally reproduces both the normalization and the small scatter of the observed $R_d-r_0$ relation at $z=0$, while yielding a slightly shallower slope. By tracking galaxies from $z=2$ to $z=0$, we identify three distinct evolutionary classes: systems undergoing disk expansion, contraction, and quasi-static evolution. Using a Bayesian hierarchical framework, we provide the first characterization of the cosmic evolution of the $R_d-r_0$ relation, tracing the evolution of its normalization, slope, and intrinsic scatter from $z=2$ to the present day. We find a mild decrease in normalization ($\sim0.07$ dex), a flattening of the slope from $\alpha \simeq 1.05$ to $\alpha \simeq 0.95$, and a weak decline in the intrinsic scatter toward lower redshift, suggesting that galaxies evolve preferentially along the relation while jointly re-balancing their stellar and dark matter scales. By comparing hydrodynamical simulations with their dark-matter-only counterparts, we isolate the impact of baryons and baryonic feedback on halo structure. Our results show that stellar feedback alone can reshape the central potential and naturally establish the observed coupling between luminous and dark matter, without requiring modifications to the dark sector.