Gravitational potential drives the concentration dependence of the stellar mass-halo mass relation

We investigate the origin of the scatter in the stellar mass-halo mass (SMHM) relation using the \colibre cosmological hydrodynamical simulations. At fixed halo mass, we find a clear positive correlation between stellar mass and halo concentration, particularly in low-mass haloes between $10^{11}$ and $10^{12}\,\rm M_\odot$, where all halo properties are computed from the corresponding dark-matter-only simulation. Two scenarios have been proposed to explain this trend: the earlier formation of higher-concentration haloes allows more time for star formation, or the deeper gravitational potential wells of higher-concentration haloes enhance baryon retention. To distinguish between them, we examine correlations between halo concentration, stellar mass, stellar age, and stellar metallicity. While, at fixed halo mass, halo concentration correlates with stellar age, stellar age itself shows only a weak correlation with stellar mass, indicating that early formation alone cannot account for the concentration-dependence in the scatter of the SMHM relation. In contrast, both stellar metallicity and halo concentration exhibit correlations with stellar mass. The connection between halo concentration and stellar metallicity persists even when simultaneously controlling for both halo mass and stellar mass. These results support the scenario in which the deeper gravitational potentials in higher-concentration haloes suppress feedback-driven outflows, thereby enhancing both baryon and metal retention.