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.

💡 Research Summary

This paper presents a detailed investigation into the origin of the intrinsic scatter observed in the stellar mass-halo mass (SMHM) relation, a fundamental scaling relation in galaxy formation theory. Using the state-of-the-art COLIBRE cosmological hydrodynamical simulations, the authors seek to determine why, at a fixed dark matter halo mass, central galaxies exhibit a range of stellar masses.

The study focuses on a key secondary halo property: concentration. It confirms a well-established but crucial trend: at fixed halo mass, galaxies residing in haloes with higher concentration tend to have higher stellar masses. This correlation is particularly strong for low-mass haloes in the range of 10^11 to 10^12 solar masses. The core of the research lies in testing two competing physical hypotheses proposed to explain this correlation. The “halo early-formation” scenario posits that haloes forming earlier become more concentrated and thus have a longer period available for star formation, leading to higher stellar mass. The “gravitational potential depth” scenario argues that more concentrated haloes have deeper gravitational potential wells, which more effectively suppress gas ejection by stellar feedback, leading to higher baryon retention and thus more efficient star formation.

To distinguish between these mechanisms, the authors employ clever diagnostics using observable galaxy properties. They examine the correlations between halo concentration, stellar mass, stellar age (a proxy for formation history), and stellar metallicity (a proxy for gas retention and recycling efficiency). Their analysis reveals a critical decoupling: while halo concentration correlates with stellar age, the stellar age itself shows only a very weak correlation with stellar mass. This indicates that simply having more time to form stars (the early-formation hypothesis) is not the primary driver of the extra stellar mass found in high-concentration haloes.

In contrast, the data strongly supports the gravitational potential depth scenario. Stellar metallicity shows a clear correlation with stellar mass. More importantly, even when statistically controlling for both halo mass and stellar mass, a significant correlation persists between halo concentration and stellar metallicity. This residual correlation is powerful evidence that high-concentration haloes are not just forming more stars; they are also better at retaining the metal-enriched gas produced by those stars. The deeper gravitational potential in these haloes impedes feedback-driven outflows, allowing for greater retention of both baryons and metals, which in turn fuels further star formation and enriches the stellar population.

Methodologically, the study strengthens its causal inference by deriving halo properties (mass and concentration) from a matched dark-matter-only simulation, thereby isolating the influence of the underlying dark matter structure from the subsequent baryonic effects like adiabatic contraction. The COLIBRE simulations themselves incorporate advanced subgrid models for physics like low-temperature cooling, star formation, and chemical enrichment, lending credibility to the detailed predictions for stellar metallicity.

In conclusion, the paper provides compelling evidence that the concentration dependence of the SMHM relation scatter is driven primarily by the depth of the gravitational potential well associated with concentrated haloes. This deeper potential quenches feedback-driven outflows, enhancing the retention of gas and metals and leading to the assembly of more massive and metal-rich central galaxies. This work underscores the importance of halo internal structure, not just halo mass, in shaping galaxy properties and offers a clear physical pathway connecting dark matter halo properties to observable galactic features.