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

TL;DR

This study tackles the origin of scatter in the SMHM relation by examining halo concentration as a secondary parameter using COLIBRE simulations. By comparing hydro runs with their DMO counterparts, the authors show that at fixed halo mass, higher concentration correlates with larger stellar masses primarily through enhanced metal retention and baryon retention in deeper potentials, rather than via earlier formation alone. The concentration–stellar metallicity link persists even when controlling for both halo and stellar mass, supporting a potential-depth driven mechanism for the SMHM scatter, particularly in haloes with $M_{200c}^{\rm DMO}\in[10^{11},10^{12}]\,\rm M_\odot$. These results are robust to numerical resolution and AGN feedback prescriptions, and point to observational avenues to test the link between halo potential depth and metallicity using stellar spectroscopy and lensing/kinematic measurements. Overall, the work clarifies a key physical driver of galaxy formation efficiency and informs models that connect halo structure to stellar content.

Abstract

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.

Figures (3)

• Figure 1: The SMHM relation for central galaxies in the COLIBREL200m6 simulation, where colour encodes the logarithm of the halo concentration smoothed over 0.1-dex stellar mass and halo mass bins. Here both halo mass and halo concentration come from the corresponding DMO run. The error bars show the median and the $16^{\rm th}-84^{\rm th}$ stellar mass quantiles within 0.1-dex-width halo mass bins. The solid line shows the best-fitting result with the functional form in equation (\ref{['eq:fitting']}). Three inset panels show the scatter plot, as well as Spearman's rank correlation coefficient, between stellar mass and halo concentration in three selected 0.1-dex-width halo mass bins, where the colour encodes the density of the scatter point distribution. The red crosses in the bottom panel show Spearman's rank correlation coefficients between stellar mass and halo concentration in 0.1-dex-width halo mass bins, where only bins with more than 30 data points are shown. The solid line is a smoothing B-spline line fitted to the data points to show the trend. There is a moderately strong correlation between stellar mass and concentration at fixed halo mass, particularly below $10^{12}\,\rm M_\odot$, and the strength declines above this mass.
• Figure 2: Pairwise Spearman's rank correlation coefficients for relations between halo and central galaxy properties within 0.1-dex-width halo mass bins from $10^{11}$ to $10^{13}\,\rm M_\odot$. The four panels correspond to correlations between halo concentration and stellar age, stellar age and stellar mass, halo concentration and stellar metallicity, and stellar metallicity and stellar mass, respectively. Here both stellar age and stellar metallicity are weighted by the mass of stellar particles, and all halo related properties are from the matched haloes in the DMO run. In the halo mass range of $10^{11-12}\,\rm M_\odot$, there is at most a weak correlation between stellar age and stellar mass while all other correlations are of moderate strength, so the correlation between halo concentration and stellar mass is mediated by stellar metallicity rather than by stellar age.
• Figure 3: Spearman's rank correlation coefficients between halo concentration and stellar metallicity (red symbols), and between halo concentration and stellar mass (blue symbols) at fixed stellar and halo mass. Results for haloes within the mass ranges $10^{11-12}\,\rm M_\odot$ and $10^{12-13}\, \rm M_\odot$ are shown with filled and open symbols, respectively. Stellar mass and halo mass are constrained within 0.1-dex and 0.3-dex bins, respectively. The two horizontal lines and the shaded regions are the mean values and standard deviations of the correlation coefficients for haloes of mass $10^{11-12}\,\rm M_\odot$. The correlation coefficient is only evaluated when more than 30 galaxies are present in the bin. All halo related quantities come from the matched haloes in the DMO run. As expected, there is no correlation between halo concentration and stellar mass when both halo mass and stellar mass are controlled. However, there is still a moderately strong correlation between concentration and stellar metallicity. The fact that this correlation is present at fixed stellar mass implies that it is due to the potential depth rather than the amount of metals produced.