CASCO: Cosmological and AStrophysical parameters from Cosmological simulations and Observations III. The physics behind the emergence of the golden mass scale

TL;DR

This work investigates the origin and evolution of the golden mass, defined by a minimum in the dark-to-stellar mass ratio, using the CAMELS simulations based on IllustrisTNG to explore how cosmology and SN/AGN feedback shape this feature across redshift. The authors demonstrate a robust U-shaped $M_{ m DM,1/2}/M_{ m star,1/2}$–$M_{\star}$ relation with a golden-mass minimum near $M_{\star}\sim10^{10.2}$–$10^{10.6}\,M_\odot$ (and $M_h\sim10^{12}\,M_\odot$) that is largely insensitive to cosmology but highly sensitive to feedback parameters, with the minimum appearing earlier in cosmic time for stronger feedback and persisting to $z\sim2$ in most models. A strong link is found between the golden mass and the size–mass relation, and a marked galaxy-type dependence emerges: passive galaxies show a clear U-shaped trend while star-forming systems often do not. The results suggest a scenario where SN and AGN feedback, together with virial shocks and cold streams, regulate gas accretion and quenching across cosmic time, and they highlight the need for larger-volume simulations to robustly probe high-mass, high-redshift regimes and refine constraints on feedback physics.

Abstract

We investigate the origin and evolution of the "golden mass" (halo mass $\sim10^{12} \, \rm M_{\odot}$, stellar mass $\sim5 \times 10^{10} \, \rm M_{\odot}$), linked to peak star formation efficiency, using \textsc{camels} simulations based on IllustrisTNG. Exploring a range of SN/AGN feedback strengths and cosmologies ($Ω_{\rm m}, σ_8$), we find a U-shaped relation between dark-to-stellar mass ratio and stellar mass, with a minimum at the golden mass, in line with observations. Cosmology affects the normalization of this relation, while feedback shapes its form and the emergence of the golden mass. Stronger SN feedback lowers its value; AGN feedback, especially radiative efficiency, alters the high-mass slope and shifts the golden mass. The golden mass appears earlier with stronger feedback, which quenches star formation more rapidly. Passive galaxies retain the U-shape; star-forming ones show decreasing dark matter fraction with stellar mass, with possible reversal at low redshift. Global stellar fractions also exhibit a U-shaped trend: in passive galaxies, the golden mass shifts to lower masses or vanishes; in star-forming ones, it emerges only at low redshift. Feedback governs the golden mass up to $z \sim 1.5-2$, with a secondary role from cold streams and virial shocks. We speculate that at $z \gtrsim 1.5-2$, a single stream-regulated scale governs galaxy growth, which later bifurcates into two: a low-mass scale tied to gas richness and a higher-mass golden mass regulating efficiency and quenching. (abridged)

Figures (9)

• Figure 1: The ratio $M_{\textrm{DM},1/2}/M_{\star,1/2}$ is plotted against $M_{\star}$ for $\textsc{camels}$ simulations, with each row showing variations in the cosmological parameters $\Omega_{\rm m}$ and $\sigma_{8}$. The green lines represent the reference $\textsc{camels}$ simulation. To examine the evolution across redshift, simulation snapshots at $z=0$, $z=0.5$, $z=1$, $z=1.5$ and $z=2$ are displayed from left to right. Medians in stellar mass bins are shown. For the reference simulation the 16-84th percentile range is also shown as a shaded green region.
• Figure 2: The ratio $M_{\textrm{DM},1/2}/M_{\star,1/2}$ is plotted against $M_{\star}$ for $\textsc{camels}$ simulations, with each row showing variations in the SN-related parameters $A_{\rm SN1}$ and $A_{\rm SN2}$. The green lines represent the reference $\textsc{camels}$ simulation. To examine the evolution across redshift, simulation snapshots at $z=0$, $z=0.5$, $z=1$, $z=1.5$ and $z=2$ are displayed from left to right. Medians in stellar mass bins are shown.
• Figure 3: The ratio $M_{\rm DM,1/2}/M_{\star,1/2}$ is plotted against $M_{\star}$, with each row showing variations in the AGN-related simulation parameters: $A_{\textrm{AGN1}}$, $A_{\textrm{AGN2}}$, $BH_{\textrm{accr}}$, $BH_{\textrm{Edd}}$, $BH_{\textrm{FF}}$, $BH_{\textrm{RE}}$, $Q_{\textrm{T}}$, and $Q_{\textrm{TP}}$ from top to bottom. The green lines represent the reference $\textsc{camels}$ simulation. To examine the evolution across redshift, simulation snapshots at $z=0$, $z=0.5$, $z=1$, $z=1.5$ and $z=2$ are displayed from left to right. Medians in stellar mass bins are shown.
• Figure 4: The half-mass radius, $R_{*,1/2}$ is plotted against $M_{\star}$, with rows showing variations in the two SN-related parameters $A_{\rm SN1}$ and $A_{\rm SN2}$ and two AGN parameters $BH_{\rm RE}$ and $Q_{\rm T}$. The green lines represent the reference $\textsc{camels}$ simulation. Simulation snapshots at $z=0$, $z=0.5$, $z=1$, $z=1.5$ and $z=2$ are displayed from left to right. Medians in stellar mass bins are shown. Dark and light gray regions indicate radii smaller than the softening length $\epsilon_{\rm min}$ and $2 \times \epsilon_{\rm min}$, respectively.
• Figure 5: The ratio $M_{\rm DM,1/2}/M_{\star,1/2}$ is plotted against $M_{\star}$, with rows showing variations in the two SN-related parameters $A_{\rm SN1}$ and $A_{\rm SN2}$ and the two AGN parameters $B_{\rm RE}$ and $Q_{\rm T}$. The green lines represent the reference $\textsc{camels}$ simulation. Simulation snapshots at $z=0$, $z=0.5$, $z=1$, $z=1.5$ and $z=2$ are displayed from left to right. The sample is divided in PGs (solid lines) and SFGs (dashed lines). Medians in stellar mass bins are shown. The binning in the two subclasses has been optimized based on the number of points in the bin, and trends based on very few data points have been omitted.