CASCO: Cosmological and AStrophysical parameters from Cosmological simulations and Observations

III. The physics behind the emergence of the golden mass scale

¹ INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Napoli, Italy
² Dipartimento di Fisica “E. Pancini”, Università degli studi di Napoli Federico II, Compl. Univ. di Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
³ INFN, Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
⁴ Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800 9700 AV Groningen, The Netherlands
⁵ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY, 10010 USA
⁶ Columbia Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY, 10027 USA
⁷ Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ, 08544 USA

^⋆ Corresponding author: crescenzo.tortora@inaf.it

Received: 12 December 2024
Accepted: 10 July 2025

Abstract

Observations reveal a characteristic ‘golden mass’ (around 10¹² M_⊙ in halo mass and 5 × 10¹⁰ M_⊙ in stellar mass) associated with a peak in star formation efficiency. Using the CAMELS simulations based on IllustrisTNG in a (50 h⁻¹ Mpc)³ volume, we investigate how this scale arises and evolves under varying supernova (SN) and active galactic nucleus (AGN) feedback strengths and cosmological parameters (Ω_m, σ₈). We find a U-shaped relation between the dark-to-stellar mass ratio (within the half-mass radius) and stellar mass, with a minimum at the golden mass, in line with observations. Cosmology primarily shifts the normalization of the scaling relation, while SN and AGN feedback modify both the shape and the emergence of the golden mass. Stronger SN feedback shifts the golden mass to lower values, while AGN feedback–especially the radiative efficiency (i.e. the fraction of the accretion rest mass released in the accretion process), followed by the black hole feedback factor (i.e. the normalization factor for the energy in the AGN feedback in the high-accretion state) and the quasar threshold (i.e. the Eddington ratio)–affects the high-mass slope and shifts the golden mass value. The golden mass appears earlier in cosmic time for simulations with stronger feedback, which more rapidly quenches star formation in massive galaxies. Splitting galaxies by star formation activity reveals that passive galaxies preserve the U-shape, while star-forming galaxies show a decreasing dark matter fraction with stellar mass, with hints of a reversal at low redshift. Global stellar fractions also follow a U-shaped trend. However, in passive systems, the golden mass disappears, shifting to lower masses, while star-forming galaxies exhibit a peak only at low redshift. Our results highlight feedback as the primary driver behind the emergence of the golden mass up to z ∼ 1.5 − 2, while stream and virial shock processes play a secondary role. Comparing our results with other theoretical expectations and observational findings, we speculate that at z ≳ 1.5 − 2, a single characteristic (stream) mass regulates galaxy evolution, which later bifurcates into two: a low-mass gas-richness scale tied to gas availability, and a higher-mass golden mass governing star formation efficiency and quenching.