Tracking the assembly of supermassive black holes: a comparison of diverse models across cosmic time

Antonio J. Porras-Valverde, Angelo Ricarte, Priyamvada Natarajan, Rachel S. Somerville, Austen Gabrielpillai, L. Y. Aaron Yung

First listed 2025-04-15 | Last updated 2025-04-15

Abstract

Galaxies grow alongside their central supermassive black holes (SMBHs), linked through fueling and feedback. However, the origins and details of this co-evolution remain unclear and differ significantly amongst modeling frameworks. Using a suite of semi-analytic models (SAMs), we trace SMBH mass assembly across $M_{\rm BH} \sim 10^{6-10}, \mathrm{M}_{\odot}$. We find significant discrepancies between observations and physics-based models of the local black hole mass function (BHMF), likely due to differences in the underlying stellar mass function and the scaling relations therefrom used to infer the BHMF. However, most physics-based models agree at $z \sim 1-4$ and align reasonably well with broad-line AGN BHMF from JWST observations at $z=4-5$. Most physics-based models reproduce the bolometric AGN luminosity evolution, except {\sc Dark Sage}, which predicts an excess deviating from models and observations. Interestingly, this pronounced ``knee' in the bolometric AGN luminosity function predicted by {\sc Dark Sage} around $L_{\rm bol} \sim 10^{46} \, \mathrm{erg \, s^{-1}}$ is consistent with the inferred luminosity of ``Little Red Dots'' at $z=5-6$, assuming that their entire emission originates from AGN activity. We analyze black hole mass build-up and accretion histories in {\sc Dark Sage}, which, unlike other models, allows for super-Eddington accretion. We report that on average, SMBHs in {\sc Dark Sage} primarily grow through secular disk instabilities and merger-driven cold gas accretion, while black hole mergers contribute 60\% of the total mass budget only for the most massive SMBHs by $z=0$.

Short digest

The authors cross-compare SMBH assembly across semi-analytic, empirical, and hydro frameworks (Dark Sage, Santa Cruz SAM, RN18, TRINITY, TNG300) over MBH ≈ 10^6–10^10 Msun. Physics-based models diverge from observationally inferred local BHMFs due to stellar-mass-function and scaling-relation systematics, but converge at z ~ 1–4 and broadly match JWST broad-line AGN BHMFs at z = 4–5. Dark Sage uniquely produces a strong knee in the bolometric AGN luminosity function near Lbol ~ 10^46 erg s^-1 that overlaps the inferred luminosities of JWST “Little Red Dots” at z = 5–6 if the emission is AGN-dominated. Within Dark Sage, SMBHs grow mainly via secular disk instabilities and merger-driven cold gas accretion, while BH–BH mergers contribute ~60% of the mass only for the most massive systems by z = 0; super-Eddington accretion is allowed.

Key figures to inspect

• Figure 3: Examine the bolometric AGN luminosity function—locate Dark Sage’s knee at Lbol ~ 10^46 erg s^-1 and compare it directly to the shaded LRD luminosity band; note that RN18 and TNG300 track the Shen et al. fits, while Santa Cruz departs at the low‑z bright end.
• Figure 2: Track the BHMF evolution versus redshift, focusing on model convergence by z ~ 1–4 and the distinct Dark Sage bump; compare to JWST broad-line AGN BHMF points at z = 4–5 (Taylor+2024) and NIRCam WFSS constraints (Matthee+2024), keeping the flagged low-mass incompleteness in mind.
• Figure 1: Contrast the local SMF, MBH–M* relation, and local BHMF across models; check how different SMF calibrations and scaling relations propagate into BHMF discrepancies, and note the Dark Sage dashed curve for halos with <200 particles.
• Figure 4: Inspect median MBH growth histories at fixed halo mass—observe order‑of‑magnitude convergence at z = 0 for most bins but larger spread in the most massive halos; use Sgr A* and M87* markers as anchors and relate differences to model seeding and accretion prescriptions.