The role of black hole feedback on galaxy star formation and the degeneracy with halo quenching

TL;DR

This work introduces DECODE, a data-driven semi-empirical framework that evolves galaxies and their central SMBHs along dark matter halo histories by linking SFR to halo accretion via abundance matching and SMBH growth to observed Eddington-ratio distributions. By quenching galaxies when their BHs reach the $M_{ m BH}-\sigma_\star$ threshold, the model reproduces observed quenched fractions and SMBH scaling relations, and it reveals a strong degeneracy between SMBH-driven quenching and halo-mass–driven quenching, with similar BHAR, SFR histories, and $M_{\rm BH}-M_\star$ trends in both scenarios. The results show BH growth peaking at $z\sim 1-2$ with typical $\langle \lambda_{\rm Edd} \rangle \sim 0.3$, modest BH growth from mergers, and a nearly redshift-invariant $M_{\rm BH}-\sigma_\star$ relation for standard radiative efficiency, suggesting that cumulative statistics alone may be insufficient to distinguish quenching channels. The DECODE framework provides a rapid, physically motivated platform to study SMBH demography across time and environments and to interpret data from upcoming surveys such as Euclid and Rubin-LSST, while outlining avenues to break degeneracies via AGN clustering and SMBH–host residual analyses.

Abstract

The interplay between the accretion of supermassive black holes (SMBHs) and the stellar mass growth of the host galaxies is still a matter of hot debate. The accretion of the SMBHs is expected to release energy under the form of AGNs. This energy is believed to impact the star formation activity and contribute to the quenching of galaxies. Here, we address this key unsolved issue with our cosmological semi-empirical model DECODE. In DECODE, we grow galaxies with their SFR linked to halo accretion rate distributions via abundance matching. SMBHs are evolved following the stellar mass growth of their host galaxies by assigning an accretion rate at each redshift from the empirical Eddington ratio distributions and duty cycles. We test the assumption that galaxies permanently quench when their central SMBHs approach the limit imposed by the observed $M_{\rm BH} - σ_\star$ relation, as a proxy of SMBH disruptive feedback. We find that simply imposing the $M_{\rm BH} - σ_\star$ condition is sufficient to generate a fraction of quenched galaxies consistent with current data, including the newest ones from Euclid. In addition, our minimal, data-driven model, also predicts SMBH scaling relations consistent in slope and normalisation with those observed, and an $M_{\rm BH} - M_\star$ relation weakly evolving with redshift. The model also naturally generates SMBH accretion rates peaking within 1 Gyr of their host SFHs. We note that all the main predictions on galaxy quenched fractions and SMBH growth histories and scaling relations are degenerate with those expected in a halo quenching model. The comprehensive data-driven model presented in this work represents an invaluable tool to investigate SMBH demography across time and environments in an accurate, physically motivated manner, ideally suited to rapidly explore the implications from large surveys, such as Euclid and Rubin-LSST.

Figures (16)

• Figure 1: Methodology followed in decode to form and evolve galaxies and supermassive black holes. The SFR-HAR relation, computed via abundance matching, is used to assign galaxies following the accretion histories of their host dark matter haloes. Observationally determined sBHAR distributions at each redshift are used to assign the accretion rates to the central SMBHs following the stellar mass growths of their host galaxies. Black hole accretion and star formation rate are halted using empirically inferred $M_{\rm BH} - \sigma_\star$ quenching relations.
• Figure 2: Star formation rate function at redshifts $z \sim 0$, $1$, $2$, $3$, $4$, and $5$. The data points with error bars include the data from VVDS (blue squares; cucciati_2012), Herschel PEP/HerMES (orange rhombuses; gruppioni_2013), PEP and HerMES (green circles; gruppioni_2015), CIGALE (red triangles; lyon_2024), Herschel-PACS (purple triangles; magnelli_2013), GALEX (brown arrows; wyder_2005), ALCS (pink pluses; fujimoto_2024), ALMA-ALPINE (grey pentagons; gruppioni_2020), SCUBA-2 (yellow stars; koprowski_2017), A$^3$COSMOS (cyan rhombuses; traina_2024), HST (blue crosses, purple, orange and green hexagons; alavi_2014bouwens_2015bouwens_2021bouwens_2022), Herschel-ATLAS (red stars; lapi_2011), Herschel+LOFAR (brown hexagons; wang_2021), JWST-CEERS (pink squares; ling_2024) and WUDS (grey rhombuses; pello_2018). The black solid lines and shaded areas show our fit to Equation (\ref{['eq:saunders']}) and $1\sigma$ uncertainty.
• Figure 3: Star formation rate-halo accretion rate relation at redshifts $z = 0$, $1$, $2$, $3$$4$ and $5$, from the abundance matching using as input the star formation rate function described in Sect. \ref{['sec:res_sfr_har']}.
• Figure 4: Average black hole mass accretion histories as predicted from decode, compared to those predicted from zou_2024. decode's results are shown both for the accretion-only scenario (solid lines) and the scenario with mergers (dotted lines). The filled circles and triangles show the redshift at which half of the black hole mass is formed. The different colours show the accretion tracks for different black mass bins at $z=0$: $\log_{10} (M_{\rm BH}/M_\odot) \simeq 6.75$ (blue lines), $\log_{10} (M_{\rm BH}/M_\odot) \simeq 7.25$ (orange lines), $\log_{10} (M_{\rm BH}/M_\odot) \simeq 7.75$ (green lines), $\log_{10} (M_{\rm BH}/M_\odot) \simeq 8.2$ (red lines), and $\log_{10} (M_{\rm BH}/M_\odot) \simeq 8.6$ (purple lines).
• Figure 5: Average of the logarithm of the Eddington ratio, $\lambda_{\rm Edd}$, as a function of redshift for different black hole mass bins at redshift $z=0$, as labelled.