<scp>Trinity</scp> VI: connection between galaxy star formation rates and supermassive black hole accretion rates from <i>z</i> = 0 − 10

ABSTRACT We infer supermassive black hole (SMBH) accretion rates and Eddington ratios as a function of SMBH/host galaxy mass and redshift with the empirical Trinity model of dark matter halo–galaxy–SMBH connection. The galaxy–SMBH mass and growth rate connection from Trinity match galaxy observables from $0\lt z\lt 13$ and SMBH observables from $0\lt z\lt 6.5$. Key findings include: (1) the ratio between cosmic SMBH accretion rate and galaxy star formation rate stays constant at $\sim 2\times 10^{-3}$ from $z=0-4$, and decreases by 2 orders of magnitude from $z=4-10$; (2) the average SMBH Eddington ratio $\overline{\eta }$ increases towards higher redshifts, nearly reaching $\overline{\eta }=1$ at $z\sim 10$; (3) at fixed redshift for $z\lt 3$, SMBHs/galaxies with higher masses have lower $\overline{\eta }$, consistent with active galactic nucleus (AGN) downsizing; (4) the average ratio of specific SMBH accretion rate ($\overline{\mathrm{SBHAR}}$) to average specific star formation rate ($\overline{\mathrm{SSFR}}$) is nearly mass-independent, with a value $\overline{\mathrm{SBHAR}}/\overline{\mathrm{SSFR}}\sim 1$, which decreases slightly from $z=10$ to $z=0$; (5) similar to galaxies, SMBHs reach their peak efficiency to convert baryons into mass when host haloes reach $10^{12} \, \mathrm{ M}_\odot$; (6) given galaxy and SMBH growth histories from Trinity, the local descendants of $1\lt z\lt 11$ overmassive JWST AGNs will remain outliers from the local SMBH mass–galaxy mass relation. These findings combine to give a simple explanation for massive ($10^9-10^{10}\, \mathrm{ M}_{\odot }$) quasars at $z\gt 6$: at these redshifts, dark matter haloes grow with an e-folding time of $\sim 45$ Myr, driving similar growth in both galaxies and SMBHs.