TRINITY VI: Connection between Galaxy Star Formation Rates and Supermassive Black Hole Accretion Rates from z=0-10

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 matches galaxy observables from $0<z<13$ and SMBH observables from $0<z<6.5$. 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 $\bar{\eta }$ increases towards higher redshifts, nearly reaching $\bar{\eta }=1$ at $z\sim 10$; 3) at fixed redshift for $z<3$, SMBHs/galaxies with higher masses have lower $\bar{\eta }$, consistent with AGN downsizing; 4) the average ratio of specific SMBH accretion rate ($\overline{\mathrm{S}\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}$) to average specific star formation rate ($\overline{\mathrm{S}\mathrm{S}\mathrm{F}\mathrm{R}}$) is nearly mass-independent, with a value $\overline{\mathrm{S}\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}\mathrm{/}\overline{\mathrm{S}\mathrm{S}\mathrm{F}\mathrm{R}}\sim 1$, 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 halos reach ${10}^{12}{M}_{\odot }$; 6) given galaxy and SMBH growth histories from TRINITY, the local descendants of $1<z<11$ overmassive JWST AGNs will remain outliers from the local SMBH mass–galaxy mass relation. These findings combine to give a simple explanation for massive (${10}^9-{10}^{10}{M}_{\odot }$) quasars at $z>6$: at these redshifts, dark matter halos grow with an $e$-folding time of $\sim 45$ Myrs, driving similar growth rates in both galaxies and SMBHs.