Mapping the Growth of Supermassive Black Holes as a Function of Galaxy Stellar Mass and Redshift

The growth of supermassive black holes is strongly linked to their galaxies. It has been shown that the population mean black-hole accretion rate ($\overline{\mathrm{BHAR}}$) primarily correlates with the galaxy stellar mass ($M_\star$) and redshift for the general galaxy population. This work aims to provide the best measurements of $\overline{\mathrm{BHAR}}$ as a function of $M_\star$ and redshift over ranges of $10^{9.5}<M_\star<10^{12}~M_\odot$ and $z<4$. We compile an unprecedentedly large sample with eight thousand active galactic nuclei (AGNs) and 1.3 million normal galaxies from nine high-quality survey fields following a wedding-cake design. We further develop a semiparametric Bayesian method that can reasonably estimate $\overline{\mathrm{BHAR}}$ and the corresponding uncertainties, even for sparsely populated regions in the parameter space. $\overline{\mathrm{BHAR}}$ is constrained by X-ray surveys sampling the AGN accretion power and UV-to-infrared multi-wavelength surveys sampling the galaxy population. Our results can independently predict the X-ray luminosity function (XLF) from the galaxy stellar mass function (SMF), and the prediction is consistent with the observed XLF. We also try adding external constraints from the observed SMF and XLF. We further measure $\overline{\mathrm{BHAR}}$ for star-forming and quiescent galaxies and show that star-forming $\overline{\mathrm{BHAR}}$ is generally larger than or at least comparable to the quiescent $\overline{\mathrm{BHAR}}$.