Linking black-hole growth with host galaxies: The accretion-stellar mass relation and its cosmic evolution

Previous studies suggest that the growth of supermassive black holes (SMBHs) may be fundamentally related to host-galaxy stellar mass ($M_{\star }$). To investigate this SMBH growth-$M_{\star }$ relation in detail, we calculate long-term SMBH accretion rate as a function of $M_{\star }$ and redshift [$\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}(M_{\star },z)$] over ranges of $\log (M_{\star }\mathrm{/}{M}_{\odot })=\text{9.5–12}$ and $z=\text{0.4–4}$. Our $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}(M_{\star },z)$ is constrained by high-quality survey data (GOODS-South, GOODS-North, and COSMOS), and by the stellar mass function and the X-ray luminosity function. At a given $M_{\star }$, $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}$ is higher at high redshift. This redshift dependence is stronger in more massive systems (for $\log (M_{\star }\mathrm{/}{M}_{\odot })\approx 11.5$, $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}$ is three decades higher at $z=4$ than at $z=0.5$), possibly due to AGN feedback. Our results indicate that the ratio between $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}$ and average star formation rate ($\overline{\mathrm{S}\mathrm{F}\mathrm{R}}$) rises toward high $M_{\star }$ at a given redshift. This $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}\mathrm{/}\overline{\mathrm{S}\mathrm{F}\mathrm{R}}$ dependence on $M_{\star }$ does not support the scenario that SMBH and galaxy growth are in lockstep. We calculate SMBH mass history [$M_{\mathrm{B}\mathrm{H}}(z)$] based on our $\overline{\mathrm{B}\mathrm{H}\mathrm{A}\mathrm{R}}(M_{\star },z)$ and the $M_{\star }(z)$ from the literature, and find that the $M_{\mathrm{B}\mathrm{H}}$-$M_{\star }$ relation has weak redshift evolution since $z\approx 2$. The $M_{\mathrm{B}\mathrm{H}}\mathrm{/}{M}_{\star }$ ratio is higher toward massive galaxies: it rises from $\approx 1\mathrm{/}5000$ at $\log M_{\star }\lesssim 10.5$ to $\approx 1/500$at$\log M_\star \gtrsim 11.2$\mathrm{.}Ourpredicted$M_{\rm BH}/M_\star$ ratio at high $M_{\star }$ is similar to that observed in local giant ellipticals, suggesting that SMBH growth from mergers is unlikely to dominate over growth from accretion.