Formation of $z \sim 6$ quasars from hierarchical galaxy mergers

The discovery of luminous quasars at redshift $z \sim 6$ indicates the presence of supermassive black holes (SMBHs) of mass $\sim 10^9 \Msun$ when the Universe was less than one billion years old. This finding presents several challenges for theoretical models, because whether such massive objects can form so early in the $\Lambda$-cold dark matter ($\Lambda$CDM) cosmology, the leading theory for cosmic structure formation, is an open question. Furthermore, whether the formation process requires exotic physics such as super-Eddington accretion remains undecided. Here, we present the first multi-scale simulations that, together with a self-regulated model for the SMBH growth, produce a luminous quasar at $z \sim 6.5$ in the $\Lambda$CDM paradigm. We follow the hierarchical assembly history of the most massive halo in a $\sim 3 \Gpc^{3}$ volume, and find that this halo of $\sim 8\times 10^{12} \Msun$ forming at $z \sim 6.5$ after several major mergers is able to reproduce a number of observed properties of SDSS J1148+5251, the most distant quasar detected at $z =6.42$ \citep{Fan2003}. Moreover, the SMBHs grow through gas accretion below the Eddington limit in a self-regulated manner owing to feedback. We find that the progenitors experience significant star formation (up to $10^4 \Msun \yr^{-1}$) preceding the major quasar phase such that the stellar mass of the quasar host reaches $10^{12} \Msun$ at $z \sim 6.5$, consistent with observations of significant metal enrichment in SDSS J1148+5251. (Abridged)