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Anti-correlation between the mass of a supermassive black hole and the mass accretion rate in type I ultraluminous infrared galaxies and nearby QSOs

We discovered a significant anti-correlation between the mass of a supermassive black hole (SMBH), $M_{\rm BH}$, and the luminosity ratio of infrared to active galactic nuclei (AGN) Eddington luminosity, $L_{\rm IR}/L_{\rm Edd}$, over four orders of magnitude for ultraluminous infrared galaxies with type I Seyfert nuclei (type I ULIRGs) and nearby QSOs. This anti-correlation ($M_{\rm BH}$ vs. $L_{\rm IR}/L_{\rm Edd}$) can be interpreted as the anti-correlation between the mass of a SMBH and the rate of mass accretion onto a SMBH normalized by the AGN Eddington rate, $\dot{M}_{\rm BH}/\dot{M}_{\rm Edd}$. In other words, the mass accretion rate $\dot{M}_{\rm BH}$ is not proportional to that of the central BH mass. Thus, this anti-correlation indicates that BH growth is determined by the external mass supply process, and not the AGN Eddington-limited mechanism. Moreover, we found an interesting tendency for type I ULIRGs to favor a super-Eddington accretion flow, whereas QSOs tended to show a sub-Eddington flow. On the basis of our findings, we suggest that a central SMBH grows by changing its mass accretion rate from super-Eddington to sub-Eddington. According to a coevolution scenario of ULIRGs and QSOs based on the radiation drag process, it has been predicted that a self-gravitating massive torus, whose mass is larger than a central BH, exists in the early phase of BH growth (type I ULIRG phase) but not in the final phase of BH growth (QSO phase). At the same time, if one considers the mass accretion rate onto a central SMBH via a turbulent viscosity, the anti-correlation ($M_{\rm BH}$ vs. $L_{\rm IR}/L_{\rm Edd}$) is well explained by the positive correlation between the mass accretion rate $\dot{M}_{\rm BH}$ and the mass ratio of a massive torus to a SMBH.