Anticorrelation between the Mass of a Supermassive Black Hole and the Mass Accretion Rate in Type 1 Ultraluminous Infrared Galaxies and Nearby QSOs

We discovered a significant anti-correlation between the mass of asupermassive black hole (SMBH), $M_{\rm BH}$, and the luminosity ratio ofinfrared to active galactic nuclei (AGN) Eddington luminosity, $L_{\rmIR}/L_{\rm Edd}$, over four orders of magnitude for ultraluminous infraredgalaxies with type I Seyfert nuclei (type I ULIRGs) and nearby QSOs. Thisanti-correlation ($M_{\rm BH}$ vs. $L_{\rm IR}/L_{\rm Edd}$) can be interpretedas the anti-correlation between the mass of a SMBH and the rate of massaccretion onto a SMBH normalized by the AGN Eddington rate, $\dot{M}_{\rmBH}/\dot{M}_{\rm Edd}$. In other words, the mass accretion rate $\dot{M}_{\rmBH}$ is not proportional to that of the central BH mass. Thus, thisanti-correlation indicates that BH growth is determined by the external masssupply process, and not the AGN Eddington-limited mechanism. Moreover, we foundan interesting tendency for type I ULIRGs to favor a super-Eddington accretionflow, whereas QSOs tended to show a sub-Eddington flow. On the basis of ourfindings, we suggest that a central SMBH grows by changing its mass accretionrate from super-Eddington to sub-Eddington. According to a coevolution scenarioof ULIRGs and QSOs based on the radiation drag process, it has been predictedthat 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 thefinal phase of BH growth (QSO phase). At the same time, if one considers themass accretion rate onto a central SMBH via a turbulent viscosity, theanti-correlation ($M_{\rm BH}$ vs. $L_{\rm IR}/L_{\rm Edd}$) is well explainedby the positive correlation between the mass accretion rate $\dot{M}_{\rm BH}$and the mass ratio of a massive torus to a SMBH.Comment: 29 pages, 4 figures, accepted for publication in Ap