Coevolution of Supermassive Black Holes and Circumnuclear Disks

We propose a new evolutionary model of a supermassive black hole (SMBH) and a circumnuclear disk (CND), taking into account the mass-supply from a host galaxy and the physical states of CND. In the model, two distinct accretion modes depending on gravitational stability of the CND play a key role on accreting gas to a SMBH. (i) If the CMD is gravitationally unstable, energy feedback from supernovae (SNe) supports a geometrically thick, turbulent gas disk. The accretion in this mode is dominated by turbulent viscosity, and it is significantly larger than that in the mode (ii), i.e., the CMD is supported by gas pressure. Once the gas supply from the host is stopped, the high accretion phase ($\sim 0.01- 0.1 M_{\odot} {\rm yr}^{-1}$) changes to the low one (mode (ii), $\sim 10^{-4} M_{\odot} {\rm yr}^{-1}$), but there is a delay with $\sim 10^{8}$ yr. Through this evolution, the gas-rich CND turns into the gas poor stellar disk. We found that not all the gas supplied from the host galaxy accrete onto the SMBH even in the high accretion phase (mode (i)), because the part of gas is used to form stars. As a result, the final SMBH mass ($M_{\rm BH,final}$) is not proportional to the total gas mass supplied from the host galaxy ($M_{\rm sup}$); $M_{\rm BH,final}/M_{\rm sup}$ decreases with $M_{\rm sup}$.This would indicate that it is difficult to form a SMBH with $\sim 10^{9} M_{\odot}$ observed at high-$z$ QSOs. The evolution of the SMBH and CND would be related to the evolutionary tracks of different type of AGNs.Comment: 11 pages, 11 figures, accepted for publication in Ap