Radiation drag driven mass accretion in clumpy interstellar medium: implications for the supermassive black hole-to-bulge relation

We quantitatively scrutinize the effects of the radiation drag arising from the radiation fields in a galactic bulge in order to examine the possibility that the radiation drag could be an effective mechanism to extract angular momentum in a spheroidal system like a bulge and allow plenty of gas to accrete onto the galactic center. For this purpose, we numerically solve the relativistic radiation hydrodynamical equation coupled with the accurate radiative transfer and quantitatively assess the radiation drag efficiency. As a result, we find that in an optically thick regime the radiation drag efficiency is sensitively dependent on the density distributions of interstellar medium (ISM). The efficiency drops according to $\tau_{\rm T}^{-2}$ in an optically thick {\it uniform} ISM, where $\tau_{\rm T}$ is the total optical depth of the dusty ISM, whereas the efficiency remains almost constant at a high level if the ISM is {\it clumpy}. Hence, if the bulge formation begins with a star formation event in a clumpy ISM, the radiation drag will effectively work to remove the angular momentum and the accreted gas may form a supermassive black hole. As a natural consequence, this mechanism reproduces a putative linear relation between the mass of a supermassive black hole and the mass of a galactic bulge, although further detailed modeling for stellar evolution is required for the more precise prediction.