Why Massive Black Holes are Small in Disk Galxies?

A potential mechanism is proposed to account for the fact that supermassive black holes (SMBHs) in disk galaxies appear to be smaller than those in elliptical galaxies in the same luminosity range. We consider the formation of SMBHs by radiation drag (Poynting-Robertson effect), which extracts angular momentum from interstellar matter and thereby drives the mass accretion onto a galactic center. In particular, we quantitatively scrutinize the efficiency of radiation drag in a galaxy composed of bulge and disk, and elucidate the relation between the final mass of SMBH and the bulge-to-disk ratio of the galaxy. As a result, it is found that the BH-to-galaxy mass ratio, $M_{\rm BH}/M_{\rm galaxy}$, decreases with a smaller bulge-to-disk ratio, due to the effects of geometrical dilution and opacity, and is reduced maximally by two orders of magnitude, resulting in $M_{\rm BH}/M_{\rm galaxy}\approx 10^{-5}$. In contrast, if only the bulge components in galaxies are focused, the BH-to-bulge mass ratio becomes $M_{\rm BH}/M_{\rm bulge}\approx 10^{-3}$, which is similar to that found in elliptical galaxies. Thus, it turns out that the mass of SMBH primarily correlates with a bulge, not with a disk, consistently with observational data.