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A number of studies have revealed the presence of central supermassive black holes in several massive disk and elliptical galaxies, and it is now believed that most (if not all) massive galaxies should have a central supermassive black hole. These works have also shown that the mass of these black holes correlate with sigma and the luminosity or mass of the elliptical galaxy (in the case of ellipticals) or the bulge (in the case of disk galaxies; see e.g. Gültekin et al. 2009 and references therein). This suggests a connected growth of black holes and bulges (and ellipticals). Essentially, black holes would accrete mass, resulting in AGN activity, until AGN feedback regulates the inflow of gas, the growth of the black hole, and the formation of stars in the bulge/elliptical (see e.g. Younger et al. 2008). In this framework, the growth of disk-like bulges would not be connected with the (bulk of) growth of black holes, and thus the properties of disk-like bulges would not correlate with the mass of black holes.

This question has been investigated by Graham (2008), Hu (2008) and Gadotti & Kauffmann (2009), and these works showed that the correlation between black hole mass and sigma is difficult to evaluate in galaxies with disk-like bulges, as the presence of bars increase sigma (in ways difficult to account for) more significantly (in relative terms) than in galaxies with classical bulges (see Graham et al. 2011). More recently, Kormendy et al. (2011) argued that the luminosities of disk-like bulges do not correlate with black hole masses, consistent with the picture outlined above. Nowak et al. (2010) and Erwin (2010) showed results indicating that, in composite bulges, the black hole mass correlates better with the luminosity of the classical bulge only, again showing that the growth of disk-like bulges is to some extent not coupled with the growth of black holes.