The black hole mass -- stellar velocity dispersion correlation: bulges versus pseudobulges

We have investigated the correlation between the supermassive black holes (SMBHs) mass ($M_{\rm bh}$) and the stellar velocity dispersion ($\sigma_*$) in two types of host galaxies: the classical bulges (or elliptical galaxies), and pseudobulges. In the form $\log (M_{\rm bh}/{\rm M_\odot})=\alpha+\beta\log(\sigma_*/200 {\rm km s^{-1}})$, the best-fit results for the 41 classical bulges/elliptical galaxies are the slope $\beta=4.17\pm0.25$ and the normalization $\alpha=8.29\pm0.04$; the best-fit results for the 12 pseudobulges are $\beta=4.17\pm0.70$, $\alpha=7.49\pm0.13$. Both relations have intrinsic scatter in $\log M_{\rm bh}$ of $\lesssim0.25$ dex. The $M_{\rm bh}$-$\sigma_*$ relation for pseudobulges is different from the relation in the classical bulges over the 3$\sigma$ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type, the pseudobulges is relatively low efficient to fuel the central SMBHs. The discrepancy between the slope of the $M_{\rm bh}$-$\sigma_*$ relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 13 ``core'' elliptical galaxies at the high mass range of the relation appears slightly steeper, which may be the imprint of their origin of dissipationless mergers.