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We investigate the correlation between the supermassive black holes (SMBHs) mass ( M  bh ) and the stellar velocity dispersion  (σ * )  in two types of host galaxies: the early‐type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo‐bulges. In the form  log ( M  bh /M ⊙ ) =α+β log (σ * /200 km s −1 ) , the best‐fitting results for the 39 early‐type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05 ; the best‐fitting results for the nine pseudo‐bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18 . Both relations have intrinsic scatter in  log  M  bh   of ≲0.27 dex. The   M  bh –σ *   relation for pseudo‐bulges is different from the relation in the early‐type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M  bh –σ *   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 ‘core’ elliptical galaxies at the high‐mass range of the relation appears steeper  (β≃ 5–6) , which may be the imprint of their origin of dissipationless mergers.

The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo‐bulges