Detection of faint broad emission lines in type 2 AGN: III. On the
  $M_{BH} - \sigma_\star$ relation of type 2 AGN
  Type 2 active galactic nuclei (AGN) represent the majority of the AGN
population. However, due to the difficulties in measuring their black hole (BH)
masses, it is still unknown whether they follow the same BH mass-host galaxy
scaling relations valid for quiescent galaxies and type 1 AGN. Here we present
the locus of type 2 AGN having virial BH mass estimates in the
$M_{BH}-\sigma_\star$ plane. Our analysis shows that the BH masses of type 2
AGN are $\sim0.9$ dex smaller than type 1 AGN at $\sigma_\star\sim 185$ km
s$^{-1}$, regardless of the (early/late) AGN host galaxy morphology.
Equivalently, type 2 AGN host galaxies have stellar velocity dispersions $\sim
0.2$ dex higher than type 1 AGN hosts at $M_{BH}\sim10^7$ M$_\odot$.
