Quasar Host Galaxies and the $M_{SMBH}$ - $\sigma_{*}$ Relation
  We analyze the emission line profiles detected in deep optical spectra of
quasars to derive the mass of their super-massive black holes (SMBH) following
the single-epoch virial method. Our sample consists in 6 radio-loud quasars and
4 radio-quiet quasars. We carefully fit a broad and narrow Gaussian component
for each emission line in both the H$\beta$ (10 objects) and H$\alpha$ regions
(5 objects). A very good agreement of the derived SMBH masses, $M_{\rm SMBH}$,
is found using the fitted broad H$\beta$ and H$\alpha$ emission lines. We
compare our $M_{\rm SMBH}$ results with those found by previous studies. We
study the relationship between the $M_{\rm SMBH}$ of the quasar and the stellar
velocity dispersion, $\sigma_{*}$, of the host galaxy. We use the measured
$M_{\rm SMBH}$ and $\sigma_{*}$ to investigate the $M_{\rm SMBH}$ -
$\sigma_{*}$ relation for both the radio-loud and radio-quiet subsamples.
Besides the scatter, we find a good agreement between radio-quiet quasars and
AGN+quiescent galaxies and between radio-loud quasars and AGN. Our analysis
does not support the hypothesis of using $\sigma$([O III] $\lambda$5007) as a
surrogate for stellar velocity dispersions in high-mass, high-luminosity
quasars. We also investigate the relationship between the 5 GHz radio-continuum
luminosity, $L_{\rm~5\,GHz}$, of the quasar host galaxy with both $M_{\rm
SMBH}$ and $\sigma_{*}$. We do not find any correlation between $L_{\rm
5\,GHz}$ and $M_{\rm SMBH}$, although we observe a trend that galaxies with
larger stellar velocity dispersions have larger $L_{\rm 5\,GHz}$. Using the
results of our fitting for the narrow emission lines of [O III] $\lambda$5007
and [N II] $\lambda$6583 we estimate the gas-phase oxygen abundance of six
quasars, being sub-solar in all cases.
