A Local Baseline of the Black Hole Mass Scaling Relations for Active
  Galaxies. III. The BH mass - $\sigma$ relation
  We create a baseline of the black hole (BH) mass (MBH) - stellar-velocity
dispersion (sigma) relation for active galaxies, using a sample of 66 local
(0.02<z<0.09) Seyfert-1 galaxies, selected from the Sloan Digital Sky Survey
(SDSS). Analysis of SDSS images yields AGN luminosities free of host-galaxy
contamination and morphological classification. 51/66 galaxies have spiral
morphology. 28 bulges have Sersic index n<2 and are considered candidate pseudo
bulges, with eight being definite pseudo bulges based on multiple
classification criteria met. Only 4/66 galaxies show sign of
interaction/merging. High signal-to-noise ratio Keck spectra provide the width
of the broad Hbeta emission line free of FeII emission and stellar absorption.
AGN luminosity and Hbeta line widths are used to estimate MBH. The Keck-based
spatially-resolved kinematics is used to determine stellar-velocity dispersion
within the spheroid effective radius. We find that sigma can vary on average by
up to 40% across definitions commonly used in the literature, emphasizing the
importance of using self-consistent definitions in comparisons and evolutionary
studies. The MBH-sigma relation for our Seyfert-1 galaxies has the same
intercept and scatter as that of reverberation-mapped AGNs as well as quiescent
galaxies, consistent with the hypothesis that our single epoch MBH estimator
and sample selection do not introduce significant biases. Barred galaxies,
merging galaxies, and those hosting pseudo bulges do not represent outliers in
the MBH-sigma relation. This is in contrast with previous work, although no
firm conclusion can be drawn due to the small sample size and limited
resolution of the SDSS images.
