Studying the [OIII]$\lambda$5007A emission-line width in a sample of
  $\sim$80 local active galaxies: A surrogate for $\sigma_{\star}$?
  For a sample of $\sim$80 local ($0.02 \leq z \leq 0.1$) Seyfert-1 galaxies
with high-quality long-slit Keck spectra and spatially-resolved
stellar-velocity dispersion ($\sigma_{\star}$) measurements, we study the
profile of the [OIII]$\lambda$5007A emission line to test the validity of using
its width as a surrogate for $\sigma_{\star}$. Such an approach has often been
used in the literature, since it is difficult to measure $\sigma_{\star}$ for
type-1 active galactic nuclei (AGNs) due to the AGN continuum outshining the
stellar-absorption lines. Fitting the [OIII] line with a single Gaussian or
Gauss-Hermite polynomials overestimates $\sigma_{\star}$ by 50-100%. When line
asymmetries from non-gravitational gas motion are excluded in a double Gaussian
fit, the average ratio between the core [OIII] width ($\sigma_{\rm
{[OIII],D}}$) and $\sigma_{\star}$ is $\sim$1, but with individual data points
off by up to a factor of two. The resulting black-hole-mass-$\sigma_{\rm
{[OIII],D}}$ relation scatters around that of quiescent galaxies and
reverberation-mapped AGNs. However, a direct comparison between
$\sigma_{\star}$ and $\sigma_{\rm {[OIII],D}}$ shows no close correlation, only
that both quantities have the same range, average and standard deviation,
probably because they feel the same gravitational potential. The large scatter
is likely due to the fact that line profiles are a luminosity-weighted average,
dependent on the light distribution and underlying kinematic field. Within the
range probed by our sample (80-260 km s$^{-1}$), our results strongly caution
against the use of [OIII] width as a surrogate for $\sigma_{\star}$ on an
individual basis. Even though our sample consists of radio-quiet AGNs, FIRST
radio-detected objects have, on average, a $\sim$10% larger [OIII] core width.
