1D Kinematics from stars and ionized gas at $z\sim0.8$ from the LEGA-C
  spectroscopic survey of massive galaxies
  We present a comparison of the observed, spatially integrated stellar and
ionized gas velocity dispersions of $\sim1000$ massive ($\log
M_{\star}/M_{\odot}\gtrsim\,10.3$) galaxies in the Large Early Galaxy
Astrophysics Census (LEGA-C) survey at $0.6\lesssim\,z\lesssim1.0$. The high
$S/N\sim20{\rm\AA^{-1}}$ afforded by 20 hour VLT/VIMOS spectra allows for joint
modeling of the stellar continuum and emission lines in all galaxies, spanning
the full range of galaxy colors and morphologies. These observed integrated
velocity dispersions (denoted as $\sigma'_{g, int}$ and $\sigma'_{\star, int}$)
are related to the intrinsic velocity dispersions of ionized gas or stars, but
also include rotational motions through beam smearing and spectral extraction.
We find good average agreement between observed velocity dispersions, with
$\langle\log(\sigma'_{g, int}/\sigma'_{\star, int})\rangle=-0.003$. This result
does not depend strongly on stellar population, structural properties, or
alignment with respect to the slit. However, in all regimes we find significant
scatter between $\sigma'_{g, int}$ and $\sigma'_{\star, int}$, with an overall
scatter of 0.13 dex of which 0.05 dex is due to observational uncertainties.
For an individual galaxy, the scatter between $\sigma'_{g, int}$ and
$\sigma'_{\star, int}$ translates to an additional uncertainty of
$\sim0.24\rm{dex}$ on dynamical mass derived from $\sigma'_{g, int}$, on top of
measurement errors and uncertainties from Virial constant or size estimates. We
measure the $z\sim0.8$ stellar mass Faber-Jackson relation and demonstrate that
emission line widths can be used to measure scaling relations. However, these
relations will exhibit increased scatter and slopes that are artificially
steepened by selecting on subsets of galaxies with progressively brighter
emission lines.
