The KMOS$^\mathrm{3D}$ Survey: rotating compact star forming galaxies
  and the decomposition of integrated line widths
  Using integral field spectroscopy we investigate the kinematic properties of
35 massive centrally-dense and compact star-forming galaxies
(${\log{\overline{M}_*}}=11.1$, $\log{(\Sigma_\mathrm{1kpc})}>9.5$,
$\log{(M_\ast/r_e^{1.5})}>10.3$) at $z\sim0.7-3.7$ within the
KMOS$^\mathrm{3D}$survey. We spatially resolve 23 compact star-forming galaxies
(SFGs) and find that the majority are dominated by rotational motions with
velocities ranging from {$95-500$ km s$^{-1}$}. The range of rotation
velocities is reflected in a similar range of integrated H$\alpha$ linewidths,
$75-400$ km s$^{-1}$, consistent with the kinematic properties of mass-matched
extended galaxies from the full KMOS$^\mathrm{3D}$ sample. The fraction of
compact SFGs that are classified as `rotation-dominated' or `disk-like' also
mirrors the fractions of the full KMOS$^\mathrm{3D}$ sample. We show that
integrated line-of-sight gas velocity dispersions from KMOS$^\mathrm{3D}$ are
best approximated by a linear combination of their rotation and turbulent
velocities with a lesser but still significant contribution from galactic scale
winds. The H$\alpha$ exponential disk sizes of compact SFGs are on average
$2.5\pm0.2$ kpc, $1-2\times$ the continuum sizes, in agreement with previous
work. The compact SFGs have a $1.4\times$ higher AGN incidence than the full
KMOS$^\mathrm{3D}$ sample at fixed stellar mass with average AGN fraction of
76\%. Given their high and centrally concentrated stellar masses as well as
stellar to dynamical mass ratios close to unity, the compact SFGs are likely to
have low molecular gas fractions and to quench on a short time scale unless
replenished with inflowing gas. The rotation in these compact systems suggests
that their direct descendants are rotating passive galaxies.
