The SAMI Galaxy Survey: Revisiting Galaxy Classification Through
  High-Order Stellar Kinematics
  Recent cosmological hydrodynamical simulations suggest that integral field
spectroscopy can connect the high-order stellar kinematic moments h3
(~skewness) and h4 (~kurtosis) in galaxies to their cosmological assembly
history. Here, we assess these results by measuring the stellar kinematics on a
sample of 315 galaxies, without a morphological selection, using 2D integral
field data from the SAMI Galaxy Survey. A proxy for the spin parameter
($\lambda_{R_e}$) and ellipticity ($\epsilon_e$) are used to separate fast and
slow rotators; there exists a good correspondence to regular and non-regular
rotators, respectively, as also seen in earlier studies. We confirm that
regular rotators show a strong h3 versus $V/\sigma$ anti-correlation, whereas
quasi-regular and non-regular rotators show a more vertical relation in h3 and
$V/\sigma$. Motivated by recent cosmological simulations, we develop an
alternative approach to kinematically classify galaxies from their individual
h3 versus $V/\sigma$ signatures. We identify five classes of high-order stellar
kinematic signatures using Gaussian mixture models. Class 1 corresponds to slow
rotators, whereas Classes 2-5 correspond to fast rotators. We find that
galaxies with similar $\lambda_{R_e}-\epsilon_e$ values can show distinctly
different h3-$V/\sigma$ signatures. Class 5 objects are previously unidentified
fast rotators that show a weak h3 versus $V/\sigma$ anti-correlation. These
objects are predicted to be disk-less galaxies formed by gas-poor mergers. From
morphological examination, however, there is evidence for large stellar disks.
Instead, Class 5 objects are more likely disturbed galaxies, have
counter-rotating bulges, or bars in edge-on galaxies. Finally, we interpret the
strong anti-correlation in h3 versus $V/\sigma$ as evidence for disks in most
fast rotators, suggesting a dearth of gas-poor mergers among fast rotators.
