The MASSIVE Survey - X. Misalignment between Kinematic and Photometric
  Axes and Intrinsic Shapes of Massive Early-Type Galaxies
  We use spatially resolved two-dimensional stellar velocity maps over a
$107"\times 107"$ field of view to investigate the kinematic features of 90
early-type galaxies above stellar mass $10^{11.5}M_\odot$ in the MASSIVE
survey. We measure the misalignment angle $\Psi$ between the kinematic and
photometric axes and identify local features such as velocity twists and
kinematically distinct components. We find 46% of the sample to be well aligned
($\Psi < 15^{\circ}$), 33% misaligned, and 21% without detectable rotation
(non-rotators). Only 24% of the sample are fast rotators, the majority of which
(91%) are aligned, whereas 57% of the slow rotators are misaligned with a
nearly flat distribution of $\Psi$ from $15^{\circ}$ to $90^{\circ}$. 11
galaxies have $\Psi \gtrsim 60^{\circ}$ and thus exhibit minor-axis ("prolate")
rotation in which the rotation is preferentially around the photometric major
axis. Kinematic misalignments occur more frequently for lower galaxy spin or
denser galaxy environments. Using the observed misalignment and ellipticity
distributions, we infer the intrinsic shape distribution of our sample and find
that MASSIVE slow rotators are consistent with being mildly triaxial, with mean
axis ratios of $b/a=0.88$ and $c/a=0.65$. In terms of local kinematic features,
51% of the sample exhibit kinematic twists of larger than $20^{\circ}$, and 2
galaxies have kinematically distinct components. The frequency of misalignment
and the broad distribution of $\Psi$ reported here suggest that the most
massive early-type galaxies are mildly triaxial, and that formation processes
resulting in kinematically misaligned slow rotators such as gas-poor mergers
occur frequently in this mass range.
