Physical Explanation for the Galaxy Distribution on the $(\lambda_{\rm
  R}, \varepsilon)$ and $(V/\sigma, \varepsilon)$ Diagrams or for the Limit on
  Orbital Anisotropy
  In the $(\lambda_{\rm R}, \varepsilon)$ and $(V/\sigma, \varepsilon)$
diagrams for characterizing dynamical states, the fast-rotator galaxies (both
early-type and spirals) are distributed within a well-defined leaf-shaped
envelope. This was explained as due to an upper limit to the orbital anisotropy
increasing with galaxy intrinsic flattening. However, a physical explanation
for this empirical trend was missing. Here we construct Jeans Anisotropic
Models (JAM), with either cylindrically or spherically aligned velocity
ellipsoid (two extreme assumptions), and each with either spatially-constant or
-variable anisotropy. We use JAM to build mock samples of axisymmetric
galaxies, assuming on average an oblate shape for the velocity ellipsoid (as
required to reproduce the rotation of real galaxies), and limiting the radial
anisotropy $\beta$ to the range allowed by physical solutions. We find that all
four mock samples naturally predict the observed galaxy distribution on the
$(\lambda_{\rm R}, \varepsilon)$ and $(V/\sigma, \varepsilon)$ diagrams,
without further assumptions. Given the similarity of the results from quite
different models, we conclude that the empirical anisotropy upper limit in real
galaxies, and the corresponding observed distributions in the $(\lambda_{\rm
R}, \varepsilon)$ and $(V/\sigma, \varepsilon)$ diagrams, are due to the lack
of physical axisymmetric equilibrium solutions at high $\beta$ anisotropy when
the velocity ellipsoid is close to oblate.
