Modeling Nearly Spherical Pure-Bulge Galaxies with a Stellar
  Mass-to-Light Ratio Gradient under the $\Lambda$CDM and MOND Paradigms: II.
  The Orbital Anisotropy of Slow Rotators within the Effective Radius
  We investigate the anisotropy of the stellar velocity dispersions within the
effective radius, $R_{\rm e}$, in 24 ATLAS$^{\rm 3D}$ pure-bulge galaxies, 16
of which are kinematic slow rotators (SRs). We allow the spherical anisotropy
parameter $\beta$ to be radially varying and allow a radial gradient in the
stellar mass-to-light ratio ($M_\star/L$) through the parameter $K$ introduced
earlier. The median anisotropy for SRs depends on $K$ as follows:
$\langle\beta_{\rm m}\rangle = a + b K$ with $a=0.19\pm 0.05$, $b=-0.13\pm
0.07$ ($\Lambda$CDM) or $a=0.21\pm 0.05$, $b=-0.26\pm 0.08$ (MOND), where
$\beta_{\rm m}$ refers to the radially averaged quantity. Under the
$\Lambda$CDM paradigm this scaling is tied to a scaling of $\langle f_{\rm
DM}\rangle = (0.16\pm 0.03) +(0.31\pm 0.06) K$, where $f_{\rm DM}$ refers to
the DM fraction within a sphere of $r=R_{\rm e}$. For $K=0$ (constant
$M_\star/L$), we obtain radially biased results with $\langle\beta_{\rm
m}\rangle \approx 0.2$ consistent with previous results. However, marginalizing
over $0 < K < 1.5$ yields $\langle\beta_{\rm m}\rangle = 0.06 ^{+0.11}_{-0.14}$
with $\langle f_{\rm DM}\rangle = 0.35 \pm 0.08$: isotropy is preferred. This
isotropy hides the fact that $\beta_{\rm m}$ is correlated with kinematic
features such as counter rotating cores (CRCs), kinematically distinct cores
(KDCs), and low-level velocities (LVs): SRs with LVs are likely to be radially
biased while SRs with CRCs are likely to be tangentially biased, and SRs with
KDCs are intermediate. Existing cosmological simulations allow us to understand
these results qualitatively in terms of their dynamical structures and
formation histories although there exist quantitative tensions. More realistic
cosmological simulations, particularly allowing for $M_\star/L$ gradients, may
be required to better understand SRs.
