  Building upon our previous MHD simulation study of magnetic channeling in
radiatively driven stellar winds, we examine here the additional dynamical
effects of stellar {\em rotation} in the (still) 2-D axisymmetric case of an
aligned dipole surface field. In addition to the magnetic confinement parameter
$\eta_{\ast}$ introduced in Paper I, we characterize the stellar rotation in
terms of a parameter $W \equiv V_{\rm{rot}}/V_{\rm{orb}}$ (the ratio of the
equatorial surface rotation speed to orbital speed), examining specifically
models with moderately strong rotation $W =$ 0.25 and 0.5, and comparing these
to analogous non-rotating cases. Defining the associated Alfv\'{e}n radius
$R_{\rm{A}} \approx \eta_{\ast}^{1/4} \Rstar$ and Kepler corotation radius
$R_{\rm{K}} \approx W^{-2/3} \Rstar$, we find rotation effects are weak for
models with $R_{\rm{A}} < R_{\rm{K}}$, but can be substantial and even dominant
for models with $R_{\rm{A}} \gtwig R_{\rm{K}}$. In particular, by extending our
simulations to magnetic confinement parameters (up to $\eta_{\ast} = 1000$)
that are well above those ($\eta_{\ast} = 10$) considered in Paper I, we are
able to study cases with $R_{\rm{A}} \gg R_{\rm{K}}$; we find that these do
indeed show clear formation of the {\em rigid-body} disk predicted in previous
analytic models, with however a rather complex, dynamic behavior characterized
by both episodes of downward infall and outward breakout that limit the buildup
of disk mass. Overall, the results provide an intriguing glimpse into the
complex interplay between rotation and magnetic confinement, and form the basis
for a full MHD description of the rigid-body disks expected in strongly
magnetic Bp stars like $\sigma$ Ori E.

Astrophysics