  We investigate the rotational dynamics of disk accretion around a strongly
magnetized neutron star with an aligned dipole field. The magnetospheric field
is assumed to thread the disk plasma both inside and outside the corotation
radius. As a result of disk-star interaction, the magnetic torque on the disk
affects the structure of accretion flow to yield the observed spin-up or
spin-down rates for a source of given fastness, magnetic field strength, and
mass accretion rate. Within the model we obtain a prescription for the
dynamical viscosity of such magnetically modified solutions for a Keplerian
disk. We then use this prescription to find a model solution for the rotation
rate profile throughout the entire disk including the non-Keplerian inner disk.
We find that the non-Keplerian angular velocity transition region is not
necessarily narrow for a source of given spin state. The boundary layer
approximation, as in the standard magnetically threaded disk model, holds only
in the case of dynamical viscosity decreasing all the way to the innermost edge
of the disk. These results are applied to several observed disk-fed X-ray
pulsars that have exhibited quasi-periodic oscillations (QPOs). The QPO
frequencies provide a constraint on the fastness parameter and enable one to
determine uniquely the width of the angular velocity transition zone for each
source within model assumptions. We discuss the implications of these results
on the value of the critical fastness parameter for a magnetized star in spin
equilibrium. Applications of our model are also made with relevant parameters
from recent numerical simulations of quasi-stationary disk-magnetized star
interactions.
