On the Rotational Dynamics of Magnetically Threaded Disks around Neutron Stars

Abstract

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.