Magnetically Torqued Thin Accretion Disks

TL;DR

This paper models the structure and torques of a thin accretion disk around a magnetized star, revealing how magnetic fields influence disk dynamics and star spin-down, applicable to various astrophysical objects.

Contribution

It introduces a simplified analytical model for magnetically torqued thin disks, deriving key properties and torque relations independent of viscosity assumptions.

Findings

Angular velocity profile tends to corotation near the star

Transition radius matches across different magnetic field models

Star spin-down can power the accretion disk in rapid rotators

Abstract

We compute the properties of a geometrically thin, steady accretion disk surrounding a central rotating, magnetized star. The magnetosphere is assumed to entrain the disk over a wide range of radii. The model is simplified in that we adopt two (alternate) ad hoc, but plausible, expressions for the azimuthal component of the magnetic field as a function of radial distance. We find a solution for the angular velocity profile tending to corotation close to the central star, and smoothly matching a Keplerian curve at a radius where the viscous stress vanishes. The value of this ''transition'' radius is nearly the same for both of our adopted B-field models. We then solve analytically for the torques on the central star and for the disk luminosity due to gravity and magnetic torques. When expressed in a dimensionless form, the resulting quantities depend on one parameter alone, the ratio of the transition radius to the corotation radius. For rapid rotators, the accretion disk may be powered mostly by spin-down of the central star. These results are independent of the viscosity prescription in the disk. We also solve for the disk structure for the special case of an optically thick alpha disk. Our results are applicable to a range of astrophysical systems including accreting neutron stars, intermediate polar cataclysmic variables, and T Tauri systems.