Induced magnetic field in accretion disks around neutron stars

A. V. Kuzin

Published 2023-10-25Version 1

There are X-ray pulsating sources that are thought to be accretion disks around neutron stars. Such disks deserve a detailed analysis. In particular, the dipole magnetic field of the central star may penetrate the disk, which, in turn, leads to the appearance of an induced magnetic field inside the disk due to the frozen-in condition. The growth of the induced field can be limited by the turbulent diffusion of the field. In the present work, I calculate the induced field in this case. The problem is reduced to the induction equation with turbulent diffusion taken into account. I have found the analytical solution of this equation, and radial and vertical structures of the field were found simultaneously. The radial structure is close to the earlier predicted dependence on the difference in angular velocities between the magnetosphere and disk: $b \propto \Omega_{\rm s} - \Omega_{\rm k}$, while the vertical structure is close to a linear dependence of an induced field on the altitude above the equator: $b \propto z$. The possibility of the existence of non-stationary quasi-periodic components of an induced field is discussed.