Induced Magnetic Field in Accretion Disks around Neutron Stars

In pulsating X-ray sources a magnetized neutron star is surrounded by an accretion disk whose
structure requires a study. In particular, the dipole magnetic field of the star can partially penetrate the disk
and, freezing into the matter, can give rise to an induced magnetic field in the disk. The field growth can be
limited by its turbulent diffusion. In this paper we calculate such an induced field. The problem is reduced to
solving the induction equation in the presence of diffusion. An analytical solution of the equation has been
obtained, with the radial and vertical structures of the induced field having been calculated simultaneously.
The radial structure is close to the previously predicted dependence on the difference of the angular velocities
of the disk and the magnetosphere: b ∝ Ωs − Ωk, while the vertical structure of the field is close to the linear
proportionality between the field and the height above the equator: b ∝ z. The possibility of the existence of
nonstationary quasi-periodic components of the induced magnetic field is discussed.